diff --git a/.editorconfig b/.editorconfig
index 11c2bd2445..086af2d930 100644
--- a/.editorconfig
+++ b/.editorconfig
@@ -8,3 +8,4 @@ charset = utf-8
indent_style = space
indent_size = 2
trim_trailing_whitespace = true
+quote_type = single
diff --git a/.eslintrc b/.eslintrc
index 076399682c..88af3ecf32 100644
--- a/.eslintrc
+++ b/.eslintrc
@@ -11,5 +11,11 @@
"class-methods-use-this": "off",
"arrow-body-style": "off",
"no-loop-func": "off"
+ },
+ "ignorePatterns": ["*.md", "*.png", "*.jpeg", "*.jpg"],
+ "settings": {
+ "react": {
+ "version": "18.2.0"
+ }
}
}
diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 912c719df3..e007b6c910 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -11,7 +11,7 @@ jobs:
runs-on: ubuntu-latest
strategy:
matrix:
- node-version: [ 14.x ]
+ node-version: [ 16.x ]
steps:
- name: Checkout repository
diff --git a/.husky/.gitignore b/.husky/.gitignore
new file mode 100644
index 0000000000..31354ec138
--- /dev/null
+++ b/.husky/.gitignore
@@ -0,0 +1 @@
+_
diff --git a/.husky/pre-commit b/.husky/pre-commit
new file mode 100755
index 0000000000..598a5dceaa
--- /dev/null
+++ b/.husky/pre-commit
@@ -0,0 +1,5 @@
+#!/bin/sh
+. "$(dirname "$0")/_/husky.sh"
+
+npm run lint
+# npm run test
diff --git a/.huskyrc.json b/.huskyrc.json
deleted file mode 100644
index 6e9b7b23b7..0000000000
--- a/.huskyrc.json
+++ /dev/null
@@ -1,5 +0,0 @@
-{
- "hooks": {
- "pre-commit": "npm run lint && npm run test"
- }
-}
diff --git a/.npmrc b/.npmrc
new file mode 100644
index 0000000000..b6f27f1359
--- /dev/null
+++ b/.npmrc
@@ -0,0 +1 @@
+engine-strict=true
diff --git a/.nvmrc b/.nvmrc
new file mode 100644
index 0000000000..7fd023741b
--- /dev/null
+++ b/.nvmrc
@@ -0,0 +1 @@
+v16.15.0
diff --git a/BACKERS.md b/BACKERS.md
index 62c397a38c..a244d3bed3 100644
--- a/BACKERS.md
+++ b/BACKERS.md
@@ -14,6 +14,24 @@
`null`
+<!--
+<table>
+ <tr>
+ <td align="center">
+ <a href="[PROFILE_URL]">
+ <img
+ src="[PROFILE_IMG_SRC]"
+ width="50"
+ height="50"
+ />
+ </a>
+ <br />
+ <a href="[PROFILE_URL]">[PROFILE_NAME]</a>
+ </td>
+ </tr>
+</table>
+-->
+
<!--
<ul>
<li>
diff --git a/README.ar-AR.md b/README.ar-AR.md
index 378334fab0..2ff0baddbd 100644
--- a/README.ar-AR.md
+++ b/README.ar-AR.md
@@ -3,7 +3,7 @@
[](https://travis-ci.org/trekhleb/javascript-algorithms)
[](https://codecov.io/gh/trekhleb/javascript-algorithms)
-تحتوي هذا مقالة على أمثلة عديدة تستند إلى الخوارزميات الشائعة وهياكل البيانات في الجافا سكريبت.
+تحتوي هذه المقالة على أمثلة عديدة تستند إلى الخوارزميات الشائعة وهياكل البيانات في الجافا سكريبت.
كل خوارزمية وهياكل البيانات لها برنامج README منفصل خاص بها
مع التفسيرات والروابط ذات الصلة لمزيد من القراءة (بما في ذلك تلك
@@ -21,7 +21,11 @@ _اقرأ هذا في لغات أخرى:_
[_Português_](README.pt-BR.md),
[_Русский_](README.ru-RU.md),
[_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
☝ ملاحضة هذا المشروع مخصص للاستخدام لأغراض التعلم والبحث
فقط ، و ** ليست ** معدة للاستخدام في **الإنتاج**
@@ -320,3 +324,5 @@ npm test -- 'playground'
> يمكنك دعم هذا المشروع عبر ❤️️ [GitHub](https://github.com/sponsors/trekhleb) أو ❤️️ [Patreon](https://www.patreon.com/trekhleb).
[الناس الذين يدعمون هذا المشروع](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.de-DE.md b/README.de-DE.md
new file mode 100644
index 0000000000..019e7d6b39
--- /dev/null
+++ b/README.de-DE.md
@@ -0,0 +1,338 @@
+# JavaScript-Algorithmen und Datenstrukturen
+
+[](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
+[](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+Dieses Repository enthält JavaScript Beispiele für viele
+gängige Algorithmen und Datenstrukturen.
+
+Jeder Algorithmus und jede Datenstruktur hat eine eigene README
+mit zugehörigen Erklärungen und weiterführenden Links (einschließlich zu YouTube-Videos).
+
+_Lies dies in anderen Sprachen:_
+[_English_](https://github.com/trekhleb/javascript-algorithms/)
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
+
+_☝ Beachte, dass dieses Projekt nur für Lern- und Forschungszwecke gedacht ist und **nicht** für den produktiven Einsatz verwendet werden soll_
+
+## Datenstrukturen
+
+Eine Datenstruktur ist eine bestimmte Art und Weise, Daten in einem Computer so zu organisieren und zu speichern, dass sie
+effizient erreicht und verändert werden können. Genauer gesagt, ist eine Datenstruktur eine Sammlung von Werten,
+den Beziehungen zwischen ihnen und den Funktionen oder Operationen, die auf die Daten angewendet werden können.
+
+`B` - Anfänger:innen, `A` - Fortgeschrittene
+
+* `B` [Verkettete Liste (Linked List)](src/data-structures/linked-list)
+* `B` [Doppelt verkettete Liste (Doubly Linked List)](src/data-structures/doubly-linked-list)
+* `B` [Warteschlange (Queue)](src/data-structures/queue)
+* `B` [Stapelspeicher (Stack)](src/data-structures/stack)
+* `B` [Hashtabelle (Hash Table)](src/data-structures/hash-table)
+* `B` [Heap-Algorithmus (Heap)](src/data-structures/heap) - max und min Heap-Versionen
+* `B` [Vorrangwarteschlange (Priority Queue)](src/data-structures/priority-queue)
+* `A` [Trie (Trie)](src/data-structures/trie)
+* `A` [Baum (Tree)](src/data-structures/tree)
+ * `A` [Binärer Suchbaum (Binary Search Tree)](src/data-structures/tree/binary-search-tree)
+ * `A` [AVL-Baum (AVL Tree)](src/data-structures/tree/avl-tree)
+ * `A` [Rot-Schwarz-Baum (Red-Black Tree)](src/data-structures/tree/red-black-tree)
+ * `A` [Segment-Baum (Segment Tree)](src/data-structures/tree/segment-tree) - mit Min/Max/Summenbereich-Abfrage Beispiel
+ * `A` [Fenwick Baum (Fenwick Tree)](src/data-structures/tree/fenwick-tree) (Binär indizierter Baum / Binary Indexed Tree)
+* `A` [Graph (Graph)](src/data-structures/graph) (sowohl gerichtet als auch ungerichtet)
+* `A` [Union-Find-Struktur (Disjoint Set)](src/data-structures/disjoint-set)
+* `A` [Bloomfilter (Bloom Filter)](src/data-structures/bloom-filter)
+
+## Algorithmen
+
+Ein Algorithmus ist eine eindeutige Spezifikation, wie eine Klasse von Problemen zu lösen ist. Er besteht
+aus einem Satz von Regeln, die eine Abfolge von Operationen genau definieren.
+
+`B` - Anfänger:innen, `A` - Fortgeschrittene
+
+### Algorithmen nach Thema
+
+* **Mathe**
+ * `B` [Bitmanipulation (Bit Manipulation)](src/algorithms/math/bits) - Bits setzen/lesen/aktualisieren/löschen, Multiplikation/Division durch zwei negieren usw..
+ * `B` [Faktoriell (Factorial)](src/algorithms/math/factorial)
+ * `B` [Fibonacci-Zahl (Fibonacci Number)](src/algorithms/math/fibonacci) - Klassische und geschlossene Version
+ * `B` [Primfaktoren (Prime Factors)](src/algorithms/math/prime-factors) - Auffinden von Primfaktoren und deren Zählung mit Hilfe des Satz von Hardy-Ramanujan (Hardy-Ramanujan's theorem)
+ * `B` [Primzahl-Test (Primality Test)](src/algorithms/math/primality-test) (Probedivision / trial division method)
+ * `B` [Euklidischer Algorithmus (Euclidean Algorithm)](src/algorithms/math/euclidean-algorithm) - Berechnen des größten gemeinsamen Teilers (ggT)
+ * `B` [Kleinstes gemeinsames Vielfaches (Least Common Multiple)](src/algorithms/math/least-common-multiple) (kgV)
+ * `B` [Sieb des Eratosthenes (Sieve of Eratosthenes)](src/algorithms/math/sieve-of-eratosthenes) - Finden aller Primzahlen bis zu einer bestimmten Grenze
+ * `B` [Power of two (Is Power of Two)](src/algorithms/math/is-power-of-two) - Prüft, ob die Zahl eine Zweierpotenz ist (naive und bitweise Algorithmen)
+ * `B` [Pascalsches Dreieck (Pascal's Triangle)](src/algorithms/math/pascal-triangle)
+ * `B` [Komplexe Zahlen (Complex Number)](src/algorithms/math/complex-number) - Komplexe Zahlen und Grundoperationen mit ihnen
+ * `B` [Bogenmaß & Grad (Radian & Degree)](src/algorithms/math/radian) - Umrechnung von Bogenmaß in Grad und zurück
+ * `B` [Fast Powering Algorithmus (Fast Powering)](src/algorithms/math/fast-powering)
+ * `B` [Horner-Schema (Horner's method)](src/algorithms/math/horner-method) - Polynomauswertung
+ * `B` [Matrizen (Matrices)](src/algorithms/math/matrix) - Matrizen und grundlegende Matrixoperationen (Multiplikation, Transposition usw.)
+ * `B` [Euklidischer Abstand (Euclidean Distance)](src/algorithms/math/euclidean-distance) - Abstand zwischen zwei Punkten/Vektoren/Matrizen
+ * `A` [Ganzzahlige Partitionierung (Integer Partition)](src/algorithms/math/integer-partition)
+ * `A` [Quadratwurzel (Square Root)](src/algorithms/math/square-root) - Newtonverfahren (Newton's method)
+ * `A` [Liu Hui π Algorithmus (Liu Hui π Algorithm)](src/algorithms/math/liu-hui) - Näherungsweise π-Berechnungen auf Basis von N-gons
+ * `A` [Diskrete Fourier-Transformation (Discrete Fourier Transform)](src/algorithms/math/fourier-transform) - Eine Funktion der Zeit (ein Signal) in die Frequenzen zerlegen, aus denen sie sich zusammensetzt
+* **Sets**
+ * `B` [Kartesisches Produkt (Cartesian Product)](src/algorithms/sets/cartesian-product) - Produkt aus mehreren Mengen
+ * `B` [Fisher-Yates-Verfahren (Fisher–Yates Shuffle)](src/algorithms/sets/fisher-yates) - Zufällige Permutation einer endlichen Folge
+ * `A` [Potenzmenge (Power Set)](src/algorithms/sets/power-set) - Alle Teilmengen einer Menge (Bitweise und Rücksetzverfahren Lösungen(backtracking solutions))
+ * `A` [Permutation (Permutations)](src/algorithms/sets/permutations) (mit und ohne Wiederholungen)
+ * `A` [Kombination (Combinations)](src/algorithms/sets/combinations) (mit und ohne Wiederholungen)
+ * `A` [Problem der längsten gemeinsamen Teilsequenz (Longest Common Subsequence)](src/algorithms/sets/longest-common-subsequence) (LCS)
+ * `A` [Längste gemeinsame Teilsequenz (Longest Increasing Subsequence)](src/algorithms/sets/longest-increasing-subsequence)
+ * `A` [Der kürzeste gemeinsame String (Shortest Common Supersequence)](src/algorithms/sets/shortest-common-supersequence) (SCS)
+ * `A` [Rucksackproblem (Knapsack Problem)](src/algorithms/sets/knapsack-problem) - "0/1" und "Ungebunden"
+ * `A` [Das Maximum-Subarray Problem (Maximum Subarray)](src/algorithms/sets/maximum-subarray) - "Brute-Force-Methode" und "Dynamische Programmierung" (Kadane' Algorithmus)
+ * `A` [Kombinationssumme (Combination Sum)](src/algorithms/sets/combination-sum) - Alle Kombinationen finden, die eine bestimmte Summe bilden
+* **Zeichenketten (Strings)**
+ * `B` [Hamming-Abstand (Hamming Distance)](src/algorithms/string/hamming-distance) - Anzahl der Positionen, an denen die Symbole unterschiedlich sind
+ * `A` [Levenshtein-Distanz (Levenshtein Distance)](src/algorithms/string/levenshtein-distance) - Minimaler Editierabstand zwischen zwei Sequenzen
+ * `A` [Knuth-Morris-Pratt-Algorithmus (Knuth–Morris–Pratt Algorithm)](src/algorithms/string/knuth-morris-pratt) (KMP Algorithmus) - Teilstringsuche (Mustervergleich / Pattern Matching)
+ * `A` [Z-Algorithmus (Z Algorithm)](src/algorithms/string/z-algorithm) - Teilstringsuche (Mustervergleich / Pattern Matching)
+ * `A` [Rabin-Karp-Algorithmus (Rabin Karp Algorithm)](src/algorithms/string/rabin-karp) - Teilstringsuche
+ * `A` [Längstes häufiges Teilzeichenfolgenproblem (Longest Common Substring)](src/algorithms/string/longest-common-substring)
+ * `A` [Regulärer Ausdruck (Regular Expression Matching)](src/algorithms/string/regular-expression-matching)
+* **Suchen**
+ * `B` [Lineare Suche (Linear Search)](src/algorithms/search/linear-search)
+ * `B` [Sprungsuche (Jump Search)](src/algorithms/search/jump-search) (oder Blocksuche) - Suche im sortierten Array
+ * `B` [Binäre Suche (Binary Search)](src/algorithms/search/binary-search) - Suche in einem sortierten Array
+ * `B` [Interpolationssuche (Interpolation Search)](src/algorithms/search/interpolation-search) - Suche in gleichmäßig verteilt sortiertem Array
+* **Sortieren**
+ * `B` [Bubblesort (Bubble Sort)](src/algorithms/sorting/bubble-sort)
+ * `B` [Selectionsort (Selection Sort)](src/algorithms/sorting/selection-sort)
+ * `B` [Einfügesortierenmethode (Insertion Sort)](src/algorithms/sorting/insertion-sort)
+ * `B` [Haldensortierung (Heap Sort)](src/algorithms/sorting/heap-sort)
+ * `B` [Mergesort (Merge Sort)](src/algorithms/sorting/merge-sort)
+ * `B` [Quicksort (Quicksort)](src/algorithms/sorting/quick-sort) - in-place und non-in-place Implementierungen
+ * `B` [Shellsort (Shellsort)](src/algorithms/sorting/shell-sort)
+ * `B` [Countingsort (Counting Sort)](src/algorithms/sorting/counting-sort)
+ * `B` [Fachverteilen (Radix Sort)](src/algorithms/sorting/radix-sort)
+* **Verkettete Liste (Linked List)**
+ * `B` [Gerade Traversierung (Straight Traversal)](src/algorithms/linked-list/traversal)
+ * `B` [Umgekehrte Traversierung (Reverse Traversal)](src/algorithms/linked-list/reverse-traversal)
+* **Bäume**
+ * `B` [Tiefensuche (Depth-First Search)](src/algorithms/tree/depth-first-search) (DFS)
+ * `B` [Breitensuche (Breadth-First Search)](src/algorithms/tree/breadth-first-search) (BFS)
+* **Graphen**
+ * `B` [Tiefensuche (Depth-First Search)](src/algorithms/graph/depth-first-search) (DFS)
+ * `B` [Breitensuche (Breadth-First Search)](src/algorithms/graph/breadth-first-search) (BFS)
+ * `B` [Algorithmus von Kruskal (Kruskal’s Algorithm)](src/algorithms/graph/kruskal) - Finden des Spannbaum (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen
+ * `A` [Dijkstra-Algorithmus (Dijkstra Algorithm)](src/algorithms/graph/dijkstra) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus
+ * `A` [Bellman-Ford-Algorithmus (Bellman-Ford Algorithm)](src/algorithms/graph/bellman-ford) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus
+ * `A` [Algorithmus von Floyd und Warshall (Floyd-Warshall Algorithm)](src/algorithms/graph/floyd-warshall) - Die kürzesten Wege zwischen allen Knotenpaaren finden
+ * `A` [Zykluserkennung (Detect Cycle)](src/algorithms/graph/detect-cycle) - Sowohl für gerichtete als auch für ungerichtete Graphen (DFS- und Disjoint-Set-basierte Versionen)
+ * `A` [Algorithmus von Prim (Prim’s Algorithm)](src/algorithms/graph/prim) - Finden des Spannbaums (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen
+ * `A` [Topologische Sortierung (Topological Sorting)](src/algorithms/graph/topological-sorting) - DFS-Verfahren
+ * `A` [Artikulationspunkte (Articulation Points)](src/algorithms/graph/articulation-points) - Algorithmus von Tarjan (Tarjan's algorithm) (DFS basiert)
+ * `A` [Brücke (Bridges)](src/algorithms/graph/bridges) - DFS-basierter Algorithmus
+ * `A` [Eulerkreisproblem (Eulerian Path and Eulerian Circuit)](src/algorithms/graph/eulerian-path) - Algorithmus von Fleury (Fleury's algorithm) - Jede Kante genau einmal durchlaufen.
+ * `A` [Hamiltonkreisproblem (Hamiltonian Cycle)](src/algorithms/graph/hamiltonian-cycle) - Jeden Eckpunkt genau einmal durchlaufen.
+ * `A` [Starke Zusammenhangskomponente (Strongly Connected Components)](src/algorithms/graph/strongly-connected-components) - Kosarajus Algorithmus
+ * `A` [Problem des Handlungsreisenden (Travelling Salesman Problem)](src/algorithms/graph/travelling-salesman) - Kürzestmögliche Route, die jede Stadt besucht und zur Ausgangsstadt zurückkehrt
+* **Kryptographie**
+ * `B` [Polynomiale Streuwertfunktion(Polynomial Hash)](src/algorithms/cryptography/polynomial-hash) - Rollierende Streuwert-Funktion basierend auf Polynom
+ * `B` [Schienenzaun Chiffre (Rail Fence Cipher)](src/algorithms/cryptography/rail-fence-cipher) - Ein Transpositionsalgorithmus zur Verschlüsselung von Nachrichten
+ * `B` [Caesar-Verschlüsselung (Caesar Cipher)](src/algorithms/cryptography/caesar-cipher) - Einfache Substitutions-Chiffre
+ * `B` [Hill-Chiffre (Hill Cipher)](src/algorithms/cryptography/hill-cipher) - Substitutionschiffre basierend auf linearer Algebra
+* **Maschinelles Lernen**
+ * `B` [Künstliches Neuron (NanoNeuron)](https://github.com/trekhleb/nano-neuron) - 7 einfache JS-Funktionen, die veranschaulichen, wie Maschinen tatsächlich lernen können (Vorwärts-/Rückwärtspropagation)
+ * `B` [Nächste-Nachbarn-Klassifikation (k-NN)](src/algorithms/ml/knn) - k-nächste-Nachbarn-Algorithmus
+ * `B` [k-Means (k-Means)](src/algorithms/ml/k-means) - k-Means-Algorithmus
+* **Image Processing**
+ * `B` [Inhaltsabhängige Bildverzerrung (Seam Carving)](src/algorithms/image-processing/seam-carving) - Algorithmus zur inhaltsabhängigen Bildgrößenänderung
+* **Unkategorisiert**
+ * `B` [Türme von Hanoi (Tower of Hanoi)](src/algorithms/uncategorized/hanoi-tower)
+ * `B` [Rotationsmatrix (Square Matrix Rotation)](src/algorithms/uncategorized/square-matrix-rotation) - In-Place-Algorithmus
+ * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game) - Backtracking, dynamische Programmierung (Top-down + Bottom-up) und gierige Beispiele
+ * `B` [Eindeutige Pfade (Unique Paths)](src/algorithms/uncategorized/unique-paths) - Backtracking, dynamische Programmierung und Pascalsches Dreieck basierte Beispiele
+ * `B` [Regenterrassen (Rain Terraces)](src/algorithms/uncategorized/rain-terraces) - Auffangproblem für Regenwasser (trapping rain water problem) (dynamische Programmierung und Brute-Force-Versionen)
+ * `B` [Rekursive Treppe (Recursive Staircase)](src/algorithms/uncategorized/recursive-staircase) - Zählen der Anzahl der Wege, die nach oben führen (4 Lösungen)
+ * `B` [Beste Zeit zum Kaufen/Verkaufen von Aktien (Best Time To Buy Sell Stocks)](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - Beispiele für "Teile und Herrsche" und Beispiele für den One-Pass-Algorithmus
+ * `A` [Damenproblem (N-Queens Problem)](src/algorithms/uncategorized/n-queens)
+ * `A` [Springerproblem (Knight's Tour)](src/algorithms/uncategorized/knight-tour)
+
+### Algorithmen nach Paradigma
+
+Ein algorithmisches Paradigma ist eine generische Methode oder ein Ansatz, der dem Entwurf einer Klasse von Algorithmen zugrunde liegt. Es ist eine Abstraktion, die höher ist als der Begriff des Algorithmus. Genauso wie ein Algorithmus eine Abstraktion ist, die höher ist als ein Computerprogramm.
+
+* **Brachiale Gewalt (Brute Force)** - schaut sich alle Möglichkeiten an und wählt die beste Lösung aus
+ * `B` [Lineare Suche (Linear Search)](src/algorithms/search/linear-search)
+ * `B` [Regenterrassen (Rain Terraces)](src/algorithms/uncategorized/rain-terraces) - Auffangproblem für Regenwasser (trapping rain water problem) (dynamische Programmierung und Brute-Force-Versionen)
+ * `B` [Rekursive Treppe (Recursive Staircase)](src/algorithms/uncategorized/recursive-staircase) - Zählen der Anzahl der Wege, die nach oben führen (4 Lösungen)
+ * `A` [Das Maximum-Subarray Problem (Maximum Subarray)](src/algorithms/sets/maximum-subarray)
+ * `A` [Problem des Handlungsreisenden (Travelling Salesman Problem)](src/algorithms/graph/travelling-salesman) - Kürzestmögliche Route, die jede Stadt besucht und zur Ausgangsstadt zurückkehrt
+ * `A` [Diskrete Fourier-Transformation (Discrete Fourier Transform)](src/algorithms/math/fourier-transform) - Eine Funktion der Zeit (ein Signal) in die Frequenzen zerlegen, aus denen sie sich zusammensetzt
+* **Gierig (Greedy)** - Wählt die beste Option zum aktuellen Zeitpunkt, ohne Rücksicht auf die Zukunft
+ * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game)
+ * `A` [Rucksackproblem (Unbound Knapsack Problem)](src/algorithms/sets/knapsack-problem)
+ * `A` [Dijkstra-Algorithmus (Dijkstra Algorithm)](src/algorithms/graph/dijkstra) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus
+ * `A` [Algorithmus von Prim (Prim’s Algorithm)](src/algorithms/graph/prim) - Finden des Spannbaums (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen
+ * `B` [Algorithmus von Kruskal (Kruskal’s Algorithm)](src/algorithms/graph/kruskal) - Finden des Spannbaum (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen
+* **Teile und herrsche** - Das Problem in kleinere Teile aufteilen und diese Teile dann lösen
+ * `B` [Binäre Suche (Binary Search)](src/algorithms/search/binary-search)
+ * `B` [Türme von Hanoi (Tower of Hanoi)](src/algorithms/uncategorized/hanoi-tower)
+ * `B` [Pascalsches Dreieck (Pascal's Triangle)](src/algorithms/math/pascal-triangle)
+ * `B` [Euklidischer Algorithmus (Euclidean Algorithm)](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
+ * `B` [Mergesort (Merge Sort)](src/algorithms/sorting/merge-sort)
+ * `B` [Quicksort (Quicksort)](src/algorithms/sorting/quick-sort)
+ * `B` [Tiefensuche (Depth-First Search)](src/algorithms/tree/depth-first-search) (DFS)
+ * `B` [Breitensuche (Breadth-First Search)](src/algorithms/graph/depth-first-search) (DFS)
+ * `B` [Matrizen (Matrices)](src/algorithms/math/matrix) - Matrizen und grundlegende Matrixoperationen (Multiplikation, Transposition usw.)
+ * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game)
+ * `B` [Fast Powering Algorithmus (Fast Powering)](src/algorithms/math/fast-powering)
+ * `B` [Beste Zeit zum Kaufen/Verkaufen von Aktien (Best Time To Buy Sell Stocks)](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - Beispiele für "Teile und Herrsche" und Beispiele für den One-Pass-Algorithmus
+ * `A` [Permutation (Permutations)](src/algorithms/sets/permutations) (mit und ohne Wiederholungen)
+ * `A` [Kombination (Combinations)](src/algorithms/sets/combinations) (mit und ohne Wiederholungen)
+* **Dynamische Programmierung** - Eine Lösung aus zuvor gefundenen Teillösungen aufbauen
+ * `B` [Fibonacci-Zahl (Fibonacci Number)](src/algorithms/math/fibonacci)
+ * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game)
+ * `B` [Eindeutige Pfade (Unique Paths)](src/algorithms/uncategorized/unique-paths)
+ * `B` [Regenterrassen (Rain Terraces)](src/algorithms/uncategorized/rain-terraces) - Auffangproblem für Regenwasser (trapping rain water problem) (dynamische Programmierung und Brute-Force-Versionen)
+ * `B` [Rekursive Treppe (Recursive Staircase)](src/algorithms/uncategorized/recursive-staircase) - Zählen der Anzahl der Wege, die nach oben führen (4 Lösungen)
+ * `B` [Inhaltsabhängige Bildverzerrung (Seam Carving)](src/algorithms/image-processing/seam-carving) - Algorithmus zur inhaltsabhängigen Bildgrößenänderung
+ * `A` [Levenshtein-Distanz (Levenshtein Distance)](src/algorithms/string/levenshtein-distance) - Minimaler Editierabstand zwischen zwei Sequenzen
+ * `A` [Problem der längsten gemeinsamen Teilsequenz (Longest Common Subsequence)](src/algorithms/sets/longest-common-subsequence) (LCS)
+ * `A` [Längstes häufiges Teilzeichenfolgenproblem (Longest Common Substring)](src/algorithms/string/longest-common-substring)
+ * `A` [Längste gemeinsame Teilsequenz (Longest Increasing Subsequence)](src/algorithms/sets/longest-increasing-subsequence)
+ * `A` [Der kürzeste gemeinsame String (Shortest Common Supersequence)](src/algorithms/sets/shortest-common-supersequence)
+ * `A` [Rucksackproblem (0/1 Knapsack Problem)](src/algorithms/sets/knapsack-problem)
+ * `A` [Ganzzahlige Partitionierung (Integer Partition)](src/algorithms/math/integer-partition)
+ * `A` [Das Maximum-Subarray Problem (Maximum Subarray)](src/algorithms/sets/maximum-subarray)
+ * `A` [Bellman-Ford-Algorithmus (Bellman-Ford Algorithm)](src/algorithms/graph/bellman-ford) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus
+ * `A` [Algorithmus von Floyd und Warshall (Floyd-Warshall Algorithm)](src/algorithms/graph/floyd-warshall) - Die kürzesten Wege zwischen allen Knotenpaaren finden
+ * `A` [Regulärer Ausdruck (Regular Expression Matching)](src/algorithms/string/regular-expression-matching)
+* **Zurückverfolgung** - Ähnlich wie bei Brute-Force versuchen Sie, alle möglichen Lösungen zu generieren, aber jedes Mal, wenn Sie die nächste Lösung generieren, testen Sie, ob sie alle Bedingungen erfüllt, und fahren erst dann mit der Generierung weiterer Lösungen fort. Andernfalls gehen Sie zurück und nehmen einen anderen Weg, um eine Lösung zu finden. Normalerweise wird das DFS-Traversal des Zustandsraums verwendet.
+ * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game)
+ * `B` [Eindeutige Pfade (Unique Paths)](src/algorithms/uncategorized/unique-paths)
+ * `A` [Potenzmenge (Power Set)](src/algorithms/sets/power-set) - Alle Teilmengen einer Menge
+ * `A` [Hamiltonkreisproblem (Hamiltonian Cycle)](src/algorithms/graph/hamiltonian-cycle) - Jeden Eckpunkt genau einmal durchlaufen.
+ * `A` [Damenproblem (N-Queens Problem)](src/algorithms/uncategorized/n-queens)
+ * `A` [Springerproblem (Knight's Tour)](src/algorithms/uncategorized/knight-tour)
+ * `A` [Kombinationssumme (Combination Sum)](src/algorithms/sets/combination-sum) - Alle Kombinationen finden, die eine bestimmte Summe bilden
+* **Verzweigung & Bindung** - Merkt sich die Lösung mit den niedrigsten Kosten, die in jeder Phase der Backtracking-Suche gefunden wurde, und verwendet die Kosten der bisher gefundenen Lösung mit den niedrigsten Kosten als untere Schranke für die Kosten einer Lösung des Problems mit den geringsten Kosten, um Teillösungen zu verwerfen, deren Kosten größer sind als die der bisher gefundenen Lösung mit den niedrigsten Kosten. Normalerweise wird das BFS-Traversal in Kombination mit dem DFS-Traversal des Zustandsraumbaums verwendet.
+
+## So verwendest du dieses Repository
+
+**Alle Abhängigkeiten installieren**
+
+```
+npm install
+```
+
+**ESLint ausführen**
+
+You may want to run it to check code quality.
+
+```
+npm run lint
+```
+
+**Alle Tests ausführen**
+
+```
+npm test
+```
+
+**Tests nach Namen ausführen**
+
+```
+npm test -- 'LinkedList'
+```
+
+**Fehlerbehebung**
+
+Falls das Linting oder Testen fehlschlägt, versuche, den Ordner "node_modules" zu löschen und die npm-Pakete neu zu installieren:
+
+```
+rm -rf ./node_modules
+npm i
+```
+
+**Spielwiese**
+
+Du kannst mit Datenstrukturen und Algorithmen in der Datei `./src/playground/playground.js` herumspielen und
+dir in dieser Datei Tests schreiben `./src/playground/__test__/playground.test.js`.
+
+Dann führe einfach folgenden Befehl aus, um zu testen, ob dein Spielwiesencode wie erwartet funktioniert:
+
+```
+npm test -- 'playground'
+```
+
+## Nützliche Informationen
+
+### Referenzen
+
+[▶ Datenstrukturen und Algorithmen auf YouTube(Englisch)](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
+### O-Notation (_Big O Notation_)
+
+Die O-Notation wird verwendet, um Algorithmen danach zu klassifizieren, wie ihre Laufzeit oder ihr Platzbedarf mit zunehmender Eingabegröße wächst. In der folgenden Tabelle finden Sie die häufigsten Wachstumsordnungen von Algorithmen, die in Big-O-Notation angegeben sind.
+
+
+
+Quelle: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+Nachfolgend finden Sie eine Liste einiger der am häufigsten verwendeten Big O-Notationen und deren Leistungsvergleiche für unterschiedliche Größen der Eingabedaten.
+
+| Big O Notation | Berechnungen für 10 Elemente | Berechnungen für 100 Elemente | Berechnungen für 1000 Elemente |
+| -------------- | ---------------------------- | ----------------------------- | ------------------------------ |
+| **O(1)** | 1 | 1 | 1 |
+| **O(log N)** | 3 | 6 | 9 |
+| **O(N)** | 10 | 100 | 1000 |
+| **O(N log N)** | 30 | 600 | 9000 |
+| **O(N^2)** | 100 | 10000 | 1000000 |
+| **O(2^N)** | 1024 | 1.26e+29 | 1.07e+301 |
+| **O(N!)** | 3628800 | 9.3e+157 | 4.02e+2567 |
+
+### Komplexität von Datenstrukturoperationen
+
+| Datenstruktur | Zugriff auf | Suche | Einfügen | Löschung | Kommentare |
+| ---------------------- | :---------: | :----: | :------: | :------: | :-------------------------------------------------------------- |
+| **Array** | 1 | n | n | n | |
+| **Stack** | n | n | 1 | 1 | |
+| **Queue** | n | n | 1 | 1 | |
+| **Linked List** | n | n | 1 | n | |
+| **Hash Table** | - | n | n | n | Im Falle einer perfekten Hash-Funktion wären die Kosten O(1) |
+| **Binary Search Tree** | n | n | n | n | Im Falle eines ausgeglichenen Baumes wären die Kosten O(log(n)) |
+| **B-Tree** | log(n) | log(n) | log(n) | log(n) | |
+| **Red-Black Tree** | log(n) | log(n) | log(n) | log(n) | |
+| **AVL Tree** | log(n) | log(n) | log(n) | log(n) | |
+| **Bloom Filter** | - | 1 | 1 | - | Falschpostive sind bei der Suche möglichen |
+
+### Komplexität von Array-Sortieralgorithmen
+
+| Name | Bester | Durchschnitt | Schlechtester | Speicher | Stabil | Kommentar |
+| ------------------ | :-----------: | :---------------------: | :-------------------------: | :------: | :----: | :------------------------------------------------------------------------- |
+| **Bubble sort** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | JA | |
+| **Insertion sort** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Ja | |
+| **Selection sort** | n<sup>2</sup> | n<sup>2</sup> | n<sup>2</sup> | 1 | Nein | |
+| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | Nein | |
+| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Ja | |
+| **Quick sort** | n log(n) | n log(n) | n<sup>2</sup> | log(n) | Nein | Quicksort wird normalerweise in-place mit O(log(n)) Stapelplatz ausgeführt |
+| **Shell sort** | n log(n) | abhängig von Spaltfolge | n (log(n))<sup>2</sup> | 1 | Nein | |
+| **Counting sort** | n + r | n + r | n + r | n + r | Ja | r - größte Zahl im Array |
+| **Radix sort** | n \* k | n \* k | n \* k | n + k | Ja | k - Länge des längsten Schlüssels |
+
+## Projekt-Unterstützer
+
+> Du kannst dieses Projekt unterstützen über ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+[Leute, die dieses Projekt unterstützen](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+
diff --git a/README.es-ES.md b/README.es-ES.md
index fa1fd340c6..3a15ada4bd 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -23,7 +23,11 @@ _Léelo en otros idiomas:_
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
*☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
y **no** para ser usado en producción.*
@@ -67,7 +71,7 @@ definen con precisión una secuencia de operaciones.
* **Matemáticas**
* `P` [Manipulación de bits](src/algorithms/math/bits) - asignar/obtener/actualizar/limpiar bits, multiplicación/división por dos, hacer negativo, etc.
* `P` [Factorial](src/algorithms/math/factorial)
- * `P` [Número de Fibonacci](src/algorithms/math/fibonacci)
+ * `P` [Sucesión de Fibonacci](src/algorithms/math/fibonacci)
* `P` [Prueba de primalidad](src/algorithms/math/primality-test) (método de división de prueba)
* `P` [Algoritmo de Euclides](src/algorithms/math/euclidean-algorithm) - calcular el Máximo común divisor (MCD)
* `P` [Mínimo común múltiplo](src/algorithms/math/least-common-multiple) (MCM)
@@ -78,7 +82,7 @@ definen con precisión una secuencia de operaciones.
* `P` [Radianes & Grados](src/algorithms/math/radian) - conversión de radianes a grados y viceversa
* `P` [Exponenciación rápida](src/algorithms/math/fast-powering)
* `A` [Partición entera](src/algorithms/math/integer-partition)
- * `A` [Algortimo π de Liu Hui](src/algorithms/math/liu-hui) - aproximar el cálculo de π basado en polígonos de N lados
+ * `A` [Algoritmo π de Liu Hui](src/algorithms/math/liu-hui) - aproximar el cálculo de π basado en polígonos de N lados
* `A` [Transformada discreta de Fourier](src/algorithms/math/fourier-transform) - descomponer una función de tiempo (señal) en las frecuencias que la componen
* **Conjuntos**
* `P` [Producto cartesiano](src/algorithms/sets/cartesian-product) - producto de múltiples conjuntos
@@ -127,7 +131,7 @@ definen con precisión una secuencia de operaciones.
* `P` [Algoritmo de Kruskal](src/algorithms/graph/kruskal) - encontrar el árbol de cubrimiento mínimo (MST) para un grafo no dirigido ponderado
* `A` [Algoritmo de Dijkstra](src/algorithms/graph/dijkstra) - encontrar los caminos más cortos a todos los vértices del grafo desde un solo vértice
* `A` [Algoritmo de Bellman-Ford](src/algorithms/graph/bellman-ford) - encontrar los caminos más cortos a todos los vértices del grafo desde un solo vértice
- * `A` [Algortimo de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - encontrar los caminos más cortos entre todos los pares de vértices
+ * `A` [Algoritmo de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - encontrar los caminos más cortos entre todos los pares de vértices
* `A` [Detectar ciclos](src/algorithms/graph/detect-cycle) - para grafos dirigidos y no dirigidos (versiones basadas en DFS y conjuntos disjuntos)
* `A` [Algoritmo de Prim](src/algorithms/graph/prim) - encontrar el árbol de cubrimiento mínimo (MST) para un grafo no dirigido ponderado
* `A` [Ordenamiento topológico](src/algorithms/graph/topological-sorting) - método DFS
@@ -137,7 +141,7 @@ definen con precisión una secuencia de operaciones.
* `A` [Ciclo hamiltoniano](src/algorithms/graph/hamiltonian-cycle) - visitar cada vértice exactamente una vez
* `A` [Componentes fuertemente conexos](src/algorithms/graph/strongly-connected-components) - algoritmo de Kosaraju
* `A` [Problema del viajante](src/algorithms/graph/travelling-salesman) - la ruta más corta posible que visita cada ciudad y vuelve a la ciudad de origen
-* **Criptografia**
+* **Criptografía**
* `P` [Hash polinomial](src/algorithms/cryptography/polynomial-hash) - función de hash rodante basada en polinomio
* **Sin categoría**
* `P` [Torre de Hanói](src/algorithms/uncategorized/hanoi-tower)
@@ -163,7 +167,7 @@ Es una abstracción superior a la noción de algoritmo, del mismo modo que un al
* `P` [Juego de los saltos](src/algorithms/uncategorized/jump-game)
* `A` [Problema de la mochila sin límite](src/algorithms/sets/knapsack-problem)
* `A` [Algoritmo de Dijkstra](src/algorithms/graph/dijkstra) - encontrar los caminos más cortos a todos los vértices del grafo desde un solo vértice
- * `A` [Algortimo de Prim](src/algorithms/graph/prim) - encontrar el árbol de cubrimiento mínimo (MST) para un grafo no dirigido ponderado
+ * `A` [Algoritmo de Prim](src/algorithms/graph/prim) - encontrar el árbol de cubrimiento mínimo (MST) para un grafo no dirigido ponderado
* `A` [Algoritmo de Kruskal](src/algorithms/graph/kruskal) - encontrar el árbol de cubrimiento mínimo (MST) para un grafo no dirigido ponderado
* **Divide y Vencerás** - divide el problema en partes más pequeñas y luego resuelve esas partes
* `P` [Búsqueda binaria](src/algorithms/search/binary-search)
@@ -202,7 +206,7 @@ Es una abstracción superior a la noción de algoritmo, del mismo modo que un al
* `A` [Problema de las N Reinas](src/algorithms/uncategorized/n-queens)
* `A` [Problema del caballo (Knight tour)](src/algorithms/uncategorized/knight-tour)
* `A` [Suma combinada](src/algorithms/sets/combination-sum) - encuentra todas las combinaciones que forman una suma específica
-* **Ramas y Limites** - recuerda la solución de menor costo encontrada en cada etapa de la búsqueda de rastreo, y utilizar el costo de la solución de menor costo encontrada hasta el momento como un límite inferior del costo de una solución de menor costo para el problema, a fin de descartar soluciones parciales con costos mayores que la solución de menor costo encontrada hasta el momento. Normalmente se utiliza un recorrido BFS en combinación con un recorrido DFS del árbol del espacio de estados.
+* **Ramas y Límites** - recuerda la solución de menor costo encontrada en cada etapa de la búsqueda de rastreo, y utilizar el costo de la solución de menor costo encontrada hasta el momento como un límite inferior del costo de una solución de menor costo para el problema, a fin de descartar soluciones parciales con costos mayores que la solución de menor costo encontrada hasta el momento. Normalmente se utiliza un recorrido BFS en combinación con un recorrido DFS del árbol del espacio de estados.
## Cómo usar este repositorio
@@ -245,7 +249,7 @@ npm test -- 'playground'
## Información útil
-### Refrencias
+### Referencias
[▶ Estructuras de datos y algoritmos en YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
@@ -298,3 +302,5 @@ frente a diferentes tamaños de los datos de entrada.
| **Shellsort** | n log(n) | depende de la secuencia de huecos | n (log(n))<sup>2</sup> | 1 | No | |
| **Ordenamiento por cuentas** | n + r | n + r | n + r | n + r | Si | r - mayor número en el arreglo |
| **Ordenamiento Radix** | n \* k | n \* k | n \* k | n + k | Si | k - largo de la llave más larga |
+
+> ℹ️ Algunos otros [proyectos](https://trekhleb.dev/projects/) y [artículos](https://trekhleb.dev/blog/) sobre JavaScript y algoritmos en [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.fr-FR.md b/README.fr-FR.md
index 024a3b1904..cb30d1833d 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -24,7 +24,11 @@ _Lisez ceci dans d'autres langues:_
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
## Data Structures
@@ -292,3 +296,5 @@ comparaisons de performance suivant différentes tailles pour les données d'ent
| **Tri Shell** | n log(n) | dépend du gap séquence | n (log(n))<sup>2</sup> | 1 | Non | |
| **Tri Comptage** | n + r | n + r | n + r | n + r | Oui | r - le plus grand nombre dans la liste |
| **Tri Radix** | n \* k | n \* k | n \* k | n + k | Non | k - longueur du plus long index |
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.he-IL.md b/README.he-IL.md
new file mode 100644
index 0000000000..43ef196e60
--- /dev/null
+++ b/README.he-IL.md
@@ -0,0 +1,370 @@
+# אלגוריתמים ומבני נתונים ב-JavaScript
+
+[](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
+[](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+
+מאגר זה מכיל דוגמאות מבוססות JavaScript של אלגוריתמים ומבני נתונים פופולריים רבים.
+
+לכל אלגוריתם ומבנה נתונים יש README משלו עם הסברים קשורים וקישורים לקריאה נוספת (כולל קישורים לסרטוני YouTube).
+
+_קרא זאת בשפות אחרות:_
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türkçe_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+
+*☝ שים לב שפרויקט זה מיועד למטרות לימוד ומחקר בלבד, ואינו מיועד לשימוש בייצור.*
+
+## מבני נתונים
+
+מבנה נתונים הוא דרך מסוימת לארגן ולאחסן נתונים במחשב כך שניתן לגשת אליהם ולשנות אותם ביעילות. ליתר דיוק, מבנה נתונים הוא אוסף של ערכי נתונים, היחסים ביניהם, והפונקציות או הפעולות שניתן ליישם על הנתונים.
+
+זכור שלכל מבנה נתונים יש את היתרונות והחסרונות שלו. חשוב לשים לב יותר לסיבה שבגללה אתה בוחר מבנה נתונים מסוים מאשר לאופן היישום שלו.
+
+`B` - מתחיל, `A` - מתקדם
+
+* `B` [רשימה מקושרת](src/data-structures/linked-list)
+* `B` [רשימה מקושרת כפולה](src/data-structures/doubly-linked-list)
+* `B` [תור](src/data-structures/queue)
+* `B` [מחסנית](src/data-structures/stack)
+* `B` [טבלת גיבוב](src/data-structures/hash-table)
+* `B` [ערימה](src/data-structures/heap) - גרסאות מקסימום ומינימום
+* `B` [תור עדיפויות](src/data-structures/priority-queue)
+* `A` [עץ תחיליות](src/data-structures/trie)
+* `A` [עץ](src/data-structures/tree)
+ * `A` [עץ חיפוש בינארי](src/data-structures/tree/binary-search-tree)
+ * `A` [עץ AVL](src/data-structures/tree/avl-tree)
+ * `A` [עץ אדום-שחור](src/data-structures/tree/red-black-tree)
+ * `A` [עץ מקטעים](src/data-structures/tree/segment-tree) - עם דוגמאות לשאילתות מינימום/מקסימום/סכום של טווח
+ * `A` [עץ פנוויק](src/data-structures/tree/fenwick-tree) (עץ בינארי מאונדקס)
+* `A` [גרף](src/data-structures/graph) (מכוון ולא מכוון)
+* `A` [קבוצה מופרדת](src/data-structures/disjoint-set) - מבנה נתונים של איחוד-מציאה או מיזוג-מציאה
+* `A` [מסנן בלום](src/data-structures/bloom-filter)
+* `A` [מטמון LRU](src/data-structures/lru-cache/) - מטמון פחות שימוש לאחרונה (LRU)
+
+## אלגוריתמים
+
+אלגוריתם הוא מפרט חד משמעי כיצד לפתור סוג של בעיות. זוהי קבוצה של כללים המגדירים במדויק רצף של פעולות.
+
+`B` - מתחיל, `A` - מתקדם
+
+### אלגוריתמים לפי נושא
+
+* **מתמטיקה**
+ * `B` [מניפולציה על ביטים](src/algorithms/math/bits) - קביעה/עדכון/ניקוי ביטים, הכפלה/חילוק ב-2, הפיכה לשלילי וכו'
+ * `B` [נקודה צפה בינארית](src/algorithms/math/binary-floating-point) - ייצוג בינארי של מספרים בנקודה צפה
+ * `B` [פקטוריאל](src/algorithms/math/factorial)
+ * `B` [מספר פיבונאצ'י](src/algorithms/math/fibonacci) - גרסאות קלאסיות וסגורות
+ * `B` [גורמים ראשוניים](src/algorithms/math/prime-factors) - מציאת גורמים ראשוניים וספירתם באמצעות משפט הארדי-רמנוג'אן
+ * `B` [בדיקת ראשוניות](src/algorithms/math/primality-test) (שיטת החלוקה הניסיונית)
+ * `B` [אלגוריתם אוקלידס](src/algorithms/math/euclidean-algorithm) - חישוב המחלק המשותף הגדול ביותר (GCD)
+ * `B` [המכפיל המשותף הקטן ביותר](src/algorithms/math/least-common-multiple) (LCM)
+ * `B` [נפה של ארטוסתנס](src/algorithms/math/sieve-of-eratosthenes) - מציאת כל המספרים הראשוניים עד לגבול כלשהו
+ * `B` [האם חזקה של שתיים](src/algorithms/math/is-power-of-two) - בדיקה אם מספר הוא חזקה של שתיים (אלגוריתמים נאיביים וביטיים)
+ * `B` [משולש פסקל](src/algorithms/math/pascal-triangle)
+ * `B` [מספר מרוכב](src/algorithms/math/complex-number) - מספרים מרוכבים ופעולות בסיסיות עליהם
+ * `B` [רדיאן ומעלות](src/algorithms/math/radian) - המרה מרדיאנים למעלות ובחזרה
+ * `B` [חזקה מהירה](src/algorithms/math/fast-powering)
+ * `B` [שיטת הורנר](src/algorithms/math/horner-method) - הערכת פולינום
+ * `B` [מטריצות](src/algorithms/math/matrix) - מטריצות ופעולות בסיסיות על מטריצות (כפל, טרנספוזיציה וכו')
+ * `B` [מרחק אוקלידי](src/algorithms/math/euclidean-distance) - מרחק בין שתי נקודות/וקטורים/מטריצות
+ * `A` [חלוקת מספר שלם](src/algorithms/math/integer-partition)
+ * `A` [שורש ריבועי](src/algorithms/math/square-root) - שיטת ניוטון
+ * `A` [אלגוריתם π של ליו הוי](src/algorithms/math/liu-hui) - חישובי π מקורבים על בסיס N-גונים
+ * `A` [התמרת פורייה הבדידה](src/algorithms/math/fourier-transform) - פירוק פונקציה של זמן (אות) לתדרים המרכיבים אותה
+
+* **קבוצות**
+ * `B` [מכפלה קרטזית](src/algorithms/sets/cartesian-product) - מכפלה של מספר קבוצות
+ * `B` [ערבוב פישר-ייטס](src/algorithms/sets/fisher-yates) - תמורה אקראית של רצף סופי
+ * `A` [קבוצת חזקה](src/algorithms/sets/power-set) - כל תתי הקבוצות של קבוצה (פתרונות ביטיים, מעקב לאחור וקסקדה)
+ * `A` [תמורות](src/algorithms/sets/permutations) (עם ובלי חזרות)
+ * `A` [צירופים](src/algorithms/sets/combinations) (עם ובלי חזרות)
+ * `A` [תת-רצף משותף ארוך ביותר](src/algorithms/sets/longest-common-subsequence) (LCS)
+ * `A` [תת-רצף עולה ארוך ביותר](src/algorithms/sets/longest-increasing-subsequence)
+ * `A` [על-רצף משותף קצר ביותר](src/algorithms/sets/shortest-common-supersequence) (SCS)
+ * `A` [בעיית התרמיל](src/algorithms/sets/knapsack-problem) - "0/1" ו"לא מוגבל"
+ * `A` [תת-מערך מקסימלי](src/algorithms/sets/maximum-subarray) - "כוח ברוטלי" ו"תכנות דינמי" (Kadane) גרסאות
+ * `A` [סכום צירוף](src/algorithms/sets/combination-sum) - מציאת כל הצירופים שיוצרים סכום ספציפי
+
+* **מחרוזות**
+ * `B` [מרחק המינג](src/algorithms/string/hamming-distance) - מספר העמדות שבהן הסמלים שונים
+ * `B` [פלינדרום](src/algorithms/string/palindrome) - בדיקה אם המחרוזת זהה בקריאה לאחור
+ * `A` [מרחק לוונשטיין](src/algorithms/string/levenshtein-distance) - מרחק העריכה המינימלי בין שתי רצפים
+ * `A` [אלגוריתם קנות'-מוריס-פראט](src/algorithms/string/knuth-morris-pratt) (אלגוריתם KMP) - חיפוש תת-מחרוזת (התאמת תבנית)
+ * `A` [אלגוריתם Z](src/algorithms/string/z-algorithm) - חיפוש תת-מחרוזת (התאמת תבנית)
+ * `A` [אלגוריתם רבין קארפ](src/algorithms/string/rabin-karp) - חיפוש תת-מחרוזת
+ * `A` [תת-מחרוזת משותפת ארוכה ביותר](src/algorithms/string/longest-common-substring)
+ * `A` [התאמת ביטוי רגולרי](src/algorithms/string/regular-expression-matching)
+
+* **חיפושים**
+ * `B` [חיפוש לינארי](src/algorithms/search/linear-search)
+ * `B` [חיפוש קפיצות](src/algorithms/search/jump-search) (או חיפוש בלוקים) - חיפוש במערך ממוין
+ * `B` [חיפוש בינארי](src/algorithms/search/binary-search) - חיפוש במערך ממוין
+ * `B` [חיפוש אינטרפולציה](src/algorithms/search/interpolation-search) - חיפוש במערך ממוין עם התפלגות אחידה
+
+* **מיון**
+ * `B` [מיון בועות](src/algorithms/sorting/bubble-sort)
+ * `B` [מיון בחירה](src/algorithms/sorting/selection-sort)
+ * `B` [מיון הכנסה](src/algorithms/sorting/insertion-sort)
+ * `B` [מיון ערימה](src/algorithms/sorting/heap-sort)
+ * `B` [מיון מיזוג](src/algorithms/sorting/merge-sort)
+ * `B` [מיון מהיר](src/algorithms/sorting/quick-sort) - יישומים במקום ולא במקום
+ * `B` [מיון צדפות](src/algorithms/sorting/shell-sort)
+ * `B` [מיון ספירה](src/algorithms/sorting/counting-sort)
+ * `B` [מיון בסיס](src/algorithms/sorting/radix-sort)
+ * `B` [מיון דלי](src/algorithms/sorting/bucket-sort)
+
+* **רשימות מקושרות**
+ * `B` [מעבר ישר](src/algorithms/linked-list/traversal)
+ * `B` [מעבר הפוך](src/algorithms/linked-list/reverse-traversal)
+
+* **עצים**
+ * `B` [חיפוש לעומק](src/algorithms/tree/depth-first-search) (DFS)
+ * `B` [חיפוש לרוחב](src/algorithms/tree/breadth-first-search) (BFS)
+
+* **גרפים**
+ * `B` [חיפוש לעומק](src/algorithms/graph/depth-first-search) (DFS)
+ * `B` [חיפוש לרוחב](src/algorithms/graph/breadth-first-search) (BFS)
+ * `B` [אלגוריתם קרוסקל](src/algorithms/graph/kruskal) - מציאת עץ פורש מינימלי (MST) עבור גרף לא מכוון משוקלל
+ * `A` [אלגוריתם דייקסטרה](src/algorithms/graph/dijkstra) - מציאת המסלולים הקצרים ביותר לכל קודקודי הגרף מקודקוד יחיד
+ * `A` [אלגוריתם בלמן-פורד](src/algorithms/graph/bellman-ford) - מציאת המסלולים הקצרים ביותר לכל קודקודי הגרף מקודקוד יחיד
+ * `A` [אלגוריתם פלויד-וורשל](src/algorithms/graph/floyd-warshall) - מציאת המסלולים הקצרים ביותר בין כל זוגות הקודקודים
+ * `A` [זיהוי מעגל](src/algorithms/graph/detect-cycle) - עבור גרפים מכוונים ולא מכוונים (גרסאות מבוססות DFS וקבוצה מופרדת)
+ * `A` [אלגוריתם פרים](src/algorithms/graph/prim) - מציאת עץ פורש מינימלי (MST) עבור גרף לא מכוון משוקלל
+ * `A` [מיון טופולוגי](src/algorithms/graph/topological-sorting) - שיטת DFS
+ * `A` [נקודות חיתוך](src/algorithms/graph/articulation-points) - אלגוריתם טרג'ן (מבוסס DFS)
+ * `A` [גשרים](src/algorithms/graph/bridges) - אלגוריתם מבוסס DFS
+ * `A` [מסלול ומעגל אוילר](src/algorithms/graph/eulerian-path) - אלגוריתם פלרי - ביקור בכל קשת בדיוק פעם אחת
+ * `A` [מעגל המילטון](src/algorithms/graph/hamiltonian-cycle) - ביקור בכל קודקוד בדיוק פעם אחת
+ * `A` [רכיבים קשירים חזק](src/algorithms/graph/strongly-connected-components) - אלגוריתם קוסרג'ו
+ * `A` [בעיית הסוכן הנוסע](src/algorithms/graph/travelling-salesman) - המסלול הקצר ביותר האפשרי שמבקר בכל עיר וחוזר לעיר המוצא
+
+* **הצפנה**
+ * `B` [גיבוב פולינומי](src/algorithms/cryptography/polynomial-hash) - פונקציית גיבוב מתגלגלת המבוססת על פולינום
+ * `B` [צופן גדר מסילה](src/algorithms/cryptography/rail-fence-cipher) - אלגוריתם הצפנת טרנספוזיציה להצפנת הודעות
+ * `B` [צופן קיסר](src/algorithms/cryptography/caesar-cipher) - צופן החלפה פשוט
+ * `B` [צופן היל](src/algorithms/cryptography/hill-cipher) - צופן החלפה המבוסס על אלגברה לינארית
+
+* **למידת מכונה**
+ * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 פונקציות JS פשוטות שמדגימות כיצד מכונות יכולות ללמוד באמת (תפוצה קדימה/אחורה)
+ * `B` [k-NN](src/algorithms/ml/knn) - אלגוריתם סיווג k-השכנים הקרובים ביותר
+ * `B` [k-Means](src/algorithms/ml/k-means) - אלגוריתם אשכול k-Means
+
+* **עיבוד תמונה**
+ * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - אלגוריתם שינוי גודל תמונה מודע תוכן
+
+* **סטטיסטיקה**
+ * `B` [משקל אקראי](src/algorithms/statistics/weighted-random) - בחירת פריט אקראי מהרשימה על בסיס משקלי הפריטים
+
+* **אלגוריתמים אבולוציוניים**
+ * `A` [אלגוריתם גנטי](https://github.com/trekhleb/self-parking-car-evolution) - דוגמה לאופן שבו ניתן ליישם אלגוריתם גנטי לאימון מכוניות בחניה עצמית
+
+* **לא מסווג**
+ * `B` [מגדלי האנוי](src/algorithms/uncategorized/hanoi-tower)
+ * `B` [סיבוב מטריצה ריבועית](src/algorithms/uncategorized/square-matrix-rotation) - אלגוריתם במקום
+ * `B` [משחק הקפיצות](src/algorithms/uncategorized/jump-game) - דוגמאות למעקב לאחור, תכנות דינמי (מלמעלה למטה + מלמטה למעלה) וחמדני
+ * `B` [מסלולים ייחודיים](src/algorithms/uncategorized/unique-paths) - דוגמאות למעקב לאחור, תכנות דינמי ומבוססות על משולש פסקל
+ * `B` [מדרגות גשם](src/algorithms/uncategorized/rain-terraces) - בעיית לכידת מי גשם (גרסאות תכנות דינמי וכוח ברוטלי)
+ * `B` [מדרגות רקורסיביות](src/algorithms/uncategorized/recursive-staircase) - ספירת מספר הדרכים להגיע לראש (4 פתרונות)
+ * `B` [הזמן הטוב ביותר לקנות ולמכור מניות](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - דוגמאות לחלוקה וכיבוש ומעבר אחד
+ * `A` [בעיית N-המלכות](src/algorithms/uncategorized/n-queens)
+ * `A` [סיור הפרש](src/algorithms/uncategorized/knight-tour)
+
+### אלגוריתמים לפי פרדיגמה
+
+פרדיגמה אלגוריתמית היא שיטה או גישה כללית המונחת בבסיס התכנון של מחלקת אלגוריתמים. זוהי הפשטה גבוהה יותר מהמושג של אלגוריתם, בדיוק כפי שאלגוריתם הוא הפשטה גבוהה יותר מתוכנית מחשב.
+
+* **כוח ברוטלי** - בודק את כל האפשרויות ובוחר את הפתרון הטוב ביותר
+ * `B` [חיפוש לינארי](src/algorithms/search/linear-search)
+ * `B` [מדרגות גשם](src/algorithms/uncategorized/rain-terraces) - בעיית לכידת מי גשם
+ * `B` [מדרגות רקורסיביות](src/algorithms/uncategorized/recursive-staircase) - ספירת מספר הדרכים להגיע לראש
+ * `A` [תת-מערך מקסימלי](src/algorithms/sets/maximum-subarray)
+ * `A` [בעיית הסוכן הנוסע](src/algorithms/graph/travelling-salesman) - המסלול הקצר ביותר האפשרי שמבקר בכל עיר וחוזר לעיר המוצא
+ * `A` [התמרת פורייה הבדידה](src/algorithms/math/fourier-transform) - פירוק פונקציה של זמן (אות) לתדרים המרכיבים אותה
+
+* **חמדני** - בוחר את האפשרות הטובה ביותר בזמן הנוכחי, ללא כל התחשבות בעתיד
+ * `B` [משחק הקפיצות](src/algorithms/uncategorized/jump-game)
+ * `A` [בעיית התרמיל הלא מוגבל](src/algorithms/sets/knapsack-problem)
+ * `A` [אלגוריתם דייקסטרה](src/algorithms/graph/dijkstra) - מציאת המסלולים הקצרים ביותר לכל קודקודי הגרף
+ * `A` [אלגוריתם פרים](src/algorithms/graph/prim) - מציאת עץ פורש מינימלי (MST) עבור גרף לא מכוון משוקלל
+ * `A` [אלגוריתם קרוסקל](src/algorithms/graph/kruskal) - מציאת עץ פורש מינימלי (MST) עבור גרף לא מכוון משוקלל
+
+* **חלוקה וכיבוש** - מחלק את הבעיה לחלקים קטנים יותר ואז פותר חלקים אלה
+ * `B` [חיפוש בינארי](src/algorithms/search/binary-search)
+ * `B` [מגדלי האנוי](src/algorithms/uncategorized/hanoi-tower)
+ * `B` [משולש פסקל](src/algorithms/math/pascal-triangle)
+ * `B` [אלגוריתם אוקלידס](src/algorithms/math/euclidean-algorithm) - חישוב המחלק המשותף הגדול ביותר (GCD)
+ * `B` [מיון מיזוג](src/algorithms/sorting/merge-sort)
+ * `B` [מיון מהיר](src/algorithms/sorting/quick-sort)
+ * `B` [חיפוש לעומק בעץ](src/algorithms/tree/depth-first-search) (DFS)
+ * `B` [חיפוש לעומק בגרף](src/algorithms/graph/depth-first-search) (DFS)
+ * `B` [מטריצות](src/algorithms/math/matrix) - יצירה ומעבר על מטריצות בצורות שונות
+ * `B` [משחק הקפיצות](src/algorithms/uncategorized/jump-game)
+ * `B` [חזקה מהירה](src/algorithms/math/fast-powering)
+ * `B` [הזמן הטוב ביותר לקנות ולמכור מניות](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - דוגמאות לחלוקה וכיבוש ומעבר אחד
+ * `A` [תמורות](src/algorithms/sets/permutations) (עם ובלי חזרות)
+ * `A` [צירופים](src/algorithms/sets/combinations) (עם ובלי חזרות)
+ * `A` [תת-מערך מקסימלי](src/algorithms/sets/maximum-subarray)
+
+* **תכנות דינמי** - בניית פתרון באמצעות תת-פתרונות שנמצאו קודם לכן
+ * `B` [מספר פיבונאצ'י](src/algorithms/math/fibonacci)
+ * `B` [משחק הקפיצות](src/algorithms/uncategorized/jump-game)
+ * `B` [מסלולים ייחודיים](src/algorithms/uncategorized/unique-paths)
+ * `B` [מדרגות גשם](src/algorithms/uncategorized/rain-terraces) - בעיית לכידת מי גשם
+ * `B` [מדרגות רקורסיביות](src/algorithms/uncategorized/recursive-staircase) - ספירת מספר הדרכים להגיע לראש
+ * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - אלגוריתם שינוי גודל תמונה מודע תוכן
+ * `A` [מרחק לוונשטיין](src/algorithms/string/levenshtein-distance) - מרחק העריכה המינימלי בין שתי רצפים
+ * `A` [תת-רצף משותף ארוך ביותר](src/algorithms/sets/longest-common-subsequence) (LCS)
+ * `A` [תת-מחרוזת משותפת ארוכה ביותר](src/algorithms/string/longest-common-substring)
+ * `A` [תת-רצף עולה ארוך ביותר](src/algorithms/sets/longest-increasing-subsequence)
+ * `A` [על-רצף משותף קצר ביותר](src/algorithms/sets/shortest-common-supersequence)
+ * `A` [בעיית התרמיל 0/1](src/algorithms/sets/knapsack-problem)
+ * `A` [חלוקת מספר שלם](src/algorithms/math/integer-partition)
+ * `A` [תת-מערך מקסימלי](src/algorithms/sets/maximum-subarray)
+ * `A` [אלגוריתם בלמן-פורד](src/algorithms/graph/bellman-ford) - מציאת המסלולים הקצרים ביותר לכל קודקודי הגרף
+ * `A` [אלגוריתם פלויד-וורשל](src/algorithms/graph/floyd-warshall) - מציאת המסלולים הקצרים ביותר בין כל זוגות הקודקודים
+ * `A` [התאמת ביטוי רגולרי](src/algorithms/string/regular-expression-matching)
+
+* **מעקב לאחור** - בדומה לכוח ברוטלי, מנסה לייצר את כל הפתרונות האפשריים, אך בכל פעם שאתה מייצר פתרון הבא אתה בודק אם הוא עומד בכל התנאים, ורק אז ממשיך לייצר פתרונות הבאים. אחרת, חוזר אחורה, והולך בנתיב אחר של מציאת פתרון. בדרך כלל מעבר DFS של מרחב המצבים משמש.
+ * `B` [משחק הקפיצות](src/algorithms/uncategorized/jump-game)
+ * `B` [מסלולים ייחודיים](src/algorithms/uncategorized/unique-paths)
+ * `B` [קבוצת חזקה](src/algorithms/sets/power-set) - כל תתי הקבוצות של קבוצה
+ * `A` [מעגל המילטון](src/algorithms/graph/hamiltonian-cycle) - ביקור בכל קודקוד בדיוק פעם אחת
+ * `A` [בעיית N-המלכות](src/algorithms/uncategorized/n-queens)
+ * `A` [סיור הפרש](src/algorithms/uncategorized/knight-tour)
+ * `A` [סכום צירוף](src/algorithms/sets/combination-sum) - מציאת כל הצירופים שיוצרים סכום ספציפי
+
+* **סניף וחסום** - זוכר את הפתרון בעלות הנמוכה ביותר שנמצא בכל שלב של החיפוש המעקב לאחור, ומשתמש בעלות של הפתרון בעלות הנמוכה ביותר שנמצא עד כה כגבול תחתון על העלות של פתרון בעלות מינימלית לבעיה, על מנת לפסול פתרונות חלקיים עם עלויות גדולות יותר מהפתרון בעלות הנמוכה ביותר שנמצא עד כה. בדרך כלל מעבר BFS בשילוב עם מעבר DFS של עץ מרחב המצבים משמש.
+
+## כיצד להשתמש במאגר זה
+
+**התקנת כל התלויות**
+
+```
+npm install
+```
+
+**הרצת ESLint**
+
+ייתכן שתרצה להריץ אותו כדי לבדוק את איכות הקוד.
+
+```
+npm run lint
+```
+
+**הרצת כל הבדיקות**
+
+```
+npm test
+```
+
+**הרצת בדיקות לפי שם**
+
+```
+npm test -- 'LinkedList'
+```
+
+**פתרון בעיות**
+
+אם הלינטינג או הבדיקות נכשלים, נסה למחוק את התיקייה `node_modules` ולהתקין מחדש את חבילות npm:
+
+```
+rm -rf ./node_modules
+npm i
+```
+
+בנוסף, ודא שאתה משתמש בגרסת Node נכונה (`>=16`). אם אתה משתמש ב-[nvm](https://github.com/nvm-sh/nvm) לניהול גרסאות Node, תוכל להריץ `nvm use` מתיקיית השורש של הפרויקט והגרסה הנכונה תיבחר.
+
+**שטח משחקים**
+
+אתה יכול לשחק עם מבני נתונים ואלגוריתמים בקובץ `./src/playground/playground.js` ולכתוב
+בדיקות עבורו ב-`./src/playground/__test__/playground.test.js`.
+
+לאחר מכן פשוט הרץ את הפקודה הבאה כדי לבדוק אם קוד שטח המשחקים שלך עובד כמצופה:
+
+```
+npm test -- 'playground'
+```
+
+## מידע שימושי
+
+### הפניות
+
+- [▶ מבני נתונים ואלגוריתמים ב-YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [✍🏻 סקיצות של מבני נתונים](https://okso.app/showcase/data-structures)
+
+### סימון ה-O הגדול
+
+סימון *ה-O הגדול* משמש לסיווג אלגוריתמים לפי כיצד זמן הריצה או דרישות המרחב שלהם גדלים ככל שגודל הקלט גדל.
+בתרשים שלהלן תוכל למצוא את הסדרים הנפוצים ביותר של צמיחת אלגוריתמים המצוינים בסימון ה-O הגדול.
+
+
+
+מקור: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+להלן רשימה של כמה מסימוני ה-O הגדול הנפוצים ביותר והשוואות הביצועים שלהם מול גדלים שונים של נתוני קלט.
+
+| סימון ה-O הגדול | חישובים ל-10 אלמנטים | חישובים ל-100 אלמנטים | חישובים ל-1000 אלמנטים |
+| ---------------- | --------------------- | ---------------------- | ----------------------- |
+| **O(1)** | 1 | 1 | 1 |
+| **O(log N)** | 3 | 6 | 9 |
+| **O(N)** | 10 | 100 | 1000 |
+| **O(N log N)** | 30 | 600 | 9000 |
+| **O(N^2)** | 100 | 10000 | 1000000 |
+| **O(2^N)** | 1024 | 1.26e+29 | 1.07e+301 |
+| **O(N!)** | 3628800 | 9.3e+157 | 4.02e+2567 |
+
+### מורכבות פעולות מבני נתונים
+
+| מבנה נתונים | גישה | חיפוש | הכנסה | מחיקה | הערות |
+| --------------------- | :-----: | :-----: | :-----: | :-----: | :------ |
+| **מערך** | 1 | n | n | n | |
+| **מחסנית** | n | n | 1 | 1 | |
+| **תור** | n | n | 1 | 1 | |
+| **רשימה מקושרת** | n | n | 1 | n | |
+| **טבלת גיבוב** | - | n | n | n | במקרה של פונקציית גיבוב מושלמת, העלויות יהיו O(1) |
+| **עץ חיפוש בינארי** | n | n | n | n | במקרה של עץ מאוזן, העלויות יהיו O(log(n)) |
+| **עץ B** | log(n) | log(n) | log(n) | log(n) | |
+| **עץ אדום-שחור** | log(n) | log(n) | log(n) | log(n) | |
+| **עץ AVL** | log(n) | log(n) | log(n) | log(n) | |
+| **מסנן בלום** | - | 1 | 1 | - | תוצאות חיוביות שגויות אפשריות בעת חיפוש |
+
+### מורכבות אלגוריתמי מיון מערכים
+
+| שם | הטוב ביותר | ממוצע | הגרוע ביותר | זיכרון | יציב | הערות |
+| ------------------- | :----------------: | :-----------------: | :------------------: | :-----: | :-----: | :------ |
+| **מיון בועות** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | כן | |
+| **מיון הכנסה** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | כן | |
+| **מיון בחירה** | n<sup>2</sup> | n<sup>2</sup> | n<sup>2</sup> | 1 | לא | |
+| **מיון ערימה** | n log(n) | n log(n) | n log(n) | 1 | לא | |
+| **מיון מיזוג** | n log(n) | n log(n) | n log(n) | n | כן | |
+| **מיון מהיר** | n log(n) | n log(n) | n<sup>2</sup> | log(n) | לא | מיון מהיר בדרך כלל מבוצע במקום עם O(log(n)) שטח מחסנית |
+| **מיון צדפות** | n log(n) | תלוי ברצף הפער | n (log(n))<sup>2</sup> | 1 | לא | |
+| **מיון ספירה** | n + r | n + r | n + r | n + r | כן | r - המספר הגדול ביותר במערך |
+| **מיון בסיס** | n * k | n * k | n * k | n + k | כן | k - אורך המפתח הארוך ביותר |
+
+## תומכי הפרויקט
+
+> אתה יכול לתמוך בפרויקט זה דרך ❤️️ [GitHub](https://github.com/sponsors/trekhleb) או ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+[אנשים שתומכים בפרויקט זה](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+
+## מחבר
+
+[@trekhleb](https://trekhleb.dev)
+
+כמה [פרויקטים](https://trekhleb.dev/projects/) ו[מאמרים](https://trekhleb.dev/blog/) נוספים על JavaScript ואלגוריתמים ב-[trekhleb.dev](https://trekhleb.dev)* `B` [משחק הקפיצות](src/algorithms/uncategor * `B` [חיפוש בינארי](src/algorithms
diff --git a/README.id-ID.md b/README.id-ID.md
index 2a258f973c..9dd908c2e6 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -5,7 +5,7 @@
Repositori ini berisi contoh-contoh algoritme dan struktur data yang populer menggunakan JavaScript.
-Setiap algoritme dan struktur data memiliki README-nya tersendiri dengan penjelasan yang berkaitan dan tautan untuk bacaan lebih lanjut (termasuk tautan menuju video YouTube).
+Setiap algoritma dan struktur data memiliki README-nya tersendiri dengan penjelasan yang berkaitan dan tautan untuk bacaan lebih lanjut (termasuk tautan menuju video YouTube).
_Baca ini dalam bahasa yang lain:_
[_English_](https://github.com/trekhleb/javascript-algorithms/),
@@ -21,7 +21,11 @@ _Baca ini dalam bahasa yang lain:_
[_Türk_](README.tr-TR.md),
[_Italiana_](README.it-IT.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
_☝ Perhatikan bahwa proyek ini hanya dimaksudkan untuk tujuan pembelajaran dan riset, dan **tidak** dimaksudkan untuk digunakan sebagai produksi._
@@ -49,24 +53,24 @@ Struktur data adalah cara tertentu untuk mengatur dan menyimpan data dalam kompu
- `L` [_Disjoint Set_](src/data-structures/disjoint-set)
- `L` [_Bloom Filter_](src/data-structures/bloom-filter)
-## Algoritme
+## Algoritma
-Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu masalah. Ia adalah sekumpulan aturan yang menjelaskan secara tepat urutan-urutan dari sebuah operasi.
+Algoritma adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu masalah. Ia adalah sekumpulan aturan yang menjelaskan secara tepat urutan-urutan dari sebuah operasi.
`P` - Pemula, `L` - Lanjutan
-### Algoritme Berdasarkanan Topik
+### Algoritma Berdasarkanan Topik
- **Matematika**
- - `P` [Manipulasi Bit](src/algorithms/math/bits) - menetapkan/mendapatkan/memperbarui/mengahpus bit, perkalian/pembagian dengan angka 2, membuat bilangan negatif etc.
+ - `P` [Manipulasi Bit](src/algorithms/math/bits) - menetapkan/mendapatkan/memperbarui/menghapus bit, perkalian/pembagian dengan angka 2, membuat bilangan negatif dan lain-lain.
- `P` [Faktorial](src/algorithms/math/Faktorial)
- `P` [Bilangan Fibonacci](src/algorithms/math/fibonacci) - versi klasik dan bentuk tertutup
- `P` [Faktor Prima](src/algorithms/math/prime-factors) - menemukan faktor prima dan menghitungnya menggunakan teorema Hardy-Ramanujan
- `P` [Pengujian Bilangan Prima](src/algorithms/math/primality-test) (metode _trial division_)
- - `P` [Algoritme Euclidean](src/algorithms/math/euclidean-algorithm) - menghitung Faktor Persekutuan Terbesar (FPB)
+ - `P` [Algoritma Euclidean](src/algorithms/math/euclidean-algorithm) - menghitung Faktor Persekutuan Terbesar (FPB)
- `P` [_Least Common Multiple_](src/algorithms/math/least-common-multiple) (LCM)
- `P` [_Sieve of Eratosthenes_](src/algorithms/math/sieve-of-eratosthenes) - menemukan semua bilangan prima hingga batas yang ditentukan
- - `P` [_Is Power of Two_](src/algorithms/math/is-power-of-two) - mengecek apakah sebuah bilangan adalah hasil dari pangkat dua (algoritme _naive_ dan _bitwise_)
+ - `P` [_Is Power of Two_](src/algorithms/math/is-power-of-two) - mengecek apakah sebuah bilangan adalah hasil dari pangkat dua (algoritma _naive_ dan _bitwise_)
- `P` [Segitiga Pascal](src/algorithms/math/pascal-triangle)
- `P` [Bilangan Kompleks](src/algorithms/math/complex-number) - bilangan kompleks dengan operasi dasarnya
- `P` [Radian & Derajat](src/algorithms/math/radian) - konversi radian ke derajat dan sebaliknya
@@ -74,7 +78,7 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
- `P` [Metode Horner](src/algorithms/math/horner-method) - evaluasi polinomial
- `L` [Partisi Bilangan Bulat](src/algorithms/math/integer-partition)
- `L` [Akar Pangkat Dua](src/algorithms/math/square-root) - metode Newton
- - `L` [Algoritme π Liu Hui](src/algorithms/math/liu-hui) - perkiraan perhitungan π berdasarkan segibanyak
+ - `L` [Algoritma π Liu Hui](src/algorithms/math/liu-hui) - perkiraan perhitungan π berdasarkan segibanyak
- `L` [Transformasi Diskrit Fourier](src/algorithms/math/fourier-transform) - menguraikan fungsi waktu (sinyal) menjadi frekuensi yang menyusunnya
- **Himpunan**
- `P` [Produk Kartesian](src/algorithms/sets/cartesian-product) - hasil dari beberapa himpunan
@@ -90,10 +94,10 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
- `L` [_Combination Sum_](src/algorithms/sets/combination-sum) - menemukan semua kombinasi yang membentuk jumlah tertentu
- **String**
- `P` [Jarak Hamming](src/algorithms/string/hamming-distance) - jumlah posisi di mana ditemukan simbol-simbol yang berbeda
- - `L` [Algoritme Jarak Levenshtein](src/algorithms/string/levenshtein-distance) - _edit distance_ minimum antara dua urutan
- - `L` [Algoritme Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (Algoritme KMP) - pencarian substring (pencocokan pola)
- - `L` [AlgoritmeZ](src/algorithms/string/z-algorithm) - pencarian substring (pencocokan pola)
- - `L` [Algoritme Rabin Karp](src/algorithms/string/rabin-karp) - pencarian substring
+ - `L` [Algoritma Jarak Levenshtein](src/algorithms/string/levenshtein-distance) - _edit distance_ minimum antara dua urutan
+ - `L` [Algoritma Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (Algoritma KMP) - pencarian substring (pencocokan pola)
+ - `L` [Algoritma Z](src/algorithms/string/z-algorithm) - pencarian substring (pencocokan pola)
+ - `L` [Algoritma Rabin Karp](src/algorithms/string/rabin-karp) - pencarian substring
- `L` [_Longest Common Substring_](src/algorithms/string/longest-common-substring)
- `L` [Pencocokan Ekspresi Reguler](src/algorithms/string/regular-expression-matching)
- **Pencarian**
@@ -120,18 +124,18 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
- **Graf**
- `P` [Pencarian Kedalaman Pertama](src/algorithms/graph/depth-first-search) (DFS)
- `P` [Pencarian Luas Pertama](src/algorithms/graph/breadth-first-search) (BFS)
- - `P` [Algoritme Kruskal](src/algorithms/graph/kruskal) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
- - `L` [Algoritme Dijkstra](src/algorithms/graph/dijkstra) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
- - `L` [Algoritme Bellman-Ford](src/algorithms/graph/bellman-ford) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
- - `L` [Algoritme Floyd-Warshall](src/algorithms/graph/floyd-warshall) - menemukan jalur terpendek antara semua pasangan sudut
+ - `P` [Algoritma Kruskal](src/algorithms/graph/kruskal) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+ - `L` [Algoritma Dijkstra](src/algorithms/graph/dijkstra) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+ - `L` [Algoritma Bellman-Ford](src/algorithms/graph/bellman-ford) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+ - `L` [Algoritma Floyd-Warshall](src/algorithms/graph/floyd-warshall) - menemukan jalur terpendek antara semua pasangan sudut
- `L` [Mendeteksi Siklus](src/algorithms/graph/detect-cycle) - untuk graf berarah dan tidak berarah (berdasarkan versi DFS dan _Disjoint Set_)
- - `L` [ALgoritme Prim](src/algorithms/graph/prim) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+ - `L` [ALgoritma Prim](src/algorithms/graph/prim) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
- `L` [Sortir Topologi](src/algorithms/graph/topological-sorting) - metode DFS
- - `L` [Poin Artikulasi](src/algorithms/graph/articulation-points) - Algoritme Tarjan (berdasarkan DFS)
- - `L` [Jembatan](src/algorithms/graph/bridges) - Algoritme berdasarkan DFS
- - `L` [Jalur dan Sirkuit Eulerian](src/algorithms/graph/eulerian-path) - Algoritme Fleury - Mengunjungi setiap tepinya tepat satu kali
+ - `L` [Poin Artikulasi](src/algorithms/graph/articulation-points) - Algoritma Tarjan (berdasarkan DFS)
+ - `L` [Jembatan](src/algorithms/graph/bridges) - Algoritma berdasarkan DFS
+ - `L` [Jalur dan Sirkuit Eulerian](src/algorithms/graph/eulerian-path) - Algoritma Fleury - Mengunjungi setiap tepinya tepat satu kali
- `L` [Siklus Hamiltonian](src/algorithms/graph/hamiltonian-cycle) - mengunjungi setiap sudutnya tepat satu kali
- - `L` [Komponen yang Terkoneksi dengan Kuat](src/algorithms/graph/strongly-connected-components) - Algoritme Kosaraju
+ - `L` [Komponen yang Terkoneksi dengan Kuat](src/algorithms/graph/strongly-connected-components) - Algoritma Kosaraju
- `L` [Permasalahan Penjual Keliling](src/algorithms/graph/travelling-salesman) - kemungkinan rute terpendek untuk mengunjungi setiap kota dan kembali lagi ke kota asal
- **Kriptografi**
- `P` [Polinomial Hash](src/algorithms/cryptography/polynomial-hash) - fungsi rolling hash berdasarkan polinomial
@@ -140,7 +144,7 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
- `P` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 fungsi JS sederhana yang mengilustrasikan bagaimana mesin-mesin dapat benar-benar belajar (perambatan maju/mundur)
- **Tidak Dikategorikan**
- `P` [Menara Hanoi](src/algorithms/uncategorized/hanoi-tower)
- - `P` [Perputaran Matriks Persegi](src/algorithms/uncategorized/square-matrix-rotation) - algoritme _in-place_
+ - `P` [Perputaran Matriks Persegi](src/algorithms/uncategorized/square-matrix-rotation) - algoritma _in-place_
- `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game) - runut-balik, pemrograman dinamis (atas ke bawah + bawah ke atas) and contoh-contoh _greedy_
- `P` [_Unique Paths_](src/algorithms/uncategorized/unique-paths) - runut-balik, pemrograman dinamis and contoh-contoh beradsarkan Segitiga Pascal
- `P` [_Rain Terraces_](src/algorithms/uncategorized/rain-terraces) - permasalahan _trapping rain water_ (versi pemrograman dinamis and _brute force_)
@@ -148,9 +152,9 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
- `L` [Permainan N-Queen](src/algorithms/uncategorized/n-queens)
- `L` [Permainan Knight's Tour](src/algorithms/uncategorized/knight-tour)
-### Algoritme Berdasarkan Paradigma
+### Algoritma Berdasarkan Paradigma
-Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari desain sebuah tingkatan algoritme. Paradigma algoritmik merupakan abstraksi yang lebih tinggi dari gagasan sebuah algoritme, seperti halnya sebuah algoritme merupakan abstraksi yang lebih tinggi dari sebuah program komputer.
+Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari desain sebuah tingkatan algoritma. Paradigma algoritmik merupakan abstraksi yang lebih tinggi dari gagasan sebuah algoritma, seperti halnya sebuah algoritma merupakan abstraksi yang lebih tinggi dari sebuah program komputer.
- **_Brute Force_** - melihat ke semua kemungkinan dan memilih solusi yang terbaik
- `P` [Pencarian Linier](src/algorithms/search/linear-search)
@@ -162,14 +166,14 @@ Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari de
- **_Greedy_** - memilih pilihan terbaik pada saat ini tanpa mempertimbangkan masa yang akan datang
- `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game)
- `L` [Permasalahan Knapsack yang Tidak Dibatasi](src/algorithms/sets/knapsack-problem)
- - `L` [Algoritme Dijkstra](src/algorithms/graph/dijkstra) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
- - `L` [Algoritme Prim](src/algorithms/graph/prim) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
- - `L` [Algoritme Kruskal](src/algorithms/graph/kruskal) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+ - `L` [Algoritma Dijkstra](src/algorithms/graph/dijkstra) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+ - `L` [Algoritma Prim](src/algorithms/graph/prim) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+ - `L` [Algoritma Kruskal](src/algorithms/graph/kruskal) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
- **Memecah dan Menaklukkan** - membagi masalah menjadi bagian-bagian yang kecil, lalu memcahkan bagian-bagian tersebut
- `P` [Pencarian Biner](src/algorithms/search/binary-search)
- `P` [Menara Hanoi](src/algorithms/uncategorized/hanoi-tower)
- `P` [Segitiga Pascal](src/algorithms/math/pascal-triangle)
- - `P` [Algoritme Euclidean](src/algorithms/math/euclidean-algorithm) - menghitung Faktor Persekutuan Terbesar (FPB)
+ - `P` [Algoritma Euclidean](src/algorithms/math/euclidean-algorithm) - menghitung Faktor Persekutuan Terbesar (FPB)
- `P` [Sortir Gabungan](src/algorithms/sorting/merge-sort)
- `P` [Sortir Cepat](src/algorithms/sorting/quick-sort)
- `P` [Pencarian Kedalaman Pertama untuk Pohon](src/algorithms/tree/depth-first-search) (DFS)
@@ -184,7 +188,7 @@ Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari de
- `P` [_Unique Paths_](src/algorithms/uncategorized/unique-paths)
- `P` [_Rain Terraces_](src/algorithms/uncategorized/rain-terraces) - permasalahan _trapping rain water_
- `P` [Tangga Rekursif](src/algorithms/uncategorized/recursive-staircase) - menghitung jumlah cara untuk mencapai ke atas tangga
- - `L` [Algoritme Jarak Levenshtein](src/algorithms/string/levenshtein-distance) - _edit distance_ minimum antara dua urutan
+ - `L` [Algoritma Jarak Levenshtein](src/algorithms/string/levenshtein-distance) - _edit distance_ minimum antara dua urutan
- `L` [_Longest Common Subsquence_](src/algorithms/sets/longest-common-subsequence) (LCS)
- `L` [_Longest Common Substring_](src/algorithms/string/longest-common-substring)
- `L` [_Longest Increasing Subsequence_](src/algorithms/sets/longest-increasing-subsequence)
@@ -192,10 +196,10 @@ Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari de
- `L` [Permasalahan Knapsack 0/1](src/algorithms/sets/knapsack-problem)
- `L` [Partisi Bilangan Bulat](src/algorithms/math/integer-partition)
- `L` [Upalarik Maksimum](src/algorithms/sets/maximum-subarray)
- - `L` [Algoritme Bellman-Ford](src/algorithms/graph/bellman-ford) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
- - `L` [Algoritme Floyd-Warshall](src/algorithms/graph/floyd-warshall) - menemukan jalur terpendek antara semua pasangan sudut
+ - `L` [Algoritma Bellman-Ford](src/algorithms/graph/bellman-ford) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+ - `L` [Algoritma Floyd-Warshall](src/algorithms/graph/floyd-warshall) - menemukan jalur terpendek antara semua pasangan sudut
- `L` [Pencocokan Ekspresi Reguler](src/algorithms/string/regular-expression-matching)
-- **Runut-balik** - sama halnya dengan _brute force_, algoritme ini mencoba untuk menghasilkan segala kemungkinan solusi, tetapi setiap kali anda menghasilkan solusi selanjutnya, anda akan menguji apakah solusi tersebut memenuhi semua kondisi dan setelah itu baru akan menghasilkan solusi berikutnya. Apabila tidak, maka akan merunut-balik dan mencari solusi di jalur yang berbeda. Biasanya menggunakan lintas DFS dari ruang keadaan.
+- **Runut-balik** - sama halnya dengan _brute force_, algoritma ini mencoba untuk menghasilkan segala kemungkinan solusi, tetapi setiap kali anda menghasilkan solusi selanjutnya, anda akan menguji apakah solusi tersebut memenuhi semua kondisi dan setelah itu baru akan menghasilkan solusi berikutnya. Apabila tidak, maka akan merunut-balik dan mencari solusi di jalur yang berbeda. Biasanya menggunakan lintas DFS dari ruang keadaan.
- `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game)
- `P` [_Unique Paths_](src/algorithms/uncategorized/unique-paths)
- `P` [Himpunan Kuasa](src/algorithms/sets/power-set) - semua himpunan bagian dari sebuah himpunan
@@ -235,7 +239,7 @@ npm test -- 'LinkedList'
**_Playground_**
-Anda dapat bermain dengan algoritme dan struktur data di _file_ `./src/playground/playground.js` dan menuliskan tesnya di `./src/playground/__test__/playground.test.js`.
+Anda dapat bermain dengan algoritma dan struktur data di _file_ `./src/playground/playground.js` dan menuliskan tesnya di `./src/playground/__test__/playground.test.js`.
Lalu, hanya tinggal menjalankan perintah berikut untuk mengetes apakah kode _playground_ anda bekerja sesuai dengan keinginan:
@@ -247,17 +251,17 @@ npm test -- 'playground'
### Referensi
-[▶ Algoritme dan Struktur Data di YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+[▶ Algoritma dan Struktur Data di YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
### Notasi _Big O_
-Notasi _Big O_ digunakan untuk mengklasifikasikan algoritme berdasarkan durasi atau ruang yang dibutuhkan seiring bertambahnya _input_. Pada grafik dibawah, anda dapat menemukan urutan pertumbuhan yang paling umum dari algoritme yang ditentukan dalam notasi _Big O_.
+Notasi _Big O_ digunakan untuk mengklasifikasikan algoritma berdasarkan durasi atau ruang yang dibutuhkan seiring bertambahnya _input_. Pada grafik dibawah, anda dapat menemukan urutan pertumbuhan yang paling umum dari algoritma yang ditentukan dalam notasi _Big O_.
Sumber: [Big O Cheat Sheet](http://bigocheatsheet.com/).
-Di bawah ini adalah daftar dari beberapa notasi _Bog O_ yang sering digunakan dan perbandingan kinerjanya terhadap berbagai ukuran _input data_.
+Di bawah ini adalah daftar dari beberapa notasi _Big O_ yang sering digunakan dan perbandingan kinerjanya terhadap berbagai ukuran _input data_.
| Notasi _Big O_ | Komputasi untuk 10 elemen | Komputasi untuk 100 elemen | Komputasi untuk 1000 elemen |
| -------------- | ------------------------- | -------------------------- | --------------------------- |
@@ -284,7 +288,7 @@ Di bawah ini adalah daftar dari beberapa notasi _Bog O_ yang sering digunakan da
| **AVL Tree** | log(n) | log(n) | log(n) | log(n) | |
| **Bloom Filter** | - | 1 | 1 | - | Positif palsu dimungkinkan saat pencarian |
-### Kompleksitas Algoritme Sortir Larik
+### Kompleksitas Algoritma Sortir Larik
| Nama | Terbaik | Rata-rata | Terburuk | Memori | Stabil | Keterangan |
| -------------------------------------- | :-----------: | :--------------------------: | :-------------------------: | :----: | :----: | :-------------------------------------------------------------------------------- |
@@ -303,3 +307,5 @@ Di bawah ini adalah daftar dari beberapa notasi _Bog O_ yang sering digunakan da
> Anda dapat mendukung proyek ini via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) atau ❤️️ [Patreon](https://www.patreon.com/trekhleb).
[Orang-orang yang mendukung proyek ini](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.it-IT.md b/README.it-IT.md
index 9d8c664f6a..d749a6aa7f 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -20,7 +20,11 @@ _Leggilo in altre lingue:_
[_Türk_](README.tr-TR.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
*☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
@@ -296,3 +300,5 @@ Nella tabella qua sotto ci sono riportate la lista delle notazioni Big O più us
| **Shell sort** | n log(n) | dipende dagli spazi vuoti nella sequenza | n (log(n))<sup>2</sup> | 1 | No | |
| **Counting sort** | n + r | n + r | n + r | n + r | Yes | r - numero più grande nell'array |
| **Radix sort** | n * k | n * k | n * k | n + k | Yes | k - lunghezza della chiave più grande |
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.ja-JP.md b/README.ja-JP.md
index af2c887c2c..acf9dee8f0 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -7,7 +7,7 @@
各アルゴリズムとデータ構造には独自のREADMEがあります。
-関連する説明と、さらに読むためのリンク (関連YouTubeのビデオ)も含まれています。
+関連する説明、そして参考資料 (YouTube動画)も含まれています。
_Read this in other languages:_
[_English_](https://github.com/trekhleb/javascript-algorithms/),
@@ -23,7 +23,11 @@ _Read this in other languages:_
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
## データ構造
@@ -99,7 +103,7 @@ _Read this in other languages:_
* `A` [正規表現マッチング](src/algorithms/string/regular-expression-matching)
* **検索**
* `B` [リニアサーチ](src/algorithms/search/linear-search)
- * `B` [ジャンプ検索](src/algorithms/search/jump-search) (or Block Search) - ソートされた配列で検索
+ * `B` [ジャンプ検索](src/algorithms/search/jump-search) (Jump Search) - ソートされた配列で検索
* `B` [バイナリ検索](src/algorithms/search/binary-search) - ソートされた配列で検索
* `B` [補間探索](src/algorithms/search/interpolation-search) - 一様分布のソート配列で検索する
* **並べ替え**
@@ -149,7 +153,7 @@ _Read this in other languages:_
### Paradigmによるアルゴリズム
アルゴリズムパラダイムは、あるクラスのアルゴリズムの設計の基礎をなす一般的な方法またはアプローチである。それは、アルゴリズムがコンピュータプログラムよりも高い抽象であるのと同様に、アルゴリズムの概念よりも高い抽象である。
-* **ブルートフォース** - べての可能性を見て最適なソリューションを選択する
+* **ブルートフォース** - すべての可能性を見て最適なソリューションを選択する
* `B` [線形探索](src/algorithms/search/linear-search)
* `B` [レインテラス](src/algorithms/uncategorized/rain-terraces) - 雨水問題
* `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - 先頭に到達する方法の数を数えます
@@ -295,3 +299,5 @@ npm test -- 'playground'
| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))<sup>2</sup> | 1 | No | |
| **Counting sort** | n + r | n + r | n + r | n + r | Yes | r - biggest number in array |
| **Radix sort** | n * k | n * k | n * k | n + k | Yes | k - length of longest key |
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 02f35d0250..d4b0d4ef14 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -5,7 +5,7 @@
이 저장소에는 많이 알려진 알고리즘 및 자료 구조의 Javascript 기반 예제를 담고 있습니다.
-각 알고리즘과 자료 구조에 대해 연관되어있는 설명이 README에 작성되어 있으며,
+각 알고리즘과 자료 구조에 대해 연관되어 있는 설명이 README에 작성되어 있으며,
링크를 통해 더 자세한 설명을 만날 수 있습니다. (관련된 YouTube 영상도 포함).
_Read this in other languages:_
@@ -22,7 +22,11 @@ _Read this in other languages:_
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
## 자료 구조
@@ -276,3 +280,5 @@ Source: [Big O Cheat Sheet](http://bigocheatsheet.com/).
| **셸 정렬** | n log(n) | 간격 순서에 영향을 받습니다. | n (log(n))<sup>2</sup> | 1 | No | |
| **계수 정렬** | n + r | n + r | n + r | n + r | Yes | r - 배열내 가장 큰 수 |
| **기수 정렬** | n * k | n * k | n * k | n + k | Yes | k - 키값의 최대 길이 |
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.md b/README.md
index 8bb2bf3cdf..3e5c5cc096 100644
--- a/README.md
+++ b/README.md
@@ -1,7 +1,17 @@
# JavaScript Algorithms and Data Structures
+> 🇺🇦 UKRAINE [IS BEING ATTACKED](https://war.ukraine.ua/) BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
+> - Help Ukraine via:
+> - [Serhiy Prytula Charity Foundation](https://prytulafoundation.org/en/)
+> - [Come Back Alive Charity Foundation](https://savelife.in.ua/en/donate-en/)
+> - [National Bank of Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
+> - More info on [war.ukraine.ua](https://war.ukraine.ua/) and [MFA of Ukraine](https://twitter.com/MFA_Ukraine)
+
+<hr/>
+
[](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
[](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
This repository contains JavaScript based examples of many
popular algorithms and data structures.
@@ -20,11 +30,15 @@ _Read this in other languages:_
[_Español_](README.es-ES.md),
[_Português_](README.pt-BR.md),
[_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md),
+[_Türkçe_](README.tr-TR.md),
+[_Italiano_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md),
+[_עברית_](README.he-IL.md)
*☝ Note that this project is meant to be used for learning and researching purposes
only, and it is **not** meant to be used for production.*
@@ -36,6 +50,8 @@ be accessed and modified efficiently. More precisely, a data structure is a coll
values, the relationships among them, and the functions or operations that can be applied to
the data.
+Remember that each data has its own trade-offs. And you need to pay attention more to why you're choosing a certain data structure than to how to implement it.
+
`B` - Beginner, `A` - Advanced
* `B` [Linked List](src/data-structures/linked-list)
@@ -53,8 +69,9 @@ the data.
* `A` [Segment Tree](src/data-structures/tree/segment-tree) - with min/max/sum range queries examples
* `A` [Fenwick Tree](src/data-structures/tree/fenwick-tree) (Binary Indexed Tree)
* `A` [Graph](src/data-structures/graph) (both directed and undirected)
-* `A` [Disjoint Set](src/data-structures/disjoint-set)
+* `A` [Disjoint Set](src/data-structures/disjoint-set) - a union–find data structure or merge–find set
* `A` [Bloom Filter](src/data-structures/bloom-filter)
+* `A` [LRU Cache](src/data-structures/lru-cache/) - Least Recently Used (LRU) cache
## Algorithms
@@ -67,6 +84,7 @@ a set of rules that precisely define a sequence of operations.
* **Math**
* `B` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc.
+ * `B` [Binary Floating Point](src/algorithms/math/binary-floating-point) - binary representation of the floating-point numbers.
* `B` [Factorial](src/algorithms/math/factorial)
* `B` [Fibonacci Number](src/algorithms/math/fibonacci) - classic and closed-form versions
* `B` [Prime Factors](src/algorithms/math/prime-factors) - finding prime factors and counting them using Hardy-Ramanujan's theorem
@@ -89,7 +107,7 @@ a set of rules that precisely define a sequence of operations.
* **Sets**
* `B` [Cartesian Product](src/algorithms/sets/cartesian-product) - product of multiple sets
* `B` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - random permutation of a finite sequence
- * `A` [Power Set](src/algorithms/sets/power-set) - all subsets of a set (bitwise and backtracking solutions)
+ * `A` [Power Set](src/algorithms/sets/power-set) - all subsets of a set (bitwise, backtracking, and cascading solutions)
* `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions)
* `A` [Combinations](src/algorithms/sets/combinations) (with and without repetitions)
* `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS)
@@ -100,6 +118,7 @@ a set of rules that precisely define a sequence of operations.
* `A` [Combination Sum](src/algorithms/sets/combination-sum) - find all combinations that form specific sum
* **Strings**
* `B` [Hamming Distance](src/algorithms/string/hamming-distance) - number of positions at which the symbols are different
+ * `B` [Palindrome](src/algorithms/string/palindrome) - check if the string is the same in reverse
* `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
* `A` [Knuth–Morris–Pratt Algorithm](src/algorithms/string/knuth-morris-pratt) (KMP Algorithm) - substring search (pattern matching)
* `A` [Z Algorithm](src/algorithms/string/z-algorithm) - substring search (pattern matching)
@@ -121,6 +140,7 @@ a set of rules that precisely define a sequence of operations.
* `B` [Shellsort](src/algorithms/sorting/shell-sort)
* `B` [Counting Sort](src/algorithms/sorting/counting-sort)
* `B` [Radix Sort](src/algorithms/sorting/radix-sort)
+ * `B` [Bucket Sort](src/algorithms/sorting/bucket-sort)
* **Linked Lists**
* `B` [Straight Traversal](src/algorithms/linked-list/traversal)
* `B` [Reverse Traversal](src/algorithms/linked-list/reverse-traversal)
@@ -152,6 +172,12 @@ a set of rules that precisely define a sequence of operations.
* `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
* `B` [k-NN](src/algorithms/ml/knn) - k-nearest neighbors classification algorithm
* `B` [k-Means](src/algorithms/ml/k-means) - k-Means clustering algorithm
+* **Image Processing**
+ * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm
+* **Statistics**
+ * `B` [Weighted Random](src/algorithms/statistics/weighted-random) - select the random item from the list based on items' weights
+* **Evolutionary algorithms**
+ * `A` [Genetic algorithm](https://github.com/trekhleb/self-parking-car-evolution) - example of how the genetic algorithm may be applied for training the self-parking cars
* **Uncategorized**
* `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
* `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
@@ -160,6 +186,7 @@ a set of rules that precisely define a sequence of operations.
* `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem (dynamic programming and brute force versions)
* `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top (4 solutions)
* `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples
+ * `B` [Valid Parentheses](src/algorithms/stack/valid-parentheses) - check if a string has valid parentheses (using stack)
* `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
* `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
@@ -172,7 +199,7 @@ algorithm is an abstraction higher than a computer program.
* **Brute Force** - look at all the possibilities and selects the best solution
* `B` [Linear Search](src/algorithms/search/linear-search)
* `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem
- * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top
+ * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach the top
* `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
* `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
* `A` [Discrete Fourier Transform](src/algorithms/math/fourier-transform) - decompose a function of time (a signal) into the frequencies that make it up
@@ -197,12 +224,14 @@ algorithm is an abstraction higher than a computer program.
* `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples
* `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions)
* `A` [Combinations](src/algorithms/sets/combinations) (with and without repetitions)
+ * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
* **Dynamic Programming** - build up a solution using previously found sub-solutions
* `B` [Fibonacci Number](src/algorithms/math/fibonacci)
* `B` [Jump Game](src/algorithms/uncategorized/jump-game)
* `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
* `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem
- * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top
+ * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach the top
+ * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm
* `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
* `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS)
* `A` [Longest Common Substring](src/algorithms/string/longest-common-substring)
@@ -214,9 +243,9 @@ algorithm is an abstraction higher than a computer program.
* `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding the shortest path to all graph vertices
* `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find the shortest paths between all pairs of vertices
* `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
-* **Backtracking** - similarly to brute force, try to generate all possible solutions, but each time you generate next solution you test
-if it satisfies all conditions, and only then continue generating subsequent solutions. Otherwise, backtrack, and go on a
-different path of finding a solution. Normally the DFS traversal of state-space is being used.
+* **Backtracking** - similarly to brute force, try to generate all possible solutions, but each time you generate the next solution, you test
+if it satisfies all conditions and only then continue generating subsequent solutions. Otherwise, backtrack and go on a
+different path to finding a solution. Normally the DFS traversal of state-space is being used.
* `B` [Jump Game](src/algorithms/uncategorized/jump-game)
* `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
* `B` [Power Set](src/algorithms/sets/power-set) - all subsets of a set
@@ -226,13 +255,14 @@ different path of finding a solution. Normally the DFS traversal of state-space
* `A` [Combination Sum](src/algorithms/sets/combination-sum) - find all combinations that form specific sum
* **Branch & Bound** - remember the lowest-cost solution found at each stage of the backtracking
search, and use the cost of the lowest-cost solution found so far as a lower bound on the cost of
-a least-cost solution to the problem, in order to discard partial solutions with costs larger than the
-lowest-cost solution found so far. Normally BFS traversal in combination with DFS traversal of state-space
+a least-cost solution to the problem in order to discard partial solutions with costs larger than the
+lowest-cost solution found so far. Normally, BFS traversal in combination with DFS traversal of state-space
tree is being used.
## How to use this repository
**Install all dependencies**
+
```
npm install
```
@@ -246,21 +276,34 @@ npm run lint
```
**Run all tests**
+
```
npm test
```
**Run tests by name**
+
```
npm test -- 'LinkedList'
```
+**Troubleshooting**
+
+If linting or testing is failing, try to delete the `node_modules` folder and re-install npm packages:
+
+```
+rm -rf ./node_modules
+npm i
+```
+
+Also, make sure that you're using the correct Node version (`>=16`). If you're using [nvm](https://github.com/nvm-sh/nvm) for Node version management you may run `nvm use` from the root folder of the project and the correct version will be picked up.
+
**Playground**
You may play with data-structures and algorithms in `./src/playground/playground.js` file and write
tests for it in `./src/playground/__test__/playground.test.js`.
-Then just simply run the following command to test if your playground code works as expected:
+Then just, simply run the following command to test if your playground code works as expected:
```
npm test -- 'playground'
@@ -270,12 +313,13 @@ npm test -- 'playground'
### References
-[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [✍🏻 Data Structure Sketches](https://okso.app/showcase/data-structures)
### Big O Notation
*Big O notation* is used to classify algorithms according to how their running time or space requirements grow as the input size grows.
-On the chart below you may find most common orders of growth of algorithms specified in Big O notation.
+On the chart below, you may find the most common orders of growth of algorithms specified in Big O notation.
@@ -283,15 +327,15 @@ Source: [Big O Cheat Sheet](http://bigocheatsheet.com/).
Below is the list of some of the most used Big O notations and their performance comparisons against different sizes of the input data.
-| Big O Notation | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements |
-| -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
-| **O(1)** | 1 | 1 | 1 |
-| **O(log N)** | 3 | 6 | 9 |
-| **O(N)** | 10 | 100 | 1000 |
-| **O(N log N)** | 30 | 600 | 9000 |
-| **O(N^2)** | 100 | 10000 | 1000000 |
-| **O(2^N)** | 1024 | 1.26e+29 | 1.07e+301 |
-| **O(N!)** | 3628800 | 9.3e+157 | 4.02e+2567 |
+| Big O Notation | Type | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements |
+| -------------- | ----------- | ---------------------------- | ----------------------------- | ------------------------------- |
+| **O(1)** | Constant | 1 | 1 | 1 |
+| **O(log N)** | Logarithmic | 3 | 6 | 9 |
+| **O(N)** | Linear | 10 | 100 | 1000 |
+| **O(N log N)** | n log(n) | 30 | 600 | 9000 |
+| **O(N^2)** | Quadratic | 100 | 10000 | 1000000 |
+| **O(2^N)** | Exponential | 1024 | 1.26e+29 | 1.07e+301 |
+| **O(N!)** | Factorial | 3628800 | 9.3e+157 | 4.02e+2567 |
### Data Structure Operations Complexity
@@ -326,4 +370,10 @@ Below is the list of some of the most used Big O notations and their performance
> You may support this project via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb).
-[Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
+[Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+
+## Author
+
+[@trekhleb](https://trekhleb.dev)
+
+A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 08dc09b6aa..56617030ab 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -24,7 +24,11 @@ _Read this in other languages:_
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
## Struktury Danych
@@ -65,7 +69,7 @@ rozwiązania problemu.
* **Matematyka**
* `B` [Manipulacja Bitami](src/algorithms/math/bits) - ustaw / uzyskaj / aktualizuj / usuwaj bity, mnożenie / dzielenie przez dwa, tworzenie negatywów itp.
- * `B` [Silna](src/algorithms/math/factorial)
+ * `B` [Silnia](src/algorithms/math/factorial)
* `B` [Ciąg Fibonacciego](src/algorithms/math/fibonacci)
* `B` [Test Pierwszorzędności](src/algorithms/math/primality-test) (metoda podziału na próby)
* `B` [Algorytm Euclideana](src/algorithms/math/euclidean-algorithm) - obliczyć Największy Wspólny Dzielnik (GCD)
@@ -288,3 +292,5 @@ Poniżej umieszczamy listę najbardziej używanych Big O notacji i ich porównan
| **Sortowanie Shella** | n log(n) | zależy od luki w układzie | n (log(n))<sup>2</sup> | 1 | No | |
| **Sortowanie przez zliczanie** | n + r | n + r | n + r | n + r | Yes | r - największy numer w tablicy|
| **Sortowanie Radix** | n * k | n * k | n * k | n + k | Yes | k -długość najdłuższego klucza |
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.pt-BR.md b/README.pt-BR.md
index baffbc3179..5b16798bc9 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -6,7 +6,7 @@
Este repositório contém exemplos baseados em JavaScript de muitos
algoritmos e estruturas de dados populares.
-Cada algoritmo e estrutura de dado possui seu próprio README
+Cada algoritmo e estrutura de dados possui seu próprio README
com explicações relacionadas e links para leitura adicional (incluindo
vídeos para YouTube)
@@ -24,14 +24,16 @@ _Leia isto em outros idiomas:_
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
## Estrutura de Dados
Uma estrutura de dados é uma maneira particular de organizar e armazenar dados em um computador para que ele possa
-ser acessado e modificado de forma eficiente. Mais precisamente, uma estrutura de dados é uma coleção de dados
-valores, as relações entre eles e as funções ou operações que podem ser aplicadas a
-os dados.
+ser acessado e modificado de forma eficiente. Mais precisamente, uma estrutura de dados é uma coleção de valores de dados, as relações entre eles e as funções ou operações que podem ser aplicadas aos dados.
`B` - Iniciante, `A` - Avançado
@@ -40,17 +42,17 @@ os dados.
* `B` [Fila (Queue)](src/data-structures/queue/README.pt-BR.md)
* `B` [Pilha (Stack)](src/data-structures/stack/README.pt-BR.md)
* `B` [Tabela de Hash (Hash Table)](src/data-structures/hash-table/README.pt-BR.md)
-* `B` [Heap](src/data-structures/heap/README.pt-BR.md)
+* `B` [Heap](src/data-structures/heap/README.pt-BR.md) - versões de heap máximo e mínimo
* `B` [Fila de Prioridade (Priority Queue)](src/data-structures/priority-queue/README.pt-BR.md)
-* `A` [Árvore de prefixos (Trie)](src/data-structures/trie/README.pt-BR.md)
+* `A` [Árvore de Prefixos (Trie)](src/data-structures/trie/README.pt-BR.md)
* `A` [Árvore (Tree)](src/data-structures/tree/README.pt-BR.md)
* `A` [Árvore de Pesquisa Binária (Binary Search Tree)](src/data-structures/tree/binary-search-tree/README.pt-BR.md)
* `A` [Árvore AVL (AVL Tree)](src/data-structures/tree/avl-tree/README.pt-BR.md)
- * `A` [Árvore Vermelha-Preta (Red-Black Tree)](src/data-structures/tree/red-black-tree/README.pt-BR.md)
+ * `A` [Árvore Rubro-Negra (Red-Black Tree)](src/data-structures/tree/red-black-tree/README.pt-BR.md)
* `A` [Árvore de Segmento (Segment Tree)](src/data-structures/tree/segment-tree/README.pt-BR.md) - com exemplos de consultas min / max / sum range
* `A` [Árvore Fenwick (Fenwick Tree)](src/data-structures/tree/fenwick-tree/README.pt-BR.md) (Árvore indexada binária)
* `A` [Grafo (Graph)](src/data-structures/graph/README.pt-BR.md) (ambos dirigidos e não direcionados)
-* `A` [Conjunto Disjuntor (Disjoint Set)](src/data-structures/disjoint-set/README.pt-BR.md)
+* `A` [Conjunto Disjunto (Disjoint Set)](src/data-structures/disjoint-set/README.pt-BR.md)
* `A` [Filtro Bloom (Bloom Filter)](src/data-structures/bloom-filter/README.pt-BR.md)
## Algoritmos
@@ -67,78 +69,79 @@ um conjunto de regras que define precisamente uma sequência de operações.
* `B` [Fatorial](src/algorithms/math/factorial)
* `B` [Número de Fibonacci](src/algorithms/math/fibonacci)
* `B` [Teste de Primalidade](src/algorithms/math/primality-test) (método de divisão experimental)
- * `B` [Algoritmo Euclidiano](src/algorithms/math/euclidean-algorithm) - calcular o maior divisor comum (GCD)
- * `B` [Mínimo múltiplo comum](src/algorithms/math/least-common-multiple) (LCM)
- * `B` [Peneira de Eratóstenes](src/algorithms/math/sieve-of-eratosthenes) - encontrar todos os números primos até um determinado limite
- * `B` [Potência de dois](src/algorithms/math/is-power-of-two) - verifique se o número é a potência de dois (algoritmos ingênuos e bit a bit)
+ * `B` [Algoritmo Euclidiano](src/algorithms/math/euclidean-algorithm) - Calcular o Máximo Divisor Comum (MDC)
+ * `B` [Mínimo Múltiplo Comum](src/algorithms/math/least-common-multiple) Calcular o Mínimo Múltiplo Comum (MMC)
+ * `B` [Peneira de Eratóstenes](src/algorithms/math/sieve-of-eratosthenes) - Encontrar todos os números primos até um determinado limite
+ * `B` [Potência de Dois](src/algorithms/math/is-power-of-two) - Verifique se o número é a potência de dois (algoritmos ingênuos e bit a bit)
* `B` [Triângulo de Pascal](src/algorithms/math/pascal-triangle)
- * `B` [Número complexo](src/algorithms/math/complex-number) - números complexos e operações básicas com eles
- * `A` [Partição inteira](src/algorithms/math/integer-partition)
- * `A` [Algoritmo Liu Hui π](src/algorithms/math/liu-hui) - cálculos aproximados de π baseados em N-gons
+ * `B` [Número Complexo](src/algorithms/math/complex-number) - Números complexos e operações básicas com eles
+ * `A` [Partição Inteira](src/algorithms/math/integer-partition)
+ * `A` [Algoritmo Liu Hui π](src/algorithms/math/liu-hui) - Cálculos aproximados de π baseados em N-gons
* **Conjuntos**
- * `B` [Produto cartesiano](src/algorithms/sets/cartesian-product) - produto de vários conjuntos
- * `B` [Permutações de Fisher–Yates](src/algorithms/sets/fisher-yates) - permutação aleatória de uma sequência finita
- * `A` [Potência e Conjunto](src/algorithms/sets/power-set) - todos os subconjuntos de um conjunto
+ * `B` [Produto Cartesiano](src/algorithms/sets/cartesian-product) - Produto de vários conjuntos
+ * `B` [Permutações de Fisher–Yates](src/algorithms/sets/fisher-yates) - Permutação aleatória de uma sequência finita
+ * `A` [Potência e Conjunto](src/algorithms/sets/power-set) - Todos os subconjuntos de um conjunto
* `A` [Permutações](src/algorithms/sets/permutations) (com e sem repetições)
* `A` [Combinações](src/algorithms/sets/combinations) (com e sem repetições)
- * `A` [Mais longa subsequência comum](src/algorithms/sets/longest-common-subsequence) (LCS)
- * `A` [Maior subsequência crescente](src/algorithms/sets/longest-increasing-subsequence)
- * `A` [Supersequência Comum mais curta](src/algorithms/sets/shortest-common-supersequence) (SCS)
- * `A` [Problema da mochila](src/algorithms/sets/knapsack-problem) - "0/1" e "Não consolidado"
- * `A` [Máximo Subarray](src/algorithms/sets/maximum-subarray) - "Força bruta" e " Programação Dinâmica" versões (Kadane's)
- * `A` [Soma de Combinação](src/algorithms/sets/combination-sum) - encontre todas as combinações que formam uma soma específica
+ * `A` [Mais Longa Subsequência Comum](src/algorithms/sets/longest-common-subsequence) (LCS)
+ * `A` [Maior Subsequência Crescente](src/algorithms/sets/longest-increasing-subsequence)
+ * `A` [Supersequência Comum Mais Curta](src/algorithms/sets/shortest-common-supersequence) (SCS)
+ * `A` [Problema da Mochila](src/algorithms/sets/knapsack-problem) - "0/1" e "Não consolidado"
+ * `A` [Subarray Máximo](src/algorithms/sets/maximum-subarray) - "Força bruta" e "Programação Dinâmica", versões de Kadane
+ * `A` [Soma de Combinação](src/algorithms/sets/combination-sum) - Encontre todas as combinações que formam uma soma específica
* **Cadeia de Caracteres**
- * `B` [Hamming Distance](src/algorithms/string/hamming-distance) - número de posições em que os símbolos são diferentes
- * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - distância mínima de edição entre duas sequências
- * `A` [Knuth–Morris–Pratt Algorithm](src/algorithms/string/knuth-morris-pratt) (Algoritmo KMP) - pesquisa de substring (correspondência de padrão)
- * `A` [Z Algorithm](src/algorithms/string/z-algorithm) - pesquisa de substring (correspondência de padrão)
- * `A` [Rabin Karp Algorithm](src/algorithms/string/rabin-karp) - pesquisa de substring
- * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring)
- * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
+ * `B` [Distância de Hamming](src/algorithms/string/hamming-distance) - Número de posições em que os símbolos são diferentes
+ * `B` [Palíndromos](src/algorithms/string/palindrome) - Verifique se a cadeia de caracteres (string) é a mesma ao contrário
+ * `A` [Distância Levenshtein](src/algorithms/string/levenshtein-distance) - Distância mínima de edição entre duas sequências
+ * `A` [Algoritmo Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (Algoritmo KMP) - Pesquisa de substring (correspondência de padrão)
+ * `A` [Z Algorithm](src/algorithms/string/z-algorithm) - Pesquisa de substring (correspondência de padrão)
+ * `A` [Algoritmo de Rabin Karp](src/algorithms/string/rabin-karp) - Pesquisa de substring
+ * `A` [Substring Comum Mais Longa](src/algorithms/string/longest-common-substring)
+ * `A` [Expressões Regulares Correspondentes](src/algorithms/string/regular-expression-matching)
* **Buscas**
- * `B` [Linear Search](src/algorithms/search/linear-search)
- * `B` [Jump Search](src/algorithms/search/jump-search) (ou Bloquear pesquisa) - pesquisar na matriz ordenada
- * `B` [Binary Search](src/algorithms/search/binary-search) - pesquisar na matriz ordenada
- * `B` [Interpolation Search](src/algorithms/search/interpolation-search) - pesquisar em matriz classificada uniformemente distribuída
+ * `B` [Busca Linear (Linear Search)](src/algorithms/search/linear-search)
+ * `B` [Busca por Saltos (Jump Search)](src/algorithms/search/jump-search) - Pesquisa em matriz ordenada
+ * `B` [Busca Binária (Binary Search)](src/algorithms/search/binary-search) - Pesquisa em matriz ordenada
+ * `B` [Busca por Interpolação (Interpolation Search)](src/algorithms/search/interpolation-search) - Pesquisa em matriz classificada uniformemente distribuída
* **Classificação**
* `B` [Bubble Sort](src/algorithms/sorting/bubble-sort)
* `B` [Selection Sort](src/algorithms/sorting/selection-sort)
* `B` [Insertion Sort](src/algorithms/sorting/insertion-sort)
* `B` [Heap Sort](src/algorithms/sorting/heap-sort)
* `B` [Merge Sort](src/algorithms/sorting/merge-sort)
- * `B` [Quicksort](src/algorithms/sorting/quick-sort) - implementações local e não local
+ * `B` [Quicksort](src/algorithms/sorting/quick-sort) - Implementações local e não local
* `B` [Shellsort](src/algorithms/sorting/shell-sort)
* `B` [Counting Sort](src/algorithms/sorting/counting-sort)
* `B` [Radix Sort](src/algorithms/sorting/radix-sort)
-* **Arvóres**
- * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
- * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS)
+* **Árvores**
+ * `B` [Busca em Profundidade (Depth-First Search)](src/algorithms/tree/depth-first-search) (DFS)
+ * `B` [Busca em Largura (Breadth-First Search)](src/algorithms/tree/breadth-first-search) (BFS)
* **Grafos**
- * `B` [Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
- * `B` [Breadth-First Search](src/algorithms/graph/breadth-first-search) (BFS)
- * `B` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
- * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
- * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
- * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - encontrar caminhos mais curtos entre todos os pares de vértices
- * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - para gráficos direcionados e não direcionados (versões baseadas em DFS e Conjunto Disjuntivo)
- * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
- * `A` [Topological Sorting](src/algorithms/graph/topological-sorting) - Métodos DFS
- * `A` [Articulation Points](src/algorithms/graph/articulation-points) -O algoritmo de Tarjan (baseado em DFS)
- * `A` [Bridges](src/algorithms/graph/bridges) - Algoritmo baseado em DFS
- * `A` [Eulerian Path and Eulerian Circuit](src/algorithms/graph/eulerian-path) - Algoritmo de Fleury - Visite todas as bordas exatamente uma vez
- * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visite todas as bordas exatamente uma vez
- * `A` [Strongly Connected Components](src/algorithms/graph/strongly-connected-components) - Algoritmo de Kosaraju's
- * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - rota mais curta possível que visita cada cidade e retorna à cidade de origem
-* **criptografia**
- * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - função de hash de rolagem baseada em polinômio
+ * `B` [Busca em Profundidade (Depth-First Search)](src/algorithms/graph/depth-first-search) (DFS)
+ * `B` [Busca em Largura (Breadth-First Search)](src/algorithms/graph/breadth-first-search) (BFS)
+ * `B` [Algoritmo de Kruskal](src/algorithms/graph/kruskal) - Encontrando Árvore Mínima de Abrangência (MST) para grafo conexo com pesos
+ * `A` [Algoritmo de Dijkstra](src/algorithms/graph/dijkstra) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
+ * `A` [Algoritmo de Bellman-Ford](src/algorithms/graph/bellman-ford) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
+ * `A` [Algoritmo de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - Encontrar caminhos mais curtos entre todos os pares de vértices
+ * `A` [Detectar Ciclo](src/algorithms/graph/detect-cycle) - Para grafos direcionados e não direcionados (versões baseadas em DFS e Conjunto Disjuntivo)
+ * `A` [Algoritmo de Prim](src/algorithms/graph/prim) - Encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
+ * `A` [Ordenação Topológica](src/algorithms/graph/topological-sorting) - Métodos DFS
+ * `A` [Pontos de Articulação](src/algorithms/graph/articulation-points) - O algoritmo de Tarjan (baseado em DFS)
+ * `A` [Pontes](src/algorithms/graph/bridges) - Algoritmo baseado em DFS
+ * `A` [Caminho e Circuito Euleriano](src/algorithms/graph/eulerian-path) - Algoritmo de Fleury - Visite todas as bordas exatamente uma vez
+ * `A` [Ciclo Hamiltoniano](src/algorithms/graph/hamiltonian-cycle) - Visite todas as bordas exatamente uma vez
+ * `A` [Componentes Fortemente Conectados](src/algorithms/graph/strongly-connected-components) - Algoritmo de Kosaraju
+ * `A` [Problema do Caixeiro Viajante](src/algorithms/graph/travelling-salesman) - Rota mais curta possível que visita cada cidade e retorna à cidade de origem
+* **Criptografia**
+ * `B` [Hash Polinomial](src/algorithms/cryptography/polynomial-hash) - Função de hash de rolagem baseada em polinômio
* **Sem categoria**
- * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
- * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - algoritmo no local
- * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, programação dinâmica (top-down + bottom-up) e exemplos gananciosos
- * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, programação dinâmica e exemplos baseados no triângulo de Pascal
- * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping problema da água da chuva (programação dinâmica e versões de força bruta)
- * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
- * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
+ * `B` [Torre de Hanoi](src/algorithms/uncategorized/hanoi-tower)
+ * `B` [Rotação de Matriz Quadrada](src/algorithms/uncategorized/square-matrix-rotation) - Algoritmo no local
+ * `B` [Jogo do Salto](src/algorithms/uncategorized/jump-game) - Backtracking, programação dinâmica (top-down + bottom-up) e exemplos gananciosos
+ * `B` [Caminhos Únicos](src/algorithms/uncategorized/unique-paths) - Backtracking, programação dinâmica e exemplos baseados no triângulo de Pascal
+ * `B` [Terraços de Chuva](src/algorithms/uncategorized/rain-terraces) - Problema de retenção da água da chuva (programação dinâmica e versões de força bruta)
+ * `A` [Problema das N-Rainhas](src/algorithms/uncategorized/n-queens)
+ * `A` [Passeio do Cavaleiro](src/algorithms/uncategorized/knight-tour)
### Algoritmos por Paradigma
@@ -146,55 +149,53 @@ Um paradigma algorítmico é um método ou abordagem genérica subjacente ao des
de algoritmos. É uma abstração maior do que a noção de um algoritmo, assim como
algoritmo é uma abstração maior que um programa de computador.
-* **Força bruta** - look at all the possibilities and selects the best solution
- * `B` [Linear Search](src/algorithms/search/linear-search)
- * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping problema da água da chuva
- * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
- * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - rota mais curta possível que visita cada cidade e retorna à cidade de origem
-* **Greedy** - choose the best option at the current time, without any consideration for the future
- * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
- * `A` [Unbound Knapsack Problem](src/algorithms/sets/knapsack-problem)
- * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
- * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
- * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
-* **Dividir p/ Conquistar** - dividir o problema em partes menores e depois resolver essas partes
- * `B` [Busca binária (Binary Search)](src/algorithms/search/binary-search)
- * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
- * `B` [Pascal's Triangle](src/algorithms/math/pascal-triangle)
- * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
+* **Força bruta** - Pense em todas as possibilidades e escolha a melhor solução
+ * `B` [Busca Linear (Linear Search)](src/algorithms/search/linear-search)
+ * `B` [Terraços de Chuva](src/algorithms/uncategorized/rain-terraces) - Problema de retenção de água da chuva (programação dinâmica e versões de força bruta)
+ * `A` [Subarray Máximo](src/algorithms/sets/maximum-subarray)
+ * `A` [Problema do Caixeiro Viajante](src/algorithms/graph/travelling-salesman) - Rota mais curta possível que visita cada cidade e retorna à cidade de origem
+* **Ganância** - Escolha a melhor opção no momento, sem qualquer consideração pelo futuro
+ * `B` [Jogo do Salto](src/algorithms/uncategorized/jump-game)
+ * `A` [Problema da Mochila](src/algorithms/sets/knapsack-problem)
+ * `A` [Algoritmo de Dijkstra](src/algorithms/graph/dijkstra) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
+ * `A` [Algoritmo de Prim](src/algorithms/graph/prim) - Encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
+ * `A` [Algoritmo de Kruskal](src/algorithms/graph/kruskal) - Encontrando Árvore Mínima de Abrangência (MST) para grafo conexo com pesos
+* **Dividir e Conquistar** - Dividir o problema em partes menores e então resolver essas partes
+ * `B` [Busca Binária (Binary Search)](src/algorithms/search/binary-search)
+ * `B` [Torre de Hanoi](src/algorithms/uncategorized/hanoi-tower)
+ * `B` [Triângulo de Pascal](src/algorithms/math/pascal-triangle)
+ * `B` [Algoritmo Euclidiano](src/algorithms/math/euclidean-algorithm) - Calcular o Máximo Divisor Comum (MDC)
* `B` [Merge Sort](src/algorithms/sorting/merge-sort)
* `B` [Quicksort](src/algorithms/sorting/quick-sort)
- * `B` [Tree Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
- * `B` [Graph Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
- * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
- * `A` [Permutations](src/algorithms/sets/permutations) (com e sem repetições)
- * `A` [Combinations](src/algorithms/sets/combinations) (com e sem repetições)
-* **Programação Dinâmica** - criar uma solução usando sub-soluções encontradas anteriormente
- * `B` [Fibonacci Number](src/algorithms/math/fibonacci)
- * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
- * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
- * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping problema da água da chuva
- * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - distância mínima de edição entre duas sequências
- * `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS)
- * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring)
- * `A` [Longest Increasing Subsequence](src/algorithms/sets/longest-increasing-subsequence)
- * `A` [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence)
- * `A` [0/1 Knapsack Problem](src/algorithms/sets/knapsack-problem)
- * `A` [Integer Partition](src/algorithms/math/integer-partition)
- * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
- * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - encontrando o caminho mais curto para todos os vértices do gráfico
- * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - encontrar caminhos mais curtos entre todos os pares de vértices
- * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
-* **Backtracking** - da mesma forma que a força bruta, tente gerar todas as soluções possíveis, mas cada vez que você gerar a próxima solução, você testará
-se satisfizer todas as condições, e só então continuar gerando soluções subseqüentes. Caso contrário, volte atrás e siga um caminho diferente para encontrar uma solução. Normalmente, a passagem DFS do espaço de estados está sendo usada.
- * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
- * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
- * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visite todos os vértices exatamente uma vez
- * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
- * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
- * `A` [Combination Sum](src/algorithms/sets/combination-sum) - encontre todas as combinações que formam uma soma específica
-* **Branch & Bound** - lembre-se da solução de menor custo encontrada em cada etapa do retrocesso
-pesquisar e usar o custo da solução de menor custo encontrada até o limite inferior do custo de
+ * `B` [Busca em Profundidade (Depth-First Search)](src/algorithms/tree/depth-first-search) (DFS)
+ * `B` [Busca em Largura (Breadth-First Search)](src/algorithms/graph/breadth-first-search) (BFS)
+ * `B` [Jogo do Salto](src/algorithms/uncategorized/jump-game)
+ * `A` [Permutações](src/algorithms/sets/permutations) (com e sem repetições)
+ * `A` [Combinações](src/algorithms/sets/combinations) (com e sem repetições)
+* **Programação Dinâmica** - Criar uma solução usando sub-soluções encontradas anteriormente
+ * `B` [Número de Fibonacci](src/algorithms/math/fibonacci)
+ * `B` [Jogo do Salto](src/algorithms/uncategorized/jump-game)
+ * `B` [Caminhos Únicos](src/algorithms/uncategorized/unique-paths)
+ * `B` [Terraços de Chuva](src/algorithms/uncategorized/rain-terraces) - Trapping problema da água da chuva
+ * `A` [Distância Levenshtein](src/algorithms/string/levenshtein-distance) - Distância mínima de edição entre duas sequências
+ * `A` [Mais Longa Subsequência Comum](src/algorithms/sets/longest-common-subsequence) (LCS)
+ * `A` [Substring Comum Mais Longa](src/algorithms/string/longest-common-substring)
+ * `A` [Maior Subsequência Crescente](src/algorithms/sets/longest-increasing-subsequence)
+ * `A` [Supersequência Comum Mais Curta](src/algorithms/sets/shortest-common-supersequence)
+ * `A` [Problema da Mochila](src/algorithms/sets/knapsack-problem)
+ * `A` [Partição Inteira](src/algorithms/math/integer-partition)
+ * `A` [Subarray Máximo](src/algorithms/sets/maximum-subarray)
+ * `A` [Algoritmo de Bellman-Ford](src/algorithms/graph/bellman-ford) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
+ * `A` [Algoritmo de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - Encontrar caminhos mais curtos entre todos os pares de vértices
+ * `A` [Expressões Regulares Correspondentes](src/algorithms/string/regular-expression-matching)
+* **Backtracking** - Da mesma forma que a força bruta, tente gerar todas as soluções possíveis, mas, cada vez que você gerar a próxima solução será necessário testar se a mesma satisfaz todas as condições, e só então continuará a gerar as soluções subsequentes. Caso contrário, volte atrás e siga um caminho diferente para encontrar uma solução. Normalmente, a passagem DFS do espaço de estados está sendo usada.
+ * `B` [Jogo do Salto](src/algorithms/uncategorized/jump-game)
+ * `B` [Caminhos Únicos](src/algorithms/uncategorized/unique-paths)
+ * `A` [Ciclo Hamiltoniano](src/algorithms/graph/hamiltonian-cycle) - Visite todos os vértices exatamente uma vez
+ * `A` [Problema das N-Rainhas](src/algorithms/uncategorized/n-queens)
+ * `A` [Passeio do Cavaleiro](src/algorithms/uncategorized/knight-tour)
+ * `A` [Soma de Combinação](src/algorithms/sets/combination-sum) - Encontre todas as combinações que formam uma soma específica
+* **Branch & Bound** - Lembre-se da solução de menor custo encontrada em cada etapa do retrocesso, pesquisar e usar o custo da solução de menor custo encontrada até o limite inferior do custo de
solução de menor custo para o problema, a fim de descartar soluções parciais com custos maiores que o
solução de menor custo encontrada até o momento. Normalmente, a travessia BFS em combinação com a passagem DFS do espaço de estados
árvore está sendo usada
@@ -223,10 +224,19 @@ npm test
```
npm test -- 'LinkedList'
```
+**Solução de problemas**
-**Parque infantil**
+Caso o linting ou o teste estejam falhando, tente excluir a pasta node_modules e reinstalar os pacotes npm:
+```
+rm -rf ./node_modules
+npm i
+```
+
+Verifique também se você está usando uma versão correta do Node (>=14.16.0). Se você estiver usando [nvm](https://github.com/nvm-sh/nvm) para gerenciamento de versão do Node, você pode executar `nvm use` a partir da pasta raiz do projeto e a versão correta será escolhida.
-Você pode brincar com estruturas de dados e algoritmos em `./src/playground/playground.js` arquivar e escrever
+**Playground**
+
+Você pode brincar com estruturas de dados e algoritmos no arquivo `./src/playground/playground.js` e escrever
testes para isso em `./src/playground/__test__/playground.test.js`.
Em seguida, basta executar o seguinte comando para testar se o código do seu playground funciona conforme o esperado:
@@ -239,15 +249,16 @@ npm test -- 'playground'
### Referências
-[▶ Estruturas de dados e algoritmos no YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [▶ Estruturas de Dados e Algoritmos no YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [✍🏻 Esboços de Estruturas de Dados](https://okso.app/showcase/data-structures)
### Notação Big O
-Ordem de crescimento dos algoritmos especificados em notação Big O.
+A notação Big O é usada para classificar algoritmos de acordo com a forma como seu tempo de execução ou requisitos de espaço crescem à medida que o tamanho da entrada aumenta. No gráfico abaixo você pode encontrar as ordens mais comuns de crescimento de algoritmos especificados na notação Big O.
-Fonte: [Notação Big-O dicas](http://bigocheatsheet.com/).
+Fonte: [Notação Big-O Dicas](http://bigocheatsheet.com/).
Abaixo está a lista de algumas das notações Big O mais usadas e suas comparações de desempenho em relação aos diferentes tamanhos dos dados de entrada.
@@ -263,29 +274,31 @@ Abaixo está a lista de algumas das notações Big O mais usadas e suas compara
### Complexidade de operações de estrutura de dados
-| estrutura de dados | Acesso | Busca | Inserção | Eliminação | comentários |
+| Estrutura de dados | Acesso | Busca | Inserção | Eliminação | Comentários |
| ----------------------- | :-------: | :-------: | :-------: | :-------: | :-------- |
| **Array** | 1 | n | n | n | |
| **Stack** | n | n | 1 | 1 | |
| **Queue** | n | n | 1 | 1 | |
| **Linked List** | n | n | 1 | 1 | |
-| **Hash Table** | - | n | n | n | Em caso de uma função hash perfeita, os custos seriam O (1) |
-| **Binary Search Tree** | n | n | n | n | No caso de custos de árvore equilibrados seria O (log (n))
+| **Hash Table** | - | n | n | n | Em caso de uma função hash perfeita, os custos seriam O(1) |
+| **Binary Search Tree** | n | n | n | n | No caso de custos de árvore equilibrados seria O(log(n))
| **B-Tree** | log(n) | log(n) | log(n) | log(n) | |
| **Red-Black Tree** | log(n) | log(n) | log(n) | log(n) | |
| **AVL Tree** | log(n) | log(n) | log(n) | log(n) | |
| **Bloom Filter** | - | 1 | 1 | - | Falsos positivos são possíveis durante a pesquisa |
-### Array Sorting Algorithms Complexity
+### Complexidade dos Algoritmos de Ordenação de Matrizes
-| Nome | Melhor | Média | Pior | Mémoria | Estável | comentários |
+| Nome | Melhor | Média | Pior | Mémoria | Estável | Comentários |
| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
| **Bubble sort** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Sim | |
| **Insertion sort** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Sim | |
| **Selection sort** | n<sup>2</sup> | n<sup>2</sup> | n<sup>2</sup> | 1 | Não | |
| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | Não | |
| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Sim | |
-| **Quick sort** | n log(n) | n log(n) | n<sup>2</sup> | log(n) | Não | O Quicksort geralmente é feito no local com o espaço de pilha O O(log(n)) stack space |
+| **Quick sort** | n log(n) | n log(n) | n<sup>2</sup> | log(n) | Não | O Quicksort geralmente é feito no local com espaço de pilha O(log(n)) |
| **Shell sort** | n log(n) | depende da sequência de lacunas | n (log(n))<sup>2</sup> | 1 | Não | |
| **Counting sort** | n + r | n + r | n + r | n + r | Sim | r - maior número na matriz |
| **Radix sort** | n * k | n * k | n * k | n + k | Sim | k - comprimento da chave mais longa |
+
+> ℹ️ Outros [projetos](https://trekhleb.dev/projects/) e [artigos](https://trekhleb.dev/blog/) sobre JavaScript e algoritmos em [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.ru-RU.md b/README.ru-RU.md
index 32f4b2f526..939ed46700 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -21,7 +21,11 @@ _Читать на других языках:_
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
*☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
@@ -35,7 +39,7 @@ _Читать на других языках:_
* `B` [Двунаправленный связный список](src/data-structures/doubly-linked-list)
* `B` [Очередь](src/data-structures/queue)
* `B` [Стек](src/data-structures/stack)
-* `B` [Хеш-табица](src/data-structures/hash-table)
+* `B` [Хеш-таблица](src/data-structures/hash-table)
* `B` [Куча](src/data-structures/heap) — максимальная и минимальная версии
* `B` [Очередь с приоритетом](src/data-structures/priority-queue)
* `A` [Префиксное дерево](src/data-structures/trie)
@@ -59,8 +63,10 @@ _Читать на других языках:_
* **Математика**
* `B` [Битовые манипуляции](src/algorithms/math/bits) — получение/запись/сброс/обновление битов, умножение/деление на 2, сделать отрицательным и т.п.
+ * `B` [Двоичное число с плавающей запятой](src/algorithms/math/binary-floating-point) - двоичное представление чисел с плавающей запятой
* `B` [Факториал](src/algorithms/math/factorial)
* `B` [Числа Фибоначчи](src/algorithms/math/fibonacci) — классическое решение, решение в замкнутой форме
+ * `B` [Простые множители](src/algorithms/math/prime-factors) - нахождение простых множителей и их подсчёт с использованием теоремы Харди-Рамануджана
* `B` [Тест простоты](src/algorithms/math/primality-test) (метод пробного деления)
* `B` [Алгоритм Евклида](src/algorithms/math/euclidean-algorithm) — нахождение наибольшего общего делителя (НОД)
* `B` [Наименьшее общее кратное](src/algorithms/math/least-common-multiple) (НОК)
@@ -70,6 +76,9 @@ _Читать на других языках:_
* `B` [Комплексные числа](src/algorithms/math/complex-number) — комплексные числа, базовые операции над ними
* `B` [Радианы и градусы](src/algorithms/math/radian) — конвертирование радианов в градусы и наоборот
* `B` [Быстрое возведение в степень](src/algorithms/math/fast-powering)
+ * `B` [Схема Горнера](src/algorithms/math/horner-method) - оценка полиномов
+ * `B` [Матрицы](src/algorithms/math/matrix) - матрицы и основные операции с матрицами (умножение, транспонирование и т.д.)
+ * `B` [Евклидово расстояние](src/algorithms/math/euclidean-distance) - расстояние между двумя точками/векторами/матрицами
* `A` [Разбиение числа](src/algorithms/math/integer-partition)
* `A` [Квадратный корень](src/algorithms/math/square-root) — метод Ньютона
* `A` [Алгоритм Лю Хуэя](src/algorithms/math/liu-hui) — расчёт числа π с заданной точностью методом вписанных правильных многоугольников
@@ -133,8 +142,19 @@ _Читать на других языках:_
* `A` [Задача коммивояжёра](src/algorithms/graph/travelling-salesman) — кратчайший маршрут, проходящий через указанные города с последующим возвратом в исходный город
* **Криптография**
* `B` [Полиноминальный хэш](src/algorithms/cryptography/polynomial-hash) — функция кольцевого хэша, основанная на полиноме
+ * `B` [Шифр ограждения рельсов](src/algorithms/cryptography/rail-fence-cipher) - алгоритм транспозиционного шифра для кодирования сообщений
+ * `B` [Шифр Цезаря](src/algorithms/cryptography/caesar-cipher) - простой подстановочный шифр
+ * `B` [Шифр Хилла](src/algorithms/cryptography/hill-cipher) - подстановочный шифр на основе линейной алгебры
* **Машинное обучение**
* `B` [Нано-нейрон](https://github.com/trekhleb/nano-neuron) — 7 простых JavaScript функций, отображающих способности машины к обучению (прямое и обратное распространение)
+ * `B` [k-NN](src/algorithms/ml/knn) - алгоритм классификации k-ближайших соседей
+ * `B` [k-Means](src/algorithms/ml/k-means) - алгоритм кластеризации по методу k-средних
+* **Обработка изображений**
+ * `B` [Резьба по шву](src/algorithms/image-processing/seam-carving) - алгоритм изменения размера изображения с учетом содержания
+* **Статистика**
+ * `B` [Взвешенная случайность](src/algorithms/statistics/weighted-random) - выбор случайного элемента из списка на основе веса элементов
+* **Эволюционные алгоритмы**
+ * `A` [Генетический алгоритм](https://github.com/trekhleb/self-parking-car-evolution) - пример применения генетического алгоритма для обучения самопаркующихся автомобилей
* **Прочие алгоритмы**
* `B` [Ханойская башня](src/algorithms/uncategorized/hanoi-tower)
* `B` [Поворот квадратной матрицы](src/algorithms/uncategorized/square-matrix-rotation) — используется дополнительная память
@@ -142,6 +162,7 @@ _Читать на других языках:_
* `B` [Поиск уникальных путей](src/algorithms/uncategorized/unique-paths) — на основе бэктрекинга, динамического программирования и треугольника Паскаля
* `B` [Подсчёт дождевой воды](src/algorithms/uncategorized/rain-terraces) — на основе перебора и динамического программирования
* `B` [Задача о рекурсивной лестнице](src/algorithms/uncategorized/recursive-staircase) — подсчёт количества путей, по которым можно достичь верха лестницы (4 способа)
+ * `B` [Лучшее время для покупки и продажи акций](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - примеры "разделяй и властвуй" и в один проход
* `A` [Задача об N ферзях](src/algorithms/uncategorized/n-queens)
* `A` [Маршрут коня](src/algorithms/uncategorized/knight-tour)
@@ -171,8 +192,10 @@ _Читать на других языках:_
* `B` [Быстрая сортировка](src/algorithms/sorting/quick-sort)
* `B` [Поиск в глубину (дерево)](src/algorithms/tree/depth-first-search)
* `B` [Поиск в глубину (граф)](src/algorithms/graph/depth-first-search)
+ * `B` [Матрицы](src/algorithms/math/matrix) - генерирование и обход матриц различной формы
* `B` [Прыжки](src/algorithms/uncategorized/jump-game)
* `B` [Быстрое возведение в степень](src/algorithms/math/fast-powering)
+ * `B` [Лучшее время для покупки и продажи акций](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - примеры "разделяй и властвуй" и в один проход
* `A` [Перестановки](src/algorithms/sets/permutations) (с повторениями и без повторений)
* `A` [Сочетания](src/algorithms/sets/combinations) (с повторениями и без повторений)
* **Динамическое программирование** — решение общей задачи конструируется на основе ранее найденных решений подзадач
@@ -181,6 +204,7 @@ _Читать на других языках:_
* `B` [Поиск уникальных путей](src/algorithms/uncategorized/unique-paths)
* `B` [Подсчёт дождевой воды](src/algorithms/uncategorized/rain-terraces)
* `B` [Задача о рекурсивной лестнице](src/algorithms/uncategorized/recursive-staircase) — подсчёт количества путей, по которым можно достичь верха лестницы
+ * `B` [Резьба по шву](src/algorithms/image-processing/seam-carving) - алгоритм изменения размера изображения с учетом содержания
* `A` [Расстояние Левенштейна](src/algorithms/string/levenshtein-distance) — метрика, измеряющая разность между двумя последовательностями
* `A` [Наибольшая общая подпоследовательность](src/algorithms/sets/longest-common-subsequence)
* `A` [Наибольшая общая подстрока](src/algorithms/string/longest-common-substring)
@@ -294,3 +318,5 @@ npm test -- 'playground'
| **Сортировка Шелла** | n log(n) | зависит от выбранных шагов | n (log(n))<sup>2</sup> | 1 | Нет | |
| **Сортировка подсчётом** | n + r | n + r | n + r | n + r | Да | r — наибольшее число в массиве |
| **Поразрядная сортировка** | n * k | n * k | n * k | n + k | Да | k — длина самого длинного ключа |
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.tr-TR.md b/README.tr-TR.md
index f7ed57fc91..53600480db 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -3,8 +3,7 @@
[](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
[](https://codecov.io/gh/trekhleb/javascript-algorithms)
-Bu repository JavaScript'e ait popüler
-algoritma ve veri yapılarını içermektedir.
+Bu repository popüler algoritmaların ve veri yapılarının birçoğunun Javascript tabanlı örneklerini bulundurur.
Her bir algoritma ve veri yapısı kendine
ait açıklama ve videoya sahip README dosyası içerir.
@@ -22,15 +21,19 @@ _Read this in other languages:_
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
*☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
-olup üretim için **yaplılmamıştır**.*
+olup üretim için **yapılmamıştır**.*
## Veri Yapıları
Bir veri yapısı, verileri bir bilgisayarda organize etmenin ve depolamanın belirli bir yoludur, böylece
-verimli bir şekilde erişilebilir ve değiştirilebilir. Daha doğrusu, bir veri yapısı bir veri koleksiyonudur,
+verimli bir şekilde erişilebilir ve değiştirilebilir. Daha iyi ifadeyle, bir veri yapısı bir veri koleksiyonudur,
aralarındaki ilişkiler, ve işlevler veya işlemler
veriye uygulanabilir.
@@ -56,8 +59,8 @@ veriye uygulanabilir.
## Algoritmalar
-Bir algoritma, bir problem sınıfının nasıl çözüleceğine dair kesin bir tanımlamadır. Bu
-bir işlem dizisini kesin olarak tanımlayan bir dizi kural.
+Bir algoritma, bir problem sınıfının nasıl çözüleceğine dair kesin bir tanımlamadır.
+Bir işlem dizisini açık olarak tanımlayan kurallar dizisidir.
`B` - Başlangıç, `A` - İleri Seviye
@@ -66,45 +69,49 @@ bir işlem dizisini kesin olarak tanımlayan bir dizi kural.
* **Matematik**
* `B` [Bit Manipülasyonu](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc.
+ * `B` [İkili Kayan Nokta](src/algorithms/math/binary-floating-point) - kayan noktalı sayıların ikilik sistemde gösterimi.
* `B` [Faktöriyel](src/algorithms/math/factorial)
* `B` [Fibonacci Sayısı](src/algorithms/math/fibonacci) - klasik ve kapalı-form versiyonları
- * `B` [Asallık Testi](src/algorithms/math/primality-test) (trial division method)
+ * `B` [Asallık Testi](src/algorithms/math/primality-test) (deneyerek bölüm metodu)
* `B` [Öklid Algoritması](src/algorithms/math/euclidean-algorithm) - En büyük ortak bölen hesaplama (EBOB)
* `B` [En küçük Ortak Kat](src/algorithms/math/least-common-multiple) (EKOK)
- * `B` [Sieve of Eratosthenes](src/algorithms/math/sieve-of-eratosthenes) - belirli bir sayıya kadarki asal sayıları bulma
+ * `B` [Eratosten Kalburu](src/algorithms/math/sieve-of-eratosthenes) - belirli bir sayıya kadarki asal sayıları bulma
* `B` [Is Power of Two](src/algorithms/math/is-power-of-two) - sayı ikinin katı mı sorgusu (naive ve bitwise algoritmaları)
* `B` [Paskal Üçgeni](src/algorithms/math/pascal-triangle)
- * `B` [Karmaşık Sayılar](src/algorithms/math/complex-number) - karmaşık sayılar ve bunlarla temel işlemler
- * `B` [Radyan & Derece](src/algorithms/math/radian) - radyandan dereceye çeviri ve tersi
+ * `B` [Karmaşık Sayılar](src/algorithms/math/complex-number) - karmaşık sayılar ve karmaşık sayılar ile temel işlemler
+ * `B` [Radyan & Derece](src/algorithms/math/radian) - radyandan dereceye çeviri ve tersine çeviri
* `B` [Fast Powering](src/algorithms/math/fast-powering)
+ * `B` [Horner's method](src/algorithms/math/horner-method) - polinomal ifadelerin değerlendirilmesi
+ * `B` [Matrices](src/algorithms/math/matrix) - matrisler ve basit matris operasyonları (çarpım, tersçapraz, vb.)
+ * `B` [Euclidean Distance](src/algorithms/math/euclidean-distance) - iki nokta/vektör/matris arasındaki mesafe
* `A` [Tamsayı Bölümü](src/algorithms/math/integer-partition)
* `A` [Karekök](src/algorithms/math/square-root) - Newton yöntemi
* `A` [Liu Hui π Algoritması](src/algorithms/math/liu-hui) - N-gons'a göre yaklaşık π hesabı
- * `A` [Ayrık Fourier Dönüşümü](src/algorithms/math/fourier-transform) - bir zaman fonksiyonunu (bir sinyal) onu oluşturan frekanslara ayırır
+ * `A` [Ayrık Fourier Dönüşümü](src/algorithms/math/fourier-transform) - bir zaman fonksiyonunu (sinyal) içerdiği frekanslara ayırın
* **Setler**
- * `B` [Kartezyen Ürün](src/algorithms/sets/cartesian-product) - product of multiple sets
+ * `B` [Kartezyen Ürün](src/algorithms/sets/cartesian-product) - birden fazla kümenin çarpımı
* `B` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - sonlu bir dizinin rastgele permütasyonu
- * `A` [Power Set](src/algorithms/sets/power-set) - all subsets of a set (bitwise and backtracking solutions)
+ * `A` [Power Set](src/algorithms/sets/power-set) - all subsets of a set (bit düzeyinde ve geri izleme yöntemleri)
* `A` [Permütasyonlar](src/algorithms/sets/permutations)(tekrarlı ve tekrarsız)
* `A` [Kombinasyonlar](src/algorithms/sets/combinations) (tekrarlı ve tekrarsız)
* `A` [En Uzun Ortak Altdizi](src/algorithms/sets/longest-common-subsequence) (LCS)
* `A` [En Uzun Artan Altdizi](src/algorithms/sets/longest-increasing-subsequence)
* `A` [En Kısa Ortak Üst Sıra](src/algorithms/sets/shortest-common-supersequence) (SCS)
- * `A` [Knapsack Problem](src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones
- * `A` [Maksimum Altdizi](src/algorithms/sets/maximum-subarray) - "Brute Force" ve "Dinamik Programlara" (Kadane'nin) versiyonu
+ * `A` [Knapsack Problem](src/algorithms/sets/knapsack-problem) - "0-1 sırt çantası problemi" ve "Sınırsız sırt çantası problemi"
+ * `A` [Maksimum Altdizi](src/algorithms/sets/maximum-subarray) - "Kaba Kuvvet" ve "Dinamik Programlara" (Kadane'nin) versiyonu
* `A` [Kombinasyon Toplamı](src/algorithms/sets/combination-sum) - belirli toplamı oluşturan tüm kombinasyonları bulun
* **Metin**
* `B` [Hamming Mesafesi](src/algorithms/string/hamming-distance) - sembollerin farklı olduğu konumların sayısı
* `A` [Levenshtein Mesafesi](src/algorithms/string/levenshtein-distance) - iki sekans arasındaki minimum düzenleme mesafesi
- * `A` [Knuth–Morris–Pratt Algoritması](src/algorithms/string/knuth-morris-pratt) (KMP Algorithm) - substring search (pattern matching)
+ * `A` [Knuth–Morris–Pratt Algoritması](src/algorithms/string/knuth-morris-pratt) (KMP Algorithm) - altmetin araması (örüntü eşleme)
* `A` [Z Algoritması](src/algorithms/string/z-algorithm) - altmetin araması (desen eşleştirme)
* `A` [Rabin Karp Algoritması](src/algorithms/string/rabin-karp) - altmetin araması
* `A` [En Uzun Ortak Alt Metin](src/algorithms/string/longest-common-substring)
* `A` [Regular Expression Eşleme](src/algorithms/string/regular-expression-matching)
* **Aramalar**
* `B` [Doğrusal Arama](src/algorithms/search/linear-search)
- * `B` [Jump Search](src/algorithms/search/jump-search) (ya da Block Search) - sıralı dizide ara
- * `B` [İkili Arama](src/algorithms/search/binary-search) - sıralı dizide ara
+ * `B` [Jump Search](src/algorithms/search/jump-search) (ya da Block Search) - sıralı dizide arama
+ * `B` [İkili Arama](src/algorithms/search/binary-search) - sıralı dizide arama
* `B` [Interpolation Search](src/algorithms/search/interpolation-search) - tekdüze dağıtılmış sıralı dizide arama
* **Sıralama**
* `B` [Bubble Sort](src/algorithms/sorting/bubble-sort)
@@ -263,7 +270,7 @@ npm test -- 'playground'
### Big O Notation
-* Big O notation *, algoritmaları, giriş boyutu büyüdükçe çalışma süresi veya alan gereksinimlerinin nasıl arttığına göre sınıflandırmak için kullanılır.
+* Big O notation *, algoritmaları, girdi boyutu büyüdükçe çalışma süresi veya alan gereksinimlerinin nasıl arttığına göre sınıflandırmak için kullanılır.
Aşağıdaki grafikte, Big O gösteriminde belirtilen algoritmaların en yaygın büyüme sıralarını bulabilirsiniz.
@@ -314,3 +321,5 @@ Altta Big O notations ve farklı input boyutlarına karşın yapılmış perform
## Projeyi Destekleme
Bu projeyi buradan destekleyebilirsiniz ❤️️ [GitHub](https://github.com/sponsors/trekhleb) veya ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.uk-UA.md b/README.uk-UA.md
index 4391ed1992..5ee5f7cbcc 100644
--- a/README.uk-UA.md
+++ b/README.uk-UA.md
@@ -21,7 +21,11 @@ _Вивчення матеріалу на інших мовах:_
[_Türk_](README.tr-TR.md),
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
*☝ Зверніть увагу! Даний проект призначений лише для навчальних та дослідницьких цілей, і він **не** призначений для виробництва (продакшн).*
@@ -304,3 +308,5 @@ npm test -- 'playground'
> Ви можете підтримати цей проект через ❤️️ [GitHub](https://github.com/sponsors/trekhleb) або ❤️️ [Patreon](https://www.patreon.com/trekhleb).
[Люди, які підтримують цей проект](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.uz-UZ.md b/README.uz-UZ.md
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+# JavaScript algoritmlari va ma'lumotlar tuzilmalari
+
+[](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
+[](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+
+Bu repozitoriyada JavaScript-ga asoslangan ko'plab mashhur algoritmlar
+va ma'lumotlar tuzilmalarining namunalari mavjud.
+
+Har bir algoritm va ma'lumotlar tuzilmasining alohida README fayli
+bo'lib, unda tegishli tushuntirishlar va qo'shimcha o'qish uchun
+havolalar (shu jumladan YouTube videolariga ham havolalar) mavjud.
+
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türkçe_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
+
+Yodda tuting, bu loyiha faqat o'quv va tadqiqot maqsadida ishlatilishi
+uchun mo'ljallangan va ishlab chiqarishda ishlatilishi **mumkin emas**.
+
+## Ma'lumotlar tuzilmalari
+
+Ma'lumotlar tuzilmasi - bu kompyuterda ma'lumotlarni samarali tarzda
+olish va o'zgartirish uchun ularni tashkil etish va saqlashning ma'lum
+bir usuli. Ayniqsa, ma'lumotlar tuzilmasi ma'lumot qiymatlarining
+to'plami, ular orasidagi munosabatlar va ma'lumotlarga qo'llanilishi
+mumkin bo'lgan funksiyalar yoki operatsiyalardir.
+
+`B` - Boshlang'ich, `A` - Ilg'or
+
+- `B` [Bog'langan ro'yxat](src/data-structures/linked-list)
+- `B` [Ikki marta bog'langan ro'yxat](src/data-structures/doubly-linked-list)
+- `B` [Navbat](src/data-structures/queue)
+- `B` [Stek](src/data-structures/stack)
+- `B` [Hash jadvali](src/data-structures/hash-table)
+- `B` [Heap](src/data-structures/heap) - maksimal va minimal heap versiyalari
+- `B` [Ustuvor navbat](src/data-structures/priority-queue)
+- `A` [Trie](src/data-structures/trie)
+- `A` [Daraxt](src/data-structures/tree)
+ - `A` [Ikkilik qidiruv daraxt](src/data-structures/tree/binary-search-tree)
+ - `A` [AVL daraxt](src/data-structures/tree/avl-tree)
+ - `A` [Qizil-qora daraxt](src/data-structures/tree/red-black-tree)
+ - `A` [Segment daraxt](src/data-structures/tree/segment-tree) - min/max/sum diapazon so'rovlari bilan misollar
+ - `A` [Fenwick daraxt](src/data-structures/tree/fenwick-tree) (ikkilik indeksli daraxt)
+- `A` [Graf](src/data-structures/graph) (yo'naltirilgan hamda yo'naltirilmagan)
+- `A` [Ajratilgan to'plam](src/data-structures/disjoint-set) - union-find ma'lumotlar strukturasi yoki merge-find to'plami
+- `A` [Bloom filtri](src/data-structures/bloom-filter)
+- `A` [LRU keshi](src/data-structures/lru-cache/) - Eng kam ishlatilgan (LRU) keshi
+
+## Algoritmlar
+
+Algoritm muammolar sinfini qanday hal qilishning aniq spetsifikatsiyasi. Bu operatsiyalar ketma-ketligini aniqlaydigan qoidalar to'plami.
+
+`B` - Boshlang'ich, `A` - Ilg'or
+
+### Mavzu bo'yicha algoritmlar
+
+- **Matematika**
+ - `B` [Bit manipulatsiyasi](src/algorithms/math/bits) - bitlarni qo'yish/olish/yangilash/tozalash, ikkilikka ko'paytirish/bo'lish, manfiy qilish va hokazo.
+ - `B` [Ikkilik suzuvchi nuqta](src/algorithms/math/binary-floating-point) - suzuvchi nuqtali sonlarning ikkilik tasviri.
+ - `B` [Faktorial](src/algorithms/math/factorial)
+ - `B` [Fibonachchi raqam](src/algorithms/math/fibonacci) - klassik va yopiq shakldagi versiyalar
+ - `B` [Asosiy omillar](src/algorithms/math/prime-factors) - tub omillarni topish va ularni Xardi-Ramanujan teoremasi yordamida sanash
+ - `B` [Birlamchilik testi](src/algorithms/math/primality-test) (sinov bo'linish usuli)
+ - `B` [Evklid algoritmi](src/algorithms/math/euclidean-algorithm) - eng katta umumiy bo'luvchini (EKUB) hisoblash
+ - `B` [Eng kichik umumiy karrali](src/algorithms/math/least-common-multiple) (EKUK)
+ - `B` [Eratosfen elagi](src/algorithms/math/sieve-of-eratosthenes) - berilgan chegaragacha barcha tub sonlarni topish
+ - `B` [Ikkining darajasimi](src/algorithms/math/is-power-of-two) - raqamning ikkining darajasi ekanligini tekshirish (sodda va bitli algoritmlar)
+ - `B` [Paskal uchburchagi](src/algorithms/math/pascal-triangle)
+ - `B` [Kompleks sonlar](src/algorithms/math/complex-number) - kompleks sonlar va ular bilan asosiy amallar
+ - `B` [Radian & Daraja](src/algorithms/math/radian) - radianlarni darajaga va orqaga aylantirish
+ - `B` [Tez ko'tarish](src/algorithms/math/fast-powering)
+ - `B` [Horner metodi](src/algorithms/math/horner-method) - polinomlarni baholash
+ - `B` [Matritsalar](src/algorithms/math/matrix) - matritsalar va asosiy matritsa operatsiyalari (ko'paytirish, transpozitsiya va boshqalar).
+ - `B` [Evklid masofasi](src/algorithms/math/euclidean-distance) - ikki nuqta/vektor/matritsa orasidagi masofa
+ - `A` [Butun sonlarni bo'lish](src/algorithms/math/integer-partition)
+ - `A` [Kvadrat ildiz](src/algorithms/math/square-root) - Nyuton metodi
+ - `A` [Liu Hui π algoritmi](src/algorithms/math/liu-hui) - N-gonlarga asoslangan π ning taxminiy hisoblari
+ - `A` [Diskret Furye transformatsiyasi](src/algorithms/math/fourier-transform) - vaqt funksiyasini (signalni) uni tashkil etuvchi chastotalarga ajratish
+- **Sets**
+ - `B` [Karteziya maxsuloti](src/algorithms/sets/cartesian-product) - bir nechta to'plamlarning ko'paytmasi
+ - `B` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - chekli ketma-ketlikni tasodifiy almashtirish
+ - `A` [Power Set](src/algorithms/sets/power-set) - to'plamning barcha kichik to'plamlari (bitwise, backtracking va kaskadli echimlar)
+ - `A` [Permutatsiyalar](src/algorithms/sets/permutations) (takroriyalash bilan va takroriyalashsiz)
+ - `A` [Kombinatsiyalar](src/algorithms/sets/combinations) (takroriyalash bilan va takroriyalashsiz)
+ - `A` [Eng uzun umumiy ketma-ketlik](src/algorithms/sets/longest-common-subsequence) (LCS)
+ - `A` [Eng uzun ortib boruvchi ketma-ketlik](src/algorithms/sets/longest-increasing-subsequence)
+ - `A` [Eng qisqa umumiy ketma-ketlik](src/algorithms/sets/shortest-common-supersequence) (SCS)
+ - `A` [Knapsack muammosi](src/algorithms/sets/knapsack-problem) - "0/1" va "Bir-biriga bog'lanmagan"
+ - `A` [Maksimal kichik massiv](src/algorithms/sets/maximum-subarray) - Toʻliq kuch va dinamik dasturlash (Kadane usuli) versiyalari
+ - `A` [Kombinatsiya yig'indisi](src/algorithms/sets/combination-sum) - ma'lum summani tashkil etuvchi barcha kombinatsiyalarni topish
+- **Stringlar**
+ - `B` [Hamming masofasi](src/algorithms/string/hamming-distance) - belgilarning bir-biridan farq qiladigan pozitsiyalar soni
+ - `B` [Palindrom](src/algorithms/string/palindrome) - satrning teskari tomoni ham bir xil ekanligini tekshirish
+ - `A` [Levenshtein masofasi](src/algorithms/string/levenshtein-distance) - ikki ketma-ketlik o'rtasidagi minimal tahrirlash masofasi
+ - `A` [Knuth–Morris–Pratt Algoritmi](src/algorithms/string/knuth-morris-pratt) (KMP Algoritmi) - kichik qatorlarni qidirish (mosh keluvchi naqshni qidirish)
+ - `A` [Z Algoritmi](src/algorithms/string/z-algorithm) - kichik qatorlarni qidirish (mosh keluvchi naqshni qidirish)
+ - `A` [Rabin Karp Algoritmi](src/algorithms/string/rabin-karp) - kichik qatorlarni qidirish
+ - `A` [Eng uzun umumiy kichik matn](src/algorithms/string/longest-common-substring)
+ - `A` [Regulyar ifoda moslashuvi](src/algorithms/string/regular-expression-matching) (RegEx)
+- **Qidiruvlar**
+ - `B` [Linear qidirish](src/algorithms/search/linear-search)
+ - `B` [Jump qidirish](src/algorithms/search/jump-search) (yoki Blok qidirish) - saralangan qatorda qidirish
+ - `B` [Ikkilik qidirish](src/algorithms/search/binary-search) - saralangan qatorda qidirish
+ - `B` [Interpolatsiya qidirish](src/algorithms/search/interpolation-search) - bir tekis taqsimlangan saralangan qatorda qidirish
+- **Tartiblash**
+ - `B` [Pufakcha tartiblash](src/algorithms/sorting/bubble-sort)
+ - `B` [Tanlash tartibi](src/algorithms/sorting/selection-sort)
+ - `B` [Kiritish tartibi](src/algorithms/sorting/insertion-sort)
+ - `B` [Heap tartibi](src/algorithms/sorting/heap-sort)
+ - `B` [Birlashtirish tartibi](src/algorithms/sorting/merge-sort)
+ - `B` [Tezkor saralash](src/algorithms/sorting/quick-sort) - joyida va joyida bo'lmagan amalga oshirish
+ - `B` [Shell tartiblash](src/algorithms/sorting/shell-sort)
+ - `B` [Sanash tartibi](src/algorithms/sorting/counting-sort)
+ - `B` [Radiksli tartiblash](src/algorithms/sorting/radix-sort)
+ - `B` [Bucket tartiblash](src/algorithms/sorting/bucket-sort)
+- **Bog'langan ro'yhatlar**
+ - `B` [To'g'ri traversal](src/algorithms/linked-list/traversal)
+ - `B` [Teskari traversal](src/algorithms/linked-list/reverse-traversal)
+- **Daraxtlar**
+ - `B` [Birinchi-pastga qarab qidirish](src/algorithms/tree/depth-first-search) (Depth-First Search)
+ - `B` [Birinchi-yonga qarab qidirish](src/algorithms/tree/breadth-first-search) (Breadth-First Search)
+- **Grafiklar**
+ - `B` [Birinchi-pastga qarab qidirish](src/algorithms/graph/depth-first-search) (Depth-First Search)
+ - `B` [Birinchi-yonga qarab qidirish](src/algorithms/graph/breadth-first-search) (Breadth-First Search)
+ - `B` [Kruskal Algoritmi](src/algorithms/graph/kruskal) - og'irlikdagi yo'naltirilmagan grafik uchun Minimal kengayuvchi daraxtni (MST) topish
+ - `A` [Dijkstra Algoritmi](src/algorithms/graph/dijkstra) - grafikning bir cho'qqisidan qolgan barcha nuqtalarga eng qisqa yo'llarni topish
+ - `A` [Bellman-Ford Algoritmi](src/algorithms/graph/bellman-ford) - grafikning bir cho'qqisidan qolgan barcha nuqtalarga eng qisqa yo'llarni topish
+ - `A` [Floyd-Warshall Algoritmi](src/algorithms/graph/floyd-warshall) - grafikning barcha uchlari orasidagi eng qisqa masofalarni topish
+ - `A` [Siklni aniqlash](src/algorithms/graph/detect-cycle) - yo'naltirilgan va yo'naltirilmagan grafiklar uchun (DFS va Disjoint Set-ga asoslangan versiyalar)
+ - `A` [Prim Algoritmi](src/algorithms/graph/prim) - og'irlikdagi yo'naltirilmagan grafik uchun Minimal kengayuvchi daraxtni (MST) topish
+ - `A` [Topologik saralash](src/algorithms/graph/topological-sorting) - DFS metodi
+ - `A` [Artikulyatsiya nuqtalari](src/algorithms/graph/articulation-points) - Tarjan algoritmi (DFS asosida)
+ - `A` [Ko'priklar](src/algorithms/graph/bridges) - DFS asosidagi algoritm
+ - `A` [Eyler yo'li va Eyler sxemasi](src/algorithms/graph/eulerian-path) - Fleury algoritmi - Har bir chekkaga bir marta tashrif buyurish
+ - `A` [Gamilton sikli](src/algorithms/graph/hamiltonian-cycle) - Har bir cho'qqiga bir marta tashrif buyurish
+ - `A` [Kuchli bog'langan komponentlar](src/algorithms/graph/strongly-connected-components) - Kosaraju algoritmi
+ - `A` [Sayohatchi sotuvchi muammosi](src/algorithms/graph/travelling-salesman) - har bir shaharga tashrif buyuradigan va kelib chiqqan shaharga qaytib keladigan eng qisqa yo'l
+- **Kriptografiya**
+ - `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - polinomga asoslangan hash funktsiyasi
+ - `B` [Rail Fence Cipher](src/algorithms/cryptography/rail-fence-cipher) - xabarlarni kodlash uchun transpozitsiya shifrlash algoritmi
+ - `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - oddiy almashtirish shifridir
+ - `B` [Hill Cipher](src/algorithms/cryptography/hill-cipher) - chiziqli algebraga asoslangan almashtirish shifri
+- **Machine Learning**
+ - `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - Mashinalar aslida qanday o'rganishi mumkinligini ko'rsatadigan 7 ta oddiy JS funksiyasi (forward/backward tarqalish)
+ - `B` [k-NN](src/algorithms/ml/knn) - eng yaqin qo'shnilarni tasniflash algoritmi
+ - `B` [k-Means](src/algorithms/ml/k-means) - k-Means kalsterlash algoritmi
+- **Tasvirga ishlov berish**
+ - `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - kontentga moslashuvchan rasm o'lchamini o'zgartirish algoritmi
+- **Statistikalar**
+ - `B` [Weighted Random](src/algorithms/statistics/weighted-random) - elementlarning og'irligi asosida ro'yxatdan tasodifiy elementni tanlash
+- **Evolyutsion algoritmlar**
+ - `A` [Genetik algoritm](https://github.com/trekhleb/self-parking-car-evolution) - avtoturargohni o'rgatish uchun genetik algoritm qanday qo'llanilishiga misol.
+- **Kategoriyasiz**
+ - `B` [Xanoy minorasi](src/algorithms/uncategorized/hanoi-tower)
+ - `B` [Kvadrat matritsaning aylanishi](src/algorithms/uncategorized/square-matrix-rotation) - joyidagi algoritm
+ - `B` [Sakrash o'yini](src/algorithms/uncategorized/jump-game) - orqaga qaytish, dinamik dasturlash (yuqoridan pastga + pastdan yuqoriga) va ochko'z misollar
+ - `B` [Noyob yo'llar](src/algorithms/uncategorized/unique-paths) - orqaga qaytish, dinamik dasturlash va Paskal uchburchagiga asoslangan misolla
+ - `B` [Yomg'ir teraslari](src/algorithms/uncategorized/rain-terraces) - yomg'ir suvini ushlab turish muammosi (dinamik dasturlash va qo'pol kuch versiyalari)
+ - `B` [Rekursiv zinapoya](src/algorithms/uncategorized/recursive-staircase) - yuqoriga chiqish yo'llari sonini hisoblash (4 ta echim)
+ - `B` [Aksiyalarni sotib olish va sotish uchun eng yaxshi vaqt](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - bo'linib-zabt etish va bir marta o'tish misollari
+ - `A` [N-Queens Muommosi](src/algorithms/uncategorized/n-queens)
+ - `A` [Ritsar sayohati](src/algorithms/uncategorized/knight-tour)
+
+### Paradigma bo'yicha algoritmlar
+
+Algorithmic paradigm - bu algoritmlar sinfini loyihalashtirishga asos bo'lib xizmat qiladigan umumiy usul yoki yondashuv. Bu algoritm tushunchasidan yuqori darajadagi abstraktsiya bo'lib, algoritm kompyuter dasturi tushunchasidan yuqori darajadagi abstraktsiya bo'lgani kabi.
+
+- **Brute Force** - barcha imkoniyatlarni ko'rib chiqib va eng yaxshi echimni tanlash
+ - `B` [Chiziqli qidirish](src/algorithms/search/linear-search)
+ - `B` [Yomg'irli teraslar](src/algorithms/uncategorized/rain-terraces) - yomg'ir suvini to'plash muammosi
+ - `B` [Rekursiv zinapoya](src/algorithms/uncategorized/recursive-staircase) - cho'qqiga chiqish yo'llari sonini hisoblash
+ - `A` [Maksimal kichik massiv](src/algorithms/sets/maximum-subarray)
+ - `A` [Sayohatchi sotuvchi muammosi](src/algorithms/graph/travelling-salesman) - har bir shaharga tashrif buyuradigan va kelib chiqqan shaharga qaytib keladigan eng qisqa yo'l
+ - `A` [Diskret Furye transformatsiyasi](src/algorithms/math/fourier-transform) - vaqt funksiyasini (signalni) uni tashkil etuvchi chastotalarga ajratish
+- **Greedy** - kelajakni o'ylamasdan, hozirgi vaqtda eng yaxshi variantni tanlash
+ - `B` [Sakrash o'yini](src/algorithms/uncategorized/jump-game)
+ - `A` [Bog'lanmagan yukxalta muammosi](src/algorithms/sets/knapsack-problem)
+ - `A` [Dijkstra Algoritmi](src/algorithms/graph/dijkstra) - grafikning bir cho'qqisidan qolgan barcha nuqtalarga eng qisqa yo'llarni topish
+ - `A` [Prim Algoritmi](src/algorithms/graph/prim) - og'irlikdagi yo'naltirilmagan grafik uchun Minimal kengayuvchi daraxtni (MST) topish
+ - `A` [Kruskal Algoritmi](src/algorithms/graph/kruskal) - og'irlikdagi yo'naltirilmagan grafik uchun Minimal kengayuvchi daraxtni (MST) topish
+- **Divide and Conquer** - muammoni kichikroq qismlarga bo'lib va keyin bu qismlarni hal qilish
+
+ - `B` [Ikkilik qidiruv](src/algorithms/search/binary-search)
+ - `B` [Xanoy minorasi](src/algorithms/uncategorized/hanoi-tower)
+ - `B` [Paskal uchburchagi](src/algorithms/math/pascal-triangle)
+ - `B` [Evklid Algoritmi](src/algorithms/math/euclidean-algorithm) - eng katta umumiy bo'luvchini (EKUB) hisoblash
+ - `B` [Birlashtirish tartibi](src/algorithms/sorting/merge-sort)
+ - `B` [Tezkor saralash](src/algorithms/sorting/quick-sort)
+ - `B` [Birinchi-pastga qarab qidirish daraxti](src/algorithms/tree/depth-first-search) (DFS)
+ - `B` [Birinchi-pastga qarab qidirish grafigi](src/algorithms/graph/depth-first-search) (DFS)
+ - `B` [Matritsalar](src/algorithms/math/matrix) - turli shakldagi matritsalarni hosil qilish va kesib o'tish
+ - `B` [Sakrash o'yini](src/algorithms/uncategorized/jump-game)
+ - `B` [Tez ko'tarish](src/algorithms/math/fast-powering)
+ - `B` [Aksiyalarni sotib olish va sotish uchun eng yaxshi vaqt](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - bo'linib-zabt etish va bir marta o'tish misollari
+ - `A` [Permutatsiyalar](src/algorithms/sets/permutations) (takroriyalash bilan va takroriyalashsiz)
+ - `A` [Kombinatsiyalar](src/algorithms/sets/combinations) (takroriyalash bilan va takroriyalashsiz)
+ - `A` [Maksimal kichik massiv](src/algorithms/sets/maximum-subarray)
+
+- **Dinamik dasturlash** - ilgari topilgan kichik yechimlar yordamida yechim yaratish
+ - `B` [Fibonachchi raqam](src/algorithms/math/fibonacci)
+ - `B` [Sakrash o'yini](src/algorithms/uncategorized/jump-game)
+ - `B` [Noyob yo'llar](src/algorithms/uncategorized/unique-paths)
+ - `B` [Yomg'ir teraslari](src/algorithms/uncategorized/rain-terraces) - yomg'ir suvini to'plash muammosi
+ - `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top
+ - `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - kontentga moslashuvchan rasm o'lchamini o'zgartirish algoritmi
+ - `A` [Levenshtein masofasi](src/algorithms/string/levenshtein-distance) - ikki ketma-ketlik o'rtasidagi minimal tahrirlash masofasi
+ - `A` [Eng uzun umumiy ketma-ketlik](src/algorithms/sets/longest-common-subsequence) (LCS)
+ - `A` [Eng uzun umumiy kichik matn](src/algorithms/string/longest-common-substring)
+ - `A` [Eng uzun ortib boruvchi ketma-ketlik](src/algorithms/sets/longest-increasing-subsequence)
+ - `A` [Eng qisqa umumiy ketma-ketlik](src/algorithms/sets/shortest-common-supersequence)
+ - `A` [0/1 Knapsak muommosi](src/algorithms/sets/knapsack-problem)
+ - `A` [Butun sonlarni bo'lish](src/algorithms/math/integer-partition)
+ - `A` [Maksimal kichik massiv](src/algorithms/sets/maximum-subarray)
+ - `A` [Bellman-Ford Algoritmi](src/algorithms/graph/bellman-ford) - grafikning bir cho'qqisidan qolgan barcha nuqtalarga eng qisqa yo'llarni topish
+ - `A` [Floyd-Warshall Algoritmi](src/algorithms/graph/floyd-warshall) -grafikning barcha uchlari orasidagi eng qisqa masofalarni topish
+ - `A` [Regulyar ifoda moslashuvi](src/algorithms/string/regular-expression-matching)
+- **Backtracking** - brute forcega o'xshab, barcha mumkin bo'lgan yechimlarni generatsiya qilishga harakat qiladi, lekin har safar keyingi yechimni yaratganingizda, yechim barcha shartlarga javob beradimi yoki yo'qligini tekshirasiz va shundan keyingina keyingi yechimlarni ishlab chiqarishni davom ettirasiz. Aks holda, orqaga qaytib, yechim topishning boshqa yo'liga o'tasiz. Odatda state-space ning DFS-qidiruvi ishlatiladi.
+ - `B` [Sakrash o'yini](src/algorithms/uncategorized/jump-game)
+ - `B` [Noyob yo'llar](src/algorithms/uncategorized/unique-paths)
+ - `B` [Power Set](src/algorithms/sets/power-set) - to'plamning barcha kichik to'plamlari
+ - `A` [Gamilton sikli](src/algorithms/graph/hamiltonian-cycle) - Har bir cho'qqiga bir marta tashrif buyurish
+ - `A` [N-Queens muommosi](src/algorithms/uncategorized/n-queens)
+ - `A` [Ritsar sayohati](src/algorithms/uncategorized/knight-tour)
+ - `A` [Kombinatsiya yig'indisi](src/algorithms/sets/combination-sum) - ma'lum summani tashkil etuvchi barcha kombinatsiyalarni topish
+- **Branch & Bound** - shu paytgacha topilgan eng arzon echimdan kattaroq xarajatlarga ega qisman echimlarni bekor qilish uchun, backtracking qidiruvining har bir bosqichida topilgan eng arzon echimni eslab qoling va shu paytgacha topilgan eng arzon yechim narxidan muammoni eng kam xarajatli yechim narxining past chegarasi sifatida foydalaning. Odatda state-space daraxtining DFS o'tishi bilan birgalikda BFS traversal qo'llaniladi.
+
+## Ushbu repozitoriyadan qanday foydalanish kerak
+
+**Barcha dependensiylarni o'rnating**
+
+```
+npm install
+```
+
+**ESLint ni ishga tushiring**
+
+Kod sifatini tekshirish uchun ESLint ni ishga tushirishingiz mumkin.
+
+```
+npm run lint
+```
+
+**Barcha testlarni ishga tushuring**
+
+```
+npm test
+```
+
+**Testlarni nom bo'yicha ishga tushirish**
+
+```
+npm test -- 'LinkedList'
+```
+
+**Muammolarni bartaraf qilish (Troubleshooting)**
+
+Agar linting yoki sinov muvaffaqiyatsiz bo'lsa, `node_modules` papkasini o'chirib, npm paketlarini qayta o'rnatishga harakat qiling:
+
+```
+rm -rf ./node_modules
+npm i
+```
+
+Shuningdek, to'g'ri Node versiyasidan foydalanayotganingizga ishonch hosil qiling (`>=16`). Agar Node versiyasini boshqarish uchun [nvm](https://github.com/nvm-sh/nvm) dan foydalanayotgan bo'lsangiz, loyihaning ildiz papkasidan `nvm use` ni ishga tushiring va to'g'ri versiya tanlanadi.
+
+**O'yin maydoni (Playground)**
+
+`./src/playground/playground.js` faylida ma'lumotlar strukturalari va algoritmlar bilan o'ynashingiz, `./src/playground/test/playground.test.js` faylida esa ular uchun testlar yozishingiz mumkin.
+
+Shundan so'ng, playground kodingiz kutilgandek ishlashini tekshirish uchun quyidagi buyruqni ishga tushirishingiz kifoya:
+
+```
+npm test -- 'playground'
+```
+
+## Foydali ma'lumotlar
+
+### Manbalar
+
+- [▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [✍🏻 Data Structure Sketches](https://okso.app/showcase/data-structures)
+
+### Big O Notation
+
+_Big O notation_ algoritmlarni kirish hajmi oshgani sayin ularning ishlash vaqti yoki bo'sh joy talablari qanday o'sishiga qarab tasniflash uchun ishlatiladi. Quyidagi jadvalda siz Big O notatsiyasida ko'rsatilgan algoritmlarning o'sishining eng keng tarqalgan tartiblarini topishingiz mumkin.
+
+
+
+Manba: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+Quyida eng ko'p qo'llaniladigan Big O notatsiyalarining ro'yxati va ularning kirish ma'lumotlarining turli o'lchamlariga nisbatan ishlashini taqqoslash keltirilgan.
+
+| Big O Notatsiya | Turi | 10 ta element uchun hisob-kitoblar | 100 ta element uchun hisob-kitoblar | 1000 ta element uchun hisob-kitoblar |
+| --------------- | ------------ | ---------------------------------- | ----------------------------------- | ------------------------------------ |
+| **O(1)** | O'zgarmas | 1 | 1 | 1 |
+| **O(log N)** | Logarifmik | 3 | 6 | 9 |
+| **O(N)** | Chiziqli | 10 | 100 | 1000 |
+| **O(N log N)** | n log(n) | 30 | 600 | 9000 |
+| **O(N^2)** | Kvadrat | 100 | 10000 | 1000000 |
+| **O(2^N)** | Eksponensial | 1024 | 1.26e+29 | 1.07e+301 |
+| **O(N!)** | Faktorial | 3628800 | 9.3e+157 | 4.02e+2567 |
+
+### Ma'lumotlar tuzilmalarining operatsiyalari murakkabligi
+
+| Ma'lumotlar tuzilmalari | Kirish | Qidirish | Kiritish | O'chirish | Izohlar |
+| --------------------------- | :----: | :------: | :------: | :-------: | :--------------------------------------------------------- |
+| **Massiv** | 1 | n | n | n | |
+| **Stak** | n | n | 1 | 1 | |
+| **Navbat** | n | n | 1 | 1 | |
+| **Bog'langan ro'yhat** | n | n | 1 | n | |
+| **Hash jadval** | - | n | n | n | Mukammal xash funksiyasi bo'lsa, xarajatlar O (1) bo'ladi. |
+| **Ikkilik qidiruv daraxti** | n | n | n | n | Balanslangan daraxt narxida O(log(n)) bo'ladi. |
+| **B-daraxti** | log(n) | log(n) | log(n) | log(n) | |
+| **Qizil-qora daraxt** | log(n) | log(n) | log(n) | log(n) | |
+| **AVL Daraxt** | log(n) | log(n) | log(n) | log(n) | |
+| **Bloom filtri** | - | 1 | 1 | - | Qidiruv paytida noto'g'ri pozitivlar bo'lishi mumkin |
+
+### Massivlarni saralash algoritmlarining murakkabligi
+
+| Nomi | Eng yaxshi | O'rta | Eng yomon | Xotira | Barqaror | Izohlar |
+| ------------------------- | :-----------: | :---------------------: | :-------------------------: | :----: | :------: | :--------------------------------------------------------------------------- |
+| **Pufakcha tartiblash** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Ha | |
+| **Kiritish tartibi** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Ha | |
+| **Tanlash tartibi** | n<sup>2</sup> | n<sup>2</sup> | n<sup>2</sup> | 1 | Yo'q | |
+| **Heap tartibi** | n log(n) | n log(n) | n log(n) | 1 | Yo'q | |
+| **Birlashtirish tartibi** | n log(n) | n log(n) | n log(n) | n | Ha | |
+| **Tezkor saralash** | n log(n) | n log(n) | n<sup>2</sup> | log(n) | Yo'q | Tezkor saralash odatda O(log(n)) stek maydoni bilan joyida amalga oshiriladi |
+| **Shell tartiblash** | n log(n) | depends on gap sequence | n (log(n))<sup>2</sup> | 1 | Yo'q | |
+| **Sanash tartibi** | n + r | n + r | n + r | n + r | Ha | r - massivdagi eng katta raqam |
+| **Radiksli tartiblash** | n \* k | n \* k | n \* k | n + k | Ha | k - eng uzun kalitning uzunligi |
+
+## Loyihani qo'llab-quvvatlovchilar
+
+> Siz ushbu loyihani ❤️️ [GitHub](https://github.com/sponsors/trekhleb) yoki ❤️️ [Patreon](https://www.patreon.com/trekhleb) orqali qo'llab-quvvatlashingiz mumkin.
+
+[Ushbu loyihani qo'llab-quvvatlagan odamlar](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+
+## Muallif
+
+[@trekhleb](https://trekhleb.dev)
+
+A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.vi-VN.md b/README.vi-VN.md
new file mode 100644
index 0000000000..4c35f467f8
--- /dev/null
+++ b/README.vi-VN.md
@@ -0,0 +1,329 @@
+# JavaScript Thuật Toán và Cấu Trúc Dữ Liệu
+
+[](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
+[](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+Repository này bao gồm nhiều ví dụ thuật toán và cấu trúc dữ liệu phổ biến
+dựa trên Javascript.
+
+Mối thuật toán và cấu trúc dữ liệu có README riêng với những lý giải và links
+liên quan để đọc thêm (bao gồm cả những videos trên Youtube).
+
+_Đọc bằng ngôn ngữ khác:_
+[_English_](README.md),
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
+[_עברית_](README.he-IL.md)
+
+*☝ Dự án này chỉ được sử dụng cho mục đích học tập và nghiên cứu, **không** được dùng
+cho mục đích thương mại.*
+
+## Cấu Trúc Dữ Liệu
+
+Cấu trúc dữ liệu là một cách cụ thể để tổ chức và lưu trữ dữ liệu trong máy tính để nó có thể
+được truy cập và sửa đổi một cách hiệu quả. Chính xác hơn, cấu trúc dữ liệu là một tập hợp
+các giá trị dữ liệu, các mối quan hệ giữa chúng và các hàm hoặc phép toán có thể được áp dụng
+cho dữ liệu.
+
+`B` - Cơ bản, `A` - Nâng cao
+
+* `B` [Danh sách liên kết](src/data-structures/linked-list)
+* `B` [Danh sách liên kết đôi](src/data-structures/doubly-linked-list)
+* `B` [Hàng đợi](src/data-structures/queue)
+* `B` [Ngăn xếp](src/data-structures/stack)
+* `B` [Bảng băm](src/data-structures/hash-table)
+* `B` [Đống](src/data-structures/heap) - max và min heap
+* `B` [Hàng đợi ưu tiên](src/data-structures/priority-queue)
+* `A` [Cây tiền tố](src/data-structures/trie)
+* `A` [Cây](src/data-structures/tree)
+ * `A` [Cây tìm kiếm nhị phân](src/data-structures/tree/binary-search-tree)
+ * `A` [Cây AVL](src/data-structures/tree/avl-tree)
+ * `A` [Cây đỏ đen](src/data-structures/tree/red-black-tree)
+ * `A` [Cây phân đoạn](src/data-structures/tree/segment-tree) - với các ví dụ truy vấn phạm vi nhỏ nhất/lớn nhất/tổng
+ * `A` [CÂy Fenwick](src/data-structures/tree/fenwick-tree) (Cây chỉ mục nhị phân)
+* `A` [Đồ thị](src/data-structures/graph) (có hướng và vô hướng)
+* `A` [Tập hợp không giao nhau](src/data-structures/disjoint-set)
+* `A` [Bộ lọc Bloom](src/data-structures/bloom-filter)
+
+## Thuật Toán
+
+Thuật toán là một đặc tả rõ ràng về cách giải quyết một lớp vấn đề. Nó là một tập hợp các
+quy tắc xác định chính xác một chuỗi phép toán.
+
+`B` - Cơ bản, `A` - Nâng cao
+
+### Thuật toán theo chủ đề
+
+* **Toán**
+ * `B` [Thao tác bit](src/algorithms/math/bits) - đặt/lấy/cập nhật/xóa bit, nhân/chia 2, đổi dấu âm,...
+ * `B` [Giai thừa](src/algorithms/math/factorial)
+ * `B` [Số Fibonacci](src/algorithms/math/fibonacci) - cổ điển và dạng đóng
+ * `B` [Thừa số nguyên tố](src/algorithms/math/prime-factors) - tìm và đếm thừa số nguyên tố sử dụng định luật Hardy-Ramanujan's
+ * `B` [Kiểm tra tính nguyên tố](src/algorithms/math/primality-test) (phân chia thử nghiệm)
+ * `B` [Thuật toán Euclid](src/algorithms/math/euclidean-algorithm) - tính ước số chung lớn nhất (GCD)
+ * `B` [Bội số chung nhỏ nhất](src/algorithms/math/least-common-multiple) (LCM)
+ * `B` [Sàng số nguyên tố](src/algorithms/math/sieve-of-eratosthenes) - tìm tất cả các số nguyên tố trong bất kỳ phạm vi nhất định nào
+ * `B` [Xác định lũy thừa của 2](src/algorithms/math/is-power-of-two) - kiểm tra xem số có phải là lũy thừa của 2 hay không (thuật toán nguyên bản và theo bit)
+ * `B` [Tam giác Pascal](src/algorithms/math/pascal-triangle)
+ * `B` [Số phức](src/algorithms/math/complex-number) - số phức và các phép toán cơ bản với số phức
+ * `B` [Radian & độ](src/algorithms/math/radian) - chuyển đổi giữa đơn vị radian và độ
+ * `B` [Tính nhanh lũy thừa](src/algorithms/math/fast-powering)
+ * `B` [Phương pháp Horner's](src/algorithms/math/horner-method) - tính giá trị đa thức
+ * `B` [Ma trận](src/algorithms/math/matrix) - ma trận và các phép toán cơ bản (phép nhân, phép chuyển vị,...)
+ * `B` [Khoảng cách Euclid](src/algorithms/math/euclidean-distance) - khoảng cách giữa hai điểm/véc-tơ/ma trận
+ * `A` [Phân hoạch](src/algorithms/math/integer-partition)
+ * `A` [Căn bậc hai](src/algorithms/math/square-root) - phương pháp Newton
+ * `A` [Thuật cắt đường tròn - Lưu Huy](src/algorithms/math/liu-hui) - phép tính gần đúng số π dựa vào đa giác
+ * `A` [Biến đổi Fourier rời rạc](src/algorithms/math/fourier-transform) - phân giải tín hiệu thời gian thành các tần số tạo nên tín hiệu đó
+* **Tập hợp**
+ * `B` [Tích Đề-các](src/algorithms/sets/cartesian-product) - tích của nhiều tập hợp
+ * `B` [Thuật toán xáo trộn](src/algorithms/sets/fisher-yates) - dãy hữu hạn hoán vị ngẫu nhiên
+ * `A` [Tập lũy thừa](src/algorithms/sets/power-set) - tập hợp chứa tất cả các tập con (theo bit và quay lui)
+ * `A` [Hoán vị](src/algorithms/sets/permutations) (lặp và không lặp)
+ * `A` [Tổ hợp](src/algorithms/sets/combinations) (lặp và không lặp)
+ * `A` [Dãy con chung dài nhất](src/algorithms/sets/longest-common-subsequence) (LCS)
+ * `A` [Dãy con chung tăng dần dài nhất](src/algorithms/sets/longest-increasing-subsequence)
+ * `A` [Dãy con chung ngắn nhất](src/algorithms/sets/shortest-common-supersequence) (SCS)
+ * `A` [Bài toán xếp ba lô](src/algorithms/sets/knapsack-problem) - dạng 0-1 và không bị chặn
+ * `A` [Mảng con lớn nhất](src/algorithms/sets/maximum-subarray) - phiên bản vét cạn và quy hoạch động (Kadane)
+ * `A` [Tổ hợp của tổng](src/algorithms/sets/combination-sum) - tìm tất cả các tổ hợp tạo thành tổng cụ thể
+* **Chuỗi**
+ * `B` [Khoảng cách Hamming](src/algorithms/string/hamming-distance) - số các vị trí các ký hiệu khác nhau
+ * `A` [Khoảng cách Levenshtein](src/algorithms/string/levenshtein-distance) - khoảng cách thay đổi nhỏ nhất giữa hai chuỗi ký tự
+ * `A` [Thuật toán Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (thuật toán KMP) - tìm chuỗi con (đối sánh mẫu)
+ * `A` [Thuật toán Z](src/algorithms/string/z-algorithm) - tìm chuỗi con (đối sánh mẫu)
+ * `A` [Thuật toán Rabin Karp](src/algorithms/string/rabin-karp) - tìm chuỗi con
+ * `A` [Xâu con chung dài nhất](src/algorithms/string/longest-common-substring)
+ * `A` [Phối biểu thức chính quy](src/algorithms/string/regular-expression-matching)
+* **Tìm kiếm**
+ * `B` [Tìm kiếm tuyến tính](src/algorithms/search/linear-search)
+ * `B` [Tìm kiếm nhảy](src/algorithms/search/jump-search) (tìm khối) - tìm kiếm trong mảng đã sắp xếp
+ * `B` [Tìm kiếm nhị phân](src/algorithms/search/binary-search) - tìm kiếm trong mảng đã sắp xếp
+ * `B` [Tìm kiếm nội suy ](src/algorithms/search/interpolation-search) - Tìm kiếm strong mảng có thứ tự được phân phối đồng nhất
+* **Sắp xếp**
+ * `B` [Sắp xếp nổi bọt](src/algorithms/sorting/bubble-sort)
+ * `B` [Sắp xếp chọn](src/algorithms/sorting/selection-sort)
+ * `B` [Sắp xếp chèn](src/algorithms/sorting/insertion-sort)
+ * `B` [Sắp xếp vun đống](src/algorithms/sorting/heap-sort)
+ * `B` [Sắp xếp trộn](src/algorithms/sorting/merge-sort)
+ * `B` [Sắp xếp nhanh](src/algorithms/sorting/quick-sort) - Tại chỗ và không tại chỗ
+ * `B` [Shellsort](src/algorithms/sorting/shell-sort)
+ * `B` [Sắp xếp đếm](src/algorithms/sorting/counting-sort)
+ * `B` [Sắp xếp theo cơ số](src/algorithms/sorting/radix-sort)
+* **Danh sách liên kết**
+ * `B` [Di chuyển chính hướng](src/algorithms/linked-list/traversal)
+ * `B` [Di chuyển ngược hướng](src/algorithms/linked-list/reverse-traversal)
+* **Cây**
+ * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
+ * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS)
+* **Đồ thị**
+ * `B` [Tìm kiếm theo chiều sâu](src/algorithms/graph/depth-first-search) (DFS)
+ * `B` [Tìm kiếm theo chiều rộng](src/algorithms/graph/breadth-first-search) (BFS)
+ * `B` [Thuật toán Kruskal](src/algorithms/graph/kruskal) - tìm cây bao trùm nhỏ nhất (MST) cho đồ thị vô hướng có trọng số
+ * `A` [Thuật toán Dijkstra Algorithm](src/algorithms/graph/dijkstra) - tìm những đường ngắn nhất từ một định tới tất cả các đỉnh
+ * `A` [Thuật toán Bellman-Ford](src/algorithms/graph/bellman-ford) - tìm những đường ngắn nhất từ một đỉnh tới tất cả các đỉnh của đồ thị
+ * `A` [Thuật toán Floyd-Warshall](src/algorithms/graph/floyd-warshall) - tìm những đường ngắn nhất giữa tất cả các cặp đỉnh
+ * `A` [Phát hiện vòng](src/algorithms/graph/detect-cycle) - cho cả đồ thị có hướng và vô hướng (dựa trên DFS và tập không giao)
+ * `A` [Thuật toán Prim](src/algorithms/graph/prim) - tìm cây bao trùm nhỏ nhất (MST) cho đồ thị vô hướng có trọng số
+ * `A` [Sắp xếp tô pô](src/algorithms/graph/topological-sorting) - phương pháp DFS
+ * `A` [Điểm khớp](src/algorithms/graph/articulation-points) - Thuật toán Tarjan (dựa trên DFS)
+ * `A` [Cầu nối](src/algorithms/graph/bridges) - dựa trên DFS
+ * `A` [Đường đi Euler và Chu trình Euler](src/algorithms/graph/eulerian-path) - thuật toán Fleury - đi qua các cạnh chỉ một lần duy nhất
+ * `A` [Chu trình Hamilton](src/algorithms/graph/hamiltonian-cycle) - đi qua các đỉnh chỉ một lần duy nhất
+ * `A` [Các thành phần kết nối chặt](src/algorithms/graph/strongly-connected-components) - Thuật toán Kosaraju
+ * `A` [Bài toán người bán hàng](src/algorithms/graph/travelling-salesman) - tuyến đường ngắn nhất có thể đến thăm từng thành phố và trở về thành phố gốc
+* **Mật mã học**
+ * `B` [Băm đa thức](src/algorithms/cryptography/polynomial-hash) - lăn hàm băm dựa trên đa thức
+ * `B` [Mật mã hàng rào đường sắt](src/algorithms/cryptography/rail-fence-cipher) - một thuật toán mật mã chuyển vị để mã hóa thông điệp
+ * `B` [Mật mã Caesar](src/algorithms/cryptography/caesar-cipher) - mật mã chuyển vị đơn giản
+ * `B` [Mật mã Hill](src/algorithms/cryptography/hill-cipher) - mật mã chuyển vị đơn giản dựa trên đại số tuyến tính
+* **Học máy**
+ * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 hàm JS đơn giản minh họa cách máy tính thực sự có thể học (truyền thuận / truyền ngược)
+ * `B` [k-NN](src/algorithms/ml/knn) - thuật toán phân loại k láng giềng gần nhất
+ * `B` [k-Means](src/algorithms/ml/k-means) - thuật toán phân cụm k-Means
+* **Khác**
+ * `B` [Tháp Hà Nội](src/algorithms/uncategorized/hanoi-tower)
+ * `B` [Xoay ma trận vuông](src/algorithms/uncategorized/square-matrix-rotation) - thuật toán tại chỗ
+ * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game) - ví dụ quay lui, quy hoạch động (từ trên xuống + từ dưới lên), dynamic programming (top-down + bottom-up) và tham lam
+ * `B` [Các đường đi đặc trưng duy nhất](src/algorithms/uncategorized/unique-paths) - ví dụ quay lui, quy hoạch động và tam giác Pascal
+ * `B` [Thu thập nước mưa](src/algorithms/uncategorized/rain-terraces) - bài toán bẫy nước mưa (phiên bản quy hoạch động và vét cạn)
+ * `B` [Cầu thang đệ quy](src/algorithms/uncategorized/recursive-staircase) - đếm số cách lên đến đỉnh (4 lời giải)
+ * `B` [Thời điểm tốt nhất để mua bán cổ phiếu ](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - ví dụ chia để trị và một đường chuyền
+ * `A` [Bài toán n quân hậu](src/algorithms/uncategorized/n-queens)
+ * `A` [Mã đi tuần](src/algorithms/uncategorized/knight-tour)
+
+### Thuật toán theo mẫu hình
+
+Mẫu hình thuật toán là một phương pháp hoặc cách tiếp cận chung làm cơ sở cho việc thiết kế một
+lớp thuật toán. Nó là một sự trừu tượng cao hơn khái niệm về một thuật toán, cũng giống như
+một thuật toán là một sự trừu tượng cao hơn một chương trình máy tính.
+
+* **Vét cạn** - xem xét tất cả các khả năng và chọn giải pháp tốt nhất
+ * `B` [Tìm kiếm tuyến tính](src/algorithms/search/linear-search)
+ * `B` [Thu thập nước mưa](src/algorithms/uncategorized/rain-terraces) - bài toán bẫy nước mưa
+ * `B` [Cầu thang đệ quy](src/algorithms/uncategorized/recursive-staircase) - đếm số cách lên đến đỉnh
+ * `A` [Mảng con lớn nhất](src/algorithms/sets/maximum-subarray)
+ * `A` [Bài toán người bán hàng](src/algorithms/graph/travelling-salesman) - tuyến đường ngắn nhất có thể đến thăm từng thành phố và trở về thành phố gốc
+ * `A` [Biến đổi Fourier rời rạc](src/algorithms/math/fourier-transform) - phân giải tín hiệu thời gian thành các tần số tạo nên tín hiệu đó
+* **Tham lam** - chọn phương án tốt nhất vào thời điểm hiện tại mà không cần cân nhắc đến tương lai
+ * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
+ * `A` [Bài xếp ba lô không bị chặn](src/algorithms/sets/knapsack-problem)
+ * `A` [Thuật toán Dijkstra](src/algorithms/graph/dijkstra) - tìm những đường ngắn nhất từ một định tới tất cả các đỉnh
+ * `A` [Thuật toán Prim](src/algorithms/graph/prim) - tìm cây bao trùm nhỏ nhất (MST) cho đồ thị vô hướng có trọng số
+ * `A` [Thuật toán Kruskal](src/algorithms/graph/kruskal) - tìm cây bao trùm nhỏ nhất (MST) cho đồ thị vô hướng có trọng số
+* **Chia để trị** - chia vấn đề thành các phần nhỏ hơn rồi giải quyết các phần đó
+ * `B` [Tìm kiếm nhị phân](src/algorithms/search/binary-search)
+ * `B` [Tháp Hà Nội](src/algorithms/uncategorized/hanoi-tower)
+ * `B` [Tam giác Pascal](src/algorithms/math/pascal-triangle)
+ * `B` [Thuật toán Euclid](src/algorithms/math/euclidean-algorithm) - tính ước số chung lớn nhất
+ * `B` [Sắp xếp trộn](src/algorithms/sorting/merge-sort)
+ * `B` [Sắp xếp nhanh](src/algorithms/sorting/quick-sort)
+ * `B` [Cây tìm kiếm theo chiều sâu](src/algorithms/tree/depth-first-search) (DFS)
+ * `B` [Đồ thị tìm kiếm theo chiều sâu](src/algorithms/graph/depth-first-search) (DFS)
+ * `B` [Ma trận](src/algorithms/math/matrix) - tạo và duyệt các ma trận có kích thước khác nhau
+ * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
+ * `B` [Tính nhanh lũy thừa](src/algorithms/math/fast-powering)
+ * `B` [Thời điểm tốt nhất để mua bán cổ phiếu](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - ví dụ chia để trị và một đường chuyền
+ * `A` [Hoán vị](src/algorithms/sets/permutations) (lặp và không lặp)
+ * `A` [Tổ hợp](src/algorithms/sets/combinations) (lặp và không lặp)
+* **Quy hoạch động** - xây dựng một giải pháp bằng cách sử dụng các giải pháp phụ đã tìm thấy trước đây
+ * `B` [Số Fibonacci](src/algorithms/math/fibonacci)
+ * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
+ * `B` [Đường đi độc nhất](src/algorithms/uncategorized/unique-paths)
+ * `B` [Thu thập nước mưa](src/algorithms/uncategorized/rain-terraces) - bài toán bẫy nước mưa
+ * `B` [Cầu thang đệ quy](src/algorithms/uncategorized/recursive-staircase) - đếm số cách lên đến đỉnh
+ * `A` [Khoảng cách Levenshtein](src/algorithms/string/levenshtein-distance) - khoảng cách thay đổi nhỏ nhất giữa hai chuỗi ký tự
+ * `A` [Dãy con chung dài nhất](src/algorithms/sets/longest-common-subsequence) (LCS)
+ * `A` [Xâu con chung dài nhất](src/algorithms/string/longest-common-substring)
+ * `A` [Dãy con chung tăng dần dài nhất](src/algorithms/sets/longest-increasing-subsequence)
+ * `A` [Dãy con chung ngắn nhất](src/algorithms/sets/shortest-common-supersequence)
+ * `A` [Bài xếp ba lô dạng 0-1](src/algorithms/sets/knapsack-problem)
+ * `A` [Integer Partition](src/algorithms/math/integer-partition)
+ * `A` [Mảng con lớn nhất](src/algorithms/sets/maximum-subarray)
+ * `A` [Thuật toán Bellman-Ford](src/algorithms/graph/bellman-ford) - tìm những đường ngắn nhất từ một đỉnh tới tất cả các đỉnh của đồ thị
+ * `A` [Thuật toán Floyd-Warshall](src/algorithms/graph/floyd-warshall) - tìm những đường ngắn nhất giữa tất cả các cặp đỉnh
+ * `A` [Phối biểu thức chính quy](src/algorithms/string/regular-expression-matching)
+* **Quay lui** - tương tự như vét cạn, cố tạo ra tất cả các giải pháp có thể, nhưng mỗi lần bạn tạo ra giải pháp tiếp theo,
+bạn sẽ kiểm tra xem nó có thỏa mãn tất cả các điều kiện hay không và chỉ khi thỏa mãn mới tiếp tục tạo ra các giải pháp tiếp theo.
+Nếu không, hãy quay lại và đi trên một con đường khác để tìm ra giải pháp. Thông thường, truyền DFS của không gian trạng thái được sử dụng.
+ * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
+ * `B` [Đường đi độc nhất](src/algorithms/uncategorized/unique-paths)
+ * `B` [Tập lũy thừa](src/algorithms/sets/power-set) - tập hợp chứa tất cả các tập con
+ * `A` [Chu trình Hamilton](src/algorithms/graph/hamiltonian-cycle) - đi qua các đỉnh một lần duy nhất
+ * `A` [Bài toán n quân hậu](src/algorithms/uncategorized/n-queens)
+ * `A` [Mã đi tuần](src/algorithms/uncategorized/knight-tour)
+ * `A` [Tổ hợp của tổng](src/algorithms/sets/combination-sum) - tìm tất cả các tổ hợp tạo thành tổng cụ thể
+* **Branch & Bound** - ghi nhớ giải pháp chi với phí thấp nhất được tìm thấy ở mỗi giai đoạn của quá trình tìm kiếm quay lui,
+sử dụng chi phí của giải pháp có chi phí thấp nhất được tìm thấy cho đến nay như một giới hạn dưới về chi phí của
+một giải pháp ít chi phí nhân cho bài toán, để loại bỏ các giải pháp từng phần với chi phí lớn hơn giải pháp chi phí thấp nhất được tìm thấy cho đến nay.
+Thông thường BFS duyệt kết hợp với duyệt DFS của cây không gian trạng thái đang được sử dụng.
+
+## Hướng dẫn sử dụng repository
+
+**Cài đặt tất cả các phụ thuộc**
+```
+npm install
+```
+
+**Chạy ESLint**
+
+Bạn có thể muốn chạy nó để kiểm tra chất lượng code.
+
+```
+npm run lint
+```
+
+**Chạy tất cả các kiểm thử**
+```
+npm test
+```
+
+**Chạy kiểm thử theo tên**
+```
+npm test -- 'LinkedList'
+```
+
+**Sân chơi**
+
+Bạn có thể chơi với các cấu trúc dữ liệu và thuật toán trong tệp `./src/playground/playground.js`
+và viết các bài kiểm thử cho nó ở `./src/playground/__test__/playground.test.js`.
+
+Sau đó, chỉ cần chạy lệnh sau để kiểm tra xem sân chơi của bạn có hoạt động như mong đợi hay không:
+
+```
+npm test -- 'playground'
+```
+
+## Thông tin hữu ích
+
+### Tham khảo
+
+[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
+### Kí hiệu O lớn
+
+*Kí hiệu O lớn* được dùng để phân loại thuật toán theo thời gian chạy hoặc yêu cầu không gian gia tăng khi kích thước đầu vào gia tăng.
+Trên biểu đồ bên dưới, bạn có thể tìm thấy hầu hết các thứ tự tăng trưởng phổ biến của các thuật toán được chỉ định trong ký hiệu O lớn.
+
+
+
+Nguồn: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+Dưới đây là danh sách một số ký hiệu O lớn thông dụng và so sánh với các kích thước khác nhau của dữ liệu đầu vào.
+
+| Kí hiệu O lớn | Tính toán cho 10 phần tử | Tính toán cho 100 phần tử | Tính toán cho 1000 phần tử |
+| -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
+| **O(1)** | 1 | 1 | 1 |
+| **O(log N)** | 3 | 6 | 9 |
+| **O(N)** | 10 | 100 | 1000 |
+| **O(N log N)** | 30 | 600 | 9000 |
+| **O(N^2)** | 100 | 10000 | 1000000 |
+| **O(2^N)** | 1024 | 1.26e+29 | 1.07e+301 |
+| **O(N!)** | 3628800 | 9.3e+157 | 4.02e+2567 |
+
+### Độ phức tạp của các phép toán cấu trúc dữ liệu
+
+| Cấu trúc dữ liệu | Truy cập | Tìm kiếm | Chèn | Xóa | Bình luận |
+| ----------------------- | :-------: | :-------: | :-------: | :-------: | :-------- |
+| **Mảng** | 1 | n | n | n | |
+| **Ngăn xếp** | n | n | 1 | 1 | |
+| **Hàng đợi** | n | n | 1 | 1 | |
+| **Danh sách liên kết** | n | n | 1 | n | |
+| **Bảng băm** | - | n | n | n | Trong trường hợp hàm băm hoàn hảo, chi phí sẽ là O(1) |
+| **Cây tìm kiếm nhị phân** | n | n | n | n | Trong trường hợp cây cân bằng, chi phí sẽ là O(log(n)) |
+| **Cây B** | log(n) | log(n) | log(n) | log(n) | |
+| **Cây đỏ đen** | log(n) | log(n) | log(n) | log(n) | |
+| **Cây AVL** | log(n) | log(n) | log(n) | log(n) | |
+| **Bộ lọc Bloom** | - | 1 | 1 | - | Có thể có kết quả dương tính giả trong khi tìm kiếm |
+
+### Độ phức tạp của các thuật toán sắp xếp mảng
+
+| Tên | Tốt nhất | Trung bình | Tệ nhất | Bộ nhớ | Ổn định | Bình luận |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Sắp xếp nổi bọt** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Có | |
+| **Sắp xếp chèn** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Có | |
+| **Sắp xếp chọn** | n<sup>2</sup> | n<sup>2</sup> | n<sup>2</sup> | 1 | Không | |
+| **Sắp xếp vun đống** | n log(n) | n log(n) | n log(n) | 1 | Không | |
+| **Sắp xếp trộn** | n log(n) | n log(n) | n log(n) | n | Có | |
+| **Sắp xếp nhanh** | n log(n) | n log(n) | n<sup>2</sup> | log(n) | Không | Sắp xếp nhanh thường được thực hiện tại chỗ với không gian ngăn xếp O (log (n)) |
+| **Shell sort** | n log(n) | phụ thuộc vào khoảng cách dãy | n (log(n))<sup>2</sup> | 1 | Không | |
+| **Sắp xếp đếm** | n + r | n + r | n + r | n + r | Có | r - số lớn nhất trong mảng |
+| **Sắp xếp theo cơ số** | n * k | n * k | n * k | n + k | Có | k - độ dài của khóa dài nhất |
+
+## Project Backers
+
+> Bạn có thể hỗ trợ dự án này qua ❤️️ [GitHub](https://github.com/sponsors/trekhleb) hoặc ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+[Những người đang ủng hộ dự án này](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
diff --git a/README.zh-CN.md b/README.zh-CN.md
index 35a3733fc3..14e0f0e36c 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -21,7 +21,11 @@ _Read this in other languages:_
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
*注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
@@ -174,7 +178,7 @@ _Read this in other languages:_
* `B` [快速算次方](src/algorithms/math/fast-powering)
* `A` [排列](src/algorithms/sets/permutations) (有/无重复)
* `A` [组合](src/algorithms/sets/combinations) (有/无重复)
-* **动态编程** - 使用以前找到的子解决方案构建解决方案
+* **动态规划(Dynamic programming)** - 使用以前找到的子解决方案构建解决方案
* `B` [斐波那契数](src/algorithms/math/fibonacci)
* `B` [跳跃游戏](src/algorithms/uncategorized/jump-game)
* `B` [独特路径](src/algorithms/uncategorized/unique-paths)
@@ -291,3 +295,5 @@ npm test -- 'playground'
| **希尔排序** | n log(n) | 取决于差距序列 | n (log(n))^2 | 1 | No | |
| **计数排序** | n + r | n + r | n + r | n + r | Yes | r - 数组里最大的数 |
| **基数排序** | n * k | n * k | n * k | n + k | Yes | k - 最长 key 的升序 |
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 4a09b8433e..aa48b40bd8 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -20,7 +20,11 @@ _Read this in other languages:_
[_Italiana_](README.it-IT.md),
[_Bahasa Indonesia_](README.id-ID.md),
[_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-IL.md)
## 資料結構
@@ -214,10 +218,12 @@ npm test -- 'playground'
| 名稱 | 最佳 | 平均 | 最差 | 記憶體 | 穩定 |
| ---------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: |
-| **氣派排序** | n | n^2 | n^2 | 1 | Yes |
+| **氣泡排序** | n | n^2 | n^2 | 1 | Yes |
| **插入排序** | n | n^2 | n^2 | 1 | Yes |
| **選擇排序** | n^2 | n^2 | n^2 | 1 | No |
| **Heap 排序** | n log(n) | n log(n) | n log(n) | 1 | No |
| **合併排序** | n log(n) | n log(n) | n log(n) | n | Yes |
| **快速排序** | n log(n) | n log(n) | n^2 | log(n) | No |
| **希爾排序** | n log(n) | 由gap sequence決定 | n (log(n))^2 | 1 | No |
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/jest.config.js b/jest.config.js
index 3fec225237..78568a1e94 100644
--- a/jest.config.js
+++ b/jest.config.js
@@ -24,7 +24,9 @@ module.exports = {
// This option sets the URL for the jsdom environment.
// It is reflected in properties such as location.href.
// @see: https://github.com/facebook/jest/issues/6769
- testURL: 'http://localhost/',
+ testEnvironmentOptions: {
+ url: 'http://localhost/',
+ },
// @see: https://jestjs.io/docs/en/configuration#coveragethreshold-object
coverageThreshold: {
diff --git a/package-lock.json b/package-lock.json
index aeeed97b47..b61d279d87 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -1,1046 +1,10232 @@
{
"name": "javascript-algorithms-and-data-structures",
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+ "lockfileVersion": 2,
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+ "packages": {
+ "": {
+ "name": "javascript-algorithms-and-data-structures",
+ "version": "0.0.4",
+ "license": "MIT",
+ "devDependencies": {
+ "@babel/cli": "7.20.7",
+ "@babel/preset-env": "7.20.2",
+ "@types/jest": "29.4.0",
+ "eslint": "8.33.0",
+ "eslint-config-airbnb": "19.0.4",
+ "eslint-plugin-import": "2.27.5",
+ "eslint-plugin-jest": "27.2.1",
+ "eslint-plugin-jsx-a11y": "6.7.1",
+ "husky": "8.0.3",
+ "jest": "29.4.1",
+ "pngjs": "^7.0.0"
+ },
+ "engines": {
+ "node": ">=16.15.0",
+ "npm": ">=8.5.5"
+ }
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- "requires": {
- "@nicolo-ribaudo/chokidar-2": "2.1.8-no-fsevents",
- "chokidar": "^3.4.0",
+ "dependencies": {
+ "@jridgewell/gen-mapping": "^0.3.0",
+ "@jridgewell/trace-mapping": "^0.3.9"
+ },
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+ }
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@@ -3609,137 +12209,178 @@
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@@ -6762,6 +14447,12 @@
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@@ -6929,51 +14546,30 @@
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"dev": true,
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@@ -7002,30 +14599,23 @@
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"dev": true,
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@@ -7083,135 +14647,44 @@
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"require-directory": "^2.1.1",
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+ "dev": true
}
}
}
diff --git a/package.json b/package.json
index 73da04e0cf..95d6d28942 100644
--- a/package.json
+++ b/package.json
@@ -2,13 +2,6 @@
"name": "javascript-algorithms-and-data-structures",
"version": "0.0.4",
"description": "Algorithms and data-structures implemented on JavaScript",
- "main": "index.js",
- "scripts": {
- "lint": "eslint ./src/**",
- "test": "jest",
- "coverage": "npm run test -- --coverage",
- "ci": "npm run lint && npm run coverage"
- },
"repository": {
"type": "git",
"url": "git+https://github.com/trekhleb/javascript-algorithms.git"
@@ -27,24 +20,35 @@
"interview",
"interview-preparation"
],
- "author": "Oleksii Trekhleb (https://www.linkedin.com/in/trekhleb/)",
+ "author": "Oleksii Trekhleb (https://trekhleb.dev)",
"license": "MIT",
"bugs": {
"url": "https://github.com/trekhleb/javascript-algorithms/issues"
},
"homepage": "https://github.com/trekhleb/javascript-algorithms#readme",
+ "main": "index.js",
+ "scripts": {
+ "lint": "eslint ./src/**",
+ "test": "jest",
+ "coverage": "npm run test -- --coverage",
+ "ci": "npm run lint && npm run coverage",
+ "prepare": "husky install"
+ },
"devDependencies": {
- "@babel/cli": "7.12.10",
- "@babel/preset-env": "7.12.11",
- "@types/jest": "26.0.19",
- "eslint": "7.16.0",
- "eslint-config-airbnb": "18.2.1",
- "eslint-plugin-import": "2.22.1",
- "eslint-plugin-jest": "24.1.3",
- "eslint-plugin-jsx-a11y": "6.4.1",
- "eslint-plugin-react": "7.21.5",
- "husky": "4.3.6",
- "jest": "26.6.3"
+ "@babel/cli": "7.20.7",
+ "@babel/preset-env": "7.20.2",
+ "@types/jest": "29.4.0",
+ "eslint": "8.33.0",
+ "eslint-config-airbnb": "19.0.4",
+ "eslint-plugin-import": "2.27.5",
+ "eslint-plugin-jest": "27.2.1",
+ "eslint-plugin-jsx-a11y": "6.7.1",
+ "husky": "8.0.3",
+ "jest": "29.4.1",
+ "pngjs": "^7.0.0"
},
- "dependencies": {}
+ "engines": {
+ "node": ">=16.15.0",
+ "npm": ">=8.5.5"
+ }
}
diff --git a/src/algorithms/cryptography/caesar-cipher/README.md b/src/algorithms/cryptography/caesar-cipher/README.md
index 428b5a9772..d648a62ee9 100644
--- a/src/algorithms/cryptography/caesar-cipher/README.md
+++ b/src/algorithms/cryptography/caesar-cipher/README.md
@@ -1,5 +1,8 @@
# Caesar Cipher Algorithm
+_Read this in other languages:_
+[_Русский_](README.ru-RU.md)
+
In cryptography, a **Caesar cipher**, also known as **Caesar's cipher**, the **shift cipher**, **Caesar's code** or **Caesar shift**, is one of the simplest and most widely known encryption techniques. It is a type of substitution cipher in which each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet. For example, with a left shift of `3`, `D` would be replaced by `A`, `E` would become `B`, and so on. The method is named after Julius Caesar, who used it in his private correspondence.
diff --git a/src/algorithms/cryptography/caesar-cipher/README.ru-RU.md b/src/algorithms/cryptography/caesar-cipher/README.ru-RU.md
new file mode 100644
index 0000000000..dee4d14cd3
--- /dev/null
+++ b/src/algorithms/cryptography/caesar-cipher/README.ru-RU.md
@@ -0,0 +1,29 @@
+# Алгоритм шифра Цезаря
+
+В криптографии **шифр Цезаря**, также известный как **шифр сдвига**, **код Цезаря** или **сдвиг Цезаря**, является одним из самых простых и широко известных методов шифрования. Это вид шифра подстановки, в котором каждый символ в открытом тексте заменяется символом, находящимся на некотором постоянном числе позиций левее или правее него в алфавите. Например, в шифре со сдвигом вправо на `3`, `D` была бы заменена на `A`, `E` станет `B`, и так далее. Метод назван в честь Юлия Цезаря, который использовал его в своей личной переписке.
+
+
+
+## Пример
+Это преобразование можно представить как выравнивание двух алфавитов; алфавит шифра - это обычный алфавит, повёрнутый влево или вправо на некоторое количество позиций. Например, здесь приведен шифр Цезаря, использующий поворот влево на три позиции, что эквивалентно сдвигу вправо на 23 (параметр сдвига используется в качестве ключа):
+
+```text
+Обычный: ABCDEFGHIJKLMNOPQRSTUVWXYZ
+Шифрованный: XYZABCDEFGHIJKLMNOPQRSTUVW
+```
+
+При шифровании человек просматривает каждую букву сообщения в "открытой" строке и записывает соответствующую букву в "шифрованной" строке.
+
+```text
+Обычный текст: THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG
+Шифрованный текст: QEB NRFZH YOLTK CLU GRJMP LSBO QEB IXWV ALD
+```
+
+## Сложность
+
+- Время: `O(|n|)`
+- Пространство: `O(|n|)`
+
+## Ссылки
+
+- [Шифр Цезаря на Wikipedia](https://ru.wikipedia.org/wiki/Шифр_Цезаря)
diff --git a/src/algorithms/graph/breadth-first-search/README.md b/src/algorithms/graph/breadth-first-search/README.md
index 32ec3e815c..06073abd8b 100644
--- a/src/algorithms/graph/breadth-first-search/README.md
+++ b/src/algorithms/graph/breadth-first-search/README.md
@@ -1,7 +1,7 @@
# Breadth-First Search (BFS)
-Breadth-first search (BFS) is an algorithm for traversing
-or searching tree or graph data structures. It starts at
+Breadth-first search (BFS) is an algorithm for traversing,
+searching tree, or graph data structures. It starts at
the tree root (or some arbitrary node of a graph, sometimes
referred to as a 'search key') and explores the neighbor
nodes first, before moving to the next level neighbors.
diff --git a/src/algorithms/graph/dijkstra/README.ko-KR.md b/src/algorithms/graph/dijkstra/README.ko-KR.md
new file mode 100644
index 0000000000..e2595bbe23
--- /dev/null
+++ b/src/algorithms/graph/dijkstra/README.ko-KR.md
@@ -0,0 +1,16 @@
+# 다익스트라 알고리즘(Dijkstra's algorithm)
+
+다익스트라 알고리즘은 도로 네트워크 등을 나타낼 수 있는 그래프에서 노드 간의 최단 경로를 찾는 알고리즘입니다.
+
+이 알고리즘은 다양한 형태로 존재합니다. 다익스트라의 원래 형태는 두 노드 간의 최단 경로를 찾았지만, 더 일반적인 형태는 단일 노드를 "소스"노드로 수정하고 그래프의 소스에서 다른 모든 노드까지의 최단 경로를 찾아 최단 경로 트리(shortest-path tree)를 생성합니다.
+
+
+
+`a`와 `b` 사이의 최단 경로를 찾는 다익스트라 알고리즘입니다.
+가장 낮은 거리를 가지며 방문하지 않은 정점(vertex)를 선택하고, 이를 통해 방문하지 않은 각 이웃까지의 거리를 계산하며, 더 작은 경우 이웃의 거리를 업데이트합니다. 이웃에 대한 작업을 마치면 방문한 것으로 표시(빨간색으로 변경)합니다.
+
+## 참조
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
+- [On YouTube by Nathaniel Fan](https://www.youtube.com/watch?v=gdmfOwyQlcI&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [On YouTube by Tushar Roy](https://www.youtube.com/watch?v=lAXZGERcDf4&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/graph/dijkstra/README.md b/src/algorithms/graph/dijkstra/README.md
index e1c5002f18..d94e2a3cdf 100644
--- a/src/algorithms/graph/dijkstra/README.md
+++ b/src/algorithms/graph/dijkstra/README.md
@@ -1,5 +1,8 @@
# Dijkstra's Algorithm
+_Read this in other languages:_
+[_한국어_](README.ko-KR.md)
+
Dijkstra's algorithm is an algorithm for finding the shortest
paths between nodes in a graph, which may represent, for example,
road networks.
diff --git a/src/algorithms/graph/kruskal/README.ko-KR.md b/src/algorithms/graph/kruskal/README.ko-KR.md
new file mode 100644
index 0000000000..eefb6a6756
--- /dev/null
+++ b/src/algorithms/graph/kruskal/README.ko-KR.md
@@ -0,0 +1,29 @@
+# 크루스칼 알고리즘
+
+크루스칼 알고리즘은 두 트리를 연결하는 최소 간선 가중치를 찾는 최소 신장 트리 알고리즘입니다.
+각 단계에서 비용을 더하는 연결된 가중 그래프에 대한 최소 신장 트리를 찾기 때문에 그래프 이론에서의 그리디 알고리즘입니다. 즉, 트리의 모든 간선의 총 가중치가 최소화되는 모든 정점을 포함하는 트리를 형성하는 간선의 하위 집합을 찾습니다. 그래프가 연결되어 있지 않으면 최소 신장 포레스트(연결된 각 구성 요소의 최소 신장 트리)를 찾습니다.
+
+
+
+
+
+유클리드 거리를 기반으로 한 크루스칼 알고리즘의 데모입니다.
+
+## 최소 신장 트리
+
+**최소 신장 트리(MST)** 또는 최소 가중치 신장 트리는 연결된 간선 가중치 무 방향 그래프의 간선의 하위 집합으로, 사이클 없이 가능한 최소 총 간선 가중치로 모든 정점을 연결합니다. 즉, 간선 가중치의 합이 가능한 작은 신장 트리입니다. 보다 일반적으로, 간선-가중치 비방향 그래프(꼭 연결되지는 않음)에는 연결된 구성 요소에 대한 최소 신장 트리의 결합인 최소 신장 포레스트(minimum spanning forest)가 있습니다.
+
+
+
+평면 그래프와 해당 최소 신장 트리입니다. 각 간선은 가중치로 레이블이 지정되며, 이 값은 길이에 거의 비례합니다.
+
+
+
+이 그림은 그래프에 최소 신장 트리가 두 개 이상 있을 수 있음을 보여 줍니다. 그림에서 그래프 아래의 두 트리는 주어진 그래프에서 최소 신장 트리가 될 수 있는 두 가지 경우입니다.
+
+## 참조
+
+- [Minimum Spanning Tree on Wikipedia](https://en.wikipedia.org/wiki/Minimum_spanning_tree)
+- [Kruskal's Algorithm on Wikipedia](https://en.wikipedia.org/wiki/Kruskal%27s_algorithm)
+- [Kruskal's Algorithm on YouTube by Tushar Roy](https://www.youtube.com/watch?v=fAuF0EuZVCk&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [Kruskal's Algorithm on YouTube by Michael Sambol](https://www.youtube.com/watch?v=71UQH7Pr9kU&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/graph/kruskal/README.md b/src/algorithms/graph/kruskal/README.md
index eb8a0ebf42..1a71390e2f 100644
--- a/src/algorithms/graph/kruskal/README.md
+++ b/src/algorithms/graph/kruskal/README.md
@@ -1,5 +1,8 @@
# Kruskal's Algorithm
+_Read this in other languages:_
+[_한국어_](README.ko-KR.md)
+
Kruskal's algorithm is a minimum-spanning-tree algorithm which
finds an edge of the least possible weight that connects any two
trees in the forest. It is a greedy algorithm in graph theory
diff --git a/src/algorithms/image-processing/seam-carving/README.md b/src/algorithms/image-processing/seam-carving/README.md
new file mode 100644
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+# Content-aware image resizing in JavaScript
+
+
+
+> There is an [interactive version of this post](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/) available where you can upload and resize your custom images.
+
+## TL;DR
+
+There are many great articles written about the *Seam Carving algorithm* already, but I couldn't resist the temptation to explore this elegant, powerful, and *yet simple* algorithm on my own, and to write about my personal experience with it. Another point that drew my attention (as a creator of [javascript-algorithms](https://github.com/trekhleb/javascript-algorithms) repo) was the fact that *Dynamic Programming (DP)* approach might be smoothly applied to solve it. And, if you're like me and still on your "learning algorithms" journey, this algorithmic solution may enrich your personal DP arsenal.
+
+So, with this article I want to do three things:
+
+1. Provide you with an interactive **content-aware resizer** so that you could play around with resizing your own images
+2. Explain the idea behind the **Seam Carving algorithm**
+3. Explain the **dynamic programming approach** to implement the algorithm (we'll be using TypeScript for it)
+
+### Content-aware image resizing
+
+*Content-aware image resizing* might be applied when it comes to changing the image proportions (i.e. reducing the width while keeping the height) and when losing some parts of the image is not desirable. Doing the straightforward image scaling in this case would distort the objects in it. To preserve the proportions of the objects while changing the image proportions we may use the [Seam Carving algorithm](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf) that was introduced by *Shai Avidan* and *Ariel Shamir*.
+
+The example below shows how the original image width was reduced by 50% using *content-aware resizing* (left image) and *straightforward scaling* (right image). In this particular case, the left image looks more natural since the proportions of the balloons were preserved.
+
+
+
+The Seam Carving algorithm's idea is to find the *seam* (continuous sequence of pixels) with the lowest contribution to the image content and then *carve* (remove) it. This process repeats over and over again until we get the required image width or height. In the example below you may see that the hot air balloon pixels contribute more to the content of the image than the sky pixels. Thus, the sky pixels are being removed first.
+
+
+
+Finding the seam with the lowest energy is a computationally expensive task (especially for large images). To make the seam search faster the *dynamic programming* approach might be applied (we will go through the implementation details below).
+
+### Objects removal
+
+The importance of each pixel (so-called pixel's energy) is being calculated based on its color (`R`, `G`, `B`, `A`) difference between two neighbor pixels. Now, if we set the pixel energy to some really low level artificially (i.e. by drawing a mask on top of them), the Seam Carving algorithm would perform an **object removal** for us for free.
+
+
+
+### JS IMAGE CARVER demo
+
+I've created the [JS IMAGE CARVER](https://trekhleb.dev/js-image-carver/) web-app (and also [open-sourced it on GitHub](https://github.com/trekhleb/js-image-carver)) that you may use to play around with resizing of your custom images.
+
+### More examples
+
+Here are some more examples of how the algorithm copes with more complex backgrounds.
+
+Mountains on the background are being shrunk smoothly without visible seams.
+
+
+
+The same goes for the ocean waves. The algorithm preserved the wave structure without distorting the surfers.
+
+
+
+We need to keep in mind that the Seam Carving algorithm is not a silver bullet, and it may fail to resize the images where *most of the pixels are edges* (look important to the algorithm). In this case, it starts distorting even the important parts of the image. In the example below the content-aware image resizing looks pretty similar to a straightforward scaling since for the algorithm all the pixels look important, and it is hard for it to distinguish Van Gogh's face from the background.
+
+
+
+## How Seam Carving algorithms works
+
+Imagine we have a `1000 x 500 px` picture, and we want to change its size to `500 x 500 px` to make it square (let's say the square ratio would better fit the Instagram feed). We might want to set up several **requirements to the resizing process** in this case:
+
+- *Preserve the important parts of the image* (i.e. if there were 5 trees before the resizing we want to have 5 trees after resizing as well).
+- *Preserve the proportions* of the important parts of the image (i.e. circle car wheels should not be squeezed to the ellipse wheels)
+
+To avoid changing the important parts of the image we may find the **continuous sequence of pixels (the seam)**, that goes from top to bottom and has *the lowest contribution to the content* of the image (avoids important parts) and then remove it. The seam removal will shrink the image by 1 pixel. We will then repeat this step until the image will get the desired width.
+
+The question is how to define *the importance of the pixel* and its contribution to the content (in the original paper the authors are using the term **energy of the pixel**). One of the ways to do it is to treat all the pixels that form the edges as important ones. In case if a pixel is a part of the edge its color would have a greater difference between the neighbors (left and right pixels) than the pixel that isn't a part of the edge.
+
+
+
+Assuming that the color of a pixel is represented by *4* numbers (`R` - red, `G` - green, `B` - blue, `A` - alpha) we may use the following formula to calculate the color difference (the pixel energy):
+
+
+
+Where:
+
+- `mEnergy` - *Energy* (importance) of the *middle* pixel (`[0..626]` if rounded)
+- `lR` - *Red* channel value for the *left* pixel (`[0..255]`)
+- `mR` - *Red* channel value for the *middle* pixel (`[0..255]`)
+- `rR` - *Red* channel value for the *right* pixel (`[0..255]`)
+- `lG` - *Green* channel value for the *left* pixel (`[0..255]`)
+- and so on...
+
+In the formula above we're omitting the alpha (transparency) channel, for now, assuming that there are no transparent pixels in the image. Later we will use the alpha channel for masking and for object removal.
+
+
+
+Now, since we know how to find the energy of one pixel, we can calculate, so-called, **energy map** which will contain the energies of each pixel of the image. On each resizing step the energy map should be re-calculated (at least partially, more about it below) and would have the same size as the image.
+
+For example, on the 1st resizing step we will have a `1000 x 500` image and a `1000 x 500` energy map. On the 2nd resizing step we will remove the seam from the image and re-calculate the energy map based on the new shrunk image. Thus, we will get a `999 x 500` image and a `999 x 500` energy map.
+
+The higher the energy of the pixel the more likely it is a part of an edge, and it is important for the image content and the less likely that we need to remove it.
+
+To visualize the energy map we may assign a brighter color to the pixels with the higher energy and darker colors to the pixels with the lower energy. Here is an artificial example of how the random part of the energy map might look like. You may see the bright line which represents the edge and which we want to preserve during the resizing.
+
+
+
+Here is a real example of the energy map for the demo image you saw above (with hot air balloons).
+
+
+
+You may play around with your custom images and see how the energy map would look like in the [interactive version of the post](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/).
+
+We may use the energy map to find the seams (one after another) with the lowest energy and by doing this to decide which pixels should be ultimately deleted.
+
+
+
+Finding the seam with the lowest energy is not a trivial task and requires exploring many possible pixel combinations before making the decision. We will apply the dynamic programming approach to speed it up.
+
+In the example below, you may see the energy map with the first lowest energy seam that was found for it.
+
+
+
+In the examples above we were reducing the width of the image. A similar approach may be taken to reduce the image height. We need to "rotate" the approach though:
+
+- start using *top* and *bottom* pixel neighbors (instead of *left* and *right* ones) to calculate the pixel energy
+- when searching for a seam we need to move from *left* to *right* (instead of from *up* to *bottom*)
+
+## Implementation in TypeScript
+
+> You may find the source code, and the functions mentioned below in the [js-image-carver](https://github.com/trekhleb/js-image-carver) repository.
+
+To implement the algorithm we will be using TypeScript. If you want a JavaScript version, you may ignore (remove) type definitions and their usages.
+
+For simplicity reasons let's implement the seam carving algorithm only for the image *width* reduction.
+
+### Content-aware width resizing (the entry function)
+
+First, let's define some common types that we're going to use while implementing the algorithm.
+
+```typescript
+// Type that describes the image size (width and height).
+type ImageSize = { w: number, h: number };
+
+// The coordinate of the pixel.
+type Coordinate = { x: number, y: number };
+
+// The seam is a sequence of pixels (coordinates).
+type Seam = Coordinate[];
+
+// Energy map is a 2D array that has the same width and height
+// as the image the map is being calculated for.
+type EnergyMap = number[][];
+
+// Type that describes the image pixel's RGBA color.
+type Color = [
+ r: number, // Red
+ g: number, // Green
+ b: number, // Blue
+ a: number, // Alpha (transparency)
+] | Uint8ClampedArray;
+```
+
+On the high level the algorithm consists of the following steps:
+
+1. Calculate the **energy map** for the current version of the image.
+2. Find the **seam** with the lowest energy based on the energy map (this is where we will apply Dynamic Programming).
+3. **Delete the seam** with the lowest energy seam from the image.
+4. **Repeat** until the image width is reduced to the desired value.
+
+```typescript
+type ResizeImageWidthArgs = {
+ img: ImageData, // Image data we want to resize.
+ toWidth: number, // Final image width we want the image to shrink to.
+};
+
+type ResizeImageWidthResult = {
+ img: ImageData, // Resized image data.
+ size: ImageSize, // Resized image size (w x h).
+};
+
+// Performs the content-aware image width resizing using the seam carving method.
+export const resizeImageWidth = (
+ { img, toWidth }: ResizeImageWidthArgs,
+): ResizeImageWidthResult => {
+ // For performance reasons we want to avoid changing the img data array size.
+ // Instead we'll just keep the record of the resized image width and height separately.
+ const size: ImageSize = { w: img.width, h: img.height };
+
+ // Calculating the number of pixels to remove.
+ const pxToRemove = img.width - toWidth;
+ if (pxToRemove < 0) {
+ throw new Error('Upsizing is not supported for now');
+ }
+
+ let energyMap: EnergyMap | null = null;
+ let seam: Seam | null = null;
+
+ // Removing the lowest energy seams one by one.
+ for (let i = 0; i < pxToRemove; i += 1) {
+ // 1. Calculate the energy map for the current version of the image.
+ energyMap = calculateEnergyMap(img, size);
+
+ // 2. Find the seam with the lowest energy based on the energy map.
+ seam = findLowEnergySeam(energyMap, size);
+
+ // 3. Delete the seam with the lowest energy seam from the image.
+ deleteSeam(img, seam, size);
+
+ // Reduce the image width, and continue iterations.
+ size.w -= 1;
+ }
+
+ // Returning the resized image and its final size.
+ // The img is actually a reference to the ImageData, so technically
+ // the caller of the function already has this pointer. But let's
+ // still return it for better code readability.
+ return { img, size };
+};
+```
+
+The image that needs to be resized is being passed to the function in [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData) format. You may draw the image on the canvas and then extract the ImageData from the canvas like this:
+
+```javascript
+const ctx = canvas.getContext('2d');
+const imgData = ctx.getImageData(0, 0, imgWidth, imgHeight);
+```
+
+> The way of uploading and drawing images in JavaScript is out of scope for this article, but you may find the complete source code of how it may be done using React in [js-image-carver](https://github.com/trekhleb/js-image-carver) repo.
+
+Let's break down each step ony be one and implement the `calculateEnergyMap()`, `findLowEnergySeam()` and `deleteSeam()` functions.
+
+### Calculating the pixel's energy
+
+Here we apply the color difference formula described above. For the left and right borders (when there are no left or right neighbors), we ignore the neighbors and don't take them into account during the energy calculation.
+
+```typescript
+// Calculates the energy of a pixel.
+const getPixelEnergy = (left: Color | null, middle: Color, right: Color | null): number => {
+ // Middle pixel is the pixel we're calculating the energy for.
+ const [mR, mG, mB] = middle;
+
+ // Energy from the left pixel (if it exists).
+ let lEnergy = 0;
+ if (left) {
+ const [lR, lG, lB] = left;
+ lEnergy = (lR - mR) ** 2 + (lG - mG) ** 2 + (lB - mB) ** 2;
+ }
+
+ // Energy from the right pixel (if it exists).
+ let rEnergy = 0;
+ if (right) {
+ const [rR, rG, rB] = right;
+ rEnergy = (rR - mR) ** 2 + (rG - mG) ** 2 + (rB - mB) ** 2;
+ }
+
+ // Resulting pixel energy.
+ return Math.sqrt(lEnergy + rEnergy);
+};
+```
+
+### Calculating the energy map
+
+The image we're working with has the [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData) format. It means that all the pixels (and their colors) are stored in a flat (*1D*) [Uint8ClampedArray](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Uint8ClampedArray) array. For readability purposes let's introduce the couple of helper functions that will allow us to work with the Uint8ClampedArray array as with a *2D* matrix instead.
+
+```typescript
+// Helper function that returns the color of the pixel.
+const getPixel = (img: ImageData, { x, y }: Coordinate): Color => {
+ // The ImageData data array is a flat 1D array.
+ // Thus we need to convert x and y coordinates to the linear index.
+ const i = y * img.width + x;
+ const cellsPerColor = 4; // RGBA
+ // For better efficiency, instead of creating a new sub-array we return
+ // a pointer to the part of the ImageData array.
+ return img.data.subarray(i * cellsPerColor, i * cellsPerColor + cellsPerColor);
+};
+
+// Helper function that sets the color of the pixel.
+const setPixel = (img: ImageData, { x, y }: Coordinate, color: Color): void => {
+ // The ImageData data array is a flat 1D array.
+ // Thus we need to convert x and y coordinates to the linear index.
+ const i = y * img.width + x;
+ const cellsPerColor = 4; // RGBA
+ img.data.set(color, i * cellsPerColor);
+};
+```
+
+To calculate the energy map we go through each image pixel and call the previously described `getPixelEnergy()` function against it.
+
+```typescript
+// Helper function that creates a matrix (2D array) of specific
+// size (w x h) and fills it with specified value.
+const matrix = <T>(w: number, h: number, filler: T): T[][] => {
+ return new Array(h)
+ .fill(null)
+ .map(() => {
+ return new Array(w).fill(filler);
+ });
+};
+
+// Calculates the energy of each pixel of the image.
+const calculateEnergyMap = (img: ImageData, { w, h }: ImageSize): EnergyMap => {
+ // Create an empty energy map where each pixel has infinitely high energy.
+ // We will update the energy of each pixel.
+ const energyMap: number[][] = matrix<number>(w, h, Infinity);
+ for (let y = 0; y < h; y += 1) {
+ for (let x = 0; x < w; x += 1) {
+ // Left pixel might not exist if we're on the very left edge of the image.
+ const left = (x - 1) >= 0 ? getPixel(img, { x: x - 1, y }) : null;
+ // The color of the middle pixel that we're calculating the energy for.
+ const middle = getPixel(img, { x, y });
+ // Right pixel might not exist if we're on the very right edge of the image.
+ const right = (x + 1) < w ? getPixel(img, { x: x + 1, y }) : null;
+ energyMap[y][x] = getPixelEnergy(left, middle, right);
+ }
+ }
+ return energyMap;
+};
+```
+
+> The energy map is going to be recalculated on every resize iteration. It means that it will be recalculated, let's say, 500 times if we need to shrink the image by 500 pixels which is not optimal. To speed up the energy map calculation on the 2nd, 3rd, and further steps, we may re-calculate the energy only for those pixels that are placed around the seam that is going to be removed. For simplicity reasons this optimization is omitted here, but you may find the example source-code in [js-image-carver](https://github.com/trekhleb/js-image-carver) repo.
+
+### Finding the seam with the lowest energy (Dynamic Programming approach)
+
+> I've described some Dynamic Programming basics in [Dynamic Programming vs Divide-and-Conquer](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/) article before. There is a DP example based on the minimum edit distance problem. You might want to check it out to get some more context.
+
+The issue we need to solve now is to find the path (the seam) on the energy map that goes from top to bottom and has the minimum sum of pixel energies.
+
+#### The naive approach
+
+The naive approach would be to check all possible paths one after another.
+
+
+
+Going from top to bottom, for each pixel, we have 3 options (↙︎ go down-left, ↓ go down, ↘︎ go down-right). This gives us the time complexity of `O(w * 3^h)` or simply `O(3^h)`, where `w` and `h` are the width and the height of the image. This approach looks slow.
+
+#### The greedy approach
+
+We may also try to choose the next pixel as a pixel with the lowest energy, hoping that the resulting seam energy will be the smallest one.
+
+
+
+This approach gives not the worst solution, but it cannot guarantee that we will find the best available solution. On the image above you may see how the greedy approach chose `5` instead of `10` at first and missed the chain of optimal pixels.
+
+The good part about this approach is that it is fast, and it has a time complexity of `O(w + h)`, where `w` and `h` are the width and the height of the image. In this case, the cost of the speed is the low quality of resizing. We need to find a minimum value in the first row (traversing `w` cells) and then we explore only 3 neighbor pixels for each row (traversing `h` rows).
+
+#### The dynamic programming approach
+
+You might have noticed that in the naive approach we summed up the same pixel energies over and over again while calculating the resulting seams' energy.
+
+
+
+In the example above you see that for the first two seams we are re-using the energy of the shorter seam (which has the energy of `235`). Instead of doing just one operation `235 + 70` to calculate the energy of the 2nd seam we're doing four operations `(5 + 0 + 80 + 150) + 70`.
+
+> This fact that we're re-using the energy of the previous seam to calculate the current seam's energy might be applied recursively to all the shorter seams up to the very top 1st row seam. When we have such overlapping sub-problems, [it is a sign](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/) that the general problem *might* be optimized by dynamic programming approach.
+
+So, we may **save the energy of the current seam** at the particular pixel in an additional `seamsEnergies` table to make it re-usable for calculating the next seams faster (the `seamsEnergies` table will have the same size as the energy map and the image itself).
+
+Let's also keep in mind that for one particular pixel on the image (i.e. the bottom left one) we may have *several* values of the previous seams energies.
+
+
+
+Since we're looking for a seam with the lowest resulting energy it would make sense to pick the previous seam with the lowest resulting energy as well.
+
+
+
+In general, we have three possible previous seems to choose from:
+
+
+
+You may think about it this way:
+
+- The cell `[1][x]`: contains the lowest possible energy of the seam that starts somewhere on the row `[0][?]` and ends up at cell `[1][x]`
+- **The current cell** `[2][3]`: contains the lowest possible energy of the seam that starts somewhere on the row `[0][?]` and ends up at cell `[2][3]`. To calculate it we need to sum up the energy of the current pixel `[2][3]` (from the energy map) with the `min(seam_energy_1_2, seam_energy_1_3, seam_energy_1_4)`
+
+If we fill the `seamsEnergies` table completely, then the minimum number in the lowest row would be the lowest possible seam energy.
+
+Let's try to fill several cells of this table to see how it works.
+
+
+
+After filling out the `seamsEnergies` table we may see that the lowest energy pixel has an energy of `50`. For convenience, during the `seamsEnergies` generation for each pixel, we may save not only the energy of the seam but also the coordinates of the previous lowest energy seam. This will give us the possibility to reconstruct the seam path from the bottom to the top easily.
+
+The time complexity of DP approach would be `O(w * h)`, where `w` and `h` are the width and the height of the image. We need to calculate energies for *every* pixel of the image.
+
+Here is an example of how this logic might be implemented:
+
+```typescript
+// The metadata for the pixels in the seam.
+type SeamPixelMeta = {
+ energy: number, // The energy of the pixel.
+ coordinate: Coordinate, // The coordinate of the pixel.
+ previous: Coordinate | null, // The previous pixel in a seam.
+};
+
+// Finds the seam (the sequence of pixels from top to bottom) that has the
+// lowest resulting energy using the Dynamic Programming approach.
+const findLowEnergySeam = (energyMap: EnergyMap, { w, h }: ImageSize): Seam => {
+ // The 2D array of the size of w and h, where each pixel contains the
+ // seam metadata (pixel energy, pixel coordinate and previous pixel from
+ // the lowest energy seam at this point).
+ const seamsEnergies: (SeamPixelMeta | null)[][] = matrix<SeamPixelMeta | null>(w, h, null);
+
+ // Populate the first row of the map by just copying the energies
+ // from the energy map.
+ for (let x = 0; x < w; x += 1) {
+ const y = 0;
+ seamsEnergies[y][x] = {
+ energy: energyMap[y][x],
+ coordinate: { x, y },
+ previous: null,
+ };
+ }
+
+ // Populate the rest of the rows.
+ for (let y = 1; y < h; y += 1) {
+ for (let x = 0; x < w; x += 1) {
+ // Find the top adjacent cell with minimum energy.
+ // This cell would be the tail of a seam with lowest energy at this point.
+ // It doesn't mean that this seam (path) has lowest energy globally.
+ // Instead, it means that we found a path with the lowest energy that may lead
+ // us to the current pixel with the coordinates x and y.
+ let minPrevEnergy = Infinity;
+ let minPrevX: number = x;
+ for (let i = (x - 1); i <= (x + 1); i += 1) {
+ if (i >= 0 && i < w && seamsEnergies[y - 1][i].energy < minPrevEnergy) {
+ minPrevEnergy = seamsEnergies[y - 1][i].energy;
+ minPrevX = i;
+ }
+ }
+
+ // Update the current cell.
+ seamsEnergies[y][x] = {
+ energy: minPrevEnergy + energyMap[y][x],
+ coordinate: { x, y },
+ previous: { x: minPrevX, y: y - 1 },
+ };
+ }
+ }
+
+ // Find where the minimum energy seam ends.
+ // We need to find the tail of the lowest energy seam to start
+ // traversing it from its tail to its head (from the bottom to the top).
+ let lastMinCoordinate: Coordinate | null = null;
+ let minSeamEnergy = Infinity;
+ for (let x = 0; x < w; x += 1) {
+ const y = h - 1;
+ if (seamsEnergies[y][x].energy < minSeamEnergy) {
+ minSeamEnergy = seamsEnergies[y][x].energy;
+ lastMinCoordinate = { x, y };
+ }
+ }
+
+ // Find the lowest energy energy seam.
+ // Once we know where the tail is we may traverse and assemble the lowest
+ // energy seam based on the "previous" value of the seam pixel metadata.
+ const seam: Seam = [];
+ if (!lastMinCoordinate) {
+ return seam;
+ }
+
+ const { x: lastMinX, y: lastMinY } = lastMinCoordinate;
+
+ // Adding new pixel to the seam path one by one until we reach the top.
+ let currentSeam = seamsEnergies[lastMinY][lastMinX];
+ while (currentSeam) {
+ seam.push(currentSeam.coordinate);
+ const prevMinCoordinates = currentSeam.previous;
+ if (!prevMinCoordinates) {
+ currentSeam = null;
+ } else {
+ const { x: prevMinX, y: prevMinY } = prevMinCoordinates;
+ currentSeam = seamsEnergies[prevMinY][prevMinX];
+ }
+ }
+
+ return seam;
+};
+```
+
+### Removing the seam with the lowest energy
+
+Once we found the lowest energy seam, we need to remove (to carve) the pixels that form it from the image. The removal is happening by shifting the pixels to the right of the seam by `1px` to the left. For performance reasons, we don't actually delete the last columns. Instead, the rendering component will just ignore the part of the image that lays beyond the resized image width.
+
+
+
+```typescript
+// Deletes the seam from the image data.
+// We delete the pixel in each row and then shift the rest of the row pixels to the left.
+const deleteSeam = (img: ImageData, seam: Seam, { w }: ImageSize): void => {
+ seam.forEach(({ x: seamX, y: seamY }: Coordinate) => {
+ for (let x = seamX; x < (w - 1); x += 1) {
+ const nextPixel = getPixel(img, { x: x + 1, y: seamY });
+ setPixel(img, { x, y: seamY }, nextPixel);
+ }
+ });
+};
+```
+
+## Objects removal
+
+The Seam Carving algorithm tries to remove the seams which consist of low energy pixels first. We could leverage this fact and by assigning low energy to some pixels manually (i.e. by drawing on the image and masking out some areas of it) we could make the Seam Carving algorithm to do *objects removal* for us for free.
+
+Currently, in `getPixelEnergy()` function we were using only the `R`, `G`, `B` color channels to calculate the pixel's energy. But there is also the `A` (alpha, transparency) parameter of the color that we didn't use yet. We may use the transparency channel to tell the algorithm that transparent pixels are the pixels we want to remove. You may check the [source-code of the energy function](https://github.com/trekhleb/js-image-carver/blob/main/src/utils/contentAwareResizer.ts#L54) that takes transparency into account.
+
+Here is how the algorithm works for object removal.
+
+
+
+## Issues and what's next
+
+The [JS IMAGE CARVER](https://github.com/trekhleb/js-image-carver) web app is far from being a production ready resizer of course. Its main purpose was to experiment with the Seam Carving algorithm interactively. So the plan for the future is to continue experimentation.
+
+The [original paper](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf) describes how the Seam Carving algorithm might be used not only for the downscaling but also for the **upscaling of the images**. The upscaling, in turn, might be used to **upscale the image back to its original width after the objects' removal**.
+
+Another interesting area of experimentation might be to make the algorithm work in a **real-time**.
+
+> Those are the plans for the future, but for now, I hope that the example with image downsizing was interesting and useful for you. I also hope that you've got the idea of using dynamic programming to implement it.
+>
+> So, good luck with your own experiments!
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+# Изменение размеров изображения с учетом его содержимого в JavaScript
+
+
+
+> Доступна [английская интерактивная версия этой статьи](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/) в которой вы можете загрузить свои собственные изображения и посмотреть, как алгоритм "справляется" с ними.
+
+## TL;DR
+
+Написано много замечательных статей об алгоритме *Seam Carving* ("Вырезание швов"), но я не смог устоять перед соблазном самостоятельно исследовать этот элегантный, мощный и в то же время простой алгоритм и написать о своем личном опыте работы с ним. Мое внимание также привлек тот факт, что для его имплементации мы можем применить *динамическое программирование (DP)*. И, если вы, как и я, все еще находитесь на пути изучения алгоритмов, то это решение может обогатить ваш личный арсенал DP.
+
+Итак, в этой статье я хочу сделать три вещи:
+
+1. Предоставить вам возможность "поиграться" с алгоритмом самостоятельно при помощи **интерактивного ресайзера**.
+2. Объяснить **идею алгоритма Seam Carving**.
+3. Объяснить как можно **применить динамическое программирование** для имплементации алгоритма (мы будем писать на TypeScript).
+
+### Изменение размеров изображений с учетом их содержимого
+
+*Изменение размера изображения с учетом содержимого* (content-aware image resizing) может быть применено, когда дело доходит до изменения пропорций изображения (например, уменьшения ширины при сохранении высоты), а также когда потеря некоторых частей изображения нежелательна. Простое масштабирование изображения в этом случае исказит находящиеся в нем объекты. Для сохранения пропорций объектов при изменении пропорций изображения можно использовать [алгоритм Seam Carving](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf), который был описан *Shai Avidan* и *Ariel Shamir*.
+
+В приведенном ниже примере показано, как ширина исходного изображения была уменьшена на 50% *с учетом содержимого изображения* (слева) и *без учета содержимого изображения* (справа, простой скейлинг). В данном случае левое изображение выглядит более естественным, так как пропорции воздушных шаров в нем были сохранены.
+
+
+
+Идея алгоритма Seam Carving заключается в том, чтобы найти *шов* (seam, непрерывную последовательность пикселей) с наименьшим влиянием на содержание изображения, а затем его *вырезать* (carve). Этот процесс повторяется снова и снова, пока мы не получим требуемую ширину или высоту изображения. В примере ниже интуитивно видно, что пиксели воздушных шаров вносят больший "вклад" в содержание и смысл изображения, чем пиксели неба. Таким образом, сначала удаляются пиксели неба.
+
+
+
+Поиск шва с наименьшей энергией (с наименьшим вкладом в содержимое изображения) является вычислительно дорогостоящей операцией (особенно для больших изображений). Для ускорения поиска шва может быть применено *динамическое программирование* (мы рассмотрим детали реализации ниже).
+
+### Удаление объектов
+
+Важность каждого пикселя (так называемая энергия пикселя) вычисляется исходя из его цветовой разницы (`R`, `G`, `B`, `A`) между двумя соседними пикселями. Если же мы вручную зададим некоторым пикселям низкий уровень энергии (например нарисовав маску поверх них), то алгоритм Seam Carving выполнит для нас **удаление помеченного объекта**, как говорится, "забесплатно".
+
+
+
+### Интерактивный ресзайзер
+
+Для этой статьи я создал приложение [JS IMAGE CARVER](https://trekhleb.dev/js-image-carver/) (доступен также и [исходный код на GitHub](https://github.com/trekhleb/js-image-carver)), которым вы можете воспользоваться для ресайза своих изображений и увидеть в реальном времени, как работает алгоритм.
+
+### Другие примеры ресайза
+
+Вот еще несколько примеров того, как алгоритм справляется с более сложным фоном.
+
+Горы на заднем плане плавно сжимаются, без видимых швов.
+
+
+
+То же самое и с океанскими волнами. Алгоритм сохранил волновую структуру, не искажая серферов.
+
+
+
+Нужно помнить, что алгоритм Seam Carving не является "волшебной таблеткой", и может не сохранить пропорции важных частей изображения в том случае, когда *большая часть пикселей выглядят как края, ребра или границы* (почти все пиксели выглядят одинаково важными с точки зрения алгоритма). В приведенном ниже примере изменение размера изображения с учетом содержимого похоже на простое масштабирование, т.к. для алгоритма все пиксели выглядят важными, и ему трудно отличить лицо Ван Гога от фона.
+
+
+
+## Как работает алгоритм Seam Carving
+
+Представим, что у нас есть картинка размером `1000 x 500 px`, и мы хотим уменьшить ее до `500 x 500 px` (допустим, квадратное изображение больше подходит для Instagram). В этом случае мы, возможно, захотим задать несколько **требований к процессу изменения размера**:
+
+- *Важные части изображения должны быть сохранены* (если до ресайза на фото было 5 деревьев, то и после ресайза мы хотим увидеть все те же 5 деревьев).
+- *Пропорции важных частей изображения должны быть сохранены* (круглые колеса автомобиля не должны стать овальными после ресайза).
+
+Чтобы избежать изменения важных частей изображения можно найти **непрерывную последовательность пикселей (шов)**, которая будет идти от верхней границы к нижней и иметь *наименьший вклад в содержимое* изображения (шов, который не проходит через важные части изображения), а затем удалить его. Удаление шва сожмет изображение на один пиксель. Далее надо повторять этот шаг до тех пор, пока изображение не станет нужной ширины.
+
+Вопрос в том, как определить *важность пикселя* и его вклад в содержание изображения (в оригинальной статье авторы используют термин **энергия пикселя**). Один из способов это сделать — рассматривать все пиксели, образующие края (границы, ребра), как важные. В случае, если пиксель является частью ребра, его цвет будет отличаться от соседей (левого и правого пикселей).
+
+
+
+Предполагая, что цвет пикселя представлен *4-мя* числами (`R` - красный, `G` - зеленый, `B` - синий, `A` - альфа, прозрачность), мы можем использовать следующую формулу для вычисления разницы в цвете (энергии пикселя):
+
+
+
+Где:
+
+- `mEnergy` - *Энергия* (важность) *среднего* пикселя (`[0..626]` если округлить)
+- `lR` - *Красный* цветовой канал *левого* пикселя (`[0..255]`)
+- `mR` - *Красный* цветовой канал *среднего* пикселя (`[0..255]`)
+- `rR` - *Красный* цветовой канал *правого* пикселя (`[0..255]`)
+- `lG` - *Зеленый* цветовой канал *левого* пикселя (`[0..255]`)
+- и так далее...
+
+В приведенной выше формуле мы пока не используем альфа-канал (прозрачность), предполагая, что изображение не содержит прозрачные пиксели. Позже мы будем использовать альфа-канал для маскировки и удаления объектов.
+
+
+
+Поскольку мы знаем, как найти энергию одного пикселя, мы можем вычислить так называемую **энергетическую карту**, которая будет содержать энергии каждого пикселя изображения. На каждом шаге изменения размера изображения карту энергий необходимо пересчитывать (по крайней мере частично, подробнее об этом ниже), и она будет иметь тот же размер, что и изображение.
+
+Например, на 1-м шаге у нас будет изображение размером `1000 x 500` и энергетическая карта размером `1000 x 500`. На 2-м шаге изменения размера мы удалим шов с изображения и пересчитаем карту энергий на основе нового уменьшенного изображения. Таким образом, мы получим изображение размером `999 x 500` и карту энергий размером `999 x 500`.
+
+Чем выше энергия пикселя, тем больше вероятность того, что он является частью ребра, важен для содержимого изображения и тем меньше вероятность того, что нам потребуется его удалить.
+
+Для визуализации карты энергий мы можем присвоить более яркий цвет пикселям с большей энергией и более темные цвета пикселям с меньшей энергией. Вот как может выглядеть часть карты энергий. Вы можете увидеть светлую линию, которая представляет край и которую мы хотим сохранить при изменении размера.
+
+
+
+Вот реальный пример энергетической карты для изображения, которое вы видели выше (с воздушными шарами).
+
+
+
+Вы можете загрузить свое изображение и посмотреть, как будет выглядеть энергетическая карта в [интерактивной версии статьи](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/).
+
+Мы можем использовать энергетическую карту, чтобы найти швы (один за другим) с наименьшей энергией и тем самым решить, какие пиксели в конечном итоге должны быть удалены.
+
+
+
+Поиск шва с наименьшими затратами энергии не является тривиальной задачей и требует перебора множества возможных комбинаций пикселей. Мы применим динамическое программирование для оптимизации поиска шва.
+
+В примере ниже вы можете увидеть карту энергий с первым найденным для нее швом с наименьшей энергией.
+
+
+
+В приведенных выше примерах мы уменьшали ширину изображения. Аналогичный подход может быть использован для уменьшения высоты изображения. Для этого нам нужно:
+
+- начать использовать соседей *сверху* и *снизу*, а не *слева* и *справа*, для вычисления энергии пикселя
+- при поиске шва нам нужно двигаться *слева* *направо*, а не *сверху* *вниз*.
+
+## Реализация алгоритма на TypeScript
+
+> Исходный код и функции, упомянутые ниже, можно найти в репозитории [js-image-carver](https://github.com/trekhleb/js-image-carver).
+
+Для реализации алгоритма мы будем использовать TypeScript. Если вам нужна версия на JavaScript, вы можете игнорировать (удалить) определения типов и их использование.
+
+Для простоты примеров мы напишем код только для уменьшения *ширины* изображения.
+
+### Уменьшение ширины с учетом содержимого изображения (исходная функция)
+
+Для начала определим некоторые общие типы, которые мы будем использовать при реализации алгоритма.
+
+```typescript
+// Type that describes the image size (width and height).
+type ImageSize = { w: number, h: number };
+
+// The coordinate of the pixel.
+type Coordinate = { x: number, y: number };
+
+// The seam is a sequence of pixels (coordinates).
+type Seam = Coordinate[];
+
+// Energy map is a 2D array that has the same width and height
+// as the image the map is being calculated for.
+type EnergyMap = number[][];
+
+// Type that describes the image pixel's RGBA color.
+type Color = [
+ r: number, // Red
+ g: number, // Green
+ b: number, // Blue
+ a: number, // Alpha (transparency)
+] | Uint8ClampedArray;
+```
+
+Для имплементации алгоритма нам необходимо выполнить следующие шаги:
+
+1. Рассчитать **карту энергии** для текущей версии изображения.
+2. Найти **шов** с наименьшей энергией на основе карты энергий (здесь мы применим динамическое программирование).
+3. **Удалить шов** с наименьшей энергией из изображения.
+4. **Повторять** до тех пор, пока ширина изображения не будет уменьшена до нужного значения.
+
+```typescript
+type ResizeImageWidthArgs = {
+ img: ImageData, // Image data we want to resize.
+ toWidth: number, // Final image width we want the image to shrink to.
+};
+
+type ResizeImageWidthResult = {
+ img: ImageData, // Resized image data.
+ size: ImageSize, // Resized image size (w x h).
+};
+
+// Performs the content-aware image width resizing using the seam carving method.
+export const resizeImageWidth = (
+ { img, toWidth }: ResizeImageWidthArgs,
+): ResizeImageWidthResult => {
+ // For performance reasons we want to avoid changing the img data array size.
+ // Instead we'll just keep the record of the resized image width and height separately.
+ const size: ImageSize = { w: img.width, h: img.height };
+
+ // Calculating the number of pixels to remove.
+ const pxToRemove = img.width - toWidth;
+ if (pxToRemove < 0) {
+ throw new Error('Upsizing is not supported for now');
+ }
+
+ let energyMap: EnergyMap | null = null;
+ let seam: Seam | null = null;
+
+ // Removing the lowest energy seams one by one.
+ for (let i = 0; i < pxToRemove; i += 1) {
+ // 1. Calculate the energy map for the current version of the image.
+ energyMap = calculateEnergyMap(img, size);
+
+ // 2. Find the seam with the lowest energy based on the energy map.
+ seam = findLowEnergySeam(energyMap, size);
+
+ // 3. Delete the seam with the lowest energy seam from the image.
+ deleteSeam(img, seam, size);
+
+ // Reduce the image width, and continue iterations.
+ size.w -= 1;
+ }
+
+ // Returning the resized image and its final size.
+ // The img is actually a reference to the ImageData, so technically
+ // the caller of the function already has this pointer. But let's
+ // still return it for better code readability.
+ return { img, size };
+};
+```
+
+Изображение, которому необходимо изменить размер, передается в функцию в формате [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData). Вы можете отобразить изображение на canvas-е, а затем извлечь ImageData из того же canvas-а следующим образом:
+
+```javascript
+const ctx = canvas.getContext('2d');
+const imgData = ctx.getImageData(0, 0, imgWidth, imgHeight);
+```
+
+> Загрузка и отрисовка изображений в JavaScript выходит за рамки данной статьи, но вы можете найти полный исходный код того, как это можно сделать с помощью React в репозитории [js-image-carver](https://github.com/trekhleb/js-image-carver).
+
+Теперь, пошагово реализуем функции `calculateEnergyMap()`, `findLowEnergySeam()` и `deleteSeam()`.
+
+### Расчет энергии пикселя
+
+Для расчета воспользуемся формулой разницы цветов, описанной выше. Для левой и правой краев изображения (когда нет левого или правого соседей) мы игнорируем соседей и не учитываем их при расчете энергии.
+
+```typescript
+// Calculates the energy of a pixel.
+const getPixelEnergy = (left: Color | null, middle: Color, right: Color | null): number => {
+ // Middle pixel is the pixel we're calculating the energy for.
+ const [mR, mG, mB] = middle;
+
+ // Energy from the left pixel (if it exists).
+ let lEnergy = 0;
+ if (left) {
+ const [lR, lG, lB] = left;
+ lEnergy = (lR - mR) ** 2 + (lG - mG) ** 2 + (lB - mB) ** 2;
+ }
+
+ // Energy from the right pixel (if it exists).
+ let rEnergy = 0;
+ if (right) {
+ const [rR, rG, rB] = right;
+ rEnergy = (rR - mR) ** 2 + (rG - mG) ** 2 + (rB - mB) ** 2;
+ }
+
+ // Resulting pixel energy.
+ return Math.sqrt(lEnergy + rEnergy);
+};
+```
+
+### Расчет энергетической карты
+
+Изображение, с которым мы работаем, имеет формат [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData). Это означает, что все пиксели (и их цвета) хранятся в одномерном массиве [Uint8ClampedArray](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Uint8ClampedArray). Для удобства чтения введем пару вспомогательных функций, которые позволят работать с массивом Uint8ClampedArray как с *2D* матрицей.
+
+```typescript
+// Helper function that returns the color of the pixel.
+const getPixel = (img: ImageData, { x, y }: Coordinate): Color => {
+ // The ImageData data array is a flat 1D array.
+ // Thus we need to convert x and y coordinates to the linear index.
+ const i = y * img.width + x;
+ const cellsPerColor = 4; // RGBA
+ // For better efficiency, instead of creating a new sub-array we return
+ // a pointer to the part of the ImageData array.
+ return img.data.subarray(i * cellsPerColor, i * cellsPerColor + cellsPerColor);
+};
+
+// Helper function that sets the color of the pixel.
+const setPixel = (img: ImageData, { x, y }: Coordinate, color: Color): void => {
+ // The ImageData data array is a flat 1D array.
+ // Thus we need to convert x and y coordinates to the linear index.
+ const i = y * img.width + x;
+ const cellsPerColor = 4; // RGBA
+ img.data.set(color, i * cellsPerColor);
+};
+```
+
+Для вычисления карты энергии мы проходим через каждый пиксель изображения и вызываем для него описанную ранее функцию `getPixelEnergy()`.
+
+```typescript
+// Helper function that creates a matrix (2D array) of specific
+// size (w x h) and fills it with specified value.
+const matrix = <T>(w: number, h: number, filler: T): T[][] => {
+ return new Array(h)
+ .fill(null)
+ .map(() => {
+ return new Array(w).fill(filler);
+ });
+};
+
+// Calculates the energy of each pixel of the image.
+const calculateEnergyMap = (img: ImageData, { w, h }: ImageSize): EnergyMap => {
+ // Create an empty energy map where each pixel has infinitely high energy.
+ // We will update the energy of each pixel.
+ const energyMap: number[][] = matrix<number>(w, h, Infinity);
+ for (let y = 0; y < h; y += 1) {
+ for (let x = 0; x < w; x += 1) {
+ // Left pixel might not exist if we're on the very left edge of the image.
+ const left = (x - 1) >= 0 ? getPixel(img, { x: x - 1, y }) : null;
+ // The color of the middle pixel that we're calculating the energy for.
+ const middle = getPixel(img, { x, y });
+ // Right pixel might not exist if we're on the very right edge of the image.
+ const right = (x + 1) < w ? getPixel(img, { x: x + 1, y }) : null;
+ energyMap[y][x] = getPixelEnergy(left, middle, right);
+ }
+ }
+ return energyMap;
+};
+```
+
+> Карта энергии будет пересчитываться при каждой итерации изменения размера. Это значит, что она будет пересчитываться, скажем, 500 раз, если нам нужно будет уменьшить изображение на 500 пикселей, что выглядит неоптимально. Чтобы ускорить вычисление карты энергии на 2-м, 3-м и последующих этапах, мы можем пересчитать энергию только для тех пикселей, которые расположены вокруг шва, который будет удален. Для простоты эта оптимизация здесь пропущена, но пример с исходным кодом можно найти в репозитории [js-image-carver](https://github.com/trekhleb/js-image-carver).
+
+### Нахождение шва с минимальной энергией (применяем динамическое программирование)
+
+> В статье [Dynamic Programming vs Divide-and-Conquer](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/) я описывал некоторые аспекты динамического программирования на примере нахождения "расстояния Левенштейна" (преобразование одной строки в другую). Возможно она будет полезна для ознакомления.
+
+Проблема, которую нам необходимо решить заключается в нахождении пути (шва) на энергетической карте, который идет от верхней границы изображения к нижней и имеет минимальную энергию (сумма энергий пикселей, составляющих шов должна быть минимальной).
+
+#### "Наивный" подход (naive)
+
+Прямолинейный ("наивный") подход — перебрать все возможные пути один за другим.
+
+
+
+Двигаясь сверху вниз, для каждого пикселя у нас есть 3 варианта (↙︎ идти вниз-влево, ↓ вниз, ↘︎ идти вниз-вправо). Это дает нам временную сложность `O (w * 3 ^ h)` или просто `O (3 ^ h)`, где `w` и` h` - ширина и высота изображения. Такой подход выглядит неоптимальным.
+
+#### "Жадный" подход (greedy)
+
+Жадный подход — выбирать следующий пиксель как пиксель с наименьшей энергией, надеясь, что результирующая энергия шва будет наименьшей.
+
+
+
+Жадный подход приведет нас к не самому худшему решению, но он не сможет гарантировать, что мы найдем наилучшее доступное решение. На картинке выше видно, как мы выбрали `5` вместо `10` и пропустили цепочку оптимальных пикселей.
+
+Плюс этого подхода в том, что он быстрый и имеет временную сложность `O(w + h)`, где `w` и `h` - это ширина и высота изображения. В этом случае плата за скорость — низкое качество ресайза (много искажений). Временная сложность обусловлена тем, что нужно найти минимальное значение в первом ряду (обход `w` ячеек), а затем исследовать только 3 соседних пикселя для каждого ряда (обход `h` рядов).
+
+#### Используем динамическое программирование
+
+Вы, наверное, заметили, что в наивном подходе мы снова и снова суммировали одни и те же энергии пикселей, вычисляя энергию образовавшихся швов.
+
+
+
+В примере выше видно, что для первых двух швов мы повторно используем энергию более короткого шва (который имеет энергию `235`). Вместо одной операции `235 + 70` для вычисления энергии 2-го шва мы делаем четыре операции `(5 + 0 + 80 + 150) + 70`.
+
+> Тот факт, что мы повторно используем энергию предыдущего шва для вычисления энергии текущего шва, может быть применен рекурсивно ко всем более коротким швам до самого верхнего 1-го ряда. Когда у нас есть такие перекрывающиеся под-проблемы, [это признак](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/), что общая задача *может* быть оптимизирована с использованием динамического программирования.
+
+Таким образом, мы можем **сохранить энергию текущего шва** для конкретного пикселя в дополнительной таблице `samsEnergies`, чтобы повторно использовать ее при расчете энергии следующих швов (таблица `samsEnergies` будет иметь тот же размер, что и энергетическая карта и само изображение).
+
+Обратите также внимание, что для большинства пикселей в изображении (например, для левого нижнего) мы можем иметь *несколько* значений энергий предыдущих швов.
+
+
+
+Так как мы ищем шов с наименьшей результирующей энергией, имеет смысл выбирать и предыдущий шов с наименьшей результирующей энергией.
+
+
+
+Как правило, у нас есть три возможных предыдущих шва, которые текущий пиксель продолжает:
+
+
+
+Можем посмотреть на это с такой стороны:
+
+- Ячейка `[1][x]`: содержит наименьшую возможную энергию шва, который начинается где-то в ряду `[0][?] ` и заканчивается в ячейке `[1][x]`.
+- **Текущая ячейка** `[2][3]`: содержит наименьшую возможную энергию шва, который начинается где-то в ряду `[0][?] ` и заканчивается в ячейке `[2][3]`. Для вычисления нужно суммировать энергию текущего пикселя `[2][3]` (из энергетической карты) с `min(seam_energy_1_2, seam_energy_1_3, seam_energy_1_4)`.
+
+Если мы заполним таблицу `ShesamsEnergies` полностью, то минимальное число в нижнем ряду будет наименьшей возможной энергией шва.
+
+Попробуем заполнить несколько ячеек этой таблицы, чтобы посмотреть, как это работает.
+
+
+
+После заполнения таблицы `ShesamsEnergies` видно, что в нижнем ряду пиксель с самой низкой энергией имеет значение `50`. Для удобства во время генерации `samsEnergies` для каждого пикселя мы можем сохранить не только энергию шва, но и координаты предыдущего шва с наименьшей энергией. Это даст нам возможность легко восстанавливать траекторию шва снизу вверх.
+
+Временная сложность DP подхода составит `O(w * h)`, где `w` и `h` - это ширина и высота изображения. Обусловлена она тем, что нужно вычислить энергии для *всех* пикселей изображения.
+
+Вот пример того, как эта логика может быть реализована:
+
+```typescript
+// The metadata for the pixels in the seam.
+type SeamPixelMeta = {
+ energy: number, // The energy of the pixel.
+ coordinate: Coordinate, // The coordinate of the pixel.
+ previous: Coordinate | null, // The previous pixel in a seam.
+};
+
+// Finds the seam (the sequence of pixels from top to bottom) that has the
+// lowest resulting energy using the Dynamic Programming approach.
+const findLowEnergySeam = (energyMap: EnergyMap, { w, h }: ImageSize): Seam => {
+ // The 2D array of the size of w and h, where each pixel contains the
+ // seam metadata (pixel energy, pixel coordinate and previous pixel from
+ // the lowest energy seam at this point).
+ const seamsEnergies: (SeamPixelMeta | null)[][] = matrix<SeamPixelMeta | null>(w, h, null);
+
+ // Populate the first row of the map by just copying the energies
+ // from the energy map.
+ for (let x = 0; x < w; x += 1) {
+ const y = 0;
+ seamsEnergies[y][x] = {
+ energy: energyMap[y][x],
+ coordinate: { x, y },
+ previous: null,
+ };
+ }
+
+ // Populate the rest of the rows.
+ for (let y = 1; y < h; y += 1) {
+ for (let x = 0; x < w; x += 1) {
+ // Find the top adjacent cell with minimum energy.
+ // This cell would be the tail of a seam with lowest energy at this point.
+ // It doesn't mean that this seam (path) has lowest energy globally.
+ // Instead, it means that we found a path with the lowest energy that may lead
+ // us to the current pixel with the coordinates x and y.
+ let minPrevEnergy = Infinity;
+ let minPrevX: number = x;
+ for (let i = (x - 1); i <= (x + 1); i += 1) {
+ if (i >= 0 && i < w && seamsEnergies[y - 1][i].energy < minPrevEnergy) {
+ minPrevEnergy = seamsEnergies[y - 1][i].energy;
+ minPrevX = i;
+ }
+ }
+
+ // Update the current cell.
+ seamsEnergies[y][x] = {
+ energy: minPrevEnergy + energyMap[y][x],
+ coordinate: { x, y },
+ previous: { x: minPrevX, y: y - 1 },
+ };
+ }
+ }
+
+ // Find where the minimum energy seam ends.
+ // We need to find the tail of the lowest energy seam to start
+ // traversing it from its tail to its head (from the bottom to the top).
+ let lastMinCoordinate: Coordinate | null = null;
+ let minSeamEnergy = Infinity;
+ for (let x = 0; x < w; x += 1) {
+ const y = h - 1;
+ if (seamsEnergies[y][x].energy < minSeamEnergy) {
+ minSeamEnergy = seamsEnergies[y][x].energy;
+ lastMinCoordinate = { x, y };
+ }
+ }
+
+ // Find the lowest energy energy seam.
+ // Once we know where the tail is we may traverse and assemble the lowest
+ // energy seam based on the "previous" value of the seam pixel metadata.
+ const seam: Seam = [];
+ if (!lastMinCoordinate) {
+ return seam;
+ }
+
+ const { x: lastMinX, y: lastMinY } = lastMinCoordinate;
+
+ // Adding new pixel to the seam path one by one until we reach the top.
+ let currentSeam = seamsEnergies[lastMinY][lastMinX];
+ while (currentSeam) {
+ seam.push(currentSeam.coordinate);
+ const prevMinCoordinates = currentSeam.previous;
+ if (!prevMinCoordinates) {
+ currentSeam = null;
+ } else {
+ const { x: prevMinX, y: prevMinY } = prevMinCoordinates;
+ currentSeam = seamsEnergies[prevMinY][prevMinX];
+ }
+ }
+
+ return seam;
+};
+```
+
+### Удаление шва с минимальной энергией
+
+Как только мы нашли шов с наименьшей суммарной энергией, нам нужно удалить (вырезать) пиксели, которые образуют его из изображения. Удаление происходит путем смещения пикселей справа от шва на `1px` влево. Из соображений производительности мы не будем удалять крайний столбик пикселей. Вместо этого, компонент, отвечающий за отрисовку уменьшенного изображения просто проигнорирует ту часть изображения, которая лежит за пределами обрезанной ширины.
+
+
+
+```typescript
+// Deletes the seam from the image data.
+// We delete the pixel in each row and then shift the rest of the row pixels to the left.
+const deleteSeam = (img: ImageData, seam: Seam, { w }: ImageSize): void => {
+ seam.forEach(({ x: seamX, y: seamY }: Coordinate) => {
+ for (let x = seamX; x < (w - 1); x += 1) {
+ const nextPixel = getPixel(img, { x: x + 1, y: seamY });
+ setPixel(img, { x, y: seamY }, nextPixel);
+ }
+ });
+};
+```
+
+## Удаление объектов с изображения
+
+Seam Carving алгоритм пытается сначала удалить швы, состоящие из низкоэнергетических пикселей. Мы могли бы использовать этот факт и, присвоив низкую энергию некоторым пикселям вручную (например, нарисовав на изображении маску), мы могли бы заставить алгоритм удалить отмеченные пиксели (*объекты*).
+
+В настоящее время в функции `getPixelEnergy()` мы используем только каналы цветов `R`, `G`, `B` для вычисления энергии пикселей. Но есть еще и параметр `A` (альфа, прозрачность), который мы не использовали. Мы можем использовать канал прозрачности, чтобы "сказать" алгоритму, что прозрачные пиксели — это те пиксели, которые мы хотим удалить. Вы можете ознакомиться с [исходным кодом функции getPixelEnergy()](https://github.com/trekhleb/js-image-carver/blob/main/src/utils/contentAwareResizer.ts#L54), которая учитывает прозрачность.
+
+Вот как при этом будет выглядеть удаление объектов:
+
+
+
+## Проблемы алгоритма и дальнейшие планы
+
+Приложение [JS IMAGE CARVER](https://github.com/trekhleb/js-image-carver) далеко от идеала и не является приложением production-ready качества. Основной его целью была возможность интерактивного экспериментирования с алгоритмом. Поэтому в дальнейших планах — использовать его именно для экспериментов.
+
+В [оригинальной статье](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf) описывается, как алгоритм может быть использован не только для уменьшения, но и для **увеличения изображения**. Увеличение (расширение) изображения, в свою очередь, может быть использовано для **автоматического расширения изображения до его исходной ширины после удаления объектов**.
+
+Еще одной интересной областью экспериментов может быть попытка ускорить алгоритм, чтобы он работал в режиме **реального времени**.
+
+> Таковы планы на будущее, но пока, надеюсь, пример с уменьшением изображения был интересен и полезен для вас. Также надеюсь, что вам было интересно увидеть применение динамического программирования в задачах, приближенных к реальности.
+>
+> Удачи с вашими собственными экспериментами!
diff --git a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.node.js b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.node.js
new file mode 100644
index 0000000000..e4f78b7a52
--- /dev/null
+++ b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.node.js
@@ -0,0 +1,85 @@
+import fs from 'fs';
+import { PNG } from 'pngjs';
+
+import resizeImageWidth from '../resizeImageWidth';
+
+const testImageBeforePath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-before.png';
+const testImageAfterPath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-after.png';
+
+/**
+ * Compares two images and finds the number of different pixels.
+ *
+ * @param {ImageData} imgA - ImageData for the first image.
+ * @param {ImageData} imgB - ImageData for the second image.
+ * @param {number} threshold - Color difference threshold [0..255]. Smaller - stricter.
+ * @returns {number} - Number of different pixels.
+ */
+function pixelsDiff(imgA, imgB, threshold = 0) {
+ if (imgA.width !== imgB.width || imgA.height !== imgB.height) {
+ throw new Error('Images must have the same size');
+ }
+
+ let differentPixels = 0;
+ const numColorParams = 4; // RGBA
+
+ for (let pixelIndex = 0; pixelIndex < imgA.data.length; pixelIndex += numColorParams) {
+ // Get pixel's color for each image.
+ const [aR, aG, aB] = imgA.data.subarray(pixelIndex, pixelIndex + numColorParams);
+ const [bR, bG, bB] = imgB.data.subarray(pixelIndex, pixelIndex + numColorParams);
+
+ // Get average pixel's color for each image (make them greyscale).
+ const aAvgColor = Math.floor((aR + aG + aB) / 3);
+ const bAvgColor = Math.floor((bR + bG + bB) / 3);
+
+ // Compare pixel colors.
+ if (Math.abs(aAvgColor - bAvgColor) > threshold) {
+ differentPixels += 1;
+ }
+ }
+
+ return differentPixels;
+}
+
+const pngLoad = (path) => new Promise((resolve) => {
+ fs.createReadStream(path)
+ .pipe(new PNG())
+ .on('parsed', function Parsed() {
+ /** @type {ImageData} */
+ const imageData = {
+ colorSpace: 'srgb',
+ width: this.width,
+ height: this.height,
+ data: this.data,
+ };
+ resolve(imageData);
+ });
+});
+
+describe('resizeImageWidth', () => {
+ it('should perform content-aware image width reduction', async () => {
+ const imgBefore = await pngLoad(testImageBeforePath);
+ const imgAfter = await pngLoad(testImageAfterPath);
+
+ const toWidth = Math.floor(imgBefore.width / 2);
+
+ const {
+ img: imgResized,
+ size: resizedSize,
+ } = resizeImageWidth({ img: imgBefore, toWidth });
+
+ expect(imgResized).toBeDefined();
+ expect(resizedSize).toBeDefined();
+
+ expect(resizedSize).toEqual({ w: toWidth, h: imgBefore.height });
+ expect(imgResized.width).toBe(imgAfter.width);
+ expect(imgResized.height).toBe(imgAfter.height);
+
+ const colorThreshold = 50;
+ const differentPixels = pixelsDiff(imgResized, imgAfter, colorThreshold);
+
+ // Allow 10% of pixels to be different
+ const pixelsThreshold = Math.floor((imgAfter.width * imgAfter.height) / 10);
+
+ expect(differentPixels).toBeLessThanOrEqual(pixelsThreshold);
+ });
+});
diff --git a/src/algorithms/image-processing/seam-carving/__tests__/test-image-after.png b/src/algorithms/image-processing/seam-carving/__tests__/test-image-after.png
new file mode 100644
index 0000000000..8b5724cd30
Binary files /dev/null and b/src/algorithms/image-processing/seam-carving/__tests__/test-image-after.png differ
diff --git a/src/algorithms/image-processing/seam-carving/__tests__/test-image-before.png b/src/algorithms/image-processing/seam-carving/__tests__/test-image-before.png
new file mode 100644
index 0000000000..20a53207dd
Binary files /dev/null and b/src/algorithms/image-processing/seam-carving/__tests__/test-image-before.png differ
diff --git a/src/algorithms/image-processing/seam-carving/resizeImageWidth.js b/src/algorithms/image-processing/seam-carving/resizeImageWidth.js
new file mode 100644
index 0000000000..9f2c92fcee
--- /dev/null
+++ b/src/algorithms/image-processing/seam-carving/resizeImageWidth.js
@@ -0,0 +1,253 @@
+import { getPixel, setPixel } from '../utils/imageData';
+
+/**
+ * The seam is a sequence of pixels (coordinates).
+ * @typedef {PixelCoordinate[]} Seam
+ */
+
+/**
+ * Energy map is a 2D array that has the same width and height
+ * as the image the map is being calculated for.
+ * @typedef {number[][]} EnergyMap
+ */
+
+/**
+ * The metadata for the pixels in the seam.
+ * @typedef {Object} SeamPixelMeta
+ * @property {number} energy - the energy of the pixel.
+ * @property {PixelCoordinate} coordinate - the coordinate of the pixel.
+ * @property {?PixelCoordinate} previous - the previous pixel in a seam.
+ */
+
+/**
+ * Type that describes the image size (width and height)
+ * @typedef {Object} ImageSize
+ * @property {number} w - image width.
+ * @property {number} h - image height.
+ */
+
+/**
+ * @typedef {Object} ResizeImageWidthArgs
+ * @property {ImageData} img - image data we want to resize.
+ * @property {number} toWidth - final image width we want the image to shrink to.
+ */
+
+/**
+ * @typedef {Object} ResizeImageWidthResult
+ * @property {ImageData} img - resized image data.
+ * @property {ImageSize} size - resized image size.
+ */
+
+/**
+ * Helper function that creates a matrix (2D array) of specific
+ * size (w x h) and fills it with specified value.
+ * @param {number} w
+ * @param {number} h
+ * @param {?(number | SeamPixelMeta)} filler
+ * @returns {?(number | SeamPixelMeta)[][]}
+ */
+const matrix = (w, h, filler) => {
+ return new Array(h)
+ .fill(null)
+ .map(() => {
+ return new Array(w).fill(filler);
+ });
+};
+
+/**
+ * Calculates the energy of a pixel.
+ * @param {?PixelColor} left
+ * @param {PixelColor} middle
+ * @param {?PixelColor} right
+ * @returns {number}
+ */
+const getPixelEnergy = (left, middle, right) => {
+ // Middle pixel is the pixel we're calculating the energy for.
+ const [mR, mG, mB] = middle;
+
+ // Energy from the left pixel (if it exists).
+ let lEnergy = 0;
+ if (left) {
+ const [lR, lG, lB] = left;
+ lEnergy = (lR - mR) ** 2 + (lG - mG) ** 2 + (lB - mB) ** 2;
+ }
+
+ // Energy from the right pixel (if it exists).
+ let rEnergy = 0;
+ if (right) {
+ const [rR, rG, rB] = right;
+ rEnergy = (rR - mR) ** 2 + (rG - mG) ** 2 + (rB - mB) ** 2;
+ }
+
+ // Resulting pixel energy.
+ return Math.sqrt(lEnergy + rEnergy);
+};
+
+/**
+ * Calculates the energy of each pixel of the image.
+ * @param {ImageData} img
+ * @param {ImageSize} size
+ * @returns {EnergyMap}
+ */
+const calculateEnergyMap = (img, { w, h }) => {
+ // Create an empty energy map where each pixel has infinitely high energy.
+ // We will update the energy of each pixel.
+ const energyMap = matrix(w, h, Infinity);
+ for (let y = 0; y < h; y += 1) {
+ for (let x = 0; x < w; x += 1) {
+ // Left pixel might not exist if we're on the very left edge of the image.
+ const left = (x - 1) >= 0 ? getPixel(img, { x: x - 1, y }) : null;
+ // The color of the middle pixel that we're calculating the energy for.
+ const middle = getPixel(img, { x, y });
+ // Right pixel might not exist if we're on the very right edge of the image.
+ const right = (x + 1) < w ? getPixel(img, { x: x + 1, y }) : null;
+ energyMap[y][x] = getPixelEnergy(left, middle, right);
+ }
+ }
+ return energyMap;
+};
+
+/**
+ * Finds the seam (the sequence of pixels from top to bottom) that has the
+ * lowest resulting energy using the Dynamic Programming approach.
+ * @param {EnergyMap} energyMap
+ * @param {ImageSize} size
+ * @returns {Seam}
+ */
+const findLowEnergySeam = (energyMap, { w, h }) => {
+ // The 2D array of the size of w and h, where each pixel contains the
+ // seam metadata (pixel energy, pixel coordinate and previous pixel from
+ // the lowest energy seam at this point).
+ const seamPixelsMap = matrix(w, h, null);
+
+ // Populate the first row of the map by just copying the energies
+ // from the energy map.
+ for (let x = 0; x < w; x += 1) {
+ const y = 0;
+ seamPixelsMap[y][x] = {
+ energy: energyMap[y][x],
+ coordinate: { x, y },
+ previous: null,
+ };
+ }
+
+ // Populate the rest of the rows.
+ for (let y = 1; y < h; y += 1) {
+ for (let x = 0; x < w; x += 1) {
+ // Find the top adjacent cell with minimum energy.
+ // This cell would be the tail of a seam with lowest energy at this point.
+ // It doesn't mean that this seam (path) has lowest energy globally.
+ // Instead, it means that we found a path with the lowest energy that may lead
+ // us to the current pixel with the coordinates x and y.
+ let minPrevEnergy = Infinity;
+ let minPrevX = x;
+ for (let i = (x - 1); i <= (x + 1); i += 1) {
+ if (i >= 0 && i < w && seamPixelsMap[y - 1][i].energy < minPrevEnergy) {
+ minPrevEnergy = seamPixelsMap[y - 1][i].energy;
+ minPrevX = i;
+ }
+ }
+
+ // Update the current cell.
+ seamPixelsMap[y][x] = {
+ energy: minPrevEnergy + energyMap[y][x],
+ coordinate: { x, y },
+ previous: { x: minPrevX, y: y - 1 },
+ };
+ }
+ }
+
+ // Find where the minimum energy seam ends.
+ // We need to find the tail of the lowest energy seam to start
+ // traversing it from its tail to its head (from the bottom to the top).
+ let lastMinCoordinate = null;
+ let minSeamEnergy = Infinity;
+ for (let x = 0; x < w; x += 1) {
+ const y = h - 1;
+ if (seamPixelsMap[y][x].energy < minSeamEnergy) {
+ minSeamEnergy = seamPixelsMap[y][x].energy;
+ lastMinCoordinate = { x, y };
+ }
+ }
+
+ // Find the lowest energy energy seam.
+ // Once we know where the tail is we may traverse and assemble the lowest
+ // energy seam based on the "previous" value of the seam pixel metadata.
+ const seam = [];
+
+ const { x: lastMinX, y: lastMinY } = lastMinCoordinate;
+
+ // Adding new pixel to the seam path one by one until we reach the top.
+ let currentSeam = seamPixelsMap[lastMinY][lastMinX];
+ while (currentSeam) {
+ seam.push(currentSeam.coordinate);
+ const prevMinCoordinates = currentSeam.previous;
+ if (!prevMinCoordinates) {
+ currentSeam = null;
+ } else {
+ const { x: prevMinX, y: prevMinY } = prevMinCoordinates;
+ currentSeam = seamPixelsMap[prevMinY][prevMinX];
+ }
+ }
+
+ return seam;
+};
+
+/**
+ * Deletes the seam from the image data.
+ * We delete the pixel in each row and then shift the rest of the row pixels to the left.
+ * @param {ImageData} img
+ * @param {Seam} seam
+ * @param {ImageSize} size
+ */
+const deleteSeam = (img, seam, { w }) => {
+ seam.forEach(({ x: seamX, y: seamY }) => {
+ for (let x = seamX; x < (w - 1); x += 1) {
+ const nextPixel = getPixel(img, { x: x + 1, y: seamY });
+ setPixel(img, { x, y: seamY }, nextPixel);
+ }
+ });
+};
+
+/**
+ * Performs the content-aware image width resizing using the seam carving method.
+ * @param {ResizeImageWidthArgs} args
+ * @returns {ResizeImageWidthResult}
+ */
+const resizeImageWidth = ({ img, toWidth }) => {
+ /**
+ * For performance reasons we want to avoid changing the img data array size.
+ * Instead we'll just keep the record of the resized image width and height separately.
+ * @type {ImageSize}
+ */
+ const size = { w: img.width, h: img.height };
+
+ // Calculating the number of pixels to remove.
+ const pxToRemove = img.width - toWidth;
+
+ let energyMap = null;
+ let seam = null;
+
+ // Removing the lowest energy seams one by one.
+ for (let i = 0; i < pxToRemove; i += 1) {
+ // 1. Calculate the energy map for the current version of the image.
+ energyMap = calculateEnergyMap(img, size);
+
+ // 2. Find the seam with the lowest energy based on the energy map.
+ seam = findLowEnergySeam(energyMap, size);
+
+ // 3. Delete the seam with the lowest energy seam from the image.
+ deleteSeam(img, seam, size);
+
+ // Reduce the image width, and continue iterations.
+ size.w -= 1;
+ }
+
+ // Returning the resized image and its final size.
+ // The img is actually a reference to the ImageData, so technically
+ // the caller of the function already has this pointer. But let's
+ // still return it for better code readability.
+ return { img, size };
+};
+
+export default resizeImageWidth;
diff --git a/src/algorithms/image-processing/utils/imageData.js b/src/algorithms/image-processing/utils/imageData.js
new file mode 100644
index 0000000000..de397b8ead
--- /dev/null
+++ b/src/algorithms/image-processing/utils/imageData.js
@@ -0,0 +1,39 @@
+/**
+ * @typedef {ArrayLike<number> | Uint8ClampedArray} PixelColor
+ */
+
+/**
+ * @typedef {Object} PixelCoordinate
+ * @property {number} x - horizontal coordinate.
+ * @property {number} y - vertical coordinate.
+ */
+
+/**
+ * Helper function that returns the color of the pixel.
+ * @param {ImageData} img
+ * @param {PixelCoordinate} coordinate
+ * @returns {PixelColor}
+ */
+export const getPixel = (img, { x, y }) => {
+ // The ImageData data array is a flat 1D array.
+ // Thus we need to convert x and y coordinates to the linear index.
+ const i = y * img.width + x;
+ const cellsPerColor = 4; // RGBA
+ // For better efficiency, instead of creating a new sub-array we return
+ // a pointer to the part of the ImageData array.
+ return img.data.subarray(i * cellsPerColor, i * cellsPerColor + cellsPerColor);
+};
+
+/**
+ * Helper function that sets the color of the pixel.
+ * @param {ImageData} img
+ * @param {PixelCoordinate} coordinate
+ * @param {PixelColor} color
+ */
+export const setPixel = (img, { x, y }, color) => {
+ // The ImageData data array is a flat 1D array.
+ // Thus we need to convert x and y coordinates to the linear index.
+ const i = y * img.width + x;
+ const cellsPerColor = 4; // RGBA
+ img.data.set(color, i * cellsPerColor);
+};
diff --git a/src/algorithms/linked-list/reverse-traversal/README.md b/src/algorithms/linked-list/reverse-traversal/README.md
index 89187e4f88..7e3f3cd6bb 100644
--- a/src/algorithms/linked-list/reverse-traversal/README.md
+++ b/src/algorithms/linked-list/reverse-traversal/README.md
@@ -1,5 +1,9 @@
# Reversed Linked List Traversal
+_Read this in other languages:_
+[_中文_](README.zh-CN.md),
+[_Português_](README.pt-BR.md)
+
The task is to traverse the given linked list in reversed order.
For example for the following linked list:
diff --git a/src/algorithms/linked-list/reverse-traversal/README.pt-BR.md b/src/algorithms/linked-list/reverse-traversal/README.pt-BR.md
new file mode 100644
index 0000000000..b2761ad720
--- /dev/null
+++ b/src/algorithms/linked-list/reverse-traversal/README.pt-BR.md
@@ -0,0 +1,23 @@
+# Travessia de Lista Encadeada Reversa
+
+_Leia isso em outros idiomas:_
+[_中文_](README.zh-CN.md),
+[_English_](README.md)
+
+A tarefa é percorrer a lista encadeada fornecida em ordem inversa.
+
+Por exemplo, para a seguinte lista vinculada:
+
+
+
+A ordem de travessia deve ser:
+
+```texto
+37 → 99 → 12
+```
+
+A complexidade de tempo é `O(n)` porque visitamos cada nó apenas uma vez.
+
+## Referência
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
diff --git a/src/algorithms/linked-list/reverse-traversal/README.zh-CN.md b/src/algorithms/linked-list/reverse-traversal/README.zh-CN.md
new file mode 100644
index 0000000000..cf0217a5b1
--- /dev/null
+++ b/src/algorithms/linked-list/reverse-traversal/README.zh-CN.md
@@ -0,0 +1,19 @@
+# 链表倒序遍历
+
+我们的任务是倒序遍历给定的链表
+
+比如下面的链表
+
+
+
+遍历的顺序应该是
+
+```text
+37 → 99 → 12
+```
+
+因为我们每个节点只访问一次，时间复杂度应该是`O(n)`
+
+## 参考
+
+- [Wikipedia](https://zh.wikipedia.org/wiki/%E9%93%BE%E8%A1%A8)
diff --git a/src/algorithms/linked-list/traversal/README.md b/src/algorithms/linked-list/traversal/README.md
index 79e7b43626..09b177494c 100644
--- a/src/algorithms/linked-list/traversal/README.md
+++ b/src/algorithms/linked-list/traversal/README.md
@@ -1,7 +1,9 @@
# Linked List Traversal
_Read this in other languages:_
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_中文_](README.zh-CN.md),
+[_Português_](README.pt-BR.md)
The task is to traverse the given linked list in straight order.
diff --git a/src/algorithms/linked-list/traversal/README.pt-BR.md b/src/algorithms/linked-list/traversal/README.pt-BR.md
new file mode 100644
index 0000000000..0fae9ed01a
--- /dev/null
+++ b/src/algorithms/linked-list/traversal/README.pt-BR.md
@@ -0,0 +1,24 @@
+# Travessia de Lista Encadeada
+
+_Leia isso em outros idiomas:_
+[_Русский_](README.ru-RU.md),
+[_中文_](README.zh-CN.md),
+[_English_](README.md)
+
+A tarefa é percorrer a lista encadeada fornecida em ordem direta.
+
+Por exemplo, para a seguinte lista vinculada:
+
+
+
+A ordem de travessia deve ser:
+
+```texto
+12 → 99 → 37
+```
+
+A complexidade de tempo é `O(n)` porque visitamos cada nó apenas uma vez.
+
+## Referência
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
diff --git a/src/algorithms/linked-list/traversal/README.zh-CN.md b/src/algorithms/linked-list/traversal/README.zh-CN.md
new file mode 100644
index 0000000000..19a01502b5
--- /dev/null
+++ b/src/algorithms/linked-list/traversal/README.zh-CN.md
@@ -0,0 +1,19 @@
+# 链表遍历
+
+我们的任务是顺序遍历给定的链表
+
+比如下面的链表
+
+
+
+遍历的顺序应该是
+
+```text
+12 → 99 → 37
+```
+
+因为我们每个节点只访问一次，时间复杂度应该是`O(n)`
+
+## 参考
+
+- [Wikipedia](https://zh.wikipedia.org/wiki/%E9%93%BE%E8%A1%A8)
\ No newline at end of file
diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md
new file mode 100644
index 0000000000..d1ae72731e
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/README.md
@@ -0,0 +1,103 @@
+# Binary representation of floating-point numbers
+
+Have you ever wondered how computers store the floating-point numbers like `3.1416` (𝝿) or `9.109 × 10⁻³¹` (the mass of the electron in kg) in the memory which is limited by a finite number of ones and zeroes (aka bits)?
+
+It seems pretty straightforward for integers (i.e. `17`). Let's say we have 16 bits (2 bytes) to store the number. In 16 bits we may store the integers in a range of `[0, 65535]`:
+
+```text
+(0000000000000000)₂ = (0)₁₀
+
+(0000000000010001)₂ =
+ (1 × 2⁴) +
+ (0 × 2³) +
+ (0 × 2²) +
+ (0 × 2¹) +
+ (1 × 2⁰) = (17)₁₀
+
+(1111111111111111)₂ =
+ (1 × 2¹⁵) +
+ (1 × 2¹⁴) +
+ (1 × 2¹³) +
+ (1 × 2¹²) +
+ (1 × 2¹¹) +
+ (1 × 2¹⁰) +
+ (1 × 2⁹) +
+ (1 × 2⁸) +
+ (1 × 2⁷) +
+ (1 × 2⁶) +
+ (1 × 2⁵) +
+ (1 × 2⁴) +
+ (1 × 2³) +
+ (1 × 2²) +
+ (1 × 2¹) +
+ (1 × 2⁰) = (65535)₁₀
+```
+
+If we need a signed integer we may use [two's complement](https://en.wikipedia.org/wiki/Two%27s_complement) and shift the range of `[0, 65535]` towards the negative numbers. In this case, our 16 bits would represent the numbers in a range of `[-32768, +32767]`.
+
+As you might have noticed, this approach won't allow you to represent the numbers like `-27.15625` (numbers after the decimal point are just being ignored).
+
+We're not the first ones who have noticed this issue though. Around ≈36 years ago some smart folks overcame this limitation by introducing the [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754) standard for floating-point arithmetic.
+
+The IEEE 754 standard describes the way (the framework) of using those 16 bits (or 32, or 64 bits) to store the numbers of wider range, including the small floating numbers (smaller than 1 and closer to 0).
+
+To get the idea behind the standard we might recall the [scientific notation](https://en.wikipedia.org/wiki/Scientific_notation) - a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form.
+
+
+
+As you may see from the image, the number representation might be split into three parts:
+
+- **sign**
+- **fraction (aka significand)** - the valuable digits (the meaning, the payload) of the number
+- **exponent** - controls how far and in which direction to move the decimal point in the fraction
+
+The **base** part we may omit by just agreeing on what it will be equal to. In our case, we'll be using `2` as a base.
+
+Instead of using all 16 bits (or 32 bits, or 64 bits) to store the fraction of the number, we may share the bits and store a sign, exponent, and fraction at the same time. Depending on the number of bits that we're going to use to store the number we end up with the following splits:
+
+| Floating-point format | Total bits | Sign bits | Exponent bits | Fraction bits | Base |
+| :-------------------- | :--------: | :-------: | :-----------: | :--------------: | :--: |
+| [Half-precision](https://en.wikipedia.org/wiki/Half-precision_floating-point_format) | 16 | 1 | 5 | 10 | 2 |
+| [Single-precision](https://en.wikipedia.org/wiki/Single-precision_floating-point_format) | 32 | 1 | 8 | 23 | 2 |
+| [Double-precision](https://en.wikipedia.org/wiki/Double-precision_floating-point_format) | 64 | 1 | 11 | 52 | 2 |
+
+With this approach, the number of bits for the fraction has been reduced (i.e. for the 16-bits number it was reduced from 16 bits to 10 bits). It means that the fraction might take a narrower range of values now (losing some precision). However, since we also have an exponent part, it will actually increase the ultimate number range and also allow us to describe the numbers between 0 and 1 (if the exponent is negative).
+
+> For example, a signed 32-bit integer variable has a maximum value of 2³¹ − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of ≈ 3.4028235 × 10³⁸.
+
+To make it possible to have a negative exponent, the IEEE 754 standard uses the [biased exponent](https://en.wikipedia.org/wiki/Exponent_bias). The idea is simple - subtract the bias from the exponent value to make it negative. For example, if the exponent has 5 bits, it might take the values from the range of `[0, 31]` (all values are positive here). But if we subtract the value of `15` from it, the range will be `[-15, 16]`. The number `15` is called bias, and it is being calculated by the following formula:
+
+```
+exponent_bias = 2 ^ (k−1) − 1
+
+k - number of exponent bits
+```
+
+I've tried to describe the logic behind the converting of floating-point numbers from a binary format back to the decimal format on the image below. Hopefully, it will give you a better understanding of how the IEEE 754 standard works. The 16-bits number is being used here for simplicity, but the same approach works for 32-bits and 64-bits numbers as well.
+
+
+
+> Checkout the [interactive version of this diagram](https://trekhleb.dev/blog/2021/binary-floating-point/) to play around with setting bits on and off, and seeing how it would influence the final result
+
+Here is the number ranges that different floating-point formats support:
+
+| Floating-point format | Exp min | Exp max | Range | Min positive |
+| :-------------------- | :------ | :------ | :--------------- | :----------- |
+| Half-precision | −14 | +15 | ±65,504 | 6.10 × 10⁻⁵ |
+| Single-precision | −126 | +127 | ±3.4028235 × 10³⁸| 1.18 × 10⁻³⁸ |
+
+Be aware that this is by no means a complete and sufficient overview of the IEEE 754 standard. It is rather a simplified and basic overview. Several corner cases were omitted in the examples above for simplicity of presentation (i.e. `-0`, `-∞`, `+∞` and `NaN` (not a number) values)
+
+## Code examples
+
+- See the [bitsToFloat.js](bitsToFloat.js) for the example of how to convert array of bits to the floating point number (the example is a bit artificial but still it gives the overview of how the conversion is going on)
+- See the [floatAsBinaryString.js](floatAsBinaryString.js) for the example of how to see the actual binary representation of the floating-point number in JavaScript
+
+## References
+
+You might also want to check out the following resources to get a deeper understanding of the binary representation of floating-point numbers:
+
+- [Interactive version of this article](https://trekhleb.dev/blog/2021/binary-floating-point/) (allows setting the bits manually and seeing the resulting floating number)
+- [Here is what you need to know about JavaScript’s Number type](https://indepth.dev/posts/1139/here-is-what-you-need-to-know-about-javascripts-number-type)
+- [Float Exposed](https://float.exposed/)
+- [IEEE754 Visualization](https://bartaz.github.io/ieee754-visualization/)
diff --git a/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js b/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js
new file mode 100644
index 0000000000..53afe691a2
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js
@@ -0,0 +1,32 @@
+import { testCases16Bits, testCases32Bits, testCases64Bits } from '../testCases';
+import { bitsToFloat16, bitsToFloat32, bitsToFloat64 } from '../bitsToFloat';
+
+describe('bitsToFloat16', () => {
+ it('should convert floating point binary bits to floating point decimal number', () => {
+ for (let testCaseIndex = 0; testCaseIndex < testCases16Bits.length; testCaseIndex += 1) {
+ const [decimal, binary] = testCases16Bits[testCaseIndex];
+ const bits = binary.split('').map((bitString) => parseInt(bitString, 10));
+ expect(bitsToFloat16(bits)).toBeCloseTo(decimal, 4);
+ }
+ });
+});
+
+describe('bitsToFloat32', () => {
+ it('should convert floating point binary bits to floating point decimal number', () => {
+ for (let testCaseIndex = 0; testCaseIndex < testCases32Bits.length; testCaseIndex += 1) {
+ const [decimal, binary] = testCases32Bits[testCaseIndex];
+ const bits = binary.split('').map((bitString) => parseInt(bitString, 10));
+ expect(bitsToFloat32(bits)).toBeCloseTo(decimal, 7);
+ }
+ });
+});
+
+describe('bitsToFloat64', () => {
+ it('should convert floating point binary bits to floating point decimal number', () => {
+ for (let testCaseIndex = 0; testCaseIndex < testCases64Bits.length; testCaseIndex += 1) {
+ const [decimal, binary] = testCases64Bits[testCaseIndex];
+ const bits = binary.split('').map((bitString) => parseInt(bitString, 10));
+ expect(bitsToFloat64(bits)).toBeCloseTo(decimal, 14);
+ }
+ });
+});
diff --git a/src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js b/src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js
new file mode 100644
index 0000000000..efb8a2ba5e
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js
@@ -0,0 +1,20 @@
+import { floatAs32BinaryString, floatAs64BinaryString } from '../floatAsBinaryString';
+import { testCases32Bits, testCases64Bits } from '../testCases';
+
+describe('floatAs32Binary', () => {
+ it('should create a binary representation of the floating numbers', () => {
+ for (let testCaseIndex = 0; testCaseIndex < testCases32Bits.length; testCaseIndex += 1) {
+ const [decimal, binary] = testCases32Bits[testCaseIndex];
+ expect(floatAs32BinaryString(decimal)).toBe(binary);
+ }
+ });
+});
+
+describe('floatAs64Binary', () => {
+ it('should create a binary representation of the floating numbers', () => {
+ for (let testCaseIndex = 0; testCaseIndex < testCases64Bits.length; testCaseIndex += 1) {
+ const [decimal, binary] = testCases64Bits[testCaseIndex];
+ expect(floatAs64BinaryString(decimal)).toBe(binary);
+ }
+ });
+});
diff --git a/src/algorithms/math/binary-floating-point/bitsToFloat.js b/src/algorithms/math/binary-floating-point/bitsToFloat.js
new file mode 100644
index 0000000000..6d1ef0d851
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/bitsToFloat.js
@@ -0,0 +1,119 @@
+/**
+ * Sequence of 0s and 1s.
+ * @typedef {number[]} Bits
+ */
+
+/**
+ * @typedef {{
+ * signBitsCount: number,
+ * exponentBitsCount: number,
+ * fractionBitsCount: number,
+ * }} PrecisionConfig
+ */
+
+/**
+ * @typedef {{
+ * half: PrecisionConfig,
+ * single: PrecisionConfig,
+ * double: PrecisionConfig
+ * }} PrecisionConfigs
+ */
+
+/**
+ * ┌───────────────── sign bit
+ * │ ┌───────────── exponent bits
+ * │ │ ┌───── fraction bits
+ * │ │ │
+ * X XXXXX XXXXXXXXXX
+ *
+ * @type {PrecisionConfigs}
+ */
+const precisionConfigs = {
+ // @see: https://en.wikipedia.org/wiki/Half-precision_floating-point_format
+ half: {
+ signBitsCount: 1,
+ exponentBitsCount: 5,
+ fractionBitsCount: 10,
+ },
+ // @see: https://en.wikipedia.org/wiki/Single-precision_floating-point_format
+ single: {
+ signBitsCount: 1,
+ exponentBitsCount: 8,
+ fractionBitsCount: 23,
+ },
+ // @see: https://en.wikipedia.org/wiki/Double-precision_floating-point_format
+ double: {
+ signBitsCount: 1,
+ exponentBitsCount: 11,
+ fractionBitsCount: 52,
+ },
+};
+
+/**
+ * Converts the binary representation of the floating point number to decimal float number.
+ *
+ * @param {Bits} bits - sequence of bits that represents the floating point number.
+ * @param {PrecisionConfig} precisionConfig - half/single/double precision config.
+ * @return {number} - floating point number decoded from its binary representation.
+ */
+function bitsToFloat(bits, precisionConfig) {
+ const { signBitsCount, exponentBitsCount } = precisionConfig;
+
+ // Figuring out the sign.
+ const sign = (-1) ** bits[0]; // -1^1 = -1, -1^0 = 1
+
+ // Calculating the exponent value.
+ const exponentBias = 2 ** (exponentBitsCount - 1) - 1;
+ const exponentBits = bits.slice(signBitsCount, signBitsCount + exponentBitsCount);
+ const exponentUnbiased = exponentBits.reduce(
+ (exponentSoFar, currentBit, bitIndex) => {
+ const bitPowerOfTwo = 2 ** (exponentBitsCount - bitIndex - 1);
+ return exponentSoFar + currentBit * bitPowerOfTwo;
+ },
+ 0,
+ );
+ const exponent = exponentUnbiased - exponentBias;
+
+ // Calculating the fraction value.
+ const fractionBits = bits.slice(signBitsCount + exponentBitsCount);
+ const fraction = fractionBits.reduce(
+ (fractionSoFar, currentBit, bitIndex) => {
+ const bitPowerOfTwo = 2 ** -(bitIndex + 1);
+ return fractionSoFar + currentBit * bitPowerOfTwo;
+ },
+ 0,
+ );
+
+ // Putting all parts together to calculate the final number.
+ return sign * (2 ** exponent) * (1 + fraction);
+}
+
+/**
+ * Converts the 16-bit binary representation of the floating point number to decimal float number.
+ *
+ * @param {Bits} bits - sequence of bits that represents the floating point number.
+ * @return {number} - floating point number decoded from its binary representation.
+ */
+export function bitsToFloat16(bits) {
+ return bitsToFloat(bits, precisionConfigs.half);
+}
+
+/**
+ * Converts the 32-bit binary representation of the floating point number to decimal float number.
+ *
+ * @param {Bits} bits - sequence of bits that represents the floating point number.
+ * @return {number} - floating point number decoded from its binary representation.
+ */
+export function bitsToFloat32(bits) {
+ return bitsToFloat(bits, precisionConfigs.single);
+}
+
+/**
+ * Converts the 64-bit binary representation of the floating point number to decimal float number.
+ *
+ * @param {Bits} bits - sequence of bits that represents the floating point number.
+ * @return {number} - floating point number decoded from its binary representation.
+ */
+export function bitsToFloat64(bits) {
+ return bitsToFloat(bits, precisionConfigs.double);
+}
diff --git a/src/algorithms/math/binary-floating-point/floatAsBinaryString.js b/src/algorithms/math/binary-floating-point/floatAsBinaryString.js
new file mode 100644
index 0000000000..aa907ac049
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/floatAsBinaryString.js
@@ -0,0 +1,61 @@
+// @see: https://en.wikipedia.org/wiki/Single-precision_floating-point_format
+const singlePrecisionBytesLength = 4; // 32 bits
+
+// @see: https://en.wikipedia.org/wiki/Double-precision_floating-point_format
+const doublePrecisionBytesLength = 8; // 64 bits
+
+const bitsInByte = 8;
+
+/**
+ * Converts the float number into its IEEE 754 binary representation.
+ * @see: https://en.wikipedia.org/wiki/IEEE_754
+ *
+ * @param {number} floatNumber - float number in decimal format.
+ * @param {number} byteLength - number of bytes to use to store the float number.
+ * @return {string} - binary string representation of the float number.
+ */
+function floatAsBinaryString(floatNumber, byteLength) {
+ let numberAsBinaryString = '';
+
+ const arrayBuffer = new ArrayBuffer(byteLength);
+ const dataView = new DataView(arrayBuffer);
+
+ const byteOffset = 0;
+ const littleEndian = false;
+
+ if (byteLength === singlePrecisionBytesLength) {
+ dataView.setFloat32(byteOffset, floatNumber, littleEndian);
+ } else {
+ dataView.setFloat64(byteOffset, floatNumber, littleEndian);
+ }
+
+ for (let byteIndex = 0; byteIndex < byteLength; byteIndex += 1) {
+ let bits = dataView.getUint8(byteIndex).toString(2);
+ if (bits.length < bitsInByte) {
+ bits = new Array(bitsInByte - bits.length).fill('0').join('') + bits;
+ }
+ numberAsBinaryString += bits;
+ }
+
+ return numberAsBinaryString;
+}
+
+/**
+ * Converts the float number into its IEEE 754 64-bits binary representation.
+ *
+ * @param {number} floatNumber - float number in decimal format.
+ * @return {string} - 64 bits binary string representation of the float number.
+ */
+export function floatAs64BinaryString(floatNumber) {
+ return floatAsBinaryString(floatNumber, doublePrecisionBytesLength);
+}
+
+/**
+ * Converts the float number into its IEEE 754 32-bits binary representation.
+ *
+ * @param {number} floatNumber - float number in decimal format.
+ * @return {string} - 32 bits binary string representation of the float number.
+ */
+export function floatAs32BinaryString(floatNumber) {
+ return floatAsBinaryString(floatNumber, singlePrecisionBytesLength);
+}
diff --git a/src/algorithms/math/binary-floating-point/images/02-half-precision-floating-point-number-explained.png b/src/algorithms/math/binary-floating-point/images/02-half-precision-floating-point-number-explained.png
new file mode 100644
index 0000000000..1bc0a5b835
Binary files /dev/null and b/src/algorithms/math/binary-floating-point/images/02-half-precision-floating-point-number-explained.png differ
diff --git a/src/algorithms/math/binary-floating-point/images/03-scientific-notation.png b/src/algorithms/math/binary-floating-point/images/03-scientific-notation.png
new file mode 100644
index 0000000000..449aa6faf5
Binary files /dev/null and b/src/algorithms/math/binary-floating-point/images/03-scientific-notation.png differ
diff --git a/src/algorithms/math/binary-floating-point/testCases.js b/src/algorithms/math/binary-floating-point/testCases.js
new file mode 100644
index 0000000000..54b9b8029b
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/testCases.js
@@ -0,0 +1,71 @@
+/**
+ * @typedef {[number, string]} TestCase
+ * @property {number} decimal
+ * @property {string} binary
+ */
+
+/**
+ * @type {TestCase[]}
+ */
+export const testCases16Bits = [
+ [-65504, '1111101111111111'],
+ [-10344, '1111000100001101'],
+ [-27.15625, '1100111011001010'],
+ [-1, '1011110000000000'],
+ [-0.09997558, '1010111001100110'],
+ [0, '0000000000000000'],
+ [5.9604644775390625e-8, '0000000000000001'],
+ [0.000004529, '0000000001001100'],
+ [0.0999755859375, '0010111001100110'],
+ [0.199951171875, '0011001001100110'],
+ [0.300048828125, '0011010011001101'],
+ [1, '0011110000000000'],
+ [1.5, '0011111000000000'],
+ [1.75, '0011111100000000'],
+ [1.875, '0011111110000000'],
+ [65504, '0111101111111111'],
+];
+
+/**
+ * @type {TestCase[]}
+ */
+export const testCases32Bits = [
+ [-3.40282346638528859812e+38, '11111111011111111111111111111111'],
+ [-10345.5595703125, '11000110001000011010011000111101'],
+ [-27.15625, '11000001110110010100000000000000'],
+ [-1, '10111111100000000000000000000000'],
+ [-0.1, '10111101110011001100110011001101'],
+ [0, '00000000000000000000000000000000'],
+ [1.40129846432481707092e-45, '00000000000000000000000000000001'],
+ [0.000004560, '00110110100110010000001000011010'],
+ [0.1, '00111101110011001100110011001101'],
+ [0.2, '00111110010011001100110011001101'],
+ [0.3, '00111110100110011001100110011010'],
+ [1, '00111111100000000000000000000000'],
+ [1.5, '00111111110000000000000000000000'],
+ [1.75, '00111111111000000000000000000000'],
+ [1.875, '00111111111100000000000000000000'],
+ [3.40282346638528859812e+38, '01111111011111111111111111111111'],
+];
+
+/**
+ * @type {TestCase[]}
+ */
+export const testCases64Bits = [
+ [-1.79769313486231570815e+308, '1111111111101111111111111111111111111111111111111111111111111111'],
+ [-10345.5595703125, '1100000011000100001101001100011110100000000000000000000000000000'],
+ [-27.15625, '1100000000111011001010000000000000000000000000000000000000000000'],
+ [-1, '1011111111110000000000000000000000000000000000000000000000000000'],
+ [-0.1, '1011111110111001100110011001100110011001100110011001100110011010'],
+ [0, '0000000000000000000000000000000000000000000000000000000000000000'],
+ [4.94065645841246544177e-324, '0000000000000000000000000000000000000000000000000000000000000001'],
+ [0.000004560, '0011111011010011001000000100001101000001011100110011110011100100'],
+ [0.1, '0011111110111001100110011001100110011001100110011001100110011010'],
+ [0.2, '0011111111001001100110011001100110011001100110011001100110011010'],
+ [0.3, '0011111111010011001100110011001100110011001100110011001100110011'],
+ [1, '0011111111110000000000000000000000000000000000000000000000000000'],
+ [1.5, '0011111111111000000000000000000000000000000000000000000000000000'],
+ [1.75, '0011111111111100000000000000000000000000000000000000000000000000'],
+ [1.875, '0011111111111110000000000000000000000000000000000000000000000000'],
+ [1.79769313486231570815e+308, '0111111111101111111111111111111111111111111111111111111111111111'],
+];
diff --git a/src/algorithms/math/bits/README.zh-CN.md b/src/algorithms/math/bits/README.zh-CN.md
index 8b71ddc21a..9ec75069c6 100644
--- a/src/algorithms/math/bits/README.zh-CN.md
+++ b/src/algorithms/math/bits/README.zh-CN.md
@@ -6,7 +6,7 @@ _Read this in other languages:_
#### Get Bit
-该方法向右移动目标位到最右边，即位数组的第0个位置上。然后在该数上与形如 `0001`的二进制形式的数进行`ADD`操作。这会清理掉除了目标位的所有其它位的数据。如果目标位是1，那么结果就是`1`，反之，结果是`0`;
+该方法向右移动目标位到最右边，即位数组的第0个位置上。然后在该数上与形如 `0001`的二进制形式的数进行`AND`操作。这会清理掉除了目标位的所有其它位的数据。如果目标位是1，那么结果就是`1`，反之，结果是`0`;
> 查看[getBit.js](getBit.js)了解更多细节。
@@ -18,7 +18,7 @@ _Read this in other languages:_
#### Clear Bit
-该方法把`1`向左移动了`bitPosition`位，生成了一个二进制形如`00100`的值。然后反转每一位的数字，得到一个二进制形如`11011`的值。接着与目标值进行`ADD`操作，就能清除掉目标位的值。
+该方法把`1`向左移动了`bitPosition`位，生成了一个二进制形如`00100`的值。然后反转每一位的数字，得到一个二进制形如`11011`的值。接着与目标值进行`AND`操作，就能清除掉目标位的值。
> 查看[clearBit.js](clearBit.js)了解更多细节。
diff --git a/src/algorithms/math/factorial/README.ka-GE.md b/src/algorithms/math/factorial/README.ka-GE.md
new file mode 100644
index 0000000000..1d02b9f7d3
--- /dev/null
+++ b/src/algorithms/math/factorial/README.ka-GE.md
@@ -0,0 +1,32 @@
+# ფაქტორიალი
+
+მათემატიკაში `n` ნატურალური რიცხვის ფაქტორიალი
+(აღინიშნება `n!` სიმბოლოთი)
+არის ყველა ნატურალური რიცხვის ნამრავლი 1-იდან `n`-ის ჩათვლით. მაგალითად:
+
+```
+5! = 5 * 4 * 3 * 2 * 1 = 120
+```
+
+| n | n! |
+| --- | ----------------: |
+| 0 | 1 |
+| 1 | 1 |
+| 2 | 2 |
+| 3 | 6 |
+| 4 | 24 |
+| 5 | 120 |
+| 6 | 720 |
+| 7 | 5 040 |
+| 8 | 40 320 |
+| 9 | 362 880 |
+| 10 | 3 628 800 |
+| 11 | 39 916 800 |
+| 12 | 479 001 600 |
+| 13 | 6 227 020 800 |
+| 14 | 87 178 291 200 |
+| 15 | 1 307 674 368 000 |
+
+## სქოლიო
+
+[Wikipedia](https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A4%E1%83%90%E1%83%A5%E1%83%A2%E1%83%9D%E1%83%A0%E1%83%98%E1%83%90%E1%83%9A%E1%83%98)
diff --git a/src/algorithms/math/factorial/README.md b/src/algorithms/math/factorial/README.md
index 107b55a3d3..9c75b41aae 100644
--- a/src/algorithms/math/factorial/README.md
+++ b/src/algorithms/math/factorial/README.md
@@ -1,7 +1,7 @@
# Factorial
_Read this in other languages:_
-[_简体中文_](README.zh-CN.md), [français](README.fr-FR.md).
+[_简体中文_](README.zh-CN.md), [_Français_](README.fr-FR.md), [_Türkçe_](README.tr-TR.md), [_ქართული_](README.ka-GE.md), [_Українська_](README.uk-UA.md).
In mathematics, the factorial of a non-negative integer `n`,
denoted by `n!`, is the product of all positive integers less
diff --git a/src/algorithms/math/factorial/README.tr-TR.md b/src/algorithms/math/factorial/README.tr-TR.md
new file mode 100644
index 0000000000..68ce21a299
--- /dev/null
+++ b/src/algorithms/math/factorial/README.tr-TR.md
@@ -0,0 +1,38 @@
+# Faktöriyel
+
+_Bunu diğer dillerde okuyun:_
+[_简体中文_](README.zh-CN.md), [français](README.fr-FR.md).
+
+Faktöriyel, matematikte, sağına ünlem işareti konulmuş sayıya
+verilen isim, daha genel olan Gama fonksiyonunun tam sayılarla
+sınırlanmış özel bir durumudur. 1'den başlayarak belirli bir
+sayma sayısına kadar olan sayıların çarpımına o sayının
+faktöriyeli denir. Basit bir şekilde faktöriyel, n tane ayrık
+elemanın kaç farklı şekilde sıralanabileceğidir.
+
+```
+5! = 5 * 4 * 3 * 2 * 1 = 120
+```
+
+| n | n! |
+| --- | ----------------: |
+| 0 | 1 |
+| 1 | 1 |
+| 2 | 2 |
+| 3 | 6 |
+| 4 | 24 |
+| 5 | 120 |
+| 6 | 720 |
+| 7 | 5 040 |
+| 8 | 40 320 |
+| 9 | 362 880 |
+| 10 | 3 628 800 |
+| 11 | 39 916 800 |
+| 12 | 479 001 600 |
+| 13 | 6 227 020 800 |
+| 14 | 87 178 291 200 |
+| 15 | 1 307 674 368 000 |
+
+## Referanslar
+
+[Wikipedia](https://en.wikipedia.org/wiki/Factorial)
diff --git a/src/algorithms/math/factorial/README.uk-UA.md b/src/algorithms/math/factorial/README.uk-UA.md
new file mode 100644
index 0000000000..bf75963113
--- /dev/null
+++ b/src/algorithms/math/factorial/README.uk-UA.md
@@ -0,0 +1,33 @@
+# Факторіал
+
+_Прочитайте це іншими мовами:_
+[_English_](README.md), [_简体中文_](README.zh-CN.md), [_Français_](README.fr-FR.md), [_Türkçe_](README.tr-TR.md), [_ქართული_](README.ka-GE.md).
+
+У математиці факторіал невід'ємного цілого числа `n`, позначений `n!`, є добутком усіх натуральних чисел, менших або рівних `n`. Наприклад:
+
+```
+5! = 5 * 4 * 3 * 2 * 1 = 120
+```
+
+| n | n! |
+| --- | ----------------: |
+| 0 | 1 |
+| 1 | 1 |
+| 2 | 2 |
+| 3 | 6 |
+| 4 | 24 |
+| 5 | 120 |
+| 6 | 720 |
+| 7 | 5 040 |
+| 8 | 40 320 |
+| 9 | 362 880 |
+| 10 | 3 628 800 |
+| 11 | 39 916 800 |
+| 12 | 479 001 600 |
+| 13 | 6 227 020 800 |
+| 14 | 87 178 291 200 |
+| 15 | 1 307 674 368 000 |
+
+## Посилання
+
+[Wikipedia](https://uk.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D1%96%D0%B0%D0%BB)
diff --git a/src/algorithms/math/fibonacci/README.fr-FR.md b/src/algorithms/math/fibonacci/README.fr-FR.md
index 1321ca24d7..81e3549b0d 100644
--- a/src/algorithms/math/fibonacci/README.fr-FR.md
+++ b/src/algorithms/math/fibonacci/README.fr-FR.md
@@ -1,7 +1,8 @@
# Nombre de Fibonacci
_Read this in other languages:_
-[english](README.md).
+[english](README.md),
+[ქართული](README.ka-GE.md).
En mathématiques, la suite de Fibonacci est une suite d'entiers
dans laquelle chaque terme (après les deux premiers)
diff --git a/src/algorithms/math/fibonacci/README.ka-GE.md b/src/algorithms/math/fibonacci/README.ka-GE.md
new file mode 100644
index 0000000000..ae7e11218b
--- /dev/null
+++ b/src/algorithms/math/fibonacci/README.ka-GE.md
@@ -0,0 +1,20 @@
+# ფიბონაჩის რიცხვი
+
+მათემატიკაში ფიბონაჩის მიმდევრობა წარმოადგენს მთელ რიცხვთა მიმდევრობას,
+რომელშიც ყოველი რიცხვი (პირველი ორი რიცხვის შემდეგ)
+მისი წინამორბედი ორი რიცხვის
+ჯამის ტოლია:
+
+`0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...`
+
+კვადრატების წყობა, სადაც ყოველი კვადრატის გვერდების სიგრძე, თანმიმდევრობით, ფიბონაჩის რიცხვებს შეესაბამება
+
+
+
+ფიბონაჩის სპირალი: ოქროს სპირალის აპროქსიმაცია, რომელიც შექმნილია კვადრატების მოპირდაპირე კუთხეებს შორის შემაერთებელი რკალების გავლებით;[4] ამ შემთხვევაში, გამოყენებულ კვადრატთა [გვერდების] ზომებია: 1, 1, 2, 3, 5, 8, 13 და 21.
+
+
+
+## სქოლიო
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_number)
diff --git a/src/algorithms/math/fibonacci/README.md b/src/algorithms/math/fibonacci/README.md
index 9a36887f71..3d476c5020 100644
--- a/src/algorithms/math/fibonacci/README.md
+++ b/src/algorithms/math/fibonacci/README.md
@@ -2,7 +2,8 @@
_Read this in other languages:_
[français](README.fr-FR.md),
-[简体中文](README.zh-CN.md).
+[简体中文](README.zh-CN.md),
+[ქართული](README.ka-GE.md).
In mathematics, the Fibonacci numbers are the numbers in the following
integer sequence, called the Fibonacci sequence, and characterized by
diff --git a/src/algorithms/math/fibonacci/README.zh-CN.md b/src/algorithms/math/fibonacci/README.zh-CN.md
index 70f74b533c..20378000d4 100644
--- a/src/algorithms/math/fibonacci/README.zh-CN.md
+++ b/src/algorithms/math/fibonacci/README.zh-CN.md
@@ -2,7 +2,8 @@
_Read this in other languages:_
[français](README.fr-FR.md),
-[english](README.md).
+[english](README.md),
+[ქართული](README.ka-GE.md).
在数学中，斐波那契数是以下整数序列（称为斐波那契数列）中的数字，其特征在于前两个数字之后的每个数字都是前两个数字的和：
diff --git a/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js b/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js
index 573f25c648..4a098eba70 100644
--- a/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js
+++ b/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js
@@ -19,7 +19,5 @@ describe('fibonacciNth', () => {
expect(fibonacciNth(73)).toBe(806515533049393);
expect(fibonacciNth(74)).toBe(1304969544928657);
expect(fibonacciNth(75)).toBe(2111485077978050);
- expect(fibonacciNth(80)).toBe(23416728348467685);
- expect(fibonacciNth(90)).toBe(2880067194370816120);
});
});
diff --git a/src/algorithms/ml/k-means/README.md b/src/algorithms/ml/k-means/README.md
index aebd60e100..fb58c1bfa4 100644
--- a/src/algorithms/ml/k-means/README.md
+++ b/src/algorithms/ml/k-means/README.md
@@ -1,5 +1,8 @@
# k-Means Algorithm
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
The **k-Means algorithm** is an unsupervised Machine Learning algorithm. It's a clustering algorithm, which groups the sample data on the basis of similarity between dimensions of vectors.
In k-Means classification, the output is a set of classes assigned to each vector. Each cluster location is continuously optimized in order to get the accurate locations of each cluster such that they represent each group clearly.
@@ -27,6 +30,11 @@ _Image source: [Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)_
The centroids are moving continuously in order to create better distinction between the different set of data points. As we can see, after a few iterations, the difference in centroids is quite low between iterations. For example between iterations `13` and `14` the difference is quite small because there the optimizer is tuning boundary cases.
+## Code Examples
+
+- [kMeans.js](./kMeans.js)
+- [kMeans.test.js](./__test__/kMeans.test.js) (test cases)
+
## References
- [k-Means neighbors algorithm on Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)
diff --git a/src/algorithms/ml/k-means/README.pt-BR.md b/src/algorithms/ml/k-means/README.pt-BR.md
new file mode 100644
index 0000000000..d814ac19bc
--- /dev/null
+++ b/src/algorithms/ml/k-means/README.pt-BR.md
@@ -0,0 +1,35 @@
+# Algoritmo k-Means
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+O **algoritmo k-Means** é um algoritmo de aprendizado de máquina não supervisionado. É um algoritmo de agrupamento, que agrupa os dados da amostra com base na semelhança entre as dimensões dos vetores.
+
+Na classificação k-Means, a saída é um conjunto de classes atribuídas a cada vetor. Cada localização de cluster é continuamente otimizada para obter as localizações precisas de cada cluster de forma que representem cada grupo claramente.
+
+A ideia é calcular a similaridade entre a localização do cluster e os vetores de dados e reatribuir os clusters com base nela. [Distância Euclidiana](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-distance) é usado principalmente para esta tarefa.
+
+
+
+_Fonte: [Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)_
+
+O algoritmo é o seguinte:
+
+1. Verifique se há erros como dados inválidos/inconsistentes
+2. Inicialize os locais do cluster `k` com pontos `k` iniciais/aleatórios
+3. Calcule a distância de cada ponto de dados de cada cluster
+4. Atribua o rótulo do cluster de cada ponto de dados igual ao do cluster em sua distância mínima
+5. Calcule o centroide de cada cluster com base nos pontos de dados que ele contém
+6. Repita cada uma das etapas acima até que as localizações do centroide estejam variando
+
+Aqui está uma visualização do agrupamento k-Means para melhor compreensão:
+
+
+
+_Fonte: [Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)_
+
+Os centroides estão se movendo continuamente para criar uma melhor distinção entre os diferentes conjuntos de pontos de dados. Como podemos ver, após algumas iterações, a diferença de centroides é bastante baixa entre as iterações. Por exemplo, entre as iterações `13` e `14` a diferença é bem pequena porque o otimizador está ajustando os casos limite.
+
+## Referências
+
+- [k-Means neighbors algorithm on Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)
diff --git a/src/algorithms/ml/knn/README.md b/src/algorithms/ml/knn/README.md
index 0d61c14fb7..1fc168eaf2 100644
--- a/src/algorithms/ml/knn/README.md
+++ b/src/algorithms/ml/knn/README.md
@@ -1,5 +1,8 @@
# k-Nearest Neighbors Algorithm
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
The **k-nearest neighbors algorithm (k-NN)** is a supervised Machine Learning algorithm. It's a classification algorithm, determining the class of a sample vector using a sample data.
In k-NN classification, the output is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its `k` nearest neighbors (`k` is a positive integer, typically small). If `k = 1`, then the object is simply assigned to the class of that single nearest neighbor.
diff --git a/src/algorithms/ml/knn/README.pt-BR.md b/src/algorithms/ml/knn/README.pt-BR.md
new file mode 100644
index 0000000000..b2abdd784f
--- /dev/null
+++ b/src/algorithms/ml/knn/README.pt-BR.md
@@ -0,0 +1,44 @@
+# Algoritmo de k-vizinhos mais próximos
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+O **algoritmo de k-vizinhos mais próximos (k-NN)** é um algoritmo de aprendizado de máquina supervisionado. É um algoritmo de classificação, determinando a classe de um vetor de amostra usando dados de amostra.
+
+Na classificação k-NN, a saída é uma associação de classe. Um objeto é classificado por uma pluralidade de votos de seus vizinhos, com o objeto sendo atribuído à classe mais comum entre seus `k` vizinhos mais próximos (`k` é um inteiro positivo, tipicamente pequeno). Se `k = 1`, então o objeto é simplesmente atribuído à classe daquele único vizinho mais próximo.
+
+The idea is to calculate the similarity between two data points on the basis of a distance metric. [Distância Euclidiana](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-distance) é usado principalmente para esta tarefa.
+
+
+
+_Fonte: [Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)_
+
+O algoritmo é o seguinte:
+
+1. Verifique se há erros como dados/rótulos inválidos.
+2. Calcule a distância euclidiana de todos os pontos de dados nos dados de treinamento com o ponto de classificação
+3. Classifique as distâncias dos pontos junto com suas classes em ordem crescente
+4. Pegue as classes iniciais `K` e encontre o modo para obter a classe mais semelhante
+5. Informe a classe mais semelhante
+
+Aqui está uma visualização da classificação k-NN para melhor compreensão:
+
+
+
+_Fonte: [Wikipedia](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)_
+
+A amostra de teste (ponto verde) deve ser classificada em quadrados azuis ou em triângulos vermelhos. Se `k = 3` (círculo de linha sólida) é atribuído aos triângulos vermelhos porque existem `2` triângulos e apenas `1` quadrado dentro do círculo interno. Se `k = 5` (círculo de linha tracejada) é atribuído aos quadrados azuis (`3` quadrados vs. `2` triângulos dentro do círculo externo).
+
+Outro exemplo de classificação k-NN:
+
+
+
+_Fonte: [GeeksForGeeks](https://media.geeksforgeeks.org/wp-content/uploads/graph2-2.png)_
+
+Aqui, como podemos ver, a classificação dos pontos desconhecidos será julgada pela proximidade com outros pontos.
+
+É importante notar que `K` é preferível ter valores ímpares para desempate. Normalmente `K` é tomado como `3` ou `5`.
+
+## Referências
+
+- [k-nearest neighbors algorithm on Wikipedia](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)
diff --git a/src/algorithms/search/binary-search/README.es-ES.md b/src/algorithms/search/binary-search/README.es-ES.md
new file mode 100644
index 0000000000..f14aef985f
--- /dev/null
+++ b/src/algorithms/search/binary-search/README.es-ES.md
@@ -0,0 +1,27 @@
+# Búsqueda binaria
+
+_Lea esto en otros idiomas:_
+[English](README.md)
+[Português brasileiro](README.pt-BR.md).
+
+En informática, la búsqueda binaria, también conocida como búsqueda de medio intervalo
+búsqueda, búsqueda logarítmica, o corte binario, es un algoritmo de búsqueda
+que encuentra la posición de un valor objetivo dentro de una matriz
+ordenada. La búsqueda binaria compara el valor objetivo con el elemento central
+de la matriz; si son desiguales, se elimina la mitad en la que
+la mitad en la que no puede estar el objetivo se elimina y la búsqueda continúa
+en la mitad restante hasta que tenga éxito. Si la búsqueda
+termina con la mitad restante vacía, el objetivo no está
+en la matriz.
+
+
+
+## Complejidad
+
+**Complejidad de tiempo**: `O(log(n))` - ya que dividimos el área de búsqueda en dos para cada
+siguiente iteración.
+
+## Referencias
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_algorithm)
+- [YouTube](https://www.youtube.com/watch?v=P3YID7liBug&index=29&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/search/binary-search/README.md b/src/algorithms/search/binary-search/README.md
index 2259b94406..34d1bd7a40 100644
--- a/src/algorithms/search/binary-search/README.md
+++ b/src/algorithms/search/binary-search/README.md
@@ -1,13 +1,17 @@
# Binary Search
-In computer science, binary search, also known as half-interval
-search, logarithmic search, or binary chop, is a search algorithm
-that finds the position of a target value within a sorted
-array. Binary search compares the target value to the middle
-element of the array; if they are unequal, the half in which
-the target cannot lie is eliminated and the search continues
-on the remaining half until it is successful. If the search
-ends with the remaining half being empty, the target is not
+_Read this in other languages:_
+[Português brasileiro](README.pt-BR.md).
+[Español](README.es-ES.md).
+
+In computer science, binary search, also known as half-interval
+search, logarithmic search, or binary chop, is a search algorithm
+that finds the position of a target value within a sorted
+array. Binary search compares the target value to the middle
+element of the array; if they are unequal, the half in which
+the target cannot lie is eliminated and the search continues
+on the remaining half until it is successful. If the search
+ends with the remaining half being empty, the target is not
in the array.
diff --git a/src/algorithms/search/binary-search/README.pt-BR.md b/src/algorithms/search/binary-search/README.pt-BR.md
new file mode 100644
index 0000000000..4f9de9f199
--- /dev/null
+++ b/src/algorithms/search/binary-search/README.pt-BR.md
@@ -0,0 +1,23 @@
+# Busca Binária
+
+_Leia isso em outras línguas:_
+[english](README.md).
+[Español](README.es-ES.md).
+
+Em ciência da computação, busca binária, também conhecida como busca de meio-intervalo, busca logarítmica ou corte binário, é um algoritmo de pesquisa
+que encontra a posição de um elemento alvo dentro de um
+vetor ordenado. O algoritmo compara o elemento alvo com o elemento central do vetor; se eles são diferentes, a metade em que
+o elemento alvo não pode estar é eliminada e a busca continua
+na metade remanescente até que o elemento alvo seja encontrado. Se a busca
+terminar com a metade remanescente vazia, o elemento alvo não está presente no vetor.
+
+
+
+## Complexidade
+
+**Complexidade de Tempo**: `O(log(n))` - pois a área de busca é dividida por dois a cada iteração.
+
+## Referências
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_algorithm)
+- [YouTube](https://www.youtube.com/watch?v=P3YID7liBug&index=29&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/search/binary-search/binarySearch.js b/src/algorithms/search/binary-search/binarySearch.js
index b9e18aab7b..5c8d48fbea 100644
--- a/src/algorithms/search/binary-search/binarySearch.js
+++ b/src/algorithms/search/binary-search/binarySearch.js
@@ -11,7 +11,7 @@ import Comparator from '../../../utils/comparator/Comparator';
export default function binarySearch(sortedArray, seekElement, comparatorCallback) {
// Let's create comparator from the comparatorCallback function.
- // Comparator object will give us common comparison methods like equal() and lessThen().
+ // Comparator object will give us common comparison methods like equal() and lessThan().
const comparator = new Comparator(comparatorCallback);
// These two indices will contain current array (sub-array) boundaries.
diff --git a/src/algorithms/search/linear-search/README.md b/src/algorithms/search/linear-search/README.md
index 942058785f..8feb422eb2 100644
--- a/src/algorithms/search/linear-search/README.md
+++ b/src/algorithms/search/linear-search/README.md
@@ -1,4 +1,8 @@
# Linear Search
+
+_Read this in other languages:_
+[Português brasileiro](README.pt-BR.md).
+
In computer science, linear search or sequential search is a
method for finding a target value within a list. It sequentially
checks each element of the list for the target value until a
diff --git a/src/algorithms/search/linear-search/README.pt-BR.md b/src/algorithms/search/linear-search/README.pt-BR.md
new file mode 100644
index 0000000000..e0af42f4ea
--- /dev/null
+++ b/src/algorithms/search/linear-search/README.pt-BR.md
@@ -0,0 +1,19 @@
+# Busca Linear
+
+_Leia isso em outras línguas:_
+[english](README.md).
+
+Na Ciência da Computação, busca linear ou busca sequencial é um método para encontrar um elemento alvo em uma lista.
+O algoritmo verifica sequencialmente cada elemento da lista procurando o elemento alvo até ele ser encontrado ou até ter verificado todos os elementos.
+A Busca linear realiza no máximo `n` comparações, onde `n` é o tamanho da lista.
+
+
+
+## Complexidade
+
+**Complexidade de Tempo**: `O(n)` - pois no pior caso devemos verificar cada elemento exatamente uma vez.
+
+## Referências
+- [Wikipedia](https://en.wikipedia.org/wiki/Linear_search)
+- [TutorialsPoint](https://www.tutorialspoint.com/data_structures_algorithms/linear_search_algorithm.htm)
+- [Youtube](https://www.youtube.com/watch?v=SGU9duLE30w)
diff --git a/src/algorithms/sets/combinations/README.md b/src/algorithms/sets/combinations/README.md
index 30243b8614..69fc0603f9 100644
--- a/src/algorithms/sets/combinations/README.md
+++ b/src/algorithms/sets/combinations/README.md
@@ -5,14 +5,14 @@ When the order doesn't matter, it is a **Combination**.
When the order **does** matter it is a **Permutation**.
**"My fruit salad is a combination of apples, grapes and bananas"**
-We don't care what order the fruits are in, they could also be
-"bananas, grapes and apples" or "grapes, apples and bananas",
+We don't care what order the fruits are in, they could also be
+"bananas, grapes and apples" or "grapes, apples and bananas",
its the same fruit salad.
## Combinations without repetitions
-This is how lotteries work. The numbers are drawn one at a
-time, and if we have the lucky numbers (no matter what order)
+This is how lotteries work. The numbers are drawn one at a
+time, and if we have the lucky numbers (no matter what order)
we win!
No Repetition: such as lottery numbers `(2,14,15,27,30,33)`
@@ -30,12 +30,12 @@ It is often called "n choose r" (such as "16 choose 3"). And is also known as th
Repetition is Allowed: such as coins in your pocket `(5,5,5,10,10)`
-Or let us say there are five flavours of ice cream:
+Or let us say there are five flavours of ice cream:
`banana`, `chocolate`, `lemon`, `strawberry` and `vanilla`.
We can have three scoops. How many variations will there be?
-Let's use letters for the flavours: `{b, c, l, s, v}`.
+Let's use letters for the flavours: `{b, c, l, s, v}`.
Example selections include:
- `{c, c, c}` (3 scoops of chocolate)
@@ -46,23 +46,21 @@ Example selections include:
-Where `n` is the number of things to choose from, and we
-choose `r` of them. Repetition allowed,
+Where `n` is the number of things to choose from, and we
+choose `r` of them. Repetition allowed,
order doesn't matter.
-## Cheat Sheets
+## Cheatsheet
-Permutations cheat sheet
+
-
+
-Combinations cheat sheet
+| | |
+| --- | --- |
+| |  |
-
-
-Permutations/combinations algorithm ideas.
-
-
+*Made with [okso.app](https://okso.app)*
## References
diff --git a/src/algorithms/sets/combinations/images/combinations-overview.jpg b/src/algorithms/sets/combinations/images/combinations-overview.jpg
new file mode 100644
index 0000000000..9f54477492
Binary files /dev/null and b/src/algorithms/sets/combinations/images/combinations-overview.jpg differ
diff --git a/src/algorithms/sets/combinations/images/combinations-with-repetitions.jpg b/src/algorithms/sets/combinations/images/combinations-with-repetitions.jpg
new file mode 100644
index 0000000000..6a80a91cd1
Binary files /dev/null and b/src/algorithms/sets/combinations/images/combinations-with-repetitions.jpg differ
diff --git a/src/algorithms/sets/combinations/images/combinations-without-repetitions.jpg b/src/algorithms/sets/combinations/images/combinations-without-repetitions.jpg
new file mode 100644
index 0000000000..9262f99c86
Binary files /dev/null and b/src/algorithms/sets/combinations/images/combinations-without-repetitions.jpg differ
diff --git a/src/algorithms/sets/combinations/images/overview.png b/src/algorithms/sets/combinations/images/overview.png
new file mode 100644
index 0000000000..fa8d6a66f5
Binary files /dev/null and b/src/algorithms/sets/combinations/images/overview.png differ
diff --git a/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequenceRecursive.test.js b/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequenceRecursive.test.js
new file mode 100644
index 0000000000..3d5c9d802a
--- /dev/null
+++ b/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequenceRecursive.test.js
@@ -0,0 +1,17 @@
+import longestCommonSubsequence from '../longestCommonSubsequenceRecursive';
+
+describe('longestCommonSubsequenceRecursive', () => {
+ it('should find longest common substring between two strings', () => {
+ expect(longestCommonSubsequence('', '')).toBe('');
+ expect(longestCommonSubsequence('ABC', '')).toBe('');
+ expect(longestCommonSubsequence('', 'ABC')).toBe('');
+ expect(longestCommonSubsequence('ABABC', 'BABCA')).toBe('BABC');
+ expect(longestCommonSubsequence('BABCA', 'ABCBA')).toBe('ABCA');
+ expect(longestCommonSubsequence('sea', 'eat')).toBe('ea');
+ expect(longestCommonSubsequence('algorithms', 'rithm')).toBe('rithm');
+ expect(longestCommonSubsequence(
+ 'Algorithms and data structures implemented in JavaScript',
+ 'Here you may find Algorithms and data structures that are implemented in JavaScript',
+ )).toBe('Algorithms and data structures implemented in JavaScript');
+ });
+});
diff --git a/src/algorithms/sets/longest-common-subsequence/longestCommonSubsequenceRecursive.js b/src/algorithms/sets/longest-common-subsequence/longestCommonSubsequenceRecursive.js
new file mode 100644
index 0000000000..580ba8c72f
--- /dev/null
+++ b/src/algorithms/sets/longest-common-subsequence/longestCommonSubsequenceRecursive.js
@@ -0,0 +1,36 @@
+/* eslint-disable no-param-reassign */
+/**
+ * Longest Common Subsequence (LCS) (Recursive Approach).
+ *
+ * @param {string} string1
+ * @param {string} string2
+ * @return {number}
+ */
+export default function longestCommonSubsequenceRecursive(string1, string2) {
+ /**
+ *
+ * @param {string} s1
+ * @param {string} s2
+ * @return {string} - returns the LCS (Longest Common Subsequence)
+ */
+ const lcs = (s1, s2, memo = {}) => {
+ if (!s1 || !s2) return '';
+
+ if (memo[`${s1}:${s2}`]) return memo[`${s1}:${s2}`];
+
+ if (s1[0] === s2[0]) {
+ return s1[0] + lcs(s1.substring(1), s2.substring(1), memo);
+ }
+
+ const nextLcs1 = lcs(s1.substring(1), s2, memo);
+ const nextLcs2 = lcs(s1, s2.substring(1), memo);
+
+ const nextLongest = nextLcs1.length >= nextLcs2.length ? nextLcs1 : nextLcs2;
+
+ memo[`${s1}:${s2}`] = nextLongest;
+
+ return nextLongest;
+ };
+
+ return lcs(string1, string2);
+}
diff --git a/src/algorithms/sets/maximum-subarray/README.md b/src/algorithms/sets/maximum-subarray/README.md
index c152f54edc..f06300f500 100644
--- a/src/algorithms/sets/maximum-subarray/README.md
+++ b/src/algorithms/sets/maximum-subarray/README.md
@@ -1,7 +1,7 @@
# Maximum subarray problem
-The maximum subarray problem is the task of finding the contiguous
-subarray within a one-dimensional array, `a[1...n]`, of numbers
+The maximum subarray problem is the task of finding the contiguous
+subarray within a one-dimensional array, `a[1...n]`, of numbers
which has the largest sum, where,
@@ -10,13 +10,20 @@ which has the largest sum, where,
## Example
-The list usually contains both positive and negative numbers along
-with `0`. For example, for the array of
-values `−2, 1, −3, 4, −1, 2, 1, −5, 4` the contiguous subarray
+The list usually contains both positive and negative numbers along
+with `0`. For example, for the array of
+values `−2, 1, −3, 4, −1, 2, 1, −5, 4` the contiguous subarray
with the largest sum is `4, −1, 2, 1`, with sum `6`.
+## Solutions
+
+- Brute Force solution `O(n^2)`: [bfMaximumSubarray.js](./bfMaximumSubarray.js)
+- Divide and Conquer solution `O(n^2)`: [dcMaximumSubarraySum.js](./dcMaximumSubarraySum.js)
+- Dynamic Programming solution `O(n)`: [dpMaximumSubarray.js](./dpMaximumSubarray.js)
+
## References
- [Wikipedia](https://en.wikipedia.org/wiki/Maximum_subarray_problem)
- [YouTube](https://www.youtube.com/watch?v=ohHWQf1HDfU&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
- [GeeksForGeeks](https://www.geeksforgeeks.org/largest-sum-contiguous-subarray/)
+- [LeetCode](https://leetcode.com/explore/interview/card/top-interview-questions-easy/97/dynamic-programming/566/discuss/1595195/C++Python-7-Simple-Solutions-w-Explanation-or-Brute-Force-+-DP-+-Kadane-+-Divide-and-Conquer)
diff --git a/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js b/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js
index e0faf0cbfe..6bff427110 100644
--- a/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js
+++ b/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js
@@ -1,7 +1,7 @@
import bfMaximumSubarray from '../bfMaximumSubarray';
describe('bfMaximumSubarray', () => {
- it('should find maximum subarray using brute force algorithm', () => {
+ it('should find maximum subarray using the brute force algorithm', () => {
expect(bfMaximumSubarray([])).toEqual([]);
expect(bfMaximumSubarray([0, 0])).toEqual([0]);
expect(bfMaximumSubarray([0, 0, 1])).toEqual([0, 0, 1]);
diff --git a/src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js b/src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js
new file mode 100644
index 0000000000..3b3ace08d3
--- /dev/null
+++ b/src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js
@@ -0,0 +1,16 @@
+import dcMaximumSubarray from '../dcMaximumSubarraySum';
+
+describe('dcMaximumSubarraySum', () => {
+ it('should find maximum subarray sum using the divide and conquer algorithm', () => {
+ expect(dcMaximumSubarray([])).toEqual(-Infinity);
+ expect(dcMaximumSubarray([0, 0])).toEqual(0);
+ expect(dcMaximumSubarray([0, 0, 1])).toEqual(1);
+ expect(dcMaximumSubarray([0, 0, 1, 2])).toEqual(3);
+ expect(dcMaximumSubarray([0, 0, -1, 2])).toEqual(2);
+ expect(dcMaximumSubarray([-1, -2, -3, -4, -5])).toEqual(-1);
+ expect(dcMaximumSubarray([1, 2, 3, 2, 3, 4, 5])).toEqual(20);
+ expect(dcMaximumSubarray([-2, 1, -3, 4, -1, 2, 1, -5, 4])).toEqual(6);
+ expect(dcMaximumSubarray([-2, -3, 4, -1, -2, 1, 5, -3])).toEqual(7);
+ expect(dcMaximumSubarray([1, -3, 2, -5, 7, 6, -1, 4, 11, -23])).toEqual(27);
+ });
+});
diff --git a/src/algorithms/sets/maximum-subarray/__test__/dpMaximumSubarray.test.js b/src/algorithms/sets/maximum-subarray/__test__/dpMaximumSubarray.test.js
index d8cf39d8e6..c00727cc66 100644
--- a/src/algorithms/sets/maximum-subarray/__test__/dpMaximumSubarray.test.js
+++ b/src/algorithms/sets/maximum-subarray/__test__/dpMaximumSubarray.test.js
@@ -1,7 +1,7 @@
import dpMaximumSubarray from '../dpMaximumSubarray';
describe('dpMaximumSubarray', () => {
- it('should find maximum subarray using dynamic programming algorithm', () => {
+ it('should find maximum subarray using the dynamic programming algorithm', () => {
expect(dpMaximumSubarray([])).toEqual([]);
expect(dpMaximumSubarray([0, 0])).toEqual([0]);
expect(dpMaximumSubarray([0, 0, 1])).toEqual([0, 0, 1]);
diff --git a/src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js b/src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js
new file mode 100644
index 0000000000..3ed9ab3ee7
--- /dev/null
+++ b/src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js
@@ -0,0 +1,33 @@
+/**
+ * Divide and Conquer solution.
+ * Complexity: O(n^2) in case if no memoization applied
+ *
+ * @param {Number[]} inputArray
+ * @return {Number[]}
+ */
+export default function dcMaximumSubarraySum(inputArray) {
+ /**
+ * We are going through the inputArray array and for each element we have two options:
+ * - to pick
+ * - not to pick
+ *
+ * Also keep in mind, that the maximum sub-array must be contiguous. It means if we picked
+ * the element, we need to continue picking the next elements or stop counting the max sum.
+ *
+ * @param {number} elementIndex - the index of the element we're deciding to pick or not
+ * @param {boolean} mustPick - to pick or not to pick the element
+ * @returns {number} - maximum subarray sum that we'll get
+ */
+ function solveRecursively(elementIndex, mustPick) {
+ if (elementIndex >= inputArray.length) {
+ return mustPick ? 0 : -Infinity;
+ }
+ return Math.max(
+ // Option #1: Pick the current element, and continue picking next one.
+ inputArray[elementIndex] + solveRecursively(elementIndex + 1, true),
+ // Option #2: Don't pick the current element.
+ mustPick ? 0 : solveRecursively(elementIndex + 1, false),
+ );
+ }
+ return solveRecursively(0, false);
+}
diff --git a/src/algorithms/sets/permutations/README.md b/src/algorithms/sets/permutations/README.md
index 8864af7240..4b6a268adc 100644
--- a/src/algorithms/sets/permutations/README.md
+++ b/src/algorithms/sets/permutations/README.md
@@ -4,13 +4,13 @@ When the order doesn't matter, it is a **Combination**.
When the order **does** matter it is a **Permutation**.
-**"The combination to the safe is 472"**. We do care about the order. `724` won't work, nor will `247`.
+**"The combination to the safe is 472"**. We do care about the order. `724` won't work, nor will `247`.
It has to be exactly `4-7-2`.
## Permutations without repetitions
-A permutation, also called an “arrangement number” or “order”, is a rearrangement of
-the elements of an ordered list `S` into a one-to-one correspondence with `S` itself.
+A permutation, also called an “arrangement number” or “order”, is a rearrangement of
+the elements of an ordered list `S` into a one-to-one correspondence with `S` itself.
Below are the permutations of string `ABC`.
@@ -37,19 +37,17 @@ For example the the lock below: it could be `333`.
n * n * n ... (r times) = n^r
```
-## Cheat Sheets
+## Cheatsheet
-Permutations cheat sheet
+
-
+
-Combinations cheat sheet
+| | |
+| --- | --- |
+| |  |
-
-
-Permutations/combinations algorithm ideas.
-
-
+*Made with [okso.app](https://okso.app)*
## References
diff --git a/src/algorithms/sets/permutations/images/overview.png b/src/algorithms/sets/permutations/images/overview.png
new file mode 100644
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diff --git a/src/algorithms/sets/permutations/images/permutations-with-repetitions.jpg b/src/algorithms/sets/permutations/images/permutations-with-repetitions.jpg
new file mode 100644
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diff --git a/src/algorithms/sets/permutations/images/permutations-without-repetitions.jpg b/src/algorithms/sets/permutations/images/permutations-without-repetitions.jpg
new file mode 100644
index 0000000000..ca70b4d8c9
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diff --git a/src/algorithms/sets/power-set/README.md b/src/algorithms/sets/power-set/README.md
index cfe791aeb2..e96961dd8f 100644
--- a/src/algorithms/sets/power-set/README.md
+++ b/src/algorithms/sets/power-set/README.md
@@ -1,7 +1,7 @@
# Power Set
Power set of a set `S` is the set of all of the subsets of `S`, including the
-empty set and `S` itself. Power set of set `S` is denoted as `P(S)`.
+empty set and `S` itself. Power set of set `S` is denoted as `P(S)`.
For example for `{x, y, z}`, the subsets
are:
@@ -21,37 +21,37 @@ are:
-Here is how we may illustrate the elements of the power set of the set `{x, y, z}` ordered with respect to
+Here is how we may illustrate the elements of the power set of the set `{x, y, z}` ordered with respect to
inclusion:
**Number of Subsets**
-If `S` is a finite set with `|S| = n` elements, then the number of subsets
-of `S` is `|P(S)| = 2^n`. This fact, which is the motivation for the
+If `S` is a finite set with `|S| = n` elements, then the number of subsets
+of `S` is `|P(S)| = 2^n`. This fact, which is the motivation for the
notation `2^S`, may be demonstrated simply as follows:
-> First, order the elements of `S` in any manner. We write any subset of `S` in
-the format `{γ1, γ2, ..., γn}` where `γi , 1 ≤ i ≤ n`, can take the value
+> First, order the elements of `S` in any manner. We write any subset of `S` in
+the format `{γ1, γ2, ..., γn}` where `γi , 1 ≤ i ≤ n`, can take the value
of `0` or `1`. If `γi = 1`, the `i`-th element of `S` is in the subset;
-otherwise, the `i`-th element is not in the subset. Clearly the number of
+otherwise, the `i`-th element is not in the subset. Clearly the number of
distinct subsets that can be constructed this way is `2^n` as `γi ∈ {0, 1}`.
## Algorithms
### Bitwise Solution
-Each number in binary representation in a range from `0` to `2^n` does exactly
-what we need: it shows by its bits (`0` or `1`) whether to include related
-element from the set or not. For example, for the set `{1, 2, 3}` the binary
+Each number in binary representation in a range from `0` to `2^n` does exactly
+what we need: it shows by its bits (`0` or `1`) whether to include related
+element from the set or not. For example, for the set `{1, 2, 3}` the binary
number of `0b010` would mean that we need to include only `2` to the current set.
| | `abc` | Subset |
| :---: | :---: | :-----------: |
| `0` | `000` | `{}` |
| `1` | `001` | `{c}` |
-| `2` | `010` | `{b}` |
+| `2` | `010` | `{b}` |
| `3` | `011` | `{c, b}` |
| `4` | `100` | `{a}` |
| `5` | `101` | `{a, c}` |
@@ -68,6 +68,44 @@ element.
> See [btPowerSet.js](./btPowerSet.js) file for backtracking solution.
+### Cascading Solution
+
+This is, arguably, the simplest solution to generate a Power Set.
+
+We start with an empty set:
+
+```text
+powerSets = [[]]
+```
+
+Now, let's say:
+
+```text
+originalSet = [1, 2, 3]
+```
+
+Let's add the 1st element from the originalSet to all existing sets:
+
+```text
+[[]] ← 1 = [[], [1]]
+```
+
+Adding the 2nd element to all existing sets:
+
+```text
+[[], [1]] ← 2 = [[], [1], [2], [1, 2]]
+```
+
+Adding the 3nd element to all existing sets:
+
+```
+[[], [1], [2], [1, 2]] ← 3 = [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
+```
+
+And so on, for the rest of the elements from the `originalSet`. On every iteration the number of sets is doubled, so we'll get `2^n` sets.
+
+> See [caPowerSet.js](./caPowerSet.js) file for cascading solution.
+
## References
* [Wikipedia](https://en.wikipedia.org/wiki/Power_set)
diff --git a/src/algorithms/sets/power-set/__test__/caPowerSet.test.js b/src/algorithms/sets/power-set/__test__/caPowerSet.test.js
new file mode 100644
index 0000000000..4fad5efe20
--- /dev/null
+++ b/src/algorithms/sets/power-set/__test__/caPowerSet.test.js
@@ -0,0 +1,28 @@
+import caPowerSet from '../caPowerSet';
+
+describe('caPowerSet', () => {
+ it('should calculate power set of given set using cascading approach', () => {
+ expect(caPowerSet([1])).toEqual([
+ [],
+ [1],
+ ]);
+
+ expect(caPowerSet([1, 2])).toEqual([
+ [],
+ [1],
+ [2],
+ [1, 2],
+ ]);
+
+ expect(caPowerSet([1, 2, 3])).toEqual([
+ [],
+ [1],
+ [2],
+ [1, 2],
+ [3],
+ [1, 3],
+ [2, 3],
+ [1, 2, 3],
+ ]);
+ });
+});
diff --git a/src/algorithms/sets/power-set/caPowerSet.js b/src/algorithms/sets/power-set/caPowerSet.js
new file mode 100644
index 0000000000..45b9eb6169
--- /dev/null
+++ b/src/algorithms/sets/power-set/caPowerSet.js
@@ -0,0 +1,37 @@
+/**
+ * Find power-set of a set using CASCADING approach.
+ *
+ * @param {*[]} originalSet
+ * @return {*[][]}
+ */
+export default function caPowerSet(originalSet) {
+ // Let's start with an empty set.
+ const sets = [[]];
+
+ /*
+ Now, let's say:
+ originalSet = [1, 2, 3].
+
+ Let's add the first element from the originalSet to all existing sets:
+ [[]] ← 1 = [[], [1]]
+
+ Adding the 2nd element to all existing sets:
+ [[], [1]] ← 2 = [[], [1], [2], [1, 2]]
+
+ Adding the 3nd element to all existing sets:
+ [[], [1], [2], [1, 2]] ← 3 = [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
+
+ And so on for the rest of the elements from originalSet.
+ On every iteration the number of sets is doubled, so we'll get 2^n sets.
+ */
+ for (let numIdx = 0; numIdx < originalSet.length; numIdx += 1) {
+ const existingSetsNum = sets.length;
+
+ for (let setIdx = 0; setIdx < existingSetsNum; setIdx += 1) {
+ const set = [...sets[setIdx], originalSet[numIdx]];
+ sets.push(set);
+ }
+ }
+
+ return sets;
+}
diff --git a/src/algorithms/sorting/bubble-sort/README.pt-BR.md b/src/algorithms/sorting/bubble-sort/README.pt-BR.md
index c7862bb957..e650523d71 100644
--- a/src/algorithms/sorting/bubble-sort/README.pt-BR.md
+++ b/src/algorithms/sorting/bubble-sort/README.pt-BR.md
@@ -1,16 +1,19 @@
# Bubble Sort
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
O bubble sort, ou ordenação por flutuação (literalmente "por bolha"), é um algoritmo de ordenação dos mais simples. A ideia é percorrer o vetor diversas vezes, e a cada passagem fazer flutuar para o topo o maior elemento da sequência. Essa movimentação lembra a forma como as bolhas em um tanque de água procuram seu próprio nível, e disso vem o nome do algoritmo.
-## Complexity
+## Complexidade
-| Name | Best | Average | Worst | Memory | Stable | Comments |
+| Nome | Melhor | Média | Pior | Memória | Estável | Comentários |
| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
-| **Bubble sort** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Yes | |
+| **Bubble sort** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Sim | |
-## References
+## Referências
- [Wikipedia](https://pt.wikipedia.org/wiki/Bubble_sort)
- [YouTube](https://www.youtube.com/watch?v=6Gv8vg0kcHc&index=27&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/sorting/bucket-sort/BucketSort.js b/src/algorithms/sorting/bucket-sort/BucketSort.js
new file mode 100644
index 0000000000..a41e5892d2
--- /dev/null
+++ b/src/algorithms/sorting/bucket-sort/BucketSort.js
@@ -0,0 +1,46 @@
+import RadixSort from '../radix-sort/RadixSort';
+
+/**
+ * Bucket Sort
+ *
+ * @param {number[]} arr
+ * @param {number} bucketsNum
+ * @return {number[]}
+ */
+export default function BucketSort(arr, bucketsNum = 1) {
+ const buckets = new Array(bucketsNum).fill(null).map(() => []);
+
+ const minValue = Math.min(...arr);
+ const maxValue = Math.max(...arr);
+
+ const bucketSize = Math.ceil(Math.max(1, (maxValue - minValue) / bucketsNum));
+
+ // Place elements into buckets.
+ for (let i = 0; i < arr.length; i += 1) {
+ const currValue = arr[i];
+ const bucketIndex = Math.floor((currValue - minValue) / bucketSize);
+
+ // Edge case for max value.
+ if (bucketIndex === bucketsNum) {
+ buckets[bucketsNum - 1].push(currValue);
+ } else {
+ buckets[bucketIndex].push(currValue);
+ }
+ }
+
+ // Sort individual buckets.
+ for (let i = 0; i < buckets.length; i += 1) {
+ // Let's use the Radix Sorter here. This may give us
+ // the average O(n + k) time complexity to sort one bucket
+ // (where k is a number of digits in the longest number).
+ buckets[i] = new RadixSort().sort(buckets[i]);
+ }
+
+ // Merge sorted buckets into final output.
+ const sortedArr = [];
+ for (let i = 0; i < buckets.length; i += 1) {
+ sortedArr.push(...buckets[i]);
+ }
+
+ return sortedArr;
+}
diff --git a/src/algorithms/sorting/bucket-sort/README.md b/src/algorithms/sorting/bucket-sort/README.md
new file mode 100644
index 0000000000..673ba80b71
--- /dev/null
+++ b/src/algorithms/sorting/bucket-sort/README.md
@@ -0,0 +1,35 @@
+# Bucket Sort
+
+**Bucket sort**, or **bin sort**, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm.
+
+## Algorithm
+
+Bucket sort works as follows:
+
+1. Set up an array of initially empty `buckets`.
+2. **Scatter:** Go over the original array, putting each object in its `bucket`.
+3. Sort each non-empty `bucket`.
+4. **Gather:** Visit the `buckets` in order and put all elements back into the original array.
+
+Elements are distributed among bins:
+
+
+
+Then, elements are sorted within each bin:
+
+
+
+
+## Complexity
+
+The computational complexity depends on the algorithm used to sort each bucket, the number of buckets to use, and whether the input is uniformly distributed.
+
+The **worst-case** time complexity of bucket sort is
+`O(n^2)` if the sorting algorithm used on the bucket is *insertion sort*, which is the most common use case since the expectation is that buckets will not have too many elements relative to the entire list. In the worst case, all elements are placed in one bucket, causing the running time to reduce to the worst-case complexity of insertion sort (all elements are in reverse order). If the worst-case running time of the intermediate sort used is `O(n * log(n))`, then the worst-case running time of bucket sort will also be
+`O(n * log(n))`.
+
+On **average**, when the distribution of elements across buckets is reasonably uniform, it can be shown that bucket sort runs on average `O(n + k)` for `k` buckets.
+
+## References
+
+- [Bucket Sort on Wikipedia](https://en.wikipedia.org/wiki/Bucket_sort)
diff --git a/src/algorithms/sorting/bucket-sort/__test__/BucketSort.test.js b/src/algorithms/sorting/bucket-sort/__test__/BucketSort.test.js
new file mode 100644
index 0000000000..9cab525d9b
--- /dev/null
+++ b/src/algorithms/sorting/bucket-sort/__test__/BucketSort.test.js
@@ -0,0 +1,33 @@
+import BucketSort from '../BucketSort';
+import {
+ equalArr,
+ notSortedArr,
+ reverseArr,
+ sortedArr,
+} from '../../SortTester';
+
+describe('BucketSort', () => {
+ it('should sort the array of numbers with different buckets amounts', () => {
+ expect(BucketSort(notSortedArr, 4)).toEqual(sortedArr);
+ expect(BucketSort(equalArr, 4)).toEqual(equalArr);
+ expect(BucketSort(reverseArr, 4)).toEqual(sortedArr);
+ expect(BucketSort(sortedArr, 4)).toEqual(sortedArr);
+
+ expect(BucketSort(notSortedArr, 10)).toEqual(sortedArr);
+ expect(BucketSort(equalArr, 10)).toEqual(equalArr);
+ expect(BucketSort(reverseArr, 10)).toEqual(sortedArr);
+ expect(BucketSort(sortedArr, 10)).toEqual(sortedArr);
+
+ expect(BucketSort(notSortedArr, 50)).toEqual(sortedArr);
+ expect(BucketSort(equalArr, 50)).toEqual(equalArr);
+ expect(BucketSort(reverseArr, 50)).toEqual(sortedArr);
+ expect(BucketSort(sortedArr, 50)).toEqual(sortedArr);
+ });
+
+ it('should sort the array of numbers with the default buckets of 1', () => {
+ expect(BucketSort(notSortedArr)).toEqual(sortedArr);
+ expect(BucketSort(equalArr)).toEqual(equalArr);
+ expect(BucketSort(reverseArr)).toEqual(sortedArr);
+ expect(BucketSort(sortedArr)).toEqual(sortedArr);
+ });
+});
diff --git a/src/algorithms/sorting/bucket-sort/images/bucket_sort_1.png b/src/algorithms/sorting/bucket-sort/images/bucket_sort_1.png
new file mode 100644
index 0000000000..da0de9172f
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diff --git a/src/algorithms/sorting/bucket-sort/images/bucket_sort_2.png b/src/algorithms/sorting/bucket-sort/images/bucket_sort_2.png
new file mode 100644
index 0000000000..7b6f32c752
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diff --git a/src/algorithms/sorting/counting-sort/README.md b/src/algorithms/sorting/counting-sort/README.md
index 098961a0e0..40a9539a22 100644
--- a/src/algorithms/sorting/counting-sort/README.md
+++ b/src/algorithms/sorting/counting-sort/README.md
@@ -1,5 +1,8 @@
# Counting Sort
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
In computer science, **counting sort** is an algorithm for sorting
a collection of objects according to keys that are small integers;
that is, it is an integer sorting algorithm. It operates by
diff --git a/src/algorithms/sorting/counting-sort/README.pt-br.md b/src/algorithms/sorting/counting-sort/README.pt-br.md
new file mode 100644
index 0000000000..af2c75f6af
--- /dev/null
+++ b/src/algorithms/sorting/counting-sort/README.pt-br.md
@@ -0,0 +1,70 @@
+# Counting Sort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+Em ciência da computação, **counting sort** é um algoritmo para ordenar
+uma coleção de objetos de acordo com chaves que são pequenos inteiros;
+ou seja, é um algoritmo de ordenação de inteiros. Ele opera por
+contando o número de objetos que têm cada valor de chave distinto,
+e usando aritmética nessas contagens para determinar as posições
+de cada valor de chave na sequência de saída. Seu tempo de execução é
+linear no número de itens e a diferença entre o
+valores de chave máximo e mínimo, portanto, é adequado apenas para
+uso em situações em que a variação de tonalidades não é significativamente
+maior que o número de itens. No entanto, muitas vezes é usado como
+sub-rotina em outro algoritmo de ordenação, radix sort, que pode
+lidar com chaves maiores de forma mais eficiente.
+
+Como a classificação por contagem usa valores-chave como índices em um vetor,
+não é uma ordenação por comparação, e o limite inferior `Ω(n log n)` para
+a ordenação por comparação não se aplica a ele. A classificação por bucket pode ser usada
+para muitas das mesmas tarefas que a ordenação por contagem, com um tempo semelhante
+análise; no entanto, em comparação com a classificação por contagem, a classificação por bucket requer
+listas vinculadas, arrays dinâmicos ou uma grande quantidade de pré-alocados
+memória para armazenar os conjuntos de itens dentro de cada bucket, enquanto
+A classificação por contagem armazena um único número (a contagem de itens)
+por balde.
+
+A classificação por contagem funciona melhor quando o intervalo de números para cada
+elemento do vetor é muito pequeno.
+
+## Algoritmo
+
+**Passo I**
+
+Na primeira etapa, calculamos a contagem de todos os elementos do
+vetor de entrada 'A'. Em seguida, armazene o resultado no vetor de contagem `C`.
+A maneira como contamos é descrita abaixo.
+
+
+
+**Passo II**
+
+Na segunda etapa, calculamos quantos elementos existem na entrada
+do vetor `A` que são menores ou iguais para o índice fornecido.
+`Ci` = números de elementos menores ou iguais a `i` no vetor de entrada.
+
+
+
+**Passo III**
+
+Nesta etapa, colocamos o elemento `A` do vetor de entrada em classificado
+posição usando a ajuda do vetor de contagem construída `C`, ou seja, o que
+construímos no passo dois. Usamos o vetor de resultados `B` para armazenar
+os elementos ordenados. Aqui nós lidamos com o índice de `B` começando de
+zero.
+
+
+
+## Complexidade
+
+| Nome | Melhor | Média | Pior | Memória | Estável | Comentários |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Counting sort** | n + r | n + r | n + r | n + r | Sim | r - Maior número no vetor |
+
+## Referências
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Counting_sort)
+- [YouTube](https://www.youtube.com/watch?v=OKd534EWcdk&index=61&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [EfficientAlgorithms](https://efficientalgorithms.blogspot.com/2016/09/lenear-sorting-counting-sort.html)
diff --git a/src/algorithms/sorting/heap-sort/README.md b/src/algorithms/sorting/heap-sort/README.md
index 6ccc50b3b0..2370776f1b 100644
--- a/src/algorithms/sorting/heap-sort/README.md
+++ b/src/algorithms/sorting/heap-sort/README.md
@@ -1,5 +1,8 @@
# Heap Sort
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
Heapsort is a comparison-based sorting algorithm.
Heapsort can be thought of as an improved selection
sort: like that algorithm, it divides its input into
diff --git a/src/algorithms/sorting/heap-sort/README.pt-BR.md b/src/algorithms/sorting/heap-sort/README.pt-BR.md
new file mode 100644
index 0000000000..6d5a2d4849
--- /dev/null
+++ b/src/algorithms/sorting/heap-sort/README.pt-BR.md
@@ -0,0 +1,20 @@
+# Heap Sort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+Heapsort é um algoritmo de ordenação baseado em comparação. O Heapsort pode ser pensado como uma seleção aprimorada sort: como esse algoritmo, ele divide sua entrada em uma região classificada e uma região não classificada, e iterativamente encolhe a região não classificada extraindo o maior elemento e movendo-o para a região classificada. A melhoria consiste no uso de uma estrutura de dados heap em vez de uma busca em tempo linear para encontrar o máximo.
+
+
+
+
+
+## Complexidade
+
+| Nome | Melhor | Média | Pior | Memória | Estável | Comentários |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | Não | |
+
+## Referências
+
+[Wikipedia](https://en.wikipedia.org/wiki/Heapsort)
diff --git a/src/algorithms/sorting/insertion-sort/README.md b/src/algorithms/sorting/insertion-sort/README.md
index cd3a74ef34..8bc922683f 100644
--- a/src/algorithms/sorting/insertion-sort/README.md
+++ b/src/algorithms/sorting/insertion-sort/README.md
@@ -1,5 +1,8 @@
# Insertion Sort
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
Insertion sort is a simple sorting algorithm that builds
the final sorted array (or list) one item at a time.
It is much less efficient on large lists than more
diff --git a/src/algorithms/sorting/insertion-sort/README.pt-BR.md b/src/algorithms/sorting/insertion-sort/README.pt-BR.md
new file mode 100644
index 0000000000..a36d2742be
--- /dev/null
+++ b/src/algorithms/sorting/insertion-sort/README.pt-BR.md
@@ -0,0 +1,22 @@
+# Insertion Sort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+A ordenação por inserção é um algoritmo de ordenação simples que criaa matriz classificada final (ou lista) um item de cada vez.
+É muito menos eficiente em grandes listas do que mais algoritmos avançados, como quicksort, heapsort ou merge
+ordenar.
+
+
+
+
+
+## Complexidade
+
+| Nome | Melhor | Média | Pior | Memória | Estável | Comentários |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Insertion sort** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Sim | |
+
+## Referências
+
+[Wikipedia](https://en.wikipedia.org/wiki/Insertion_sort)
diff --git a/src/algorithms/sorting/merge-sort/README.ko-KR.md b/src/algorithms/sorting/merge-sort/README.ko-KR.md
new file mode 100644
index 0000000000..5447fd217e
--- /dev/null
+++ b/src/algorithms/sorting/merge-sort/README.ko-KR.md
@@ -0,0 +1,22 @@
+# 병합 정렬
+
+컴퓨터과학에서, 병합 정렬(일반적으로 mergesort라고 쓰는)은 효율적이고, 범용적인, 비교 기반의 정렬 알고리즘입니다. 대부분의 구현들은 안정적인 정렬을 만들어내며, 이는 정렬된 산출물에서 동일한 요소들의 입력 순서가 유지된다는 것을 의미합니다. 병합 정렬은 1945년에 John von Neumann이 만든 분할 정복 알고리즘입니다.
+
+병합 정렬의 예시입니다. 우선 리스트를 가장 작은 단위로 나누고(한 개의 요소), 두 개의 인접한 리스트를 정렬하고 병합하기 위해 각 요소와 인접한 리스트를 비교합니다. 마지막으로 모든 요소들은 정렬되고 병합됩니다.
+
+
+
+재귀적인 병합 정렬 알고리즘은 7개의 정수값을 가진 배열을 정렬하는데 사용됩니다. 다음은 합병 정렬을 모방하기 위해 사람이 취하는 단계입니다.(하향식)
+
+
+
+## 복잡도
+
+| Name | Best | Average | Worst | Memory | Stable | Comments |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Yes | |
+
+## 참조
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Merge_sort)
+- [YouTube](https://www.youtube.com/watch?v=KF2j-9iSf4Q&index=27&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/sorting/merge-sort/README.md b/src/algorithms/sorting/merge-sort/README.md
index f4ed837a22..2931329482 100644
--- a/src/algorithms/sorting/merge-sort/README.md
+++ b/src/algorithms/sorting/merge-sort/README.md
@@ -1,23 +1,27 @@
# Merge Sort
-In computer science, merge sort (also commonly spelled
-mergesort) is an efficient, general-purpose,
-comparison-based sorting algorithm. Most implementations
-produce a stable sort, which means that the implementation
-preserves the input order of equal elements in the sorted
-output. Mergesort is a divide and conquer algorithm that
+_Read this in other languages:_
+[_한국어_](README.ko-KR.md),
+[_Português_](README.pt-BR.md)
+
+In computer science, merge sort (also commonly spelled
+mergesort) is an efficient, general-purpose,
+comparison-based sorting algorithm. Most implementations
+produce a stable sort, which means that the implementation
+preserves the input order of equal elements in the sorted
+output. Mergesort is a divide and conquer algorithm that
was invented by John von Neumann in 1945.
-An example of merge sort. First divide the list into
-the smallest unit (1 element), then compare each
-element with the adjacent list to sort and merge the
-two adjacent lists. Finally all the elements are sorted
+An example of merge sort. First divide the list into
+the smallest unit (1 element), then compare each
+element with the adjacent list to sort and merge the
+two adjacent lists. Finally all the elements are sorted
and merged.
-A recursive merge sort algorithm used to sort an array of 7
-integer values. These are the steps a human would take to
+A recursive merge sort algorithm used to sort an array of 7
+integer values. These are the steps a human would take to
emulate merge sort (top-down).
diff --git a/src/algorithms/sorting/merge-sort/README.pt-BR.md b/src/algorithms/sorting/merge-sort/README.pt-BR.md
new file mode 100644
index 0000000000..f7be449f04
--- /dev/null
+++ b/src/algorithms/sorting/merge-sort/README.pt-BR.md
@@ -0,0 +1,38 @@
+# Merge Sort
+
+_Leia isso em outros idiomas:_
+[_한국어_](README.ko-KR.md),
+[_English_](README.md)
+
+Em ciência da computação, merge sort (também comumente escrito
+mergesort) é uma ferramenta eficiente, de propósito geral,
+algoritmo de ordenação baseado em comparação. A maioria das implementações
+produzir uma classificação estável, o que significa que a implementação
+preserva a ordem de entrada de elementos iguais na ordenação
+resultado. Mergesort é um algoritmo de divisão e conquista que
+foi inventado por John von Neumann em 1945.
+
+Um exemplo de classificação de mesclagem. Primeiro divida a lista em
+a menor unidade (1 elemento), então compare cada
+elemento com a lista adjacente para classificar e mesclar o
+duas listas adjacentes. Finalmente todos os elementos são ordenados
+e mesclado.
+
+
+
+Um algoritmo de classificação de mesclagem recursivo usado para classificar uma matriz de 7
+valores inteiros. Estes são os passos que um ser humano daria para
+emular merge sort (top-down).
+
+
+
+## Complexidade
+
+| Nome | Melhor | Média | Pior | Memória | Estável | Comentários |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Sim | |
+
+## Referências
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Merge_sort)
+- [YouTube](https://www.youtube.com/watch?v=KF2j-9iSf4Q&index=27&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/sorting/quick-sort/QuickSortInPlace.js b/src/algorithms/sorting/quick-sort/QuickSortInPlace.js
index cc1f5e5068..d02298b230 100644
--- a/src/algorithms/sorting/quick-sort/QuickSortInPlace.js
+++ b/src/algorithms/sorting/quick-sort/QuickSortInPlace.js
@@ -4,7 +4,7 @@ export default class QuickSortInPlace extends Sort {
/** Sorting in place avoids unnecessary use of additional memory, but modifies input array.
*
* This process is difficult to describe, but much clearer with a visualization:
- * @see: http://www.algomation.com/algorithm/quick-sort-visualization
+ * @see: https://www.hackerearth.com/practice/algorithms/sorting/quick-sort/visualize/
*
* @param {*[]} originalArray - Not sorted array.
* @param {number} inputLowIndex
diff --git a/src/algorithms/sorting/quick-sort/README.md b/src/algorithms/sorting/quick-sort/README.md
index 88c768aa37..9dcec0f12f 100644
--- a/src/algorithms/sorting/quick-sort/README.md
+++ b/src/algorithms/sorting/quick-sort/README.md
@@ -1,5 +1,9 @@
# Quicksort
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_Português_](README.pt-BR.md)
+
Quicksort is a divide and conquer algorithm.
Quicksort first divides a large array into two smaller
sub-arrays: the low elements and the high elements.
diff --git a/src/algorithms/sorting/quick-sort/README.pt-BR.md b/src/algorithms/sorting/quick-sort/README.pt-BR.md
new file mode 100644
index 0000000000..ca3a45699f
--- /dev/null
+++ b/src/algorithms/sorting/quick-sort/README.pt-BR.md
@@ -0,0 +1,39 @@
+# Quicksort
+
+_Leia isso em outros idiomas:_
+[_简体中文_](README.zh-CN.md),
+[_English_](README.md)
+
+Quicksort é um algoritmo de dividir para conquistar.
+Quicksort primeiro divide uma grande matriz em duas menores
+submatrizes: os elementos baixos e os elementos altos.
+O Quicksort pode então classificar recursivamente as submatrizes.
+
+As etapas são:
+
+1. Escolha um elemento, denominado pivô, na matriz.
+2. Particionamento: reordene a matriz para que todos os elementos com
+valores menores que o pivô estejam antes do pivô, enquanto todos
+elementos com valores maiores do que o pivô vêm depois dele
+(valores iguais podem ser usados em qualquer direção). Após este particionamento,
+o pivô está em sua posição final. Isso é chamado de
+operação de partição.
+3. Aplique recursivamente as etapas acima à submatriz de
+elementos com valores menores e separadamente para o
+submatriz de elementos com valores maiores.
+
+Visualização animada do algoritmo quicksort.
+As linhas horizontais são valores dinâmicos.
+
+
+
+## Complexidade
+
+| Nome | Melhor | Média | Pior | Memória | Estável | Comentários |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Quick sort** | n log(n) | n log(n) | n<sup>2</sup> | log(n) | Não | Quicksort geralmente é feito no local com espaço de pilha O(log(n)) |
+
+## Referências
+
+- [Wikipedia](https://pt.wikipedia.org/wiki/Quicksort)
+- [YouTube](https://www.youtube.com/watch?v=SLauY6PpjW4&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/sorting/quick-sort/README.zh-CN.md b/src/algorithms/sorting/quick-sort/README.zh-CN.md
new file mode 100644
index 0000000000..96b2e44de8
--- /dev/null
+++ b/src/algorithms/sorting/quick-sort/README.zh-CN.md
@@ -0,0 +1,27 @@
+# 快速排序
+
+快速排序是一种分而治之的算法。快速排序首先将一个大数组分成两个较小的子数组：比某个数小的元素和比某个数大的元素。然后快速排序可以递归地对子数组进行排序。
+
+步骤是：
+
+1. 从数组中选择一个元素，称为基点
+
+2. 分区：对数组重新排序，使所有值小于基点的元素都在它左边，而所有值大于基点的元素都在它右边（相等的值可以放在任何一边）。在此分区之后，基点处于其最终位置（左边和右边的中间位置）。这称为分区操作。
+
+3. 递归地将上述步骤应用于左边的数组和右边的数组。
+
+快速排序算法的动画可视化。水平线是基点值。
+
+
+
+## 复杂度
+
+| Name | Best | Average | Worst | Memory | Stable | Comments |
+| -------------- | :-----------: | :-----------: | :-----------: | :----: | :----: | :------------------------------------------------------------ |
+| **Quick sort** | n log(n) | n log(n) | n<sup>2</sup> | log(n) | No | Quicksort is usually done in-place with O(log(n)) stack space |
+
+## 引用
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Quicksort)
+
+- [YouTube](https://www.youtube.com/watch?v=SLauY6PpjW4&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/sorting/radix-sort/README.md b/src/algorithms/sorting/radix-sort/README.md
index 2da1f5504b..108d7d19b6 100644
--- a/src/algorithms/sorting/radix-sort/README.md
+++ b/src/algorithms/sorting/radix-sort/README.md
@@ -1,36 +1,39 @@
# Radix Sort
-In computer science, **radix sort** is a non-comparative integer sorting
-algorithm that sorts data with integer keys by grouping keys by the individual
+_Read this in other languages:_
+[_Português_](README.pt-BR.md),
+
+In computer science, **radix sort** is a non-comparative integer sorting
+algorithm that sorts data with integer keys by grouping keys by the individual
digits which share the same significant position and value. A positional notation
-is required, but because integers can represent strings of characters
-(e.g., names or dates) and specially formatted floating point numbers, radix
+is required, but because integers can represent strings of characters
+(e.g., names or dates) and specially formatted floating point numbers, radix
sort is not limited to integers.
*Where does the name come from?*
In mathematical numeral systems, the *radix* or base is the number of unique digits,
-including the digit zero, used to represent numbers in a positional numeral system.
-For example, a binary system (using numbers 0 and 1) has a radix of 2 and a decimal
+including the digit zero, used to represent numbers in a positional numeral system.
+For example, a binary system (using numbers 0 and 1) has a radix of 2 and a decimal
system (using numbers 0 to 9) has a radix of 10.
## Efficiency
-The topic of the efficiency of radix sort compared to other sorting algorithms is
-somewhat tricky and subject to quite a lot of misunderstandings. Whether radix
-sort is equally efficient, less efficient or more efficient than the best
-comparison-based algorithms depends on the details of the assumptions made.
-Radix sort complexity is `O(wn)` for `n` keys which are integers of word size `w`.
-Sometimes `w` is presented as a constant, which would make radix sort better
-(for sufficiently large `n`) than the best comparison-based sorting algorithms,
-which all perform `O(n log n)` comparisons to sort `n` keys. However, in
-general `w` cannot be considered a constant: if all `n` keys are distinct,
-then `w` has to be at least `log n` for a random-access machine to be able to
-store them in memory, which gives at best a time complexity `O(n log n)`. That
-would seem to make radix sort at most equally efficient as the best
+The topic of the efficiency of radix sort compared to other sorting algorithms is
+somewhat tricky and subject to quite a lot of misunderstandings. Whether radix
+sort is equally efficient, less efficient or more efficient than the best
+comparison-based algorithms depends on the details of the assumptions made.
+Radix sort complexity is `O(wn)` for `n` keys which are integers of word size `w`.
+Sometimes `w` is presented as a constant, which would make radix sort better
+(for sufficiently large `n`) than the best comparison-based sorting algorithms,
+which all perform `O(n log n)` comparisons to sort `n` keys. However, in
+general `w` cannot be considered a constant: if all `n` keys are distinct,
+then `w` has to be at least `log n` for a random-access machine to be able to
+store them in memory, which gives at best a time complexity `O(n log n)`. That
+would seem to make radix sort at most equally efficient as the best
comparison-based sorts (and worse if keys are much longer than `log n`).
-
+
## Complexity
diff --git a/src/algorithms/sorting/radix-sort/README.pt-BR.md b/src/algorithms/sorting/radix-sort/README.pt-BR.md
new file mode 100644
index 0000000000..2274440984
--- /dev/null
+++ b/src/algorithms/sorting/radix-sort/README.pt-BR.md
@@ -0,0 +1,48 @@
+# Radix Sort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+Em ciência da computação, **radix sort** é uma classificação inteira não comparativa
+algoritmo que classifica os dados com chaves inteiras agrupando as chaves pelo indivíduo
+dígitos que compartilham a mesma posição e valor significativos. Uma notação posicional
+é necessário, mas porque os números inteiros podem representar cadeias de caracteres
+(por exemplo, nomes ou datas) e números de ponto flutuante especialmente formatados, base
+sort não está limitado a inteiros.
+
+*De onde vem o nome?*
+
+Em sistemas numéricos matemáticos, a *radix* ou base é o número de dígitos únicos,
+incluindo o dígito zero, usado para representar números em um sistema de numeração posicional.
+Por exemplo, um sistema binário (usando números 0 e 1) tem uma raiz de 2 e um decimal
+sistema (usando números de 0 a 9) tem uma raiz de 10.
+
+## Eficiência
+
+O tópico da eficiência do radix sort comparado a outros algoritmos de ordenação é
+um pouco complicado e sujeito a muitos mal-entendidos. Se raiz
+sort é igualmente eficiente, menos eficiente ou mais eficiente do que o melhor
+algoritmos baseados em comparação depende dos detalhes das suposições feitas.
+A complexidade de classificação de raiz é `O(wn)` para chaves `n` que são inteiros de tamanho de palavra `w`.
+Às vezes, `w` é apresentado como uma constante, o que tornaria a classificação radix melhor
+(para `n` suficientemente grande) do que os melhores algoritmos de ordenação baseados em comparação,
+que todos realizam comparações `O(n log n)` para classificar chaves `n`. No entanto, em
+geral `w` não pode ser considerado uma constante: se todas as chaves `n` forem distintas,
+então `w` tem que ser pelo menos `log n` para que uma máquina de acesso aleatório seja capaz de
+armazená-los na memória, o que dá na melhor das hipóteses uma complexidade de tempo `O(n log n)`. Este
+parece tornar a ordenação radix no máximo tão eficiente quanto a melhor
+ordenações baseadas em comparação (e pior se as chaves forem muito mais longas que `log n`).
+
+
+
+## Complexidade
+
+| Nome | Melhor | Média | Pior | Memória | Estável | Comentários |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Radix sort** | n * k | n * k | n * k | n + k | Sim | k - comprimento da chave mais longa |
+
+## Referências
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Radix_sort)
+- [YouTube](https://www.youtube.com/watch?v=XiuSW_mEn7g&index=62&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [ResearchGate](https://www.researchgate.net/figure/Simplistic-illustration-of-the-steps-performed-in-a-radix-sort-In-this-example-the_fig1_291086231)
diff --git a/src/algorithms/sorting/radix-sort/images/radix-sort.png b/src/algorithms/sorting/radix-sort/images/radix-sort.png
new file mode 100644
index 0000000000..0cf9bf9e4d
Binary files /dev/null and b/src/algorithms/sorting/radix-sort/images/radix-sort.png differ
diff --git a/src/algorithms/sorting/selection-sort/README.md b/src/algorithms/sorting/selection-sort/README.md
index 6a708d2579..005c616131 100644
--- a/src/algorithms/sorting/selection-sort/README.md
+++ b/src/algorithms/sorting/selection-sort/README.md
@@ -1,5 +1,8 @@
# Selection Sort
+_Read this in other languages:_
+[_Português_](README.pt-BR.md).
+
Selection sort is a sorting algorithm, specifically an
in-place comparison sort. It has O(n2) time complexity,
making it inefficient on large lists, and generally
diff --git a/src/algorithms/sorting/selection-sort/README.pt-BR.md b/src/algorithms/sorting/selection-sort/README.pt-BR.md
new file mode 100644
index 0000000000..0c45b73f61
--- /dev/null
+++ b/src/algorithms/sorting/selection-sort/README.pt-BR.md
@@ -0,0 +1,20 @@
+# Selection Sort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md).
+
+Selection Sort é um algoritmo de ordenação, mais especificamente um algoritmo de ordenação por comparação in-place (requer uma quantidade constante de espaço de memória adicional). Tem complexidade O(n²), tornando-o ineficiente em listas grandes e, geralmente, tem desempenho inferior ao similar Insertion Sort. O Selection Sort é conhecido por sua simplicidade e tem vantagens de desempenho sobre algoritmos mais complexos em certas situações, particularmente quando a memória auxiliar é limitada.
+
+
+
+
+
+## Complexidade
+
+| Nome | Melhor | Médio | Pior | Memória | Estável | Comentários |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :----------: |
+| **Selection sort** | n<sup>2</sup> | n<sup>2</sup> | n<sup>2</sup> | 1 | Não | |
+
+## Referências
+
+[Wikipedia](https://en.wikipedia.org/wiki/Selection_sort)
diff --git a/src/algorithms/sorting/shell-sort/README.md b/src/algorithms/sorting/shell-sort/README.md
index 386fc9f066..f93338e2eb 100644
--- a/src/algorithms/sorting/shell-sort/README.md
+++ b/src/algorithms/sorting/shell-sort/README.md
@@ -1,5 +1,8 @@
# Shellsort
+_Read this in other languages:_
+[_Português_](README.pt-BR.md).
+
Shellsort, also known as Shell sort or Shell's method,
is an in-place comparison sort. It can be seen as either a
generalization of sorting by exchange (bubble sort) or sorting
diff --git a/src/algorithms/sorting/shell-sort/README.pt-BR.md b/src/algorithms/sorting/shell-sort/README.pt-BR.md
new file mode 100644
index 0000000000..14de1a517e
--- /dev/null
+++ b/src/algorithms/sorting/shell-sort/README.pt-BR.md
@@ -0,0 +1,60 @@
+# Shellsort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md).
+
+Shellsort, também conhecido como Shell sort ou método de Shell,
+é uma classificação de comparação in-loco. Pode ser visto tanto como um
+generalização da ordenação por troca (bubble sort) ou ordenação
+por inserção (ordenação por inserção). O método começa classificando
+pares de elementos distantes um do outro, então progressivamente
+reduzindo a distância entre os elementos a serem comparados. Iniciando
+com elementos distantes, pode mover alguns fora do lugar
+elementos em posição mais rápido do que um simples vizinho mais próximo
+intercâmbio
+
+
+
+## Como o Shellsort funciona?
+
+Para nosso exemplo e facilidade de compreensão, tomamos o intervalo
+de `4`. Faça uma sub-lista virtual de todos os valores localizados no
+intervalo de 4 posições. Aqui esses valores são
+`{35, 14}`, `{33, 19}`, `{42, 27}` e `{10, 44}`
+
+
+
+Comparamos valores em cada sublista e os trocamos (se necessário)
+na matriz original. Após esta etapa, o novo array deve
+parece com isso
+
+
+
+Então, pegamos o intervalo de 2 e essa lacuna gera duas sub-listas
+- `{14, 27, 35, 42}`, `{19, 10, 33, 44}`
+
+
+
+Comparamos e trocamos os valores, se necessário, no array original.
+Após esta etapa, a matriz deve ficar assim
+
+
+
+> OBS: Na imagem abaixo há um erro de digitação e a matriz de resultados deve ser `[14, 10, 27, 19, 35, 33, 42, 44]`.
+
+Finalmente, ordenamos o resto do array usando o intervalo de valor 1.
+A classificação de shell usa a classificação por inserção para classificar a matriz.
+
+
+
+## Complexidade
+
+| Nome | Melhor | Média | Pior | Memória | Estável | Comentários |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))<sup>2</sup> | 1 | Não | |
+
+## Referências
+
+- [Tutorials Point](https://www.tutorialspoint.com/data_structures_algorithms/shell_sort_algorithm.htm)
+- [Wikipedia](https://en.wikipedia.org/wiki/Shellsort)
+- [YouTube by Rob Edwards](https://www.youtube.com/watch?v=ddeLSDsYVp8&index=79&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/stack/valid-parentheses/README.md b/src/algorithms/stack/valid-parentheses/README.md
new file mode 100644
index 0000000000..31d7fd60f3
--- /dev/null
+++ b/src/algorithms/stack/valid-parentheses/README.md
@@ -0,0 +1,44 @@
+# Valid Parentheses Problem
+
+Given a string s containing just the characters '(', ')', '{', '}', '[' and ']', determine if the input string is valid.
+
+An input string is valid if:
+
+Open brackets must be closed by the same type of brackets.
+Open brackets must be closed in the correct order.
+Every close bracket has a corresponding open bracket of the same type.
+
+
+Example 1:
+
+`Input: s = "()"`
+
+Output: true
+
+Example 2:
+
+`Input: s = "()[]{}"`
+
+Output: true
+
+Example 3:
+
+`Input: s = "(]"`
+
+Output: false
+
+This is actually a very common interview question and a very good example of how to use a stack data structure to solve problems.
+
+## Solution
+The problem can be solved in two ways
+
+### Bruteforce Approach
+We can iterate through the string and then for each character in the string, we check for it's last closing character in the the string. Once we find the last closing character in the string, we remove both characters and then repeat the iteration, if we don't find a closing character for an opening character, then the string is invalid. The time complexity of this would be O(n^2) which is not so efficient.
+
+### Using a Stack
+We can use a hashtable to store all opening characters and the value would be the respective closing character. We can then iterate through the string and if we encounter an opening parantheses, we push it's closing character to the stack. If we ecounter a closing paraentheses, then we pop the stack and confirm that the popped element is equal to the current closing parentheses character. If it is not then the string is invalid. At the end of the iteration, we also need to check that the stack is empty. If it is not then the string is invalid. If it is, then the string is valid. This is a more efficient approach with a Time complexity and Space complexity of O(n).
+
+
+## References
+
+- [Leetcode](https://leetcode.com/problems/valid-parentheses/)
diff --git a/src/algorithms/stack/valid-parentheses/__test__/validParentheses.test.js b/src/algorithms/stack/valid-parentheses/__test__/validParentheses.test.js
new file mode 100644
index 0000000000..e286688dfd
--- /dev/null
+++ b/src/algorithms/stack/valid-parentheses/__test__/validParentheses.test.js
@@ -0,0 +1,23 @@
+import isValid from '../validParentheses';
+
+describe('validParentheses', () => {
+ it('should return false when string is empty', () => {
+ expect(isValid('')).toBe(false);
+ });
+
+ it('should return true when string contains valid parentheses in correct order', () => {
+ expect(isValid('()')).toBe(true);
+ expect(isValid('()[]{}')).toBe(true);
+ expect(isValid('((({[]})))')).toBe(true);
+ });
+
+ it('should return false when string contains invalid parentheses', () => {
+ expect(isValid('(]')).toBe(false);
+ expect(isValid('()[]{} }')).toBe(false);
+ expect(isValid('((({[(]})))')).toBe(false);
+ });
+
+ it('should return false when string contains valid parentheses in wrong order', () => {
+ expect(isValid('({)}')).toBe(false);
+ });
+});
diff --git a/src/algorithms/stack/valid-parentheses/validParentheses.js b/src/algorithms/stack/valid-parentheses/validParentheses.js
new file mode 100644
index 0000000000..a327780768
--- /dev/null
+++ b/src/algorithms/stack/valid-parentheses/validParentheses.js
@@ -0,0 +1,42 @@
+import Stack from '../../../data-structures/stack/Stack';
+import HashTable from '../../../data-structures/hash-table/HashTable';
+
+// Declare hashtable containg opening parentheses as key and it's closing parentheses as value.
+const hashTable = new HashTable(3);
+hashTable.set('{', '}');
+hashTable.set('(', ')');
+hashTable.set('[', ']');
+
+/**
+ * Check if string has valid parentheses.
+ *
+ * @param {string} parenthesesString
+ * @return {boolean}
+ */
+export default function isValid(parenthesesString) {
+ // If string is empty return false
+ if (parenthesesString.length === 0) {
+ return false;
+ }
+ // Create stack
+ const stack = new Stack();
+
+ // Loop through each character of string
+ for (let i = 0; i < parenthesesString.length; i += 1) {
+ const currentCharacter = parenthesesString[i];
+ // If character is opening parentheses push it's closing parentheses to stack
+ if (hashTable.has(currentCharacter)) {
+ stack.push(hashTable.get(currentCharacter));
+ } else {
+ /* If character is a closing parentheses then,:
+ check If stack is empty, if it is return false.
+ if stack is not empty, pop from stack and compare it with current character.
+ If they are not same return false. */
+ if (stack.isEmpty() || stack.pop() !== currentCharacter) {
+ return false;
+ }
+ }
+ }
+ // If stack is empty return true else return false
+ return stack.isEmpty();
+}
diff --git a/src/algorithms/statistics/weighted-random/README.md b/src/algorithms/statistics/weighted-random/README.md
new file mode 100644
index 0000000000..16e459704b
--- /dev/null
+++ b/src/algorithms/statistics/weighted-random/README.md
@@ -0,0 +1,143 @@
+# Weighted Random
+
+
+
+## What is "Weighted Random"
+
+Let's say you have a list of **items**. Item could be anything. For example, we may have a list of fruits and vegetables that you like to eat: `[ '🍌', '🍎', '🥕' ]`.
+
+The list of **weights** represent the weight (or probability, or importance) of each item. Weights are numbers. For example, the weights like `[3, 7, 1]` would say that:
+
+- you would like to eat `🍎 apples` more often (`7` out of `3 + 7 + 1 = 11` times),
+- then you would like to eat `bananas 🍌` less often (only `3` out of `11` times),
+- and the `carrots 🥕` you really don't like (want to eat it only `1` out of `11` times).
+
+> If we speak in terms of probabilities than the weights list might be an array of floats that sum up to `1` (i.e. `[0.1, 0.5, 0.2, 0.2]`).
+
+The **Weighted Random** in this case will be the function that will randomly return you the item from the list, and it will take each item's weight into account, so that items with the higher weight will be picked more often.
+
+Example of the function interface:
+
+```javascript
+const items = [ '🍌', '🍎', '🥕' ];
+const weights = [ 3, 7, 1 ];
+
+function weightedRandom(items, weights) {
+ // implementation goes here ...
+}
+
+const nextSnackToEat = weightedRandom(items, weights); // Could be '🍎'
+```
+
+## Applications of Weighted Random
+
+- In [Genetic Algorithm](https://en.wikipedia.org/wiki/Genetic_algorithm) the weighted random is used during the "Selection" phase, when we need to select the fittest/strongest individuums based on their fitness score for mating and for producing the next stronger generation. You may find an **example** in the [Self-Parking Car in 500 Lines of Code](https://trekhleb.dev/blog/2021/self-parking-car-evolution/) article.
+- In [Recurrent Neural Networks (RNN)](https://en.wikipedia.org/wiki/Recurrent_neural_network) when trying to decide what letter to choose next (to form the sentence) based on the next letter probability. You may find an **example** in the [Recipe Generation using Recurrent Neural Network (RNN)](https://nbviewer.org/github/trekhleb/machine-learning-experiments/blob/master/experiments/recipe_generation_rnn/recipe_generation_rnn.ipynb) Jupyter notebook.
+- In [Nginx Load Balancing](https://docs.nginx.com/nginx/admin-guide/load-balancer/http-load-balancer/) to send HTTP requests more often to the servers with the higher weights.
+- And more...
+
+## The Algorithm
+
+The **straightforward approach** would be to:
+
+1. Repeat each item in the list according to its weight.
+2. Pick the random item from the list.
+
+For example in our case with fruits and vegetables we could generate the following list of size `3 + 7 + 1 = 11`:
+
+```javascript
+const items = [ '🍌', '🍎', '🥕' ];
+const weights = [ 3, 7, 1 ];
+
+// Repeating the items based on weights.
+const weightedItems = [
+ '🍌', '🍌', '🍌',
+ '🍎', '🍎', '🍎', '🍎', '🍎', '🍎', '🍎',
+ '🥕',
+];
+
+// And now just pick the random item from weightedItems array.
+```
+
+However, as you may see, this approach may require a lot of memory, in case if we have a lot of items to repeat in `weightedItems` list. Think of it as if you would need to repeat a string like `"some-random-string"` (`18` bytes) a ten million times. You will need to allocate around `180Mb` of additional memory space just for this array.
+
+The **more efficient approach** would be to:
+
+1. Prepare the list of cumulative weights for each item (i.e. the `cumulativeWeights` list which will have the same number of elements as the original `weights` list). In our case it will look like this: `cumulativeWeights = [3, 3 + 7, 3 + 7 + 1] = [3, 10, 11]`
+2. Generate the random number `randomNumber` from `0` to the highest cumulative weight value. In our case the random number will be in a range of `[0..11]`. Let's say that we have `randomNumber = 8`.
+3. Go through the `cumulativeWeights` list from left to right and pick the first element which is higher or equal to the `randomNumber`. The index of such element we will use to pick the item from the `items` array.
+
+The idea behind this approach is that the higher weights will "occupy" more numeric space. Therefore, there is a higher chance that the random number will fall into the "higher weight numeric bucket".
+
+```javascript
+const weights = [3, 7, 1 ];
+const cumulativeWeights = [3, 10, 11];
+
+// In a pseudo-representation we may think about the cumulativeWeights array like this.
+const pseudoCumulativeWeights = [
+ 1, 2, 3, // <-- [3] numbers
+ 4, 5, 6, 7, 8, 9, 10, // <-- [7] numbers
+ 11, // <-- [1] number
+];
+```
+
+Here is an example of how the `weightedRandom` function might be implemented:
+
+```javascript
+/**
+ * Picks the random item based on its weight.
+ * The items with higher weight will be picked more often (with a higher probability).
+ *
+ * For example:
+ * - items = ['banana', 'orange', 'apple']
+ * - weights = [0, 0.2, 0.8]
+ * - weightedRandom(items, weights) in 80% of cases will return 'apple', in 20% of cases will return
+ * 'orange' and it will never return 'banana' (because probability of picking the banana is 0%)
+ *
+ * @param {any[]} items
+ * @param {number[]} weights
+ * @returns {{item: any, index: number}}
+ */
+export default function weightedRandom(items, weights) {
+ if (items.length !== weights.length) {
+ throw new Error('Items and weights must be of the same size');
+ }
+
+ if (!items.length) {
+ throw new Error('Items must not be empty');
+ }
+
+ // Preparing the cumulative weights array.
+ // For example:
+ // - weights = [1, 4, 3]
+ // - cumulativeWeights = [1, 5, 8]
+ const cumulativeWeights = [];
+ for (let i = 0; i < weights.length; i += 1) {
+ cumulativeWeights[i] = weights[i] + (cumulativeWeights[i - 1] || 0);
+ }
+
+ // Getting the random number in a range of [0...sum(weights)]
+ // For example:
+ // - weights = [1, 4, 3]
+ // - maxCumulativeWeight = 8
+ // - range for the random number is [0...8]
+ const maxCumulativeWeight = cumulativeWeights[cumulativeWeights.length - 1];
+ const randomNumber = maxCumulativeWeight * Math.random();
+
+ // Picking the random item based on its weight.
+ // The items with higher weight will be picked more often.
+ for (let itemIndex = 0; itemIndex < items.length; itemIndex += 1) {
+ if (cumulativeWeights[itemIndex] >= randomNumber) {
+ return {
+ item: items[itemIndex],
+ index: itemIndex,
+ };
+ }
+ }
+}
+```
+
+## Implementation
+
+- Check the [weightedRandom.js](weightedRandom.js) file for the implementation of the `weightedRandom()` function.
+- Check the [weightedRandom.test.js](__test__/weightedRandom.test.js) file for the tests-cases.
diff --git a/src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js b/src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js
new file mode 100644
index 0000000000..1b0b267627
--- /dev/null
+++ b/src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js
@@ -0,0 +1,64 @@
+import weightedRandom from '../weightedRandom';
+
+describe('weightedRandom', () => {
+ it('should throw an error when the number of weights does not match the number of items', () => {
+ const getWeightedRandomWithInvalidInputs = () => {
+ weightedRandom(['a', 'b', 'c'], [10, 0]);
+ };
+ expect(getWeightedRandomWithInvalidInputs).toThrow('Items and weights must be of the same size');
+ });
+
+ it('should throw an error when the number of weights or items are empty', () => {
+ const getWeightedRandomWithInvalidInputs = () => {
+ weightedRandom([], []);
+ };
+ expect(getWeightedRandomWithInvalidInputs).toThrow('Items must not be empty');
+ });
+
+ it('should correctly do random selection based on wights in straightforward cases', () => {
+ expect(weightedRandom(['a', 'b', 'c'], [1, 0, 0])).toEqual({ index: 0, item: 'a' });
+ expect(weightedRandom(['a', 'b', 'c'], [0, 1, 0])).toEqual({ index: 1, item: 'b' });
+ expect(weightedRandom(['a', 'b', 'c'], [0, 0, 1])).toEqual({ index: 2, item: 'c' });
+ expect(weightedRandom(['a', 'b', 'c'], [0, 1, 1])).not.toEqual({ index: 0, item: 'a' });
+ expect(weightedRandom(['a', 'b', 'c'], [1, 0, 1])).not.toEqual({ index: 1, item: 'b' });
+ expect(weightedRandom(['a', 'b', 'c'], [1, 1, 0])).not.toEqual({ index: 2, item: 'c' });
+ });
+
+ it('should correctly do random selection based on wights', () => {
+ // Number of times we're going to select the random items based on their weights.
+ const ATTEMPTS_NUM = 1000;
+ // The +/- delta in the number of times each item has been actually selected.
+ // I.e. if we want the item 'a' to be selected 300 times out of 1000 cases (30%)
+ // then 267 times is acceptable since it is bigger that 250 (which is 300 - 50)
+ // ans smaller than 350 (which is 300 + 50)
+ const THRESHOLD = 50;
+
+ const items = ['a', 'b', 'c']; // The actual items values don't matter.
+ const weights = [0.1, 0.3, 0.6];
+
+ const counter = [];
+ for (let i = 0; i < ATTEMPTS_NUM; i += 1) {
+ const randomItem = weightedRandom(items, weights);
+ if (!counter[randomItem.index]) {
+ counter[randomItem.index] = 1;
+ } else {
+ counter[randomItem.index] += 1;
+ }
+ }
+
+ for (let itemIndex = 0; itemIndex < items.length; itemIndex += 1) {
+ /*
+ i.e. item with the index of 0 must be selected 100 times (ideally)
+ or with the threshold of [100 - 50, 100 + 50] times.
+
+ i.e. item with the index of 1 must be selected 300 times (ideally)
+ or with the threshold of [300 - 50, 300 + 50] times.
+
+ i.e. item with the index of 2 must be selected 600 times (ideally)
+ or with the threshold of [600 - 50, 600 + 50] times.
+ */
+ expect(counter[itemIndex]).toBeGreaterThan(ATTEMPTS_NUM * weights[itemIndex] - THRESHOLD);
+ expect(counter[itemIndex]).toBeLessThan(ATTEMPTS_NUM * weights[itemIndex] + THRESHOLD);
+ }
+ });
+});
diff --git a/src/algorithms/statistics/weighted-random/images/cover.png b/src/algorithms/statistics/weighted-random/images/cover.png
new file mode 100644
index 0000000000..a4bf41b65f
Binary files /dev/null and b/src/algorithms/statistics/weighted-random/images/cover.png differ
diff --git a/src/algorithms/statistics/weighted-random/weightedRandom.js b/src/algorithms/statistics/weighted-random/weightedRandom.js
new file mode 100644
index 0000000000..0d58a504f8
--- /dev/null
+++ b/src/algorithms/statistics/weighted-random/weightedRandom.js
@@ -0,0 +1,52 @@
+/**
+ * Picks the random item based on its weight.
+ * The items with higher weight will be picked more often (with a higher probability).
+ *
+ * For example:
+ * - items = ['banana', 'orange', 'apple']
+ * - weights = [0, 0.2, 0.8]
+ * - weightedRandom(items, weights) in 80% of cases will return 'apple', in 20% of cases will return
+ * 'orange' and it will never return 'banana' (because probability of picking the banana is 0%)
+ *
+ * @param {any[]} items
+ * @param {number[]} weights
+ * @returns {{item: any, index: number}}
+ */
+/* eslint-disable consistent-return */
+export default function weightedRandom(items, weights) {
+ if (items.length !== weights.length) {
+ throw new Error('Items and weights must be of the same size');
+ }
+
+ if (!items.length) {
+ throw new Error('Items must not be empty');
+ }
+
+ // Preparing the cumulative weights array.
+ // For example:
+ // - weights = [1, 4, 3]
+ // - cumulativeWeights = [1, 5, 8]
+ const cumulativeWeights = [];
+ for (let i = 0; i < weights.length; i += 1) {
+ cumulativeWeights[i] = weights[i] + (cumulativeWeights[i - 1] || 0);
+ }
+
+ // Getting the random number in a range of [0...sum(weights)]
+ // For example:
+ // - weights = [1, 4, 3]
+ // - maxCumulativeWeight = 8
+ // - range for the random number is [0...8]
+ const maxCumulativeWeight = cumulativeWeights[cumulativeWeights.length - 1];
+ const randomNumber = maxCumulativeWeight * Math.random();
+
+ // Picking the random item based on its weight.
+ // The items with higher weight will be picked more often.
+ for (let itemIndex = 0; itemIndex < items.length; itemIndex += 1) {
+ if (cumulativeWeights[itemIndex] >= randomNumber) {
+ return {
+ item: items[itemIndex],
+ index: itemIndex,
+ };
+ }
+ }
+}
diff --git a/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js b/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js
index e4344b7730..a3a39904a4 100644
--- a/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js
+++ b/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js
@@ -50,7 +50,7 @@ export default function knuthMorrisPratt(text, word) {
} else if (wordIndex > 0) {
wordIndex = patternTable[wordIndex - 1];
} else {
- wordIndex = 0;
+ // wordIndex = 0;
textIndex += 1;
}
}
diff --git a/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstring.test.js b/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstring.test.js
index a24c0df55c..8c1cb20703 100644
--- a/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstring.test.js
+++ b/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstring.test.js
@@ -7,6 +7,8 @@ describe('longestCommonSubstring', () => {
expect(longestCommonSubstring('', 'ABC')).toBe('');
expect(longestCommonSubstring('ABABC', 'BABCA')).toBe('BABC');
expect(longestCommonSubstring('BABCA', 'ABCBA')).toBe('ABC');
+ expect(longestCommonSubstring('sea', 'eat')).toBe('ea');
+ expect(longestCommonSubstring('algorithms', 'rithm')).toBe('rithm');
expect(longestCommonSubstring(
'Algorithms and data structures implemented in JavaScript',
'Here you may find Algorithms and data structures that are implemented in JavaScript',
diff --git a/src/algorithms/string/longest-common-substring/longestCommonSubstring.js b/src/algorithms/string/longest-common-substring/longestCommonSubstring.js
index 1d68ede9e3..6afeccf398 100644
--- a/src/algorithms/string/longest-common-substring/longestCommonSubstring.js
+++ b/src/algorithms/string/longest-common-substring/longestCommonSubstring.js
@@ -1,4 +1,6 @@
/**
+ * Longest Common Substring (LCS) (Dynamic Programming Approach).
+ *
* @param {string} string1
* @param {string} string2
* @return {string}
diff --git a/src/algorithms/string/palindrome/README.md b/src/algorithms/string/palindrome/README.md
new file mode 100644
index 0000000000..0ce77d42b6
--- /dev/null
+++ b/src/algorithms/string/palindrome/README.md
@@ -0,0 +1,29 @@
+# Palindrome Check
+
+A [Palindrome](https://en.wikipedia.org/wiki/Palindrome) is a string that reads the same forwards and backwards.
+This means that the second half of the string is the reverse of the
+first half.
+
+## Examples
+
+The following are palindromes (thus would return `TRUE`):
+
+```
+- "a"
+- "pop" -> p + o + p
+- "deed" -> de + ed
+- "kayak" -> ka + y + ak
+- "racecar" -> rac + e + car
+```
+
+The following are NOT palindromes (thus would return `FALSE`):
+
+```
+- "rad"
+- "dodo"
+- "polo"
+```
+
+## References
+
+- [GeeksForGeeks - Check if a number is Palindrome](https://www.geeksforgeeks.org/check-if-a-number-is-palindrome/)
diff --git a/src/algorithms/string/palindrome/__test__/isPalindrome.test.js b/src/algorithms/string/palindrome/__test__/isPalindrome.test.js
new file mode 100644
index 0000000000..0a49d5be5d
--- /dev/null
+++ b/src/algorithms/string/palindrome/__test__/isPalindrome.test.js
@@ -0,0 +1,15 @@
+import isPalindrome from '../isPalindrome';
+
+describe('palindromeCheck', () => {
+ it('should return whether or not the string is a palindrome', () => {
+ expect(isPalindrome('a')).toBe(true);
+ expect(isPalindrome('pop')).toBe(true);
+ expect(isPalindrome('deed')).toBe(true);
+ expect(isPalindrome('kayak')).toBe(true);
+ expect(isPalindrome('racecar')).toBe(true);
+
+ expect(isPalindrome('rad')).toBe(false);
+ expect(isPalindrome('dodo')).toBe(false);
+ expect(isPalindrome('polo')).toBe(false);
+ });
+});
diff --git a/src/algorithms/string/palindrome/isPalindrome.js b/src/algorithms/string/palindrome/isPalindrome.js
new file mode 100644
index 0000000000..327fd6bbf2
--- /dev/null
+++ b/src/algorithms/string/palindrome/isPalindrome.js
@@ -0,0 +1,19 @@
+/**
+ * @param {string} string
+ * @return {boolean}
+ */
+
+export default function isPalindrome(string) {
+ let left = 0;
+ let right = string.length - 1;
+
+ while (left < right) {
+ if (string[left] !== string[right]) {
+ return false;
+ }
+ left += 1;
+ right -= 1;
+ }
+
+ return true;
+}
diff --git a/src/algorithms/tree/breadth-first-search/breadthFirstSearch.js b/src/algorithms/tree/breadth-first-search/breadthFirstSearch.js
index 503ec34f96..e1c7b70e14 100644
--- a/src/algorithms/tree/breadth-first-search/breadthFirstSearch.js
+++ b/src/algorithms/tree/breadth-first-search/breadthFirstSearch.js
@@ -3,9 +3,9 @@ import Queue from '../../../data-structures/queue/Queue';
/**
* @typedef {Object} Callbacks
* @property {function(node: BinaryTreeNode, child: BinaryTreeNode): boolean} allowTraversal -
- * Determines whether DFS should traverse from the node to its child.
- * @property {function(node: BinaryTreeNode)} enterNode - Called when DFS enters the node.
- * @property {function(node: BinaryTreeNode)} leaveNode - Called when DFS leaves the node.
+ * Determines whether BFS should traverse from the node to its child.
+ * @property {function(node: BinaryTreeNode)} enterNode - Called when BFS enters the node.
+ * @property {function(node: BinaryTreeNode)} leaveNode - Called when BFS leaves the node.
*/
/**
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
index 9446993e98..975eade3a4 100644
--- a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
@@ -46,7 +46,7 @@ Let's say we have an array of prices `[7, 6, 4, 3, 1]` and we're on the _1st_ da
1. _Option 1: Keep the money_ → profit would equal to the profit from buying/selling the rest of the stocks → `keepProfit = profit([6, 4, 3, 1])`.
2. _Option 2: Buy/sell at current price_ → profit in this case would equal to the profit from buying/selling the rest of the stocks plus (or minus, depending on whether we're selling or buying) the current stock price → `buySellProfit = -7 + profit([6, 4, 3, 1])`.
-The overall profit would be equal to → `overalProfit = Max(keepProfit, buySellProfit)`.
+The overall profit would be equal to → `overallProfit = Max(keepProfit, buySellProfit)`.
As you can see the `profit([6, 4, 3, 1])` task is being solved in the same recursive manner.
diff --git a/src/algorithms/uncategorized/n-queens/README.md b/src/algorithms/uncategorized/n-queens/README.md
index 077e26d73d..399256768e 100644
--- a/src/algorithms/uncategorized/n-queens/README.md
+++ b/src/algorithms/uncategorized/n-queens/README.md
@@ -59,7 +59,7 @@ and return false.
queen here leads to a solution.
b) If placing queen in [row, column] leads to a solution then return
true.
- c) If placing queen doesn't lead to a solution then umark this [row,
+ c) If placing queen doesn't lead to a solution then unmark this [row,
column] (Backtrack) and go to step (a) to try other rows.
3) If all rows have been tried and nothing worked, return false to trigger
backtracking.
diff --git a/src/data-structures/bloom-filter/README.md b/src/data-structures/bloom-filter/README.md
index 17c666775e..7880a7f7be 100644
--- a/src/data-structures/bloom-filter/README.md
+++ b/src/data-structures/bloom-filter/README.md
@@ -2,38 +2,39 @@
_Read this in other languages:_
[_Русский_](README.ru-RU.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Українська_](README.uk-UA.md)
-A **bloom filter** is a space-efficient probabilistic
-data structure designed to test whether an element
-is present in a set. It is designed to be blazingly
+A **bloom filter** is a space-efficient probabilistic
+data structure designed to test whether an element
+is present in a set. It is designed to be blazingly
fast and use minimal memory at the cost of potential
false positives. False positive matches are possible,
but false negatives are not – in other words, a query
returns either "possibly in set" or "definitely not in set".
-Bloom proposed the technique for applications where the
+Bloom proposed the technique for applications where the
amount of source data would require an impractically large
-amount of memory if "conventional" error-free hashing
+amount of memory if "conventional" error-free hashing
techniques were applied.
## Algorithm description
-An empty Bloom filter is a bit array of `m` bits, all
+An empty Bloom filter is a bit array of `m` bits, all
set to `0`. There must also be `k` different hash functions
-defined, each of which maps or hashes some set element to
-one of the `m` array positions, generating a uniform random
-distribution. Typically, `k` is a constant, much smaller
-than `m`, which is proportional to the number of elements
-to be added; the precise choice of `k` and the constant of
-proportionality of `m` are determined by the intended
+defined, each of which maps or hashes some set element to
+one of the `m` array positions, generating a uniform random
+distribution. Typically, `k` is a constant, much smaller
+than `m`, which is proportional to the number of elements
+to be added; the precise choice of `k` and the constant of
+proportionality of `m` are determined by the intended
false positive rate of the filter.
-Here is an example of a Bloom filter, representing the
-set `{x, y, z}`. The colored arrows show the positions
-in the bit array that each set element is mapped to. The
-element `w` is not in the set `{x, y, z}`, because it
-hashes to one bit-array position containing `0`. For
+Here is an example of a Bloom filter, representing the
+set `{x, y, z}`. The colored arrows show the positions
+in the bit array that each set element is mapped to. The
+element `w` is not in the set `{x, y, z}`, because it
+hashes to one bit-array position containing `0`. For
this figure, `m = 18` and `k = 3`.
@@ -92,7 +93,7 @@ three factors: the size of the bloom filter, the
number of hash functions we use, and the number
of items that have been inserted into the filter.
-The formula to calculate probablity of a false positive is:
+The formula to calculate probability of a false positive is:
( 1 - e <sup>-kn/m</sup> ) <sup>k</sup>
diff --git a/src/data-structures/bloom-filter/README.pt-BR.md b/src/data-structures/bloom-filter/README.pt-BR.md
index 77c4232262..0c8522b958 100644
--- a/src/data-structures/bloom-filter/README.pt-BR.md
+++ b/src/data-structures/bloom-filter/README.pt-BR.md
@@ -3,7 +3,7 @@
O **bloom filter** é uma estrutura de dados probabilística
espaço-eficiente designada para testar se um elemento está
ou não presente em um conjunto de dados. Foi projetado para ser
-incrivelmente rápido e utilizar o mínimo de memória ao
+incrivelmente rápida e utilizar o mínimo de memória ao
potencial custo de um falso-positivo. Correspondências
_falsas positivas_ são possíveis, contudo _falsos negativos_
não são - em outras palavras, a consulta retorna
@@ -12,7 +12,7 @@ não são - em outras palavras, a consulta retorna
Bloom propôs a técnica para aplicações onde a quantidade
de entrada de dados exigiria uma alocação de memória
impraticavelmente grande se as "convencionais" técnicas
-error-free hashing fossem aplicado.
+error-free hashing fossem aplicadas.
## Descrição do algoritmo
diff --git a/src/data-structures/bloom-filter/README.uk-UA.md b/src/data-structures/bloom-filter/README.uk-UA.md
new file mode 100644
index 0000000000..aa9075a094
--- /dev/null
+++ b/src/data-structures/bloom-filter/README.uk-UA.md
@@ -0,0 +1,54 @@
+# Фільтр Блума
+
+**Фільтр Блума** - це просторово-ефективна ймовірна структура даних, створена для перевірки наявності елемента
+у множині. Він спроектований неймовірно швидким за мінімального використання пам'яті ціною потенційних помилкових спрацьовувань.
+Існує можливість отримати хибнопозитивне спрацьовування (елемента в безлічі немає, але структура даних повідомляє,
+що він є), але не хибнонегативне. Іншими словами, черга повертає або "можливо в наборі", або "певно не
+у наборі". Фільтр Блума може використовувати будь-який обсяг пам'яті, проте чим він більший, тим менша вірогідність помилкового
+спрацьовування.
+
+Блум запропонував цю техніку для застосування в областях, де кількість вихідних даних потребувала б непрактично багато
+пам'яті, у разі застосування умовно безпомилкових технік хешування.
+
+## Опис алгоритму
+
+Порожній фільтр Блума представлений бітовим масивом з `m` бітів, всі біти якого обнулені. Має бути визначено `k`
+незалежних хеш-функцій, що відображають кожен елемент множини в одну з `m` позицій у масиві, генеруючи однакове
+випадковий розподіл. Зазвичай `k` задана константою, яка набагато менше `m` і пропорційна
+кількості елементів, що додаються; точний вибір `k` та постійної пропорційності `m` визначаються рівнем хибних
+спрацьовувань фільтра.
+
+Ось приклад Блум фільтра, що представляє набір `{x, y, z}`. Кольорові стрілки показують позиції в бітовому масиві,
+яким прив'язаний кожен елемент набору. Елемент `w` не в наборі `{x, y, z}`, тому що він прив'язаний до позиції в бітовому
+масиві, що дорівнює `0`. Для цієї форми, `m = 18`, а `k = 3`.
+
+Фільтр Блума є бітовий масив з `m` біт. Спочатку, коли структура даних зберігає порожню множину, всі
+m біт обнулені. Користувач повинен визначити `k` незалежних хеш-функцій `h1`, …, `hk`,
+що відображають кожен елемент в одну з m позицій бітового масиву досить рівномірним чином.
+
+Для додавання елемента e необхідно записати одиниці на кожну з позицій `h1(e)`, …, `hk(e)`
+бітового масиву.
+
+Для перевірки приналежності елемента `e` до безлічі елементів, що зберігаються, необхідно перевірити стан бітів
+`h1(e)`, …, `hk(e)`. Якщо хоча б один з них дорівнює нулю, елемент не може належати множині
+(інакше при його додаванні всі ці біти були встановлені). Якщо вони рівні одиниці, то структура даних повідомляє,
+що `е` належить безлічі. При цьому може виникнути дві ситуації: або елемент дійсно належить множині,
+або всі ці біти виявилися встановлені випадково при додаванні інших елементів, що і є джерелом помилкових
+спрацьовувань у цій структурі даних.
+
+
+
+## Застосування
+
+Фільтр Блума може бути використаний для блогів. Якщо мета полягає в тому, щоб показати читачам лише ті статті,
+які вони ще не бачили, фільтр блуму ідеальний. Він може містити значення, що хешуються, відповідні статті. Після
+того, як користувач прочитав кілька статей, вони можуть бути поміщені у фільтр. Наступного разу, коли користувач
+відвідає сайт, ці статті можуть бути вилучені з результатів за допомогою фільтра.
+
+Деякі статті неминуче будуть відфільтровані помилково, але ціна прийнятна. Те, що користувач не побачить дещо
+статей цілком прийнятно, беручи до уваги той факт, що йому завжди показуються інші нові статті при кожному
+новому відвідуванні.
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%A4%D1%96%D0%BB%D1%8C%D1%82%D1%80_%D0%91%D0%BB%D1%83%D0%BC%D0%B0)
diff --git a/src/data-structures/disjoint-set/DisjointSetAdhoc.js b/src/data-structures/disjoint-set/DisjointSetAdhoc.js
new file mode 100644
index 0000000000..9653418042
--- /dev/null
+++ b/src/data-structures/disjoint-set/DisjointSetAdhoc.js
@@ -0,0 +1,78 @@
+/**
+ * The minimalistic (ad hoc) version of a DisjointSet (or a UnionFind) data structure
+ * that doesn't have external dependencies and that is easy to copy-paste and
+ * use during the coding interview if allowed by the interviewer (since many
+ * data structures in JS are missing).
+ *
+ * Time Complexity:
+ *
+ * - Constructor: O(N)
+ * - Find: O(α(N))
+ * - Union: O(α(N))
+ * - Connected: O(α(N))
+ *
+ * Where N is the number of vertices in the graph.
+ * α refers to the Inverse Ackermann function.
+ * In practice, we assume it's a constant.
+ * In other words, O(α(N)) is regarded as O(1) on average.
+ */
+class DisjointSetAdhoc {
+ /**
+ * Initializes the set of specified size.
+ * @param {number} size
+ */
+ constructor(size) {
+ // The index of a cell is an id of the node in a set.
+ // The value of a cell is an id (index) of the root node.
+ // By default, the node is a parent of itself.
+ this.roots = new Array(size).fill(0).map((_, i) => i);
+
+ // Using the heights array to record the height of each node.
+ // By default each node has a height of 1 because it has no children.
+ this.heights = new Array(size).fill(1);
+ }
+
+ /**
+ * Finds the root of node `a`
+ * @param {number} a
+ * @returns {number}
+ */
+ find(a) {
+ if (a === this.roots[a]) return a;
+ this.roots[a] = this.find(this.roots[a]);
+ return this.roots[a];
+ }
+
+ /**
+ * Joins the `a` and `b` nodes into same set.
+ * @param {number} a
+ * @param {number} b
+ * @returns {number}
+ */
+ union(a, b) {
+ const aRoot = this.find(a);
+ const bRoot = this.find(b);
+
+ if (aRoot === bRoot) return;
+
+ if (this.heights[aRoot] > this.heights[bRoot]) {
+ this.roots[bRoot] = aRoot;
+ } else if (this.heights[aRoot] < this.heights[bRoot]) {
+ this.roots[aRoot] = bRoot;
+ } else {
+ this.roots[bRoot] = aRoot;
+ this.heights[aRoot] += 1;
+ }
+ }
+
+ /**
+ * Checks if `a` and `b` belong to the same set.
+ * @param {number} a
+ * @param {number} b
+ */
+ connected(a, b) {
+ return this.find(a) === this.find(b);
+ }
+}
+
+export default DisjointSetAdhoc;
diff --git a/src/data-structures/disjoint-set/README.md b/src/data-structures/disjoint-set/README.md
index 535960c7bb..772f68191b 100644
--- a/src/data-structures/disjoint-set/README.md
+++ b/src/data-structures/disjoint-set/README.md
@@ -2,22 +2,27 @@
_Read this in other languages:_
[_Русский_](README.ru-RU.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Українська_](README.uk-UA.md)
-
-**Disjoint-set** data structure (also called a union–find data structure or merge–find set) is a data
-structure that tracks a set of elements partitioned into a number of disjoint (non-overlapping) subsets.
-It provides near-constant-time operations (bounded by the inverse Ackermann function) to *add new sets*,
-to *merge existing sets*, and to *determine whether elements are in the same set*.
+**Disjoint-set** data structure (also called a union–find data structure or merge–find set) is a data
+structure that tracks a set of elements partitioned into a number of disjoint (non-overlapping) subsets.
+It provides near-constant-time operations (bounded by the inverse Ackermann function) to _add new sets_,
+to _merge existing sets_, and to _determine whether elements are in the same set_.
In addition to many other uses (see the Applications section), disjoint-sets play a key role in Kruskal's algorithm for finding the minimum spanning tree of a graph.
-*MakeSet* creates 8 singletons.
+_MakeSet_ creates 8 singletons.
-After some operations of *Union*, some sets are grouped together.
+After some operations of _Union_, some sets are grouped together.
+
+## Implementation
+
+- [DisjointSet.js](./DisjointSet.js)
+- [DisjointSetAdhoc.js](./DisjointSetAdhoc.js) - The minimalistic (ad hoc) version of a DisjointSet (or a UnionFind) data structure that doesn't have external dependencies and that is easy to copy-paste and use during the coding interview if allowed by the interviewer (since many data structures in JS are missing).
## References
diff --git a/src/data-structures/disjoint-set/README.pt-BR.md b/src/data-structures/disjoint-set/README.pt-BR.md
index 130b8aea6c..a7d827a8a2 100644
--- a/src/data-structures/disjoint-set/README.pt-BR.md
+++ b/src/data-structures/disjoint-set/README.pt-BR.md
@@ -1,8 +1,8 @@
-# Conjunto Disjuntor (Disjoint Set)
+# Conjunto Disjunto (Disjoint Set)
-**Conjunto Disjuntor**
+**Conjunto Disjunto**
-**Conjunto Disjuntor** é uma estrutura de dados (também chamado de
+**Conjunto Disjunto** é uma estrutura de dados (também chamado de
estrutura de dados de union–find ou merge–find) é uma estrutura de dados
que rastreia um conjunto de elementos particionados em um número de
subconjuntos separados (sem sobreposição).
@@ -10,9 +10,9 @@ Ele fornece operações de tempo quase constante (limitadas pela função
inversa de Ackermann) para *adicionar novos conjuntos*, para
*mesclar/fundir conjuntos existentes* e para *determinar se os elementos
estão no mesmo conjunto*.
-Além de muitos outros usos (veja a seção Applications), conjunto disjuntor
+Além de muitos outros usos (veja a seção Applications), conjuntos disjuntos
desempenham um papel fundamental no algoritmo de Kruskal para encontrar a
-árvore geradora mínima de um gráfico (graph).
+árvore geradora mínima de um grafo (graph).
diff --git a/src/data-structures/disjoint-set/README.uk-UA.md b/src/data-structures/disjoint-set/README.uk-UA.md
new file mode 100644
index 0000000000..c721b66420
--- /dev/null
+++ b/src/data-structures/disjoint-set/README.uk-UA.md
@@ -0,0 +1,22 @@
+# Система неперетинних множин
+
+**Система неперетинних множин** це структура даних (також звана структурою даної пошуку перетину або
+безліччю пошуку злиття), яка управляє безліччю елементів, розбитих на кілька підмножин, що не перетинаються.
+Вона надає близько-константний час виконання операцій (обмежений зворотною функцією Акерманна) за додаванням
+нових множин, *злиття існуючих множин і *випередження, чи відносяться елементи до одного і того ж безлічі.
+
+Застосовується для зберігання компонентів зв'язності в графах, зокрема, алгоритму Фарбала необхідна подібна структура
+даних для ефективної реалізації.
+
+Основні операції:
+
+- _MakeSet(x)_ - створює одноелементне безліч {x},
+- _Find(x)_ - повертає ідентифікатор множини, що містить елемент x,
+- _Union(x,y)_ - об'єднання множин, що містять x та y.
+
+Після деяких операцій _об'єднання_, деякі множини зібрані разом.
+
+## Посилання
+
+- [СНМ на Wikipedia](https://uk.wikipedia.org/wiki/%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D0%BD%D0%B5%D0%BF%D0%B5%D1%80%D0%B5%D1%82%D0%B8%D0%BD%D0%BD%D0%B8%D1%85_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B8%D0%BD)
+- [СНМ на YouTube](https://www.youtube.com/watch?v=5XwRPwLnK6I)
diff --git a/src/data-structures/disjoint-set/__test__/DisjointSetAdhoc.test.js b/src/data-structures/disjoint-set/__test__/DisjointSetAdhoc.test.js
new file mode 100644
index 0000000000..f7be0fcde9
--- /dev/null
+++ b/src/data-structures/disjoint-set/__test__/DisjointSetAdhoc.test.js
@@ -0,0 +1,50 @@
+import DisjointSetAdhoc from '../DisjointSetAdhoc';
+
+describe('DisjointSetAdhoc', () => {
+ it('should create unions and find connected elements', () => {
+ const set = new DisjointSetAdhoc(10);
+
+ // 1-2-5-6-7 3-8-9 4
+ set.union(1, 2);
+ set.union(2, 5);
+ set.union(5, 6);
+ set.union(6, 7);
+
+ set.union(3, 8);
+ set.union(8, 9);
+
+ expect(set.connected(1, 5)).toBe(true);
+ expect(set.connected(5, 7)).toBe(true);
+ expect(set.connected(3, 8)).toBe(true);
+
+ expect(set.connected(4, 9)).toBe(false);
+ expect(set.connected(4, 7)).toBe(false);
+
+ // 1-2-5-6-7 3-8-9-4
+ set.union(9, 4);
+
+ expect(set.connected(4, 9)).toBe(true);
+ expect(set.connected(4, 3)).toBe(true);
+ expect(set.connected(8, 4)).toBe(true);
+
+ expect(set.connected(8, 7)).toBe(false);
+ expect(set.connected(2, 3)).toBe(false);
+ });
+
+ it('should keep the height of the tree small', () => {
+ const set = new DisjointSetAdhoc(10);
+
+ // 1-2-6-7-9 1 3 4 5
+ set.union(7, 6);
+ set.union(1, 2);
+ set.union(2, 6);
+ set.union(1, 7);
+ set.union(9, 1);
+
+ expect(set.connected(1, 7)).toBe(true);
+ expect(set.connected(6, 9)).toBe(true);
+ expect(set.connected(4, 9)).toBe(false);
+
+ expect(Math.max(...set.heights)).toBe(3);
+ });
+});
diff --git a/src/data-structures/doubly-linked-list/README.es-ES.md b/src/data-structures/doubly-linked-list/README.es-ES.md
new file mode 100644
index 0000000000..490466d74b
--- /dev/null
+++ b/src/data-structures/doubly-linked-list/README.es-ES.md
@@ -0,0 +1,104 @@
+# Lista doblemente enlazada
+
+_Lea esto en otros idiomas:_
+[_Русский_](README.ru-RU.md),
+[_简体中文_](README.zh-CN.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md)
+[_한국어_](README.ko-KR.md)
+
+En informática, una **lista doblemente enlazada** es una estructura de datos relacionados que consta de un conjunto de registros conectados secuencialmente llamados nodos. Cada nodo contiene dos campos, llamados enlaces, que son referencias al nodo anterior y al siguiente en la secuencia de nodos. Los enlaces anterior y siguiente de los nodos inicial y final, apuntan respectivamente a algún tipo de terminador (normalmente un nodo centinela o nulo), facilitando así el recorrido de la lista. Si solo hay un nodo nulo, la lista se enlaza circularmente a través este. Puede conceptualizarse como dos listas enlazadas individualmente formadas a partir de los mismos elementos de datos, pero en órdenes secuenciales opuestos.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+Los dos enlaces de un nodo permiten recorrer la lista en cualquier dirección. Si bien agregar o eliminar un nodo en una lista doblemente enlazada requiere cambiar más enlaces que las mismas operaciones en una lista enlazada individualmente, las operaciones son más simples y potencialmente más eficientes (para nodos que no sean los primeros) porque no hay necesidad de realizar un seguimiento del nodo anterior durante el recorrido o no es necesario recorrer la lista para encontrar el nodo anterior, de modo que se pueda modificar su enlace.
+
+## Pseudocódigo para operaciones básicas
+
+### Insertar
+
+```text
+Add(value)
+ Pre: value is the value to add to the list
+ Post: value has been placed at the tail of the list
+ n ← node(value)
+ if head = ø
+ head ← n
+ tail ← n
+ else
+ n.previous ← tail
+ tail.next ← n
+ tail ← n
+ end if
+end Add
+```
+
+### Eliminar
+
+```text
+Remove(head, value)
+ Pre: head is the head node in the list
+ value is the value to remove from the list
+ Post: value is removed from the list, true; otherwise false
+ if head = ø
+ return false
+ end if
+ if value = head.value
+ if head = tail
+ head ← ø
+ tail ← ø
+ else
+ head ← head.next
+ head.previous ← ø
+ end if
+ return true
+ end if
+ n ← head.next
+ while n != ø and value !== n.value
+ n ← n.next
+ end while
+ if n = tail
+ tail ← tail.previous
+ tail.next ← ø
+ return true
+ else if n != ø
+ n.previous.next ← n.next
+ n.next.previous ← n.previous
+ return true
+ end if
+ return false
+end Remove
+```
+
+### Recorrido Inverso
+
+```text
+ReverseTraversal(tail)
+ Pre: tail is the node of the list to traverse
+ Post: the list has been traversed in reverse order
+ n ← tail
+ while n != ø
+ yield n.value
+ n ← n.previous
+ end while
+end Reverse Traversal
+```
+
+## Complejidades
+
+## Complejidad del Tiempo
+
+| Acceso | Búsqueda | Inserción | Eliminación |
+| :----: | :------: | :-------: | :---------: |
+| O(n) | O(n) | O(1) | O(n) |
+
+### Complejidad del Espacio
+
+O(n)
+
+## Referencias
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Doubly_linked_list)
+- [YouTube](https://www.youtube.com/watch?v=JdQeNxWCguQ&t=7s&index=72&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/doubly-linked-list/README.ja-JP.md b/src/data-structures/doubly-linked-list/README.ja-JP.md
index ede22817ba..0ff96628c9 100644
--- a/src/data-structures/doubly-linked-list/README.ja-JP.md
+++ b/src/data-structures/doubly-linked-list/README.ja-JP.md
@@ -2,7 +2,9 @@
コンピュータサイエンスにおいて、**双方向リスト**はノードと呼ばれる一連のリンクレコードからなる連結データ構造です。各ノードはリンクと呼ばれる2つのフィールドを持っていて、これらは一連のノード内における前のノードと次のノードを参照しています。最初のノードの前のリンクと最後のノードの次のリンクはある種の終端を示していて、一般的にはダミーノードやnullが格納され、リストのトラバースを容易に行えるようにしています。もしダミーノードが1つしかない場合、リストはその1つのノードを介して循環的にリンクされます。これは、それぞれ逆の順番の単方向のリンクリストが2つあるものとして考えることができます。
-
+
+
+*Made with [okso.app](https://okso.app)*
2つのリンクにより、リストをどちらの方向にもトラバースすることができます。双方向リストはノードの追加や削除の際に、片方向リンクリストと比べてより多くのリンクを変更する必要があります。しかし、その操作は簡単で、より効率的な(最初のノード以外の場合)可能性があります。前のノードのリンクを更新する際に前のノードを保持したり、前のノードを見つけるためにリストをトラバースする必要がありません。
@@ -25,7 +27,7 @@ Add(value)
end if
end Add
```
-
+
### 削除
```text
@@ -62,7 +64,7 @@ Remove(head, value)
return false
end Remove
```
-
+
### 逆トラバース
```text
@@ -76,7 +78,7 @@ ReverseTraversal(tail)
end while
end Reverse Traversal
```
-
+
## 計算量
## 時間計算量
diff --git a/src/data-structures/doubly-linked-list/README.ko-KR.md b/src/data-structures/doubly-linked-list/README.ko-KR.md
index 192b189817..9f60e54f32 100644
--- a/src/data-structures/doubly-linked-list/README.ko-KR.md
+++ b/src/data-structures/doubly-linked-list/README.ko-KR.md
@@ -12,7 +12,9 @@ _Read this in other languages:_
센티넬 노드가 하나만 있으면, 목록이 센티넬 노드를 통해서 원형으로 연결됩니다.
동일한 데이터 항목으로 구성되어 있지만, 반대 순서로 두 개의 단일 연결 리스트로 개념화 할 수 있습니다.
-
+
+
+*Made with [okso.app](https://okso.app)*
두 개의 노드 링크를 사용하면 어느 방향으로든 리스트를 순회할 수 있습니다.
이중 연결 리스트에서 노드를 추가하거나 제거하려면, 단일 연결 리스트에서 동일한 작업보다 더 많은 링크를 변경해야 하지만, 첫 번째 노드 이외의 노드인 경우 작업을 추적할 필요가 없으므로 작업이 더 단순해져 잠재적으로 더 효율적입니다.
@@ -37,7 +39,7 @@ Add(value)
end if
end Add
```
-
+
### 삭제
```text
@@ -74,7 +76,7 @@ Remove(head, value)
return false
end Remove
```
-
+
### 역순회
```text
@@ -88,7 +90,7 @@ ReverseTraversal(tail)
end while
end Reverse Traversal
```
-
+
## 복잡도
## 시간 복잡도
diff --git a/src/data-structures/doubly-linked-list/README.md b/src/data-structures/doubly-linked-list/README.md
index c64b51262d..1610d1e497 100644
--- a/src/data-structures/doubly-linked-list/README.md
+++ b/src/data-structures/doubly-linked-list/README.md
@@ -4,26 +4,30 @@ _Read this in other languages:_
[_Русский_](README.ru-RU.md),
[_简体中文_](README.zh-CN.md),
[_日本語_](README.ja-JP.md),
-[_Português_](README.pt-BR.md)
-[_한국어_](README.ko-KR.md)
-
-In computer science, a **doubly linked list** is a linked data structure that
-consists of a set of sequentially linked records called nodes. Each node contains
-two fields, called links, that are references to the previous and to the next
-node in the sequence of nodes. The beginning and ending nodes' previous and next
-links, respectively, point to some kind of terminator, typically a sentinel
-node or null, to facilitate the traversal of the list. If there is only one
-sentinel node, then the list is circularly linked via the sentinel node. It can
-be conceptualized as two singly linked lists formed from the same data items,
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Español_](README.es-ES.md),
+[_Українська_](README.uk-UA.md)
+
+In computer science, a **doubly linked list** is a linked data structure that
+consists of a set of sequentially linked records called nodes. Each node contains
+two fields, called links, that are references to the previous and to the next
+node in the sequence of nodes. The beginning and ending nodes' previous and next
+links, respectively, point to some kind of terminator, typically a sentinel
+node or null, to facilitate the traversal of the list. If there is only one
+sentinel node, then the list is circularly linked via the sentinel node. It can
+be conceptualized as two singly linked lists formed from the same data items,
but in opposite sequential orders.
-
+
+
+_Made with [okso.app](https://okso.app)_
-The two node links allow traversal of the list in either direction. While adding
-or removing a node in a doubly linked list requires changing more links than the
-same operations on a singly linked list, the operations are simpler and
-potentially more efficient (for nodes other than first nodes) because there
-is no need to keep track of the previous node during traversal or no need
+The two node links allow traversal of the list in either direction. While adding
+or removing a node in a doubly linked list requires changing more links than the
+same operations on a singly linked list, the operations are simpler and
+potentially more efficient (for nodes other than first nodes) because there
+is no need to keep track of the previous node during traversal or no need
to traverse the list to find the previous node, so that its link can be modified.
## Pseudocode for Basic Operations
@@ -45,7 +49,7 @@ Add(value)
end if
end Add
```
-
+
### Delete
```text
@@ -82,7 +86,7 @@ Remove(head, value)
return false
end Remove
```
-
+
### Reverse Traversal
```text
@@ -96,14 +100,14 @@ ReverseTraversal(tail)
end while
end Reverse Traversal
```
-
+
## Complexities
## Time Complexity
-| Access | Search | Insertion | Deletion |
-| :-------: | :-------: | :-------: | :-------: |
-| O(n) | O(n) | O(1) | O(n) |
+| Access | Search | Insertion | Deletion |
+| :----: | :----: | :-------: | :------: |
+| O(n) | O(n) | O(1) | O(n) |
### Space Complexity
diff --git a/src/data-structures/doubly-linked-list/README.pt-BR.md b/src/data-structures/doubly-linked-list/README.pt-BR.md
index 73c86f5386..c4294decf4 100644
--- a/src/data-structures/doubly-linked-list/README.pt-BR.md
+++ b/src/data-structures/doubly-linked-list/README.pt-BR.md
@@ -4,21 +4,23 @@ Na ciência da computação, uma **lista duplamente conectada** é uma estrutura
de dados vinculada que se consistem em um conjunto de registros
sequencialmente vinculados chamados de nós (nodes). Em cada nó contém dois
campos, chamados de ligações, que são referenciados ao nó anterior e posterior
-de uma sequência de nós. O começo e o fim dos nós anteriormente e posteiormente
+de uma sequência de nós. O começo e o fim dos nós anteriormente e posteriormente
ligados, respectiviamente, apontam para algum tipo de terminação, normalmente
um nó sentinela ou nulo, para facilitar a travessia da lista. Se existe
somente um nó sentinela, então a lista é ligada circularmente através do nó
sentinela. Ela pode ser conceitualizada como duas listas individualmente ligadas
e formadas a partir dos mesmos itens, mas em ordem sequencial opostas.
-
+
+
+*Made with [okso.app](https://okso.app)*
Os dois nós ligados permitem a travessia da lista em qualquer direção.
Enquanto adicionar ou remover um nó de uma lista duplamente vinculada requer
alterar mais ligações (conexões) do que em uma lista encadeada individualmente
(singly linked list), as operações são mais simples e potencialmente mais
eficientes (para nós que não sejam nós iniciais) porque não há necessidade
-de se manter rastreamento do nó anterior durante a travessia ou não há
+de manter um rastreamento do nó anterior durante a travessia ou não há
necessidade de percorrer a lista para encontrar o nó anterior, para que
então sua ligação/conexão possa ser modificada.
@@ -41,8 +43,8 @@ Add(value)
end if
end Add
```
-
-### Deletar
+
+### Remoção
```text
Remove(head, value)
@@ -78,7 +80,7 @@ Remove(head, value)
return false
end Remove
```
-
+
### Travessia reversa
```text
@@ -92,7 +94,7 @@ ReverseTraversal(tail)
end while
end Reverse Traversal
```
-
+
## Complexidades
## Complexidade de Tempo
diff --git a/src/data-structures/doubly-linked-list/README.ru-RU.md b/src/data-structures/doubly-linked-list/README.ru-RU.md
index 66637691fa..b69d0da393 100644
--- a/src/data-structures/doubly-linked-list/README.ru-RU.md
+++ b/src/data-structures/doubly-linked-list/README.ru-RU.md
@@ -3,21 +3,23 @@
**Двусвязный список** — связная структура данных в информатике, состоящая из набора
последовательно связанных записей, называемых узлами. Каждый узел содержит два поля,
называемых ссылками, которые указывают на предыдущий и последующий элементы в
-последовательности узлов. Ссылка на предыдущий элемент корневого узла ссылка на
-последующий элемент последнего узла, указывают на некого рода прерыватель, обычно
+последовательности узлов. Ссылка на предыдущий элемент корневого узла и ссылка на
+последующий элемент последнего узла указывают на некого рода прерыватель, обычно
сторожевой узел или null, для облегчения обхода списка. Если в списке только один
-сторожевой узел, тогда список циклически связана через него.
-Двусвязный список можно представить, как два связных списка, которые образованны из
+сторожевой узел, тогда список циклически связан через него.
+Двусвязный список можно представить, как два связных списка, которые образованы из
одних и тех же данных, но расположенных в противоположном порядке.
-
+
+
+*Made with [okso.app](https://okso.app)*
Две ссылки позволяют обходить список в обоих направлениях. Добавление и
удаление узла в двусвязном списке требует изменения большего количества ссылок,
чем аналогичные операции в связном списке. Однако данные операции проще и потенциально
более эффективны (для некорневых узлов) - при обходе не нужно следить за предыдущим
узлом или повторно обходить список в поиске предыдущего узла, плюс его ссылка
-может быть изменена.
+может быть изменена.
## Псевдокод основных операций
@@ -38,7 +40,7 @@ Add(value)
end if
end Add
```
-
+
### Удаление
```text
@@ -75,7 +77,7 @@ Remove(head, value)
return false
end Remove
```
-
+
### Обратный обход
```text
@@ -89,7 +91,7 @@ ReverseTraversal(tail)
end while
end Reverse Traversal
```
-
+
## Сложность
## Временная сложность
diff --git a/src/data-structures/doubly-linked-list/README.uk-UA.md b/src/data-structures/doubly-linked-list/README.uk-UA.md
new file mode 100644
index 0000000000..a52a8015e0
--- /dev/null
+++ b/src/data-structures/doubly-linked-list/README.uk-UA.md
@@ -0,0 +1,109 @@
+# Двобічно зв'язаний список
+
+**Двобічно зв'язаний список** — зв'язкова структура даних в інформатиці, що складається з набору
+послідовно пов'язаних записів, званих вузлами. Кожен вузол містить два поля,
+званих посиланнями, які вказують на попередній і наступний елементи
+послідовність вузлів. Посилання на попередній елемент кореневого вузла та посилання на
+Наступний елемент останнього вузла вказують на деякого роду переривник, зазвичай
+сторожовий вузол або null для полегшення обходу списку. Якщо у списку лише один
+сторожовий вузол, тоді перелік циклічно пов'язаний через нього.
+Двобічно зв'язаний список можна уявити, як два зв'язкові списки, які утворені з
+одних і тих самих даних, але розташованих у протилежному порядку.
+
+
+
+_Made with [okso.app](https://okso.app)_
+
+Два посилання дозволяють обходити список в обох напрямках. Додавання та
+видалення вузла у двозв'язному списку вимагає зміни більшої кількості посилань,
+ніж аналогічні операції у зв'язковому списку. Однак дані операції простіше та потенційно
+більш ефективні (для некореневих вузлів) – при обході не потрібно стежити за попереднім
+вузлом або повторно обходити список у пошуку попереднього вузла, плюс його посилання
+може бути змінено.
+
+## Псевдокод основних операцій
+
+### Вставка
+
+```text
+Add(value)
+ Pre: value - значення, що додається
+ Post: value поміщено в кінець списку
+ n ← node(value)
+ if head = ø
+ head ← n
+ tail ← n
+ else
+ n.previous ← tail
+ tail.next ← n
+ tail ← n
+ end if
+end Add
+```
+
+### Видалення
+
+```text
+Remove(head, value)
+ Pre: head - перший вузол у списку
+ value - значення, яке слід видалити
+ Post: true - value видалено зі списку, інакше false
+ if head = ø
+ return false
+ end if
+ if value = head.value
+ if head = tail
+ head ← ø
+ tail ← ø
+ else
+ head ← head.next
+ head.previous ← ø
+ end if
+ return true
+ end if
+ n ← head.next
+ while n = ø and value = n.value
+ n ← n.next
+ end while
+ if n = tail
+ tail ← tail.previous
+ tail.next ← ø
+ return true
+ else if n = ø
+ n.previous.next ← n.next
+ n.next.previous ← n.previous
+ return true
+ end if
+ return false
+end Remove
+```
+
+### Зворотний обхід
+
+```text
+ReverseTraversal(tail)
+ Pre: tail - кінцевий елемент обхідного списку
+ Post: елементи списку пройдено у зворотному порядку
+ n ← tail
+ while n = ø
+ yield n.value
+ n ← n.previous
+ end while
+end Reverse Traversal
+```
+
+## Складність
+
+## Часова складність
+
+| Читання | Пошук | Вставка | Видалення |
+| :-----: | :---: | :-----: | :-------: |
+| O(n) | O(n) | O(1) | O(n) |
+
+### Просторова складність
+
+O(n)
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%94%D0%B2%D0%BE%D0%B1%D1%96%D1%87%D0%BD%D0%BE_%D0%B7%D0%B2%27%D1%8F%D0%B7%D0%B0%D0%BD%D0%B8%D0%B9_%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA#:~:text=%D0%94%D0%B2%D0%BE%D0%B1%D1%96%D1%87%D0%BD%D0%BE%20%D0%B7%D0%B2'%D1%8F%D0%B7%D0%B0%D0%BD%D0%B8%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%20%E2%80%94%20%D0%B2%D0%B8%D0%B4,%D0%BD%D0%B0%20%D0%BF%D0%BE%D0%B4%D0%B0%D0%BB%D1%8C%D1%88%D0%B8%D0%B9%20%D0%B2%D1%83%D0%B7%D0%BE%D0%BB%20%D1%83%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D1%83.)
diff --git a/src/data-structures/doubly-linked-list/README.zh-CN.md b/src/data-structures/doubly-linked-list/README.zh-CN.md
index 03dd53c11d..3e669f4c45 100644
--- a/src/data-structures/doubly-linked-list/README.zh-CN.md
+++ b/src/data-structures/doubly-linked-list/README.zh-CN.md
@@ -2,7 +2,9 @@
在计算机科学中, 一个 **双向链表(doubly linked list)** 是由一组称为节点的顺序链接记录组成的链接数据结构。每个节点包含两个字段，称为链接，它们是对节点序列中上一个节点和下一个节点的引用。开始节点和结束节点的上一个链接和下一个链接分别指向某种终止节点，通常是前哨节点或null，以方便遍历列表。如果只有一个前哨节点，则列表通过前哨节点循环链接。它可以被概念化为两个由相同数据项组成的单链表，但顺序相反。
-
+
+
+*Made with [okso.app](https://okso.app)*
两个节点链接允许在任一方向上遍历列表。
@@ -19,7 +21,7 @@ Add(value)
Pre: value is the value to add to the list
Post: value has been placed at the tail of the list
n ← node(value)
- if head = ø
+ if head != ø
head ← n
tail ← n
else
@@ -29,7 +31,7 @@ Add(value)
end if
end Add
```
-
+
### 删除
```text
@@ -51,14 +53,14 @@ Remove(head, value)
return true
end if
n ← head.next
- while n = ø and value !== n.value
+ while n != ø and value !== n.value
n ← n.next
end while
if n = tail
tail ← tail.previous
tail.next ← ø
return true
- else if n = ø
+ else if n != ø
n.previous.next ← n.next
n.next.previous ← n.previous
return true
@@ -66,7 +68,7 @@ Remove(head, value)
return false
end Remove
```
-
+
### 反向遍历
```text
@@ -74,13 +76,13 @@ ReverseTraversal(tail)
Pre: tail is the node of the list to traverse
Post: the list has been traversed in reverse order
n ← tail
- while n = ø
+ while n != ø
yield n.value
n ← n.previous
end while
end Reverse Traversal
```
-
+
## 复杂度
## 时间复杂度
diff --git a/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg b/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg
new file mode 100644
index 0000000000..3483e69fb8
Binary files /dev/null and b/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg differ
diff --git a/src/data-structures/graph/README.fr-FR.md b/src/data-structures/graph/README.fr-FR.md
new file mode 100644
index 0000000000..c6a6c90892
--- /dev/null
+++ b/src/data-structures/graph/README.fr-FR.md
@@ -0,0 +1,25 @@
+# Graph
+
+En informatique, un **graphe** est une structure de
+données abstraite qui implémente les concepts de
+graphe orienté et de graphe non-orienté venant
+des mathématiques, plus précisément du domaine de
+la théorie des graphes.
+
+La structure de données abstraite de graphe consiste
+en un ensemble fini, éventuellement mutable de sommets
+ou nœuds ou points, avec un ensemble de paires ordonnées
+ou non de tels éléments. Ces paires sont des arêtes, arcs
+non orientés, ou lignes pour un graphe non orienté, et
+flèches, arêtes orientées , arcs, ou lignes orientées
+dans le cas orienté. Les sommets peuvent faire partie
+de la structure, ou être des entités extérieures,
+représentées par des entiers ou des références.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## References
+
+- [Wikipedia](https://fr.wikipedia.org/wiki/Graphe_(type_abstrait))
diff --git a/src/data-structures/graph/README.md b/src/data-structures/graph/README.md
index 98acf43616..790602b536 100644
--- a/src/data-structures/graph/README.md
+++ b/src/data-structures/graph/README.md
@@ -3,25 +3,30 @@
_Read this in other languages:_
[_简体中文_](README.zh-CN.md),
[_Русский_](README.ru-RU.md),
-[_Português_](README.pt-BR.md)
+[_Français_](README.fr-FR.md),
+[_Português_](README.pt-BR.md),
+[_Українська_](README.uk-UA.md)
-In computer science, a **graph** is an abstract data type
-that is meant to implement the undirected graph and
+
+In computer science, a **graph** is an abstract data type
+that is meant to implement the undirected graph and
directed graph concepts from mathematics, specifically
the field of graph theory
-A graph data structure consists of a finite (and possibly
-mutable) set of vertices or nodes or points, together
-with a set of unordered pairs of these vertices for an
-undirected graph or a set of ordered pairs for a
-directed graph. These pairs are known as edges, arcs,
-or lines for an undirected graph and as arrows,
-directed edges, directed arcs, or directed lines
-for a directed graph. The vertices may be part of
-the graph structure, or may be external entities
+A graph data structure consists of a finite (and possibly
+mutable) set of vertices or nodes or points, together
+with a set of unordered pairs of these vertices for an
+undirected graph or a set of ordered pairs for a
+directed graph. These pairs are known as edges, arcs,
+or lines for an undirected graph and as arrows,
+directed edges, directed arcs, or directed lines
+for a directed graph. The vertices may be part of
+the graph structure, or may be external entities
represented by integer indices or references.
-
+
+
+*Made with [okso.app](https://okso.app)*
## References
diff --git a/src/data-structures/graph/README.pt-BR.md b/src/data-structures/graph/README.pt-BR.md
index 194a4eb04c..de7947cba8 100644
--- a/src/data-structures/graph/README.pt-BR.md
+++ b/src/data-structures/graph/README.pt-BR.md
@@ -17,7 +17,9 @@ para um grafo direcionado.
Os vértices podem fazer parte a estrutura do grafo, ou podem
ser entidades externas representadas por índices inteiros ou referências.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Referências
diff --git a/src/data-structures/graph/README.ru-RU.md b/src/data-structures/graph/README.ru-RU.md
index 2f656730c2..950198451b 100644
--- a/src/data-structures/graph/README.ru-RU.md
+++ b/src/data-structures/graph/README.ru-RU.md
@@ -3,7 +3,7 @@
**Граф** в информатике - абстрактный тип данных, который должен реализовывать концепции направленного и ненаправленного
графа в математике, особенно в области теории графов.
-Структура данных графа состоит из конечного (и возможно изменяющегося) набора вершин или узлов, или точек, совместно с
+Структура данных графа состоит из конечного (и возможно изменяющегося) набора вершин или узлов, или точек, совместно с
набором ненаправленных пар этих вершин для ненаправленного графа или с набором направленных пар для направленного графа.
Эти пары известны как рёбра, арки или линии для ненаправленного графа и как стрелки, направленные рёбра, направленные
арки или направленные линии для направленного графа. Эти вершины могут быть частью структуры графа, или внешними
@@ -14,7 +14,9 @@
информатике, могут быть представлены графами. Например, строение Википедии можно смоделировать при помощи
ориентированного графа, в котором вершины — это статьи, а дуги (ориентированные рёбра) — гиперссылки.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Ссылки
diff --git a/src/data-structures/graph/README.uk-UA.md b/src/data-structures/graph/README.uk-UA.md
new file mode 100644
index 0000000000..9886cd904c
--- /dev/null
+++ b/src/data-structures/graph/README.uk-UA.md
@@ -0,0 +1,24 @@
+# Граф
+
+**Граф** в інформатиці - абстрактний тип даних, який має реалізовувати концепції спрямованого та неспрямованого
+графа у математиці, особливо у галузі теорії графів.
+
+Структура даних графа складається з кінцевого (і можливо, що змінюється) набору вершин або вузлів, або точок, спільно з
+набором ненаправлених пар цих вершин для ненаправленого графа або набором спрямованих пар для спрямованого графа.
+Ці пари відомі як ребра, арки або лінії для ненаправленого графа та як стрілки, спрямовані ребра, спрямовані
+арки чи спрямовані лінії для спрямованого графа. Ці вершини можуть бути частиною структури графа, або зовнішніми
+сутностями, представленими цілими індексами або посиланнями.
+
+Для різних областей застосування види графів можуть відрізнятися спрямованістю, обмеженнями на кількість зв'язків та
+додатковими даними про вершини або ребра. Багато структур, що становлять практичний інтерес у математиці та
+інформатики можуть бути представлені графами. Наприклад, будову Вікіпедії можна змоделювати за допомогою
+орієнтованого графа, в якому вершини – це статті, а дуги (орієнтовані ребра) – гіперпосилання.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## Посилання
+
+- [Граф у математиці на Wikipedia](https://uk.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D1%84_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0))
+- [Структура даних Graph / Граф](https://www.youtube.com/watch?v=D0U8aFEhgKQ)
diff --git a/src/data-structures/graph/README.zh-CN.md b/src/data-structures/graph/README.zh-CN.md
index 49c977157e..1f885a43b9 100644
--- a/src/data-structures/graph/README.zh-CN.md
+++ b/src/data-structures/graph/README.zh-CN.md
@@ -11,9 +11,9 @@
如果顶点对之间的边是有权重的,该图可称为加权图。
+
-
-
+*Made with [okso.app](https://okso.app)*
## 参考
diff --git a/src/data-structures/graph/images/graph.jpeg b/src/data-structures/graph/images/graph.jpeg
new file mode 100644
index 0000000000..e49ecc0b9c
Binary files /dev/null and b/src/data-structures/graph/images/graph.jpeg differ
diff --git a/src/data-structures/hash-table/README.fr-FR.md b/src/data-structures/hash-table/README.fr-FR.md
index f32d8e5624..2fd41c8838 100644
--- a/src/data-structures/hash-table/README.fr-FR.md
+++ b/src/data-structures/hash-table/README.fr-FR.md
@@ -17,11 +17,13 @@ hachage où la fonction de hachage génère le même index
pour plusieurs clés. De telles collisions doivent être
accommodées d'une manière ou d'une autre.
-
+
Collision de hachage résolue par chaînage séparé.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Références
diff --git a/src/data-structures/hash-table/README.ja-JP.md b/src/data-structures/hash-table/README.ja-JP.md
index 85bf71d19c..d71cb273b9 100644
--- a/src/data-structures/hash-table/README.ja-JP.md
+++ b/src/data-structures/hash-table/README.ja-JP.md
@@ -1,14 +1,16 @@
# ハッシュテーブル
-
+
コンピュータサイエンスにおいて、**ハッシュテーブル**（ハッシュマップ)は*キーを値にマッピング*できる*連想配列*の機能を持ったデータ構造です。ハッシュテーブルは*ハッシュ関数*を使ってバケットやスロットの配列へのインデックスを計算し、そこから目的の値を見つけることができます。
理想的には、ハッシュ関数は各キーを一意のバケットに割り当てますが、ほとんどのハッシュテーブルは不完全なハッシュ関数を採用しているため、複数のキーに対して同じインデックスを生成した時にハッシュの衝突が起こります。このような衝突は何らかの方法で対処する必要があります。
-
+
チェイン法によるハッシュの衝突の解決例
-
+
+
+*Made with [okso.app](https://okso.app)*
## 参考
diff --git a/src/data-structures/hash-table/README.ko-KR.md b/src/data-structures/hash-table/README.ko-KR.md
new file mode 100644
index 0000000000..b3a8c94066
--- /dev/null
+++ b/src/data-structures/hash-table/README.ko-KR.md
@@ -0,0 +1,27 @@
+# Hash Table
+
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Français_](README.fr-FR.md),
+[_Português_](README.pt-BR.md)
+
+컴퓨팅에서, **해시 테이블**(해시 맵)은 키를 값에 매핑할 수 있는 구조인 *연관 배열*을 구현하는 자료 구조입니다. 해시 테이블은 *해시 함수*를 사용해 원하는 값을 담을 수 있는 버킷 또는 슬롯 배열의 인덱스를 계산합니다.
+
+이상적으로, 해시 함수는 각 키들을 고유 버킷에 할당하지만 대부분의 해시 테이블은 불완전한 해시 함수를 사용하기 때문에 해시 함수를 통해 두 개 이상의 키에 대해 동일한 인덱스를 생성하는 해시 충돌이 발생할 수 있습니다. 이러한 해시 충돌은 어떠한 방법으로든 해결되어야 합니다.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+다음은 분리 연결법을 통해 해시 충돌을 해결한 예시입니다.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## 참고
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Hash_table)
+- [YouTube](https://www.youtube.com/watch?v=shs0KM3wKv8&index=4&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/hash-table/README.md b/src/data-structures/hash-table/README.md
index 37d20a6199..f0d0c9932d 100644
--- a/src/data-structures/hash-table/README.md
+++ b/src/data-structures/hash-table/README.md
@@ -5,27 +5,31 @@ _Read this in other languages:_
[_Русский_](README.ru-RU.md),
[_日本語_](README.ja-JP.md),
[_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
-
-In computing, a **hash table** (hash map) is a data
-structure which implements an *associative array*
-abstract data type, a structure that can *map keys
-to values*. A hash table uses a *hash function* to
-compute an index into an array of buckets or slots,
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
+
+In computing, a **hash table** (hash map) is a data
+structure which implements an _associative array_
+abstract data type, a structure that can _map keys
+to values_. A hash table uses a _hash function_ to
+compute an index into an array of buckets or slots,
from which the desired value can be found
-Ideally, the hash function will assign each key to a
-unique bucket, but most hash table designs employ an
-imperfect hash function, which might cause hash
+Ideally, the hash function will assign each key to a
+unique bucket, but most hash table designs employ an
+imperfect hash function, which might cause hash
collisions where the hash function generates the same
index for more than one key. Such collisions must be
accommodated in some way.
-
+
Hash collision resolved by separate chaining.
-
+
+
+_Made with [okso.app](https://okso.app)_
## References
diff --git a/src/data-structures/hash-table/README.pt-BR.md b/src/data-structures/hash-table/README.pt-BR.md
index 0adf9ca96b..c89faf6ca1 100644
--- a/src/data-structures/hash-table/README.pt-BR.md
+++ b/src/data-structures/hash-table/README.pt-BR.md
@@ -1,6 +1,6 @@
# Tabela de Hash (Hash Table)
-Na ciência da computação, uma **tabela de hash** (hash map) é uma
+Na ciência da computação, uma **tabela de hash** (hash table) é uma
estrutura de dados pela qual implementa um tipo de dado abstrado de
*array associativo*, uma estrutura que pode *mapear chaves para valores*.
Uma tabela de hash utiliza uma *função de hash* para calcular um índice
@@ -10,14 +10,16 @@ pode ser encontrado.
Idealmente, a função de hash irá atribuir a cada chave a um bucket único,
mas a maioria dos designs de tabela de hash emprega uma função de hash
imperfeita, pela qual poderá causar colisões de hashes onde a função de hash
-gera o mesmo índice para mais de uma chave.Tais colisões devem ser
+gera o mesmo índice para mais de uma chave. Tais colisões devem ser
acomodados de alguma forma.
-
+
Colisão de hash resolvida por encadeamento separado.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Referências
diff --git a/src/data-structures/hash-table/README.ru-RU.md b/src/data-structures/hash-table/README.ru-RU.md
index d5487cb900..e1e21129da 100644
--- a/src/data-structures/hash-table/README.ru-RU.md
+++ b/src/data-structures/hash-table/README.ru-RU.md
@@ -2,10 +2,10 @@
**Хеш-таблица** - структура данных, реализующая абстрактный тип данных *ассоциативный массив*, т.е. структура, которая
*связывает ключи со значениями*. Хеш-таблица использует *хеш-функцию* для вычисления индекса в массиве, в котором может
-быть найдено желаемое значение. Ниже представлена хеш-таблица, в которой ключём выступает имя человека, а значениями
+быть найдено желаемое значение. Ниже представлена хеш-таблица, в которой ключом выступает имя человека, а значениями
являются телефонные номера. Хеш-функция преобразует ключ-имя в индекс массива с телефонными номерами.
-
+
В идеале хеш-функция будет присваивать элементу массива уникальный ключ. Однако большинство реальных хеш-таблиц
используют несовершенные хеш-функции. Это может привести к ситуациям, когда хеш-функция генерирует одинаковый индекс для
@@ -14,9 +14,13 @@
Существует два варианта решения коллизий - хеш-таблица с цепочками и с открытой адресацией.
Метод цепочек подразумевает хранение значений, соответствующих одному и тому же индексу в виде связного списка(цепочки).
-
+
+
+
+*Made with [okso.app](https://okso.app)*
Метод открытой адресации помещает значение, для которого получен дублирующий индекс, в первую свободную ячейку.
+
## Ссылки
diff --git a/src/data-structures/hash-table/README.uk-UA.md b/src/data-structures/hash-table/README.uk-UA.md
new file mode 100644
index 0000000000..2ab3183599
--- /dev/null
+++ b/src/data-structures/hash-table/README.uk-UA.md
@@ -0,0 +1,29 @@
+# Геш таблиця
+
+**Геш таблиця** - структура даних, що реалізує абстрактний тип даних асоціативний масив, тобто. структура, яка
+_зв'язує ключі зі значеннями_. Геш-таблиця використовує _геш-функцію_ для обчислення індексу в масиві, в якому може
+бути знайдено бажане значення. Нижче представлена геш-таблиця, у якій ключем виступає ім'я людини, а значеннями
+телефонні номери. Геш-функція перетворює ключ-ім'я на індекс масиву з телефонними номерами.
+
+
+
+В ідеалі геш-функція присвоюватиме елементу масиву унікальний ключ. Проте більшість реальних геш-таблиць
+використовують недосконалі геш-функції. Це може призвести до ситуацій, коли геш-функція генерує однаковий індекс для
+кількох ключів. Ці ситуації називаються колізіями і мають бути якось вирішені.
+
+Існує два варіанти вирішення колізій - геш-таблиця з ланцюжками та з відкритою адресацією.
+
+Метод ланцюжків передбачає зберігання значень, відповідних одному й тому індексу як зв'язкового списку(ланцюжка).
+
+
+
+_Made with [okso.app](https://okso.app)_
+
+Метод відкритої адресації поміщає значення, для якого отримано дублюючий індекс, в першу вільну комірку.
+
+
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%93%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%8F)
+- [YouTube](https://www.youtube.com/watch?v=WTYaboK-NMk)
diff --git a/src/data-structures/hash-table/README.zh-CN.md b/src/data-structures/hash-table/README.zh-CN.md
index 5de3cc5ea2..c53214aa88 100644
--- a/src/data-structures/hash-table/README.zh-CN.md
+++ b/src/data-structures/hash-table/README.zh-CN.md
@@ -1,7 +1,7 @@
# 哈希表
-在计算中, 一个 **哈希表(hash table 或hash map)** 是一种实现 *关联数组(associative array)*
-的抽象数据；类型, 该结构可以将 *键映射到值*。
+在计算中, 一个 **哈希表(hash table 或hash map)** 是一种实现 *关联数组(associative array)*
+的抽象数据类型, 该结构可以将 *键映射到值*。
哈希表使用 *哈希函数/散列函数* 来计算一个值在数组或桶(buckets)中或槽(slots)中对应的索引,可使用该索引找到所需的值。
@@ -9,11 +9,15 @@
以某种方式进行处理。
-
+
+
+*Made with [okso.app](https://okso.app)*
通过单独的链接解决哈希冲突
-
+
+
+*Made with [okso.app](https://okso.app)*
## 参考
diff --git a/src/data-structures/hash-table/images/collision-resolution.jpeg b/src/data-structures/hash-table/images/collision-resolution.jpeg
new file mode 100644
index 0000000000..1e0c979289
Binary files /dev/null and b/src/data-structures/hash-table/images/collision-resolution.jpeg differ
diff --git a/src/data-structures/hash-table/images/hash-table.jpeg b/src/data-structures/hash-table/images/hash-table.jpeg
new file mode 100644
index 0000000000..f350453c10
Binary files /dev/null and b/src/data-structures/hash-table/images/hash-table.jpeg differ
diff --git a/src/data-structures/heap/Heap.js b/src/data-structures/heap/Heap.js
index 45dfcfa267..b978739ec8 100644
--- a/src/data-structures/heap/Heap.js
+++ b/src/data-structures/heap/Heap.js
@@ -279,7 +279,7 @@ export default class Heap {
/* istanbul ignore next */
pairIsInCorrectOrder(firstElement, secondElement) {
throw new Error(`
- You have to implement heap pair comparision method
+ You have to implement heap pair comparison method
for ${firstElement} and ${secondElement} values.
`);
}
diff --git a/src/data-structures/heap/MaxHeapAdhoc.js b/src/data-structures/heap/MaxHeapAdhoc.js
new file mode 100644
index 0000000000..b9d69c59e0
--- /dev/null
+++ b/src/data-structures/heap/MaxHeapAdhoc.js
@@ -0,0 +1,115 @@
+/**
+ * The minimalistic (ad hoc) version of a MaxHeap data structure that doesn't have
+ * external dependencies and that is easy to copy-paste and use during the
+ * coding interview if allowed by the interviewer (since many data
+ * structures in JS are missing).
+ */
+class MaxHeapAdhoc {
+ constructor(heap = []) {
+ this.heap = [];
+ heap.forEach(this.add);
+ }
+
+ add(num) {
+ this.heap.push(num);
+ this.heapifyUp();
+ }
+
+ peek() {
+ return this.heap[0];
+ }
+
+ poll() {
+ if (this.heap.length === 0) return undefined;
+ const top = this.heap[0];
+ this.heap[0] = this.heap[this.heap.length - 1];
+ this.heap.pop();
+ this.heapifyDown();
+ return top;
+ }
+
+ isEmpty() {
+ return this.heap.length === 0;
+ }
+
+ toString() {
+ return this.heap.join(',');
+ }
+
+ heapifyUp() {
+ let nodeIndex = this.heap.length - 1;
+ while (nodeIndex > 0) {
+ const parentIndex = this.getParentIndex(nodeIndex);
+ if (this.heap[parentIndex] >= this.heap[nodeIndex]) break;
+ this.swap(parentIndex, nodeIndex);
+ nodeIndex = parentIndex;
+ }
+ }
+
+ heapifyDown() {
+ let nodeIndex = 0;
+
+ while (
+ (
+ this.hasLeftChild(nodeIndex) && this.heap[nodeIndex] < this.leftChild(nodeIndex)
+ )
+ || (
+ this.hasRightChild(nodeIndex) && this.heap[nodeIndex] < this.rightChild(nodeIndex)
+ )
+ ) {
+ const leftIndex = this.getLeftChildIndex(nodeIndex);
+ const rightIndex = this.getRightChildIndex(nodeIndex);
+ const left = this.leftChild(nodeIndex);
+ const right = this.rightChild(nodeIndex);
+
+ if (this.hasLeftChild(nodeIndex) && this.hasRightChild(nodeIndex)) {
+ if (left >= right) {
+ this.swap(leftIndex, nodeIndex);
+ nodeIndex = leftIndex;
+ } else {
+ this.swap(rightIndex, nodeIndex);
+ nodeIndex = rightIndex;
+ }
+ } else if (this.hasLeftChild(nodeIndex)) {
+ this.swap(leftIndex, nodeIndex);
+ nodeIndex = leftIndex;
+ }
+ }
+ }
+
+ getLeftChildIndex(parentIndex) {
+ return (2 * parentIndex) + 1;
+ }
+
+ getRightChildIndex(parentIndex) {
+ return (2 * parentIndex) + 2;
+ }
+
+ getParentIndex(childIndex) {
+ return Math.floor((childIndex - 1) / 2);
+ }
+
+ hasLeftChild(parentIndex) {
+ return this.getLeftChildIndex(parentIndex) < this.heap.length;
+ }
+
+ hasRightChild(parentIndex) {
+ return this.getRightChildIndex(parentIndex) < this.heap.length;
+ }
+
+ leftChild(parentIndex) {
+ return this.heap[this.getLeftChildIndex(parentIndex)];
+ }
+
+ rightChild(parentIndex) {
+ return this.heap[this.getRightChildIndex(parentIndex)];
+ }
+
+ swap(indexOne, indexTwo) {
+ const tmp = this.heap[indexTwo];
+ this.heap[indexTwo] = this.heap[indexOne];
+ this.heap[indexOne] = tmp;
+ }
+}
+
+export default MaxHeapAdhoc;
diff --git a/src/data-structures/heap/MinHeapAdhoc.js b/src/data-structures/heap/MinHeapAdhoc.js
new file mode 100644
index 0000000000..c70692f3de
--- /dev/null
+++ b/src/data-structures/heap/MinHeapAdhoc.js
@@ -0,0 +1,117 @@
+/**
+ * The minimalistic (ad hoc) version of a MinHeap data structure that doesn't have
+ * external dependencies and that is easy to copy-paste and use during the
+ * coding interview if allowed by the interviewer (since many data
+ * structures in JS are missing).
+ */
+class MinHeapAdhoc {
+ constructor(heap = []) {
+ this.heap = [];
+ heap.forEach(this.add);
+ }
+
+ add(num) {
+ this.heap.push(num);
+ this.heapifyUp();
+ }
+
+ peek() {
+ return this.heap[0];
+ }
+
+ poll() {
+ if (this.heap.length === 0) return undefined;
+ const top = this.heap[0];
+ this.heap[0] = this.heap[this.heap.length - 1];
+ this.heap.pop();
+ this.heapifyDown();
+ return top;
+ }
+
+ isEmpty() {
+ return this.heap.length === 0;
+ }
+
+ toString() {
+ return this.heap.join(',');
+ }
+
+ heapifyUp() {
+ let nodeIndex = this.heap.length - 1;
+ while (nodeIndex > 0) {
+ const parentIndex = this.getParentIndex(nodeIndex);
+ if (this.heap[parentIndex] <= this.heap[nodeIndex]) break;
+ this.swap(parentIndex, nodeIndex);
+ nodeIndex = parentIndex;
+ }
+ }
+
+ heapifyDown() {
+ let nodeIndex = 0;
+
+ while (
+ (
+ this.hasLeftChild(nodeIndex)
+ && this.heap[nodeIndex] > this.leftChild(nodeIndex)
+ )
+ || (
+ this.hasRightChild(nodeIndex)
+ && this.heap[nodeIndex] > this.rightChild(nodeIndex)
+ )
+ ) {
+ const leftIndex = this.getLeftChildIndex(nodeIndex);
+ const rightIndex = this.getRightChildIndex(nodeIndex);
+ const left = this.leftChild(nodeIndex);
+ const right = this.rightChild(nodeIndex);
+
+ if (this.hasLeftChild(nodeIndex) && this.hasRightChild(nodeIndex)) {
+ if (left <= right) {
+ this.swap(leftIndex, nodeIndex);
+ nodeIndex = leftIndex;
+ } else {
+ this.swap(rightIndex, nodeIndex);
+ nodeIndex = rightIndex;
+ }
+ } else if (this.hasLeftChild(nodeIndex)) {
+ this.swap(leftIndex, nodeIndex);
+ nodeIndex = leftIndex;
+ }
+ }
+ }
+
+ getLeftChildIndex(parentIndex) {
+ return 2 * parentIndex + 1;
+ }
+
+ getRightChildIndex(parentIndex) {
+ return 2 * parentIndex + 2;
+ }
+
+ getParentIndex(childIndex) {
+ return Math.floor((childIndex - 1) / 2);
+ }
+
+ hasLeftChild(parentIndex) {
+ return this.getLeftChildIndex(parentIndex) < this.heap.length;
+ }
+
+ hasRightChild(parentIndex) {
+ return this.getRightChildIndex(parentIndex) < this.heap.length;
+ }
+
+ leftChild(parentIndex) {
+ return this.heap[this.getLeftChildIndex(parentIndex)];
+ }
+
+ rightChild(parentIndex) {
+ return this.heap[this.getRightChildIndex(parentIndex)];
+ }
+
+ swap(indexOne, indexTwo) {
+ const tmp = this.heap[indexTwo];
+ this.heap[indexTwo] = this.heap[indexOne];
+ this.heap[indexOne] = tmp;
+ }
+}
+
+export default MinHeapAdhoc;
diff --git a/src/data-structures/heap/README.fr-FR.md b/src/data-structures/heap/README.fr-FR.md
index 49ad73cc9f..56f184b593 100644
--- a/src/data-structures/heap/README.fr-FR.md
+++ b/src/data-structures/heap/README.fr-FR.md
@@ -4,11 +4,15 @@ En informatique, un **tas** est une structure de données arborescente spéciali
Dans un *tas minimal* (en anglais *min heap*), si `P` est un nœud parent de `C`, alors la clé (la valeur) de `P` est inférieure ou égale à la clé de `C`.
-
+
+
+*Made with [okso.app](https://okso.app)*
Dans un *tas maximal* (en anglais *max heap*), la clé de `P` est supérieure ou égale à la clé de `C`.
-
+
+
+
Le nœud au «sommet» du tas sans parents est appelé le nœud racine.
diff --git a/src/data-structures/heap/README.ja-JP.md b/src/data-structures/heap/README.ja-JP.md
index 465e11a049..13d3e36338 100644
--- a/src/data-structures/heap/README.ja-JP.md
+++ b/src/data-structures/heap/README.ja-JP.md
@@ -4,11 +4,15 @@
*最小ヒープ*では、もし`P`が`C`の親ノードの場合、`P`のキー(値)は`C`のキーより小さい、または等しくなります。
-
+
+
+*Made with [okso.app](https://okso.app)*
*最大ヒープ*では、`P`のキーは`C`のキーより大きい、もしくは等しくなります。
-
+
+
+
ヒープの「トップ」のノードには親ノードが存在せず、ルートノードと呼ばれます。
diff --git a/src/data-structures/heap/README.ko-KR.md b/src/data-structures/heap/README.ko-KR.md
new file mode 100644
index 0000000000..136a87b420
--- /dev/null
+++ b/src/data-structures/heap/README.ko-KR.md
@@ -0,0 +1,23 @@
+# 힙 (자료구조)
+
+컴퓨터 과학에서의 **힙**은 아래에 설명된 힙 속성을 만족하는 전문화된 트리 기반 데이터구조입니다.
+
+*최소 힙*에서 `P`가 `C`의 상위 노드라면 `P`의 키(값)는 `C`의 키보다 작거나 같습니다.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+*최대 힙*에서 `P`의 키는 `C`의 키보다 크거나 같습니다.
+
+
+
+
+
+상위 노드가 없는 힙의 "상단"에 있는 노드를 루트 노드라고 합니다.
+
+## 참조
+
+- [Wikipedia](<https://en.wikipedia.org/wiki/Heap_(data_structure)>)
+- [YouTube](https://www.youtube.com/watch?v=t0Cq6tVNRBA&index=5&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
diff --git a/src/data-structures/heap/README.md b/src/data-structures/heap/README.md
index b125fad7a7..392c5c96bc 100644
--- a/src/data-structures/heap/README.md
+++ b/src/data-structures/heap/README.md
@@ -5,9 +5,13 @@ _Read this in other languages:_
[_Русский_](README.ru-RU.md),
[_日本語_](README.ja-JP.md),
[_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Türkçe_](README.tr-TR.md),
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
-In computer science, a **heap** is a specialized tree-based
+
+In computer science, a **heap** is a specialized tree-based
data structure that satisfies the heap property described
below.
@@ -15,16 +19,50 @@ In a *min heap*, if `P` is a parent node of `C`, then the
key (the value) of `P` is less than or equal to the
key of `C`.
-
+
+
+*Made with [okso.app](https://okso.app)*
In a *max heap*, the key of `P` is greater than or equal
to the key of `C`
-
+
+
+
-The node at the "top" of the heap with no parents is
+The node at the "top" of the heap with no parents is
called the root node.
+## Time Complexities
+
+Here are time complexities of various heap data structures. Function names assume a max-heap.
+
+| Operation | find-max | delete-max | insert| increase-key| meld |
+| --------- | -------- | ---------- | ----- | ----------- | ---- |
+| [Binary](https://en.wikipedia.org/wiki/Binary_heap) | `Θ(1)` | `Θ(log n)` | `O(log n)` | `O(log n)` | `Θ(n)` |
+| [Leftist](https://en.wikipedia.org/wiki/Leftist_tree) | `Θ(1)` | `Θ(log n)` | `Θ(log n)` | `O(log n)` | `Θ(log n)` |
+| [Binomial](https://en.wikipedia.org/wiki/Binomial_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `O(log n)` | `O(log n)` |
+| [Fibonacci](https://en.wikipedia.org/wiki/Fibonacci_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
+| [Pairing](https://en.wikipedia.org/wiki/Pairing_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `o(log n)` | `Θ(1)` |
+| [Brodal](https://en.wikipedia.org/wiki/Brodal_queue) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
+| [Rank-pairing](https://en.wikipedia.org/w/index.php?title=Rank-pairing_heap&action=edit&redlink=1) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
+| [Strict Fibonacci](https://en.wikipedia.org/wiki/Fibonacci_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
+| [2-3 heap](https://en.wikipedia.org/wiki/2%E2%80%933_heap) | `O(log n)` | `O(log n)` | `O(log n)` | `Θ(1)` | `?` |
+
+Where:
+- **find-max (or find-min):** find a maximum item of a max-heap, or a minimum item of a min-heap, respectively (a.k.a. *peek*)
+- **delete-max (or delete-min):** removing the root node of a max heap (or min heap), respectively
+- **insert:** adding a new key to the heap (a.k.a., *push*)
+- **increase-key or decrease-key:** updating a key within a max- or min-heap, respectively
+- **meld:** joining two heaps to form a valid new heap containing all the elements of both, destroying the original heaps.
+
+> In this repository, the [MaxHeap.js](./MaxHeap.js) and [MinHeap.js](./MinHeap.js) are examples of the **Binary** heap.
+
+## Implementation
+
+- [MaxHeap.js](./MaxHeap.js) and [MinHeap.js](./MinHeap.js)
+- [MaxHeapAdhoc.js](./MaxHeapAdhoc.js) and [MinHeapAdhoc.js](./MinHeapAdhoc.js) - The minimalistic (ad hoc) version of a MinHeap/MaxHeap data structure that doesn't have external dependencies and that is easy to copy-paste and use during the coding interview if allowed by the interviewer (since many data structures in JS are missing).
+
## References
- [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))
diff --git a/src/data-structures/heap/README.pt-BR.md b/src/data-structures/heap/README.pt-BR.md
index e78f6c199a..f229048d3a 100644
--- a/src/data-structures/heap/README.pt-BR.md
+++ b/src/data-structures/heap/README.pt-BR.md
@@ -6,12 +6,16 @@ baseada em uma árvore especializada que satisfaz a propriedade _heap_ descrita
Em um *heap mínimo* (min heap), caso `P` é um nó pai de `C`, então a chave
(o valor) de `P` é menor ou igual a chave de `C`.
-
+
+
+*Made with [okso.app](https://okso.app)*
Em uma *heap máximo* (max heap), a chave de `P` é maior ou igual
a chave de `C`.
-
+
+
+
O nó no "topo" do _heap_, cujo não possui pais, é chamado de nó raiz.
diff --git a/src/data-structures/heap/README.ru-RU.md b/src/data-structures/heap/README.ru-RU.md
index 760fc479ab..4c074d1f7c 100644
--- a/src/data-structures/heap/README.ru-RU.md
+++ b/src/data-structures/heap/README.ru-RU.md
@@ -4,11 +4,15 @@
если B является узлом-потомком узла A, то ключ(A) ≥ ключ(B). Из этого следует, что элемент с наибольшим ключом всегда
является корневым узлом кучи, поэтому иногда такие кучи называют max-кучами.
-
+
+
+
Если сравнение перевернуть, то наименьший элемент будет всегда корневым узлом, такие кучи называют min-кучами.
-
+
+
+*Made with [okso.app](https://okso.app)*
Не существует никаких ограничений относительно того, сколько узлов-потомков имеет каждый узел кучи. На практике их
число обычно не более двух. Куча является максимально эффективной реализацией абстрактного типа данных, который
diff --git a/src/data-structures/heap/README.tr-TR.md b/src/data-structures/heap/README.tr-TR.md
new file mode 100644
index 0000000000..05906391e8
--- /dev/null
+++ b/src/data-structures/heap/README.tr-TR.md
@@ -0,0 +1,22 @@
+# Heap (data-structure)
+
+Bilgisayar biliminde, **yığın (heap)** aşağıda açıklanan özellikleri karşılayan ağaç tabanlı(tree-based) özel bir veri yapısıdır.
+
+*min heap*, Eğer `P`, `C`'nin üst düğümü ise, `P`'nin anahtarı (değeri) `C`'nin anahtarından (değerinden) küçük veya ona eşittir.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+*max heap*, `P`'nin anahtarı `C`'nin anahtarından büyük veya eşittir.
+
+
+
+
+
+Yığının (Heap) "en üstündeki" ebeveyni olmayan düğüme kök düğüm (root node) denir.
+
+## Referanslar
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))
+- [YouTube](https://www.youtube.com/watch?v=t0Cq6tVNRBA&index=5&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/heap/README.uk-UA.md b/src/data-structures/heap/README.uk-UA.md
new file mode 100644
index 0000000000..f35995d8ae
--- /dev/null
+++ b/src/data-structures/heap/README.uk-UA.md
@@ -0,0 +1,25 @@
+# Купа (структура даних)
+
+У комп'ютерних науках купа - це спеціалізована структура даних на кшталт дерева, яка задовольняє властивості купи:
+якщо B є вузлом-нащадком вузла A, то ключ (A) ≥ ключ (B). З цього випливає, що елемент із найбільшим ключем завжди
+є кореневим вузлом купи, тому іноді такі купи називають max-купами.
+
+
+
+
+
+Якщо порівняння перевернути, то найменший елемент завжди буде кореневим вузлом, такі купи називають min-купами.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+Не існує жодних обмежень щодо того, скільки вузлів-нащадків має кожен вузол купи. На практиці їх
+число зазвичай трохи більше двох. Купа є максимально ефективною реалізацією абстрактного типу даних, який
+називається чергою із пріоритетом.
+
+Вузол на вершині купи, який не має батьків, називається кореневим вузлом.
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%9A%D1%83%D0%BF%D0%B0_(%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0_%D0%B4%D0%B0%D0%BD%D0%B8%D1%85))
diff --git a/src/data-structures/heap/README.zh-CN.md b/src/data-structures/heap/README.zh-CN.md
index 4c1ecaf068..8ba42dfb05 100644
--- a/src/data-structures/heap/README.zh-CN.md
+++ b/src/data-structures/heap/README.zh-CN.md
@@ -1,19 +1,23 @@
-# 堆 (数据结构)
-
-在计算机科学中, 一个 **堆(heap)** 是一种特殊的基于树的数据结构，它满足下面描述的堆属性。
-
-在一个 *最小堆(min heap)* 中, 如果 `P` 是 `C` 的一个父级节点, 那么 `P` 的key(或value)应小于或等于 `C` 的对应值.
-
-
-
-在一个 *最大堆(max heap)* 中, `P` 的key(或value)大于 `C` 的对应值。
-
-
-
-
-在堆“顶部”的没有父级节点的节点,被称之为根节点。
-
-## 参考
-
-- [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))
-- [YouTube](https://www.youtube.com/watch?v=t0Cq6tVNRBA&index=5&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+# 堆 (数据结构)
+
+在计算机科学中, 一个 **堆(heap)** 是一种特殊的基于树的数据结构，它满足下面描述的堆属性。
+
+在一个 *最小堆(min heap)* 中, 如果 `P` 是 `C` 的一个父级节点, 那么 `P` 的key(或value)应小于或等于 `C` 的对应值.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+在一个 *最大堆(max heap)* 中, `P` 的key(或value)大于 `C` 的对应值。
+
+
+
+
+
+
+在堆“顶部”的没有父级节点的节点,被称之为根节点。
+
+## 参考
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))
+- [YouTube](https://www.youtube.com/watch?v=t0Cq6tVNRBA&index=5&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/heap/__test__/MaxHeapAdhoc.test.js b/src/data-structures/heap/__test__/MaxHeapAdhoc.test.js
new file mode 100644
index 0000000000..0217a98ddf
--- /dev/null
+++ b/src/data-structures/heap/__test__/MaxHeapAdhoc.test.js
@@ -0,0 +1,91 @@
+import MaxHeap from '../MaxHeapAdhoc';
+
+describe('MaxHeapAdhoc', () => {
+ it('should create an empty max heap', () => {
+ const maxHeap = new MaxHeap();
+
+ expect(maxHeap).toBeDefined();
+ expect(maxHeap.peek()).toBe(undefined);
+ expect(maxHeap.isEmpty()).toBe(true);
+ });
+
+ it('should add items to the heap and heapify it up', () => {
+ const maxHeap = new MaxHeap();
+
+ maxHeap.add(5);
+ expect(maxHeap.isEmpty()).toBe(false);
+ expect(maxHeap.peek()).toBe(5);
+ expect(maxHeap.toString()).toBe('5');
+
+ maxHeap.add(3);
+ expect(maxHeap.peek()).toBe(5);
+ expect(maxHeap.toString()).toBe('5,3');
+
+ maxHeap.add(10);
+ expect(maxHeap.peek()).toBe(10);
+ expect(maxHeap.toString()).toBe('10,3,5');
+
+ maxHeap.add(1);
+ expect(maxHeap.peek()).toBe(10);
+ expect(maxHeap.toString()).toBe('10,3,5,1');
+
+ maxHeap.add(1);
+ expect(maxHeap.peek()).toBe(10);
+ expect(maxHeap.toString()).toBe('10,3,5,1,1');
+
+ expect(maxHeap.poll()).toBe(10);
+ expect(maxHeap.toString()).toBe('5,3,1,1');
+
+ expect(maxHeap.poll()).toBe(5);
+ expect(maxHeap.toString()).toBe('3,1,1');
+
+ expect(maxHeap.poll()).toBe(3);
+ expect(maxHeap.toString()).toBe('1,1');
+ });
+
+ it('should poll items from the heap and heapify it down', () => {
+ const maxHeap = new MaxHeap();
+
+ maxHeap.add(5);
+ maxHeap.add(3);
+ maxHeap.add(10);
+ maxHeap.add(11);
+ maxHeap.add(1);
+
+ expect(maxHeap.toString()).toBe('11,10,5,3,1');
+
+ expect(maxHeap.poll()).toBe(11);
+ expect(maxHeap.toString()).toBe('10,3,5,1');
+
+ expect(maxHeap.poll()).toBe(10);
+ expect(maxHeap.toString()).toBe('5,3,1');
+
+ expect(maxHeap.poll()).toBe(5);
+ expect(maxHeap.toString()).toBe('3,1');
+
+ expect(maxHeap.poll()).toBe(3);
+ expect(maxHeap.toString()).toBe('1');
+
+ expect(maxHeap.poll()).toBe(1);
+ expect(maxHeap.toString()).toBe('');
+
+ expect(maxHeap.poll()).toBe(undefined);
+ expect(maxHeap.toString()).toBe('');
+ });
+
+ it('should heapify down through the right branch as well', () => {
+ const maxHeap = new MaxHeap();
+
+ maxHeap.add(3);
+ maxHeap.add(12);
+ maxHeap.add(10);
+
+ expect(maxHeap.toString()).toBe('12,3,10');
+
+ maxHeap.add(11);
+ expect(maxHeap.toString()).toBe('12,11,10,3');
+
+ expect(maxHeap.poll()).toBe(12);
+ expect(maxHeap.toString()).toBe('11,3,10');
+ });
+});
diff --git a/src/data-structures/heap/__test__/MinHeapAdhoc.test.js b/src/data-structures/heap/__test__/MinHeapAdhoc.test.js
new file mode 100644
index 0000000000..766b307ff0
--- /dev/null
+++ b/src/data-structures/heap/__test__/MinHeapAdhoc.test.js
@@ -0,0 +1,91 @@
+import MinHeapAdhoc from '../MinHeapAdhoc';
+
+describe('MinHeapAdhoc', () => {
+ it('should create an empty min heap', () => {
+ const minHeap = new MinHeapAdhoc();
+
+ expect(minHeap).toBeDefined();
+ expect(minHeap.peek()).toBe(undefined);
+ expect(minHeap.isEmpty()).toBe(true);
+ });
+
+ it('should add items to the heap and heapify it up', () => {
+ const minHeap = new MinHeapAdhoc();
+
+ minHeap.add(5);
+ expect(minHeap.isEmpty()).toBe(false);
+ expect(minHeap.peek()).toBe(5);
+ expect(minHeap.toString()).toBe('5');
+
+ minHeap.add(3);
+ expect(minHeap.peek()).toBe(3);
+ expect(minHeap.toString()).toBe('3,5');
+
+ minHeap.add(10);
+ expect(minHeap.peek()).toBe(3);
+ expect(minHeap.toString()).toBe('3,5,10');
+
+ minHeap.add(1);
+ expect(minHeap.peek()).toBe(1);
+ expect(minHeap.toString()).toBe('1,3,10,5');
+
+ minHeap.add(1);
+ expect(minHeap.peek()).toBe(1);
+ expect(minHeap.toString()).toBe('1,1,10,5,3');
+
+ expect(minHeap.poll()).toBe(1);
+ expect(minHeap.toString()).toBe('1,3,10,5');
+
+ expect(minHeap.poll()).toBe(1);
+ expect(minHeap.toString()).toBe('3,5,10');
+
+ expect(minHeap.poll()).toBe(3);
+ expect(minHeap.toString()).toBe('5,10');
+ });
+
+ it('should poll items from the heap and heapify it down', () => {
+ const minHeap = new MinHeapAdhoc();
+
+ minHeap.add(5);
+ minHeap.add(3);
+ minHeap.add(10);
+ minHeap.add(11);
+ minHeap.add(1);
+
+ expect(minHeap.toString()).toBe('1,3,10,11,5');
+
+ expect(minHeap.poll()).toBe(1);
+ expect(minHeap.toString()).toBe('3,5,10,11');
+
+ expect(minHeap.poll()).toBe(3);
+ expect(minHeap.toString()).toBe('5,11,10');
+
+ expect(minHeap.poll()).toBe(5);
+ expect(minHeap.toString()).toBe('10,11');
+
+ expect(minHeap.poll()).toBe(10);
+ expect(minHeap.toString()).toBe('11');
+
+ expect(minHeap.poll()).toBe(11);
+ expect(minHeap.toString()).toBe('');
+
+ expect(minHeap.poll()).toBe(undefined);
+ expect(minHeap.toString()).toBe('');
+ });
+
+ it('should heapify down through the right branch as well', () => {
+ const minHeap = new MinHeapAdhoc();
+
+ minHeap.add(3);
+ minHeap.add(12);
+ minHeap.add(10);
+
+ expect(minHeap.toString()).toBe('3,12,10');
+
+ minHeap.add(11);
+ expect(minHeap.toString()).toBe('3,11,10,12');
+
+ expect(minHeap.poll()).toBe(3);
+ expect(minHeap.toString()).toBe('10,11,12');
+ });
+});
diff --git a/src/data-structures/heap/images/array-representation.jpeg b/src/data-structures/heap/images/array-representation.jpeg
new file mode 100644
index 0000000000..8914e7102e
Binary files /dev/null and b/src/data-structures/heap/images/array-representation.jpeg differ
diff --git a/src/data-structures/heap/images/max-heap.jpeg b/src/data-structures/heap/images/max-heap.jpeg
new file mode 100644
index 0000000000..c1585d0302
Binary files /dev/null and b/src/data-structures/heap/images/max-heap.jpeg differ
diff --git a/src/data-structures/heap/images/min-heap.jpeg b/src/data-structures/heap/images/min-heap.jpeg
new file mode 100644
index 0000000000..646923b2df
Binary files /dev/null and b/src/data-structures/heap/images/min-heap.jpeg differ
diff --git a/src/data-structures/linked-list/LinkedList.js b/src/data-structures/linked-list/LinkedList.js
index 1fb0b5eaf4..ba7d0e3ee1 100644
--- a/src/data-structures/linked-list/LinkedList.js
+++ b/src/data-structures/linked-list/LinkedList.js
@@ -54,6 +54,40 @@ export default class LinkedList {
return this;
}
+ /**
+ * @param {*} value
+ * @param {number} index
+ * @return {LinkedList}
+ */
+ insert(value, rawIndex) {
+ const index = rawIndex < 0 ? 0 : rawIndex;
+ if (index === 0) {
+ this.prepend(value);
+ } else {
+ let count = 1;
+ let currentNode = this.head;
+ const newNode = new LinkedListNode(value);
+ while (currentNode) {
+ if (count === index) break;
+ currentNode = currentNode.next;
+ count += 1;
+ }
+ if (currentNode) {
+ newNode.next = currentNode.next;
+ currentNode.next = newNode;
+ } else {
+ if (this.tail) {
+ this.tail.next = newNode;
+ this.tail = newNode;
+ } else {
+ this.head = newNode;
+ this.tail = newNode;
+ }
+ }
+ }
+ return this;
+ }
+
/**
* @param {*} value
* @return {LinkedListNode}
@@ -65,7 +99,7 @@ export default class LinkedList {
let deletedNode = null;
- // If the head must be deleted then make next node that is differ
+ // If the head must be deleted then make next node that is different
// from the head to be a new head.
while (this.head && this.compare.equal(this.head.value, value)) {
deletedNode = this.head;
diff --git a/src/data-structures/linked-list/README.es-ES.md b/src/data-structures/linked-list/README.es-ES.md
index 978e234ddf..6c6ba7ee87 100644
--- a/src/data-structures/linked-list/README.es-ES.md
+++ b/src/data-structures/linked-list/README.es-ES.md
@@ -1,33 +1,34 @@
# Lista Enlazada (Linked List)
-_Lee esto en otros idiomas:_
+_Lee este artículo en otros idiomas:_
[_简体中文_](README.zh-CN.md),
[_Русский_](README.ru-RU.md),
[_日本語_](README.ja-JP.md),
[_Português_](README.pt-BR.md)
[_English_](README.md)
-En ciencias de la computaciòn una **lista enlazada** es una coleccion linear
-de elemntos de datos, en los cuales el orden linear no es dado por
-su posciòn fisica en memoria. En cambio, cada
-elemento señala al siguiente. Es una estructura de datos
+En ciencias de la computación una **lista enlazada** es una colección lineal
+de elementos, en los cuales el orden lineal no es dado por
+su posición física en memoria. En cambio, cada
+elemento señala al siguiente. Es una estructura de datos
que consiste en un grupo de nodos los cuales juntos representan
-una secuencia. Bajo la forma mas simple, cada nodo es
-compuesto de datos y una referencia (en otras palabras,
-un lazo) al siguiente nodo en la secuencia. Esta estructura
-permite la insercion o remocion de elementos
-desde cualquier posicion en la secuencia durante la iteracion.
-Variantes mas complejas agregan lazos adicionales, permitiendo
-una eficiente insercion o remocion desde referencias arbitrarias
-del elemento. Una desventaja de las listas lazadas es que el tiempo de
-acceso es linear (y dificil de canalizar) Un acceso
-mas rapido, como un acceso aleatorio, no es factible. Los arreglos
-tienen una mejor locazion comparados con las listas lazadas.
+una secuencia. En su forma más sencilla, cada nodo está
+compuesto de datos y una referencia (en otras palabras,
+un enlace) al siguiente nodo en la secuencia. Esta estructura
+permite la inserción o eliminación de elementos
+desde cualquier posición en la secuencia durante la iteración.
+Las variantes más complejas agregan enlaces adicionales, permitiendo
+una eficiente inserción o eliminación desde referencias arbitrarias
+del elemento. Una desventaja de las listas enlazadas es que el tiempo de
+acceso es lineal (y difícil de canalizar). Un acceso
+más rápido, como un acceso aleatorio, no es factible. Los arreglos
+tienen una mejor localización en caché comparados con las listas enlazadas.
+
-
+*Made with [okso.app](https://okso.app)*
-## Pseudocodigo para operacones basicas
+## Pseudocódigo para operaciones básicas
### Insertar
@@ -76,7 +77,7 @@ Contains(head, value)
return true
end Contains
```
-
+
### Borrar
```text
@@ -111,7 +112,7 @@ Remove(head, value)
end Remove
```
-### Atrevesar
+### Atravesar
```text
Traverse(head)
@@ -146,19 +147,19 @@ ReverseTraversal(head, tail)
end ReverseTraversal
```
-## Complexities
+## Complejidades
-### Time Complexity
+### Complejidad de Tiempo
-| Access | Search | Insertion | Deletion |
-| :-------: | :-------: | :-------: | :-------: |
-| O(n) | O(n) | O(1) | O(n) |
+| Acceso | Búsqueda | Inserción | Eliminación |
+| :----: | :------: | :-------: | :---------: |
+| O(n) | O(n) | O(1) | O(n) |
-### Space Complexity
+### Complejidad Espacial
O(n)
-## References
+## Referencias
- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
- [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/linked-list/README.ja-JP.md b/src/data-structures/linked-list/README.ja-JP.md
index e68b64fa6a..c78997042b 100644
--- a/src/data-structures/linked-list/README.ja-JP.md
+++ b/src/data-structures/linked-list/README.ja-JP.md
@@ -2,7 +2,9 @@
コンピュータサイエンスにおいて、**リンクリスト**はデータ要素の線形コレクションです。要素の順番はメモリ内の物理的な配置によっては決まりません。代わりに、各要素が次の要素を指しています。リンクリストはノードのグループからなるデータ構造です。最も単純な形式では、各ノードはデータとシーケンス内における次のノードへの参照(つまり、リンク)で構成されています。この構造はイテレーションにおいて任意の位置へ要素を効率的に挿入、削除することを可能にしています。より複雑なリンクリストではリンクをさらに追加することで、任意の要素の参照から要素を効率的に挿入、削除することを可能にしています。リンクリストの欠点はアクセスタイムが線形である(そして、パイプライン処理が難しい)ことです。ランダムアクセスのような高速なアクセスは実現不可能です。配列の方がリンクリストと比較して参照の局所性が優れています。
-
+
+
+*Made with [okso.app](https://okso.app)*
## 基本操作の擬似コード
@@ -53,7 +55,7 @@ Contains(head, value)
return true
end Contains
```
-
+
### 削除
```text
diff --git a/src/data-structures/linked-list/README.ko-KR.md b/src/data-structures/linked-list/README.ko-KR.md
index dc03327501..f68d8a464d 100644
--- a/src/data-structures/linked-list/README.ko-KR.md
+++ b/src/data-structures/linked-list/README.ko-KR.md
@@ -8,7 +8,9 @@ _Read this in other languages:_
컴퓨터과학에서, **링크드 리스트**는 데이터 요소의 선형 집합이며, 이 집합에서 논리적 저장 순서는 메모리의 물리적 저장 순서와 일치하지 않습니다. 그 대신, 각각의 원소들은 자기 자신 다음의 원소를 가리킵니다. **링크드 리스트**는 순서를 표현하는 노드들의 집합으로 이루어져 있습니다. 간단하게, 각각의 노드들은 데이터와 다음 순서의 노드를 가리키는 레퍼런스로 이루어져 있습니다. (링크라고 부릅니다.) 이 자료구조는 순회하는 동안 순서에 상관없이 효율적인 삽입이나 삭제가 가능합니다. 더 복잡한 변형은 추가적인 링크를 더해, 임의의 원소 참조로부터 효율적인 삽입과 삭제를 가능하게 합니다. 링크드 리스트의 단점은 접근 시간이 선형이라는 것이고, 병렬처리도 하지 못합니다. 임의 접근처럼 빠른 접근은 불가능합니다. 링크드 리스트에 비해 배열이 더 나은 캐시 지역성을 가지고 있습니다.
-
+
+
+*Made with [okso.app](https://okso.app)*
## 기본 연산에 대한 수도코드
@@ -60,7 +62,7 @@ Contains(head, value)
return true
end Contains
```
-
+
### 삭제
```text
@@ -137,7 +139,7 @@ end ReverseTraversal
| 접근 | 탐색 | 삽입 | 삭제 |
| :---: | :---: | :---: | :---: |
-| O(n) | O(n) | O(1) | O(1) |
+| O(n) | O(n) | O(1) | O(n) |
### 공간 복잡도
diff --git a/src/data-structures/linked-list/README.md b/src/data-structures/linked-list/README.md
index 656ad68f58..825a0272f4 100644
--- a/src/data-structures/linked-list/README.md
+++ b/src/data-structures/linked-list/README.md
@@ -7,6 +7,8 @@ _Read this in other languages:_
[_Português_](README.pt-BR.md),
[_한국어_](README.ko-KR.md),
[_Español_](README.es-ES.md),
+[_Türkçe_](README.tr-TR.md),
+[_Українська_](README.uk-UA.md)
In computer science, a **linked list** is a linear collection
of data elements, in which linear order is not given by
@@ -25,7 +27,9 @@ time is linear (and difficult to pipeline). Faster
access, such as random access, is not feasible. Arrays
have better cache locality as compared to linked lists.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Pseudocode for Basic Operations
@@ -104,8 +108,9 @@ Remove(head, value)
if n.next = tail
tail ← n
tail.next = null
+ else
+ n.next ← n.next.next
end if
- n.next ← n.next.next
return true
end if
return false
diff --git a/src/data-structures/linked-list/README.pt-BR.md b/src/data-structures/linked-list/README.pt-BR.md
index 03fec359df..579a4fce8c 100644
--- a/src/data-structures/linked-list/README.pt-BR.md
+++ b/src/data-structures/linked-list/README.pt-BR.md
@@ -1,24 +1,26 @@
# Lista Encadeada (Linked List)
Na ciência da computação, uma **lista encadeada** é uma coleção linear de
-elementos de dado, em que a ordem linear não é dada por sua locação
+elementos de dados, em que a ordem linear não é dada por sua locação
física na memória. Em vez disso, cada elemento aponta para o próximo.
É uma estrutura de dados consistindo em um grupo de nós
que juntos representam uma sequência. Sob a forma mais simples,
cada nó é composto de dados e uma referência (em outras palavras,
-uma ligação/conexão) para o próximo nó na sequência. Esta estrutua
-permite uma eficiente inserção e remoção de elementos de qualquer
+uma ligação/conexão) para o próximo nó na sequência. Esta estrutura
+permite inserção ou remoção eficiente de elementos de qualquer
posição na sequência durante a iteração.
Variantes mais complexas adicionam ligações adicionais, permitindo
uma inserção ou remoção mais eficiente a partir de referências
-de elementos arbitrárias. Uma desvantagem das listas vinculadas
+de elementos arbitrárias. Uma desvantagem das listas encadeadas
é que o tempo de acesso é linear (e difícil de inserir em uma
-pipeline). Acessos mais rápidos, como acesso aleatório, não é viável.
+pipeline). Acesso mais rápido, como acesso aleatório, não é viável.
Arrays possuem uma melhor localização de cache em comparação
-com lista encadeada (linked list).
+com listas encadeadas (linked lists).
-
+
+
+*Made with [okso.app](https://okso.app)*
## Pseudo código para Operações Básicas
diff --git a/src/data-structures/linked-list/README.ru-RU.md b/src/data-structures/linked-list/README.ru-RU.md
index fa8e277e0d..98ad6c4727 100644
--- a/src/data-structures/linked-list/README.ru-RU.md
+++ b/src/data-structures/linked-list/README.ru-RU.md
@@ -6,7 +6,9 @@
Недостатком связных списков является то, что время доступа линейно (и затруднительно для реализации конвейеров). Быстрый доступ(случайный) невозможен.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Псевдокод основных операций
@@ -57,7 +59,7 @@ Contains(head, value)
return true
end Contains
```
-
+
### Удаление
```text
@@ -133,7 +135,7 @@ end ReverseTraversal
| Чтение | Поиск | Вставка | Удаление |
| :--------: | :-------: | :--------: | :-------: |
-| O(n) | O(n) | O(1) | O(1) |
+| O(n) | O(n) | O(1) | O(n) |
### Пространственная сложность
diff --git a/src/data-structures/linked-list/README.tr-TR.md b/src/data-structures/linked-list/README.tr-TR.md
new file mode 100644
index 0000000000..e5ed05623d
--- /dev/null
+++ b/src/data-structures/linked-list/README.tr-TR.md
@@ -0,0 +1,161 @@
+# Bağlantılı Liste
+
+_Bunu diğer dillerde okuyun:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Español_](README.es-ES.md),
+
+Bilgisayar bilimlerinde, **Bağlantılı liste**, her biri hem gerçek verileri
+hem de listedeki bir sonraki düğümün bir bağlantısını içeren dinamik bir
+veri yapısıdır. Bu yapı, yineleme sırasında rastgele bir konumda
+öğeleri verimli bir şekilde eklemenize ve kaldırmanıza olanak tanır.
+Daha karmaşık seçenekler için, isteğe bağlı öğeleri verimli bir şekilde
+eklemek ve kaldırmak için ek bağlantılar içerir.
+
+Bağlantılı listelerin bir dezavantajı, erişim süresinin doğrusal olmasıdır
+(ve ardışık düzene geçirilmesi zordur). Rastgele erişim gibi daha hızlı erişim
+mümkün değildir. Diziler, bağlantılı listelere kıyasla daha iyi önbellek konumuna sahiptir.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## Temel İşlemler için Sözde Kod
+
+### Ekleme
+
+```text
+Add(value)
+ Pre: value is the value to add to the list
+ Post: value has been placed at the tail of the list
+ n ← node(value)
+ if head = ø
+ head ← n
+ tail ← n
+ else
+ tail.next ← n
+ tail ← n
+ end if
+end Add
+```
+
+```text
+Prepend(value)
+ Pre: value is the value to add to the list
+ Post: value has been placed at the head of the list
+ n ← node(value)
+ n.next ← head
+ head ← n
+ if tail = ø
+ tail ← n
+ end
+end Prepend
+```
+
+### Arama
+
+```text
+Contains(head, value)
+ Pre: head is the head node in the list
+ value is the value to search for
+ Post: the item is either in the linked list, true; otherwise false
+ n ← head
+ while n != ø and n.value != value
+ n ← n.next
+ end while
+ if n = ø
+ return false
+ end if
+ return true
+end Contains
+```
+
+### Silme
+
+```text
+Remove(head, value)
+ Pre: head is the head node in the list
+ value is the value to remove from the list
+ Post: value is removed from the list, true, otherwise false
+ if head = ø
+ return false
+ end if
+ n ← head
+ if n.value = value
+ if head = tail
+ head ← ø
+ tail ← ø
+ else
+ head ← head.next
+ end if
+ return true
+ end if
+ while n.next != ø and n.next.value != value
+ n ← n.next
+ end while
+ if n.next != ø
+ if n.next = tail
+ tail ← n
+ tail.next = null
+ end if
+ n.next ← n.next.next
+ return true
+ end if
+ return false
+end Remove
+```
+
+### Geçiş
+
+```text
+Traverse(head)
+ Pre: head is the head node in the list
+ Post: the items in the list have been traversed
+ n ← head
+ while n != ø
+ yield n.value
+ n ← n.next
+ end while
+end Traverse
+```
+
+### Ters Geçiş
+
+```text
+ReverseTraversal(head, tail)
+ Pre: head and tail belong to the same list
+ Post: the items in the list have been traversed in reverse order
+ if tail != ø
+ curr ← tail
+ while curr != head
+ prev ← head
+ while prev.next != curr
+ prev ← prev.next
+ end while
+ yield curr.value
+ curr ← prev
+ end while
+ yield curr.value
+ end if
+end ReverseTraversal
+```
+
+## Karmaşıklıklar
+
+### Zaman Karmaşıklığı
+
+| Erişim | Arama | Ekleme | Silme |
+| :-------: | :-------: | :-------: | :-------: |
+| O(n) | O(n) | O(1) | O(n) |
+
+### Uzay Karmaşıklığı
+
+O(n)
+
+## Referanslar
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
+- [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/linked-list/README.uk-UA.md b/src/data-structures/linked-list/README.uk-UA.md
new file mode 100644
index 0000000000..9b34a6d828
--- /dev/null
+++ b/src/data-structures/linked-list/README.uk-UA.md
@@ -0,0 +1,147 @@
+# Зв'язаний список
+
+Зв'язаний список — базова динамічна структура даних в інформатиці, що складається з вузлів, кожен з яких містить як дані, так і посилання («зв'язку») на наступний вузол списку. Ця структура даних дозволяє ефективно додавати та видаляти елементи на довільній позиції у послідовності у процесі ітерації. Більш складні варіанти включають додаткові посилання, що дозволяють ефективно додавати та видаляти довільні елементи.
+
+Принциповою перевагою перед масивом є структурна гнучкість: порядок елементів зв'язаного списку може збігатися з порядком розташування елементів даних у пам'яті комп'ютера, а порядок обходу списку завжди явно задається його внутрішніми зв'язками. Це важливо, бо у багатьох мовах створення масиву вимагає вказати його розмір заздалегідь. Зв'язаний список дозволяє обійти це обмеження.
+
+Недоліком зв'язаних списків є те, що час доступу є лінійним (і важко для реалізації конвеєрів). Неможливий швидкий доступ (випадковий).
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## Псевдокод основних операцій
+
+### Вставка
+
+```text
+Add(value)
+ Pre: value - значення, що додається
+ Post: value додано в кінець списку
+ n ← node(value)
+ if head = ø
+ head ← n
+ tail ← n
+ else
+ tail.next ← n
+ tail ← n
+ end if
+end Add
+```
+
+```text
+Prepend(value)
+ Pre: value - значення, що додається
+ Post: value додано на початку списку
+ n ← node(value)
+ n.next ← head
+ head ← n
+ if tail = ø
+ tail ← n
+ end
+end Prepend
+```
+
+### Пошук
+
+```text
+Contains(head, value)
+ Pre: head - перший вузол у списку
+ value - значення, яке слід знайти
+ Post: true - value знайдено у списку, інакше false
+ n ← head
+ while n != ø and n.value != value
+ n ← n.next
+ end while
+ if n = ø
+ return false
+ end if
+ return true
+end Contains
+```
+
+### Видалення
+
+```text
+Remove(head, value)
+ Pre: head - перший вузол у списку
+ value - значення, яке слід видалити
+ Post: true - value видалено зі списку, інакше false
+ if head = ø
+ return false
+ end if
+ n ← head
+ if n.value = value
+ if head = tail
+ head ← ø
+ tail ← ø
+ else
+ head ← head.next
+ end if
+ return true
+ end if
+ while n.next != ø and n.next.value != value
+ n ← n.next
+ end while
+ if n.next != ø
+ if n.next = tail
+ tail ← n
+ end if
+ n.next ← n.next.next
+ return true
+ end if
+ return false
+end Remove
+```
+
+### Обхід
+
+```text
+Traverse(head)
+ Pre: head - перший вузол у списку
+ Post: елементи списку пройдені
+ n ← head
+ while n != ø
+ yield n.value
+ n ← n.next
+ end while
+end Traverse
+```
+
+### Зворотній обхід
+
+```text
+ReverseTraversal(head, tail)
+ Pre: head і tail відносяться до одного списку
+ Post: елементи списку пройдено у зворотньому порядку
+ if tail != ø
+ curr ← tail
+ while curr != head
+ prev ← head
+ while prev.next != curr
+ prev ← prev.next
+ end while
+ yield curr.value
+ curr ← prev
+ end while
+ yield curr.value
+ end if
+end ReverseTraversal
+```
+
+## Складність
+
+### Часова складність
+
+| Читання | Пошук | Вставка | Вилучення |
+| :--------: | :-------: | :--------: | :-------: |
+| O(n) | O(n) | O(1) | O(n) |
+
+### Просторова складність
+
+O(n)
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/Зв'язаний_список)
+- [YouTube](https://www.youtube.com/watch?v=6snsMa4E1Os)
diff --git a/src/data-structures/linked-list/README.vi-VN.md b/src/data-structures/linked-list/README.vi-VN.md
new file mode 100644
index 0000000000..005838c6c1
--- /dev/null
+++ b/src/data-structures/linked-list/README.vi-VN.md
@@ -0,0 +1,155 @@
+# Danh sách liên kết (Linked List)
+
+_Đọc bằng ngôn ngữ khác:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Español_](README.es-ES.md),
+[_Türkçe_](README.tr-TR.md),
+[_Українська_](README.uk-UA.md)
+
+
+Trong khoa học máy tính, một danh sách liên kết là một bộ sưu tập tuyến tính
+các phần tử dữ liệu, trong đó thứ tự tuyến tính không được xác định bởi
+vị trí vật lý của chúng trong bộ nhớ. Thay vào đó, mỗi
+phần tử trỏ đến phần tử tiếp theo. Đây là một cấu trúc dữ liệu
+bao gồm một nhóm các nút cùng đại diện cho
+một chuỗi. Dưới dạng đơn giản nhất, mỗi nút
+bao gồm dữ liệu và một tham chiếu (nói cách khác,
+một liên kết) đến nút tiếp theo trong chuỗi. Cấu trúc này
+cho phép việc chèn hoặc loại bỏ các phần tử một cách hiệu quả
+từ bất kỳ vị trí nào trong chuỗi trong quá trình lặp.
+Các biến thể phức tạp hơn thêm các liên kết bổ sung, cho phép
+việc chèn hoặc loại bỏ một cách hiệu quả từ bất kỳ phần tử nào
+trong chuỗi dựa trên tham chiếu. Một nhược điểm của danh sách liên kết
+là thời gian truy cập tuyến tính (và khó điều chỉnh). Truy cập nhanh hơn,
+như truy cập ngẫu nhiên, là không khả thi. Mảng
+có độ tương phản cache tốt hơn so với danh sách liên kết.
+
+
+*Được làm từ [okso.app](https://okso.app)*
+
+## Mã giải (Pseudocode) cho Các Hoạt Động Cơ Bản
+ *head = đầu,
+ *tail = đuôi,
+ *next = kế tiếp,
+ *node = nút,
+ *value = giá trị
+
+### Chèn (Insert)
+
+```
+ThêmGiáTrị(giá trị) (Add(value))
+ Trước(Pre): giá trị là giá trị muốn thêm vào danh sách
+ Sau(Post): giá trị đã được đặt ở cuối danh sách
+
+ n ← node(value)
+ if head = ø
+ head ← n
+ tail ← n
+ else
+ tail.next ← n
+ tail ← n
+ end if
+end ThêmGiáTrị(Add)
+```
+
+```
+ChènVàoĐầu(giá trị)
+ Trước(Pre): giá trị là giá trị muốn thêm vào danh sách
+ Sau(Post): giá trị đã được đặt ở đầu danh sách
+
+ n ← node(value)
+ n.next ← head
+ head ← n
+ if tail = ø
+ tail ← n
+ end
+end ChènVàoĐầu
+```
+
+### Tìm Kiếm (Search)
+```
+Chứa(đầu, giá trị)
+ Trước: đầu là nút đầu trong danh sách
+ giá trị là giá trị cần tìm kiếm
+ Sau: mục đó có thể ở trong danh sách liên kết, true; nếu không, là false
+ n ← head
+ while n != ø and n.value != value
+ n ← n.next
+ end while
+ if n = ø
+ return false
+ end if
+ return true
+end Contains
+```
+
+### Xóa (Delete)
+```
+Xóa(đầu, giá trị)
+ Trước: đầu là nút đầu trong danh sách
+ giá trị là giá trị cần xóa khỏi danh sách
+ Sau: giá trị đã được xóa khỏi danh sách, true; nếu không, là false
+ if head = ø
+ return false
+ end if
+ n ← head
+ if n.value = value
+ if head = tail
+ head ← ø
+ tail ← ø
+ else
+ head ← head.next
+ end if
+ return true
+ end if
+ while n.next != ø and n.next.value != value
+ n ← n.next
+ end while
+ if n.next != ø
+ if n.next = tail
+ tail ← n
+ tail.next = null
+ else
+ n.next ← n.next.next
+ end if
+ return true
+ end if
+ return false
+end Remove
+```
+
+### Duyệt(raverse)
+Duyệt(đầu)
+ Trước: đầu là nút đầu trong danh sách
+ Sau: các mục trong danh sách đã được duyệt
+ n ← head
+ while n != ø
+ yield n.value
+ n ← n.next
+ end while
+end Traverse
+
+### Duyệt Ngược (Traverse in Reverse)
+DuyệtNgược(đầu, đuôi)
+ Trước: đầu và đuôi thuộc cùng một danh sách
+ Sau: các mục trong danh sách đã được duyệt theo thứ tự ngược lại
+
+## Độ Phức Tạp
+
+### Độ Phức Tạp Thời Gian (Time Complexity)
+
+| Access | Search | Insertion | Deletion |
+| :-------: | :-------: | :-------: | :-------: |
+| O(n) | O(n) | O(1) | O(n) |
+
+## Độ Phức Tạp Không Gian (Space Complexity)
+O(n)
+
+## Tham Khảo
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
+- [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/linked-list/README.zh-CN.md b/src/data-structures/linked-list/README.zh-CN.md
index 81f036ab08..f0b75121e7 100644
--- a/src/data-structures/linked-list/README.zh-CN.md
+++ b/src/data-structures/linked-list/README.zh-CN.md
@@ -8,7 +8,9 @@
更快的访问，如随机访问，是不可行的。与链表相比，数组具有更好的缓存位置。
-
+
+
+*Made with [okso.app](https://okso.app)*
## 基本操作的伪代码
@@ -59,7 +61,7 @@ Contains(head, value)
return true
end Contains
```
-
+
### 删除
```text
@@ -107,7 +109,7 @@ Traverse(head)
end while
end Traverse
```
-
+
### 反向遍历
```text
diff --git a/src/data-structures/linked-list/__test__/LinkedList.test.js b/src/data-structures/linked-list/__test__/LinkedList.test.js
index f4eb83e2bd..6ac41ddf05 100644
--- a/src/data-structures/linked-list/__test__/LinkedList.test.js
+++ b/src/data-structures/linked-list/__test__/LinkedList.test.js
@@ -32,6 +32,21 @@ describe('LinkedList', () => {
expect(linkedList.toString()).toBe('3,2,1');
});
+ it('should insert node to linked list', () => {
+ const linkedList = new LinkedList();
+
+ linkedList.insert(4, 3);
+ expect(linkedList.head.toString()).toBe('4');
+ expect(linkedList.tail.toString()).toBe('4');
+
+ linkedList.insert(3, 2);
+ linkedList.insert(2, 1);
+ linkedList.insert(1, -7);
+ linkedList.insert(10, 9);
+
+ expect(linkedList.toString()).toBe('1,4,2,3,10');
+ });
+
it('should delete node by value from linked list', () => {
const linkedList = new LinkedList();
@@ -215,7 +230,7 @@ describe('LinkedList', () => {
expect(node).toBeDefined();
expect(node.value.value).toBe(2);
expect(node.value.customValue).toBe('test2');
- expect(linkedList.find({ value: 2, customValue: 'test5' })).toBeNull();
+ expect(linkedList.find({ value: { value: 2, customValue: 'test5' } })).toBeNull();
});
it('should find preferring callback over compare function', () => {
diff --git a/src/data-structures/linked-list/images/linked-list.jpeg b/src/data-structures/linked-list/images/linked-list.jpeg
new file mode 100644
index 0000000000..61a0712066
Binary files /dev/null and b/src/data-structures/linked-list/images/linked-list.jpeg differ
diff --git a/src/data-structures/lru-cache/LRUCache.js b/src/data-structures/lru-cache/LRUCache.js
new file mode 100644
index 0000000000..d6b4b3c6be
--- /dev/null
+++ b/src/data-structures/lru-cache/LRUCache.js
@@ -0,0 +1,153 @@
+/* eslint-disable no-param-reassign, max-classes-per-file */
+
+/**
+ * Simple implementation of the Doubly-Linked List Node
+ * that is used in LRUCache class below.
+ */
+class LinkedListNode {
+ /**
+ * Creates a doubly-linked list node.
+ * @param {string} key
+ * @param {any} val
+ * @param {LinkedListNode} prev
+ * @param {LinkedListNode} next
+ */
+ constructor(key, val, prev = null, next = null) {
+ this.key = key;
+ this.val = val;
+ this.prev = prev;
+ this.next = next;
+ }
+}
+
+/**
+ * Implementation of the LRU (Least Recently Used) Cache
+ * based on the HashMap and Doubly Linked List data-structures.
+ *
+ * Current implementation allows to have fast O(1) (in average) read and write operations.
+ *
+ * At any moment in time the LRU Cache holds not more that "capacity" number of items in it.
+ */
+class LRUCache {
+ /**
+ * Creates a cache instance of a specific capacity.
+ * @param {number} capacity
+ */
+ constructor(capacity) {
+ this.capacity = capacity; // How many items to store in cache at max.
+ this.nodesMap = {}; // The quick links to each linked list node in cache.
+ this.size = 0; // The number of items that is currently stored in the cache.
+ this.head = new LinkedListNode(); // The Head (first) linked list node.
+ this.tail = new LinkedListNode(); // The Tail (last) linked list node.
+ }
+
+ /**
+ * Returns the cached value by its key.
+ * Time complexity: O(1) in average.
+ * @param {string} key
+ * @returns {any}
+ */
+ get(key) {
+ if (this.nodesMap[key] === undefined) return undefined;
+ const node = this.nodesMap[key];
+ this.promote(node);
+ return node.val;
+ }
+
+ /**
+ * Sets the value to cache by its key.
+ * Time complexity: O(1) in average.
+ * @param {string} key
+ * @param {any} val
+ */
+ set(key, val) {
+ if (this.nodesMap[key]) {
+ const node = this.nodesMap[key];
+ node.val = val;
+ this.promote(node);
+ } else {
+ const node = new LinkedListNode(key, val);
+ this.append(node);
+ }
+ }
+
+ /**
+ * Promotes the node to the end of the linked list.
+ * It means that the node is most frequently used.
+ * It also reduces the chance for such node to get evicted from cache.
+ * @param {LinkedListNode} node
+ */
+ promote(node) {
+ this.evict(node);
+ this.append(node);
+ }
+
+ /**
+ * Appends a new node to the end of the cache linked list.
+ * @param {LinkedListNode} node
+ */
+ append(node) {
+ this.nodesMap[node.key] = node;
+
+ if (!this.head.next) {
+ // First node to append.
+ this.head.next = node;
+ this.tail.prev = node;
+ node.prev = this.head;
+ node.next = this.tail;
+ } else {
+ // Append to an existing tail.
+ const oldTail = this.tail.prev;
+ oldTail.next = node;
+ node.prev = oldTail;
+ node.next = this.tail;
+ this.tail.prev = node;
+ }
+
+ this.size += 1;
+
+ if (this.size > this.capacity) {
+ this.evict(this.head.next);
+ }
+ }
+
+ /**
+ * Evicts (removes) the node from cache linked list.
+ * @param {LinkedListNode} node
+ */
+ evict(node) {
+ delete this.nodesMap[node.key];
+ this.size -= 1;
+
+ const prevNode = node.prev;
+ const nextNode = node.next;
+
+ // If one and only node.
+ if (prevNode === this.head && nextNode === this.tail) {
+ this.head.next = null;
+ this.tail.prev = null;
+ this.size = 0;
+ return;
+ }
+
+ // If this is a Head node.
+ if (prevNode === this.head) {
+ nextNode.prev = this.head;
+ this.head.next = nextNode;
+ return;
+ }
+
+ // If this is a Tail node.
+ if (nextNode === this.tail) {
+ prevNode.next = this.tail;
+ this.tail.prev = prevNode;
+ return;
+ }
+
+ // If the node is in the middle.
+ prevNode.next = nextNode;
+ nextNode.prev = prevNode;
+ }
+}
+
+export default LRUCache;
diff --git a/src/data-structures/lru-cache/LRUCacheOnMap.js b/src/data-structures/lru-cache/LRUCacheOnMap.js
new file mode 100644
index 0000000000..8e4e226129
--- /dev/null
+++ b/src/data-structures/lru-cache/LRUCacheOnMap.js
@@ -0,0 +1,53 @@
+/* eslint-disable no-restricted-syntax, no-unreachable-loop */
+
+/**
+ * Implementation of the LRU (Least Recently Used) Cache
+ * based on the (ordered) Map data-structure.
+ *
+ * Current implementation allows to have fast O(1) (in average) read and write operations.
+ *
+ * At any moment in time the LRU Cache holds not more that "capacity" number of items in it.
+ */
+class LRUCacheOnMap {
+ /**
+ * Creates a cache instance of a specific capacity.
+ * @param {number} capacity
+ */
+ constructor(capacity) {
+ this.capacity = capacity; // How many items to store in cache at max.
+ this.items = new Map(); // The ordered hash map of all cached items.
+ }
+
+ /**
+ * Returns the cached value by its key.
+ * Time complexity: O(1) in average.
+ * @param {string} key
+ * @returns {any}
+ */
+ get(key) {
+ if (!this.items.has(key)) return undefined;
+ const val = this.items.get(key);
+ this.items.delete(key);
+ this.items.set(key, val);
+ return val;
+ }
+
+ /**
+ * Sets the value to cache by its key.
+ * Time complexity: O(1).
+ * @param {string} key
+ * @param {any} val
+ */
+ set(key, val) {
+ this.items.delete(key);
+ this.items.set(key, val);
+ if (this.items.size > this.capacity) {
+ for (const headKey of this.items.keys()) {
+ this.items.delete(headKey);
+ break;
+ }
+ }
+ }
+}
+
+export default LRUCacheOnMap;
diff --git a/src/data-structures/lru-cache/README.ko-KR.md b/src/data-structures/lru-cache/README.ko-KR.md
new file mode 100644
index 0000000000..93957bc0ed
--- /dev/null
+++ b/src/data-structures/lru-cache/README.ko-KR.md
@@ -0,0 +1,51 @@
+# LRU 캐시 알고리즘
+
+**LRU 캐시 알고리즘** 은 사용된 순서대로 아이템을 정리함으로써, 오랜 시간 동안 사용되지 않은 아이템을 빠르게 찾아낼 수 있도록 한다.
+
+한방향으로만 옷을 걸 수 있는 옷걸이 행거를 생각해봅시다. 가장 오랫동안 입지 않은 옷을 찾기 위해서는, 행거의 반대쪽 끝을 보면 됩니다.
+
+## 문제 정의
+
+LRUCache 클래스를 구현해봅시다:
+
+- `LRUCache(int capacity)` LRU 캐시를 **양수** 의 `capacity` 로 초기화합니다.
+- `int get(int key)` `key` 가 존재할 경우 `key` 값을 반환하고, 그렇지 않으면 `undefined` 를 반환합니다.
+- `void set(int key, int value)` `key` 가 존재할 경우 `key` 값을 업데이트 하고, 그렇지 않으면 `key-value` 쌍을 캐시에 추가합니다. 만약 이 동작으로 인해 키 개수가 `capacity` 를 넘는 경우, 가장 오래된 키 값을 **제거** 합니다.
+
+`get()` 과 `set()` 함수는 무조건 평균 `O(1)` 의 시간 복잡도 내에 실행되어야 합니다.
+
+## 구현
+
+### 버전 1: 더블 링크드 리스트 + 해시맵
+
+[LRUCache.js](./LRUCache.js) 에서 `LRUCache` 구현체 예시를 확인할 수 있습니다. 예시에서는 (평균적으로) 빠른 `O(1)` 캐시 아이템 접근을 위해 `HashMap` 을 사용했고, (평균적으로) 빠른 `O(1)` 캐시 아이템 수정과 제거를 위해 `DoublyLinkedList` 를 사용했습니다. (허용된 최대의 캐시 용량을 유지하기 위해)
+
+
+
+_[okso.app](https://okso.app) 으로 만듦_
+
+LRU 캐시가 어떻게 작동하는지 더 많은 예시로 확인하고 싶다면 LRUCache.test.js](./**test**/LRUCache.test.js) 파일을 참고하세요.
+
+### 버전 2: 정렬된 맵
+
+더블 링크드 리스트로 구현한 첫번째 예시는 어떻게 평균 `O(1)` 시간 복잡도가 `set()` 과 `get()` 으로 나올 수 있는지 학습 목적과 이해를 돕기 위해 좋은 예시입니다.
+
+그러나, 더 쉬운 방법은 자바스크립트의 [Map](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Map) 객체를 사용하는 것입니다. 이 `Map` 객체는 키-값 쌍과 키를 **추가하는 순서 원본** 을 지닙니다. 우리는 이걸 아이템을 제거하거나 다시 추가하면서 맵의 "가장 마지막" 동작에서 최근에 사용된 아이템을 유지하기 위해 사용할 수 있습니다. `Map` 의 시작점에 있는 아이템은 캐시 용량이 넘칠 경우 가장 먼저 제거되는 대상입니다. 아이템의 순서는 `map.keys()` 와 같은 `IterableIterator` 을 사용해 확인할 수 있습니다.
+
+해당 구현체는 [LRUCacheOnMap.js](./LRUCacheOnMap.js) 의 `LRUCacheOnMap` 예시에서 확인할 수 있습니다.
+
+이 LRU 캐시 방식이 어떻게 작동하는지 더 많은 테스트 케이스를 확인하고 싶다면 [LRUCacheOnMap.test.js](./__test__/LRUCacheOnMap.test.js) 파일을 참고하세요.
+
+## 복잡도
+
+| | 평균 |
+| --------------- | ------ |
+| 공간 | `O(n)` |
+| 아이템 찾기 | `O(1)` |
+| 아이템 설정하기 | `O(1)` |
+
+## 참조
+
+- [LRU Cache on LeetCode](https://leetcode.com/problems/lru-cache/solutions/244744/lru-cache/)
+- [LRU Cache on InterviewCake](https://www.interviewcake.com/concept/java/lru-cache)
+- [LRU Cache on Wiki](https://en.wikipedia.org/wiki/Cache_replacement_policies)
diff --git a/src/data-structures/lru-cache/README.md b/src/data-structures/lru-cache/README.md
new file mode 100644
index 0000000000..eaa075f809
--- /dev/null
+++ b/src/data-structures/lru-cache/README.md
@@ -0,0 +1,54 @@
+# Least Recently Used (LRU) Cache
+
+_Read this in other languages:_
+[한국어](README.ko-KR.md),
+
+A **Least Recently Used (LRU) Cache** organizes items in order of use, allowing you to quickly identify which item hasn't been used for the longest amount of time.
+
+Picture a clothes rack, where clothes are always hung up on one side. To find the least-recently used item, look at the item on the other end of the rack.
+
+## The problem statement
+
+Implement the LRUCache class:
+
+- `LRUCache(int capacity)` Initialize the LRU cache with **positive** size `capacity`.
+- `int get(int key)` Return the value of the `key` if the `key` exists, otherwise return `undefined`.
+- `void set(int key, int value)` Update the value of the `key` if the `key` exists. Otherwise, add the `key-value` pair to the cache. If the number of keys exceeds the `capacity` from this operation, **evict** the least recently used key.
+
+The functions `get()` and `set()` must each run in `O(1)` average time complexity.
+
+## Implementation
+
+### Version 1: Doubly Linked List + Hash Map
+
+See the `LRUCache` implementation example in [LRUCache.js](./LRUCache.js). The solution uses a `HashMap` for fast `O(1)` (in average) cache items access, and a `DoublyLinkedList` for fast `O(1)` (in average) cache items promotions and eviction (to keep the maximum allowed cache capacity).
+
+
+
+_Made with [okso.app](https://okso.app)_
+
+You may also find more test-case examples of how the LRU Cache works in [LRUCache.test.js](./__test__/LRUCache.test.js) file.
+
+### Version 2: Ordered Map
+
+The first implementation that uses doubly linked list is good for learning purposes and for better understanding of how the average `O(1)` time complexity is achievable while doing `set()` and `get()`.
+
+However, the simpler approach might be to use a JavaScript [Map](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Map) object. The `Map` object holds key-value pairs and **remembers the original insertion order** of the keys. We can use this fact in order to keep the recently-used items in the "end" of the map by removing and re-adding items. The item at the beginning of the `Map` is the first one to be evicted if cache capacity overflows. The order of the items may checked by using the `IterableIterator` like `map.keys()`.
+
+See the `LRUCacheOnMap` implementation example in [LRUCacheOnMap.js](./LRUCacheOnMap.js).
+
+You may also find more test-case examples of how the LRU Cache works in [LRUCacheOnMap.test.js](./__test__/LRUCacheOnMap.test.js) file.
+
+## Complexities
+
+| | Average |
+| -------- | ------- |
+| Space | `O(n)` |
+| Get item | `O(1)` |
+| Set item | `O(1)` |
+
+## References
+
+- [LRU Cache on LeetCode](https://leetcode.com/problems/lru-cache/solutions/244744/lru-cache/)
+- [LRU Cache on InterviewCake](https://www.interviewcake.com/concept/java/lru-cache)
+- [LRU Cache on Wiki](https://en.wikipedia.org/wiki/Cache_replacement_policies)
diff --git a/src/data-structures/lru-cache/__test__/LRUCache.test.js b/src/data-structures/lru-cache/__test__/LRUCache.test.js
new file mode 100644
index 0000000000..438fd50378
--- /dev/null
+++ b/src/data-structures/lru-cache/__test__/LRUCache.test.js
@@ -0,0 +1,150 @@
+import LRUCache from '../LRUCache';
+
+describe('LRUCache', () => {
+ it('should set and get values to and from the cache', () => {
+ const cache = new LRUCache(100);
+ expect(cache.get('key-1')).toBeUndefined();
+
+ cache.set('key-1', 15);
+ cache.set('key-2', 16);
+ cache.set('key-3', 17);
+ expect(cache.get('key-1')).toBe(15);
+ expect(cache.get('key-2')).toBe(16);
+ expect(cache.get('key-3')).toBe(17);
+ expect(cache.get('key-3')).toBe(17);
+ expect(cache.get('key-2')).toBe(16);
+ expect(cache.get('key-1')).toBe(15);
+
+ cache.set('key-1', 5);
+ cache.set('key-2', 6);
+ cache.set('key-3', 7);
+ expect(cache.get('key-1')).toBe(5);
+ expect(cache.get('key-2')).toBe(6);
+ expect(cache.get('key-3')).toBe(7);
+ });
+
+ it('should evict least recently used items from cache with cache size of 1', () => {
+ const cache = new LRUCache(1);
+ expect(cache.get('key-1')).toBeUndefined();
+
+ cache.set('key-1', 15);
+ expect(cache.get('key-1')).toBe(15);
+
+ cache.set('key-2', 16);
+ expect(cache.get('key-1')).toBeUndefined();
+ expect(cache.get('key-2')).toBe(16);
+
+ cache.set('key-2', 17);
+ expect(cache.get('key-2')).toBe(17);
+
+ cache.set('key-3', 18);
+ cache.set('key-4', 19);
+ expect(cache.get('key-2')).toBeUndefined();
+ expect(cache.get('key-3')).toBeUndefined();
+ expect(cache.get('key-4')).toBe(19);
+ });
+
+ it('should evict least recently used items from cache with cache size of 2', () => {
+ const cache = new LRUCache(2);
+ expect(cache.get('key-21')).toBeUndefined();
+
+ cache.set('key-21', 15);
+ expect(cache.get('key-21')).toBe(15);
+
+ cache.set('key-22', 16);
+ expect(cache.get('key-21')).toBe(15);
+ expect(cache.get('key-22')).toBe(16);
+
+ cache.set('key-22', 17);
+ expect(cache.get('key-22')).toBe(17);
+
+ cache.set('key-23', 18);
+ expect(cache.size).toBe(2);
+ expect(cache.get('key-21')).toBeUndefined();
+ expect(cache.get('key-22')).toBe(17);
+ expect(cache.get('key-23')).toBe(18);
+
+ cache.set('key-24', 19);
+ expect(cache.size).toBe(2);
+ expect(cache.get('key-21')).toBeUndefined();
+ expect(cache.get('key-22')).toBeUndefined();
+ expect(cache.get('key-23')).toBe(18);
+ expect(cache.get('key-24')).toBe(19);
+ });
+
+ it('should evict least recently used items from cache with cache size of 3', () => {
+ const cache = new LRUCache(3);
+
+ cache.set('key-1', 1);
+ cache.set('key-2', 2);
+ cache.set('key-3', 3);
+ expect(cache.get('key-1')).toBe(1);
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-3')).toBe(3);
+
+ cache.set('key-3', 4);
+ expect(cache.get('key-1')).toBe(1);
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-3')).toBe(4);
+
+ cache.set('key-4', 5);
+ expect(cache.get('key-1')).toBeUndefined();
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-3')).toBe(4);
+ expect(cache.get('key-4')).toBe(5);
+ });
+
+ it('should promote the node while calling set() method', () => {
+ const cache = new LRUCache(2);
+
+ cache.set('2', 1);
+ cache.set('1', 1);
+ cache.set('2', 3);
+ cache.set('4', 1);
+ expect(cache.get('1')).toBeUndefined();
+ expect(cache.get('2')).toBe(3);
+ });
+
+ it('should promote the recently accessed item with cache size of 3', () => {
+ const cache = new LRUCache(3);
+
+ cache.set('key-1', 1);
+ cache.set('key-2', 2);
+ cache.set('key-3', 3);
+ expect(cache.get('key-1')).toBe(1);
+
+ cache.set('key-4', 4);
+ expect(cache.get('key-1')).toBe(1);
+ expect(cache.get('key-3')).toBe(3);
+ expect(cache.get('key-4')).toBe(4);
+ expect(cache.get('key-2')).toBeUndefined();
+ });
+
+ it('should promote the recently accessed item with cache size of 4', () => {
+ const cache = new LRUCache(4);
+
+ cache.set('key-1', 1);
+ cache.set('key-2', 2);
+ cache.set('key-3', 3);
+ cache.set('key-4', 4);
+ expect(cache.get('key-4')).toBe(4);
+ expect(cache.get('key-3')).toBe(3);
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-1')).toBe(1);
+
+ cache.set('key-5', 5);
+ expect(cache.get('key-1')).toBe(1);
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-3')).toBe(3);
+ expect(cache.get('key-4')).toBeUndefined();
+ expect(cache.get('key-5')).toBe(5);
+
+ cache.set('key-6', 6);
+ expect(cache.get('key-1')).toBeUndefined();
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-3')).toBe(3);
+ expect(cache.get('key-4')).toBeUndefined();
+ expect(cache.get('key-5')).toBe(5);
+ expect(cache.get('key-6')).toBe(6);
+ });
+});
diff --git a/src/data-structures/lru-cache/__test__/LRUCacheOnMap.test.js b/src/data-structures/lru-cache/__test__/LRUCacheOnMap.test.js
new file mode 100644
index 0000000000..8912a1199a
--- /dev/null
+++ b/src/data-structures/lru-cache/__test__/LRUCacheOnMap.test.js
@@ -0,0 +1,148 @@
+import LRUCache from '../LRUCacheOnMap';
+
+describe('LRUCacheOnMap', () => {
+ it('should set and get values to and from the cache', () => {
+ const cache = new LRUCache(100);
+ expect(cache.get('key-1')).toBeUndefined();
+
+ cache.set('key-1', 15);
+ cache.set('key-2', 16);
+ cache.set('key-3', 17);
+ expect(cache.get('key-1')).toBe(15);
+ expect(cache.get('key-2')).toBe(16);
+ expect(cache.get('key-3')).toBe(17);
+ expect(cache.get('key-3')).toBe(17);
+ expect(cache.get('key-2')).toBe(16);
+ expect(cache.get('key-1')).toBe(15);
+
+ cache.set('key-1', 5);
+ cache.set('key-2', 6);
+ cache.set('key-3', 7);
+ expect(cache.get('key-1')).toBe(5);
+ expect(cache.get('key-2')).toBe(6);
+ expect(cache.get('key-3')).toBe(7);
+ });
+
+ it('should evict least recently used items from cache with cache size of 1', () => {
+ const cache = new LRUCache(1);
+ expect(cache.get('key-1')).toBeUndefined();
+
+ cache.set('key-1', 15);
+ expect(cache.get('key-1')).toBe(15);
+
+ cache.set('key-2', 16);
+ expect(cache.get('key-1')).toBeUndefined();
+ expect(cache.get('key-2')).toBe(16);
+
+ cache.set('key-2', 17);
+ expect(cache.get('key-2')).toBe(17);
+
+ cache.set('key-3', 18);
+ cache.set('key-4', 19);
+ expect(cache.get('key-2')).toBeUndefined();
+ expect(cache.get('key-3')).toBeUndefined();
+ expect(cache.get('key-4')).toBe(19);
+ });
+
+ it('should evict least recently used items from cache with cache size of 2', () => {
+ const cache = new LRUCache(2);
+ expect(cache.get('key-21')).toBeUndefined();
+
+ cache.set('key-21', 15);
+ expect(cache.get('key-21')).toBe(15);
+
+ cache.set('key-22', 16);
+ expect(cache.get('key-21')).toBe(15);
+ expect(cache.get('key-22')).toBe(16);
+
+ cache.set('key-22', 17);
+ expect(cache.get('key-22')).toBe(17);
+
+ cache.set('key-23', 18);
+ expect(cache.get('key-21')).toBeUndefined();
+ expect(cache.get('key-22')).toBe(17);
+ expect(cache.get('key-23')).toBe(18);
+
+ cache.set('key-24', 19);
+ expect(cache.get('key-21')).toBeUndefined();
+ expect(cache.get('key-22')).toBeUndefined();
+ expect(cache.get('key-23')).toBe(18);
+ expect(cache.get('key-24')).toBe(19);
+ });
+
+ it('should evict least recently used items from cache with cache size of 3', () => {
+ const cache = new LRUCache(3);
+
+ cache.set('key-1', 1);
+ cache.set('key-2', 2);
+ cache.set('key-3', 3);
+ expect(cache.get('key-1')).toBe(1);
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-3')).toBe(3);
+
+ cache.set('key-3', 4);
+ expect(cache.get('key-1')).toBe(1);
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-3')).toBe(4);
+
+ cache.set('key-4', 5);
+ expect(cache.get('key-1')).toBeUndefined();
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-3')).toBe(4);
+ expect(cache.get('key-4')).toBe(5);
+ });
+
+ it('should promote the node while calling set() method', () => {
+ const cache = new LRUCache(2);
+
+ cache.set('2', 1);
+ cache.set('1', 1);
+ cache.set('2', 3);
+ cache.set('4', 1);
+ expect(cache.get('1')).toBeUndefined();
+ expect(cache.get('2')).toBe(3);
+ });
+
+ it('should promote the recently accessed item with cache size of 3', () => {
+ const cache = new LRUCache(3);
+
+ cache.set('key-1', 1);
+ cache.set('key-2', 2);
+ cache.set('key-3', 3);
+ expect(cache.get('key-1')).toBe(1);
+
+ cache.set('key-4', 4);
+ expect(cache.get('key-1')).toBe(1);
+ expect(cache.get('key-3')).toBe(3);
+ expect(cache.get('key-4')).toBe(4);
+ expect(cache.get('key-2')).toBeUndefined();
+ });
+
+ it('should promote the recently accessed item with cache size of 4', () => {
+ const cache = new LRUCache(4);
+
+ cache.set('key-1', 1);
+ cache.set('key-2', 2);
+ cache.set('key-3', 3);
+ cache.set('key-4', 4);
+ expect(cache.get('key-4')).toBe(4);
+ expect(cache.get('key-3')).toBe(3);
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-1')).toBe(1);
+
+ cache.set('key-5', 5);
+ expect(cache.get('key-1')).toBe(1);
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-3')).toBe(3);
+ expect(cache.get('key-4')).toBeUndefined();
+ expect(cache.get('key-5')).toBe(5);
+
+ cache.set('key-6', 6);
+ expect(cache.get('key-1')).toBeUndefined();
+ expect(cache.get('key-2')).toBe(2);
+ expect(cache.get('key-3')).toBe(3);
+ expect(cache.get('key-4')).toBeUndefined();
+ expect(cache.get('key-5')).toBe(5);
+ expect(cache.get('key-6')).toBe(6);
+ });
+});
diff --git a/src/data-structures/lru-cache/images/lru-cache.jpg b/src/data-structures/lru-cache/images/lru-cache.jpg
new file mode 100644
index 0000000000..6a2fcfceb4
Binary files /dev/null and b/src/data-structures/lru-cache/images/lru-cache.jpg differ
diff --git a/src/data-structures/priority-queue/README.ko-KR.md b/src/data-structures/priority-queue/README.ko-KR.md
new file mode 100644
index 0000000000..50a064d05a
--- /dev/null
+++ b/src/data-structures/priority-queue/README.ko-KR.md
@@ -0,0 +1,12 @@
+# 우선 순위 큐
+
+컴퓨터 과학에서 **우선 순위 큐**는 일반 큐 또는 스택 데이터 구조와 같은 추상 데이터 유형이지만, 여기서 각 요소에는 "우선 순위"가 연결됩니다.
+우선 순위 큐에서는 우선 순위가 높은 요소가 낮은 요소 앞에 제공됩니다. 두 요소가 동일한 우선 순위를 가질 경우 큐의 순서에 따라 제공됩니다.
+
+우선 순위 큐는 종종 힙을 사용하여 구현되지만 개념적으로는 힙과 구별됩니다. 우선 순위 대기열은 "리스트(list)" 또는 "맵(map)"과 같은 추상적인 개념입니다;
+리스트가 링크드 리스트나 배열로 구현될 수 있는 것처럼 우선 순위 큐는 힙이나 정렬되지 않은 배열과 같은 다양한 다른 방법으로 구현될 수 있습니다.
+
+## 참조
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Priority_queue)
+- [YouTube](https://www.youtube.com/watch?v=wptevk0bshY&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=6)
diff --git a/src/data-structures/priority-queue/README.md b/src/data-structures/priority-queue/README.md
index a487678ad8..6d0901960d 100644
--- a/src/data-structures/priority-queue/README.md
+++ b/src/data-structures/priority-queue/README.md
@@ -5,20 +5,22 @@ _Read this in other languages:_
[_Русский_](README.ru-RU.md),
[_日本語_](README.ja-JP.md),
[_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
-In computer science, a **priority queue** is an abstract data type
-which is like a regular queue or stack data structure, but where
-additionally each element has a "priority" associated with it.
-In a priority queue, an element with high priority is served before
-an element with low priority. If two elements have the same
+In computer science, a **priority queue** is an abstract data type
+which is like a regular queue or stack data structure, but where
+additionally each element has a "priority" associated with it.
+In a priority queue, an element with high priority is served before
+an element with low priority. If two elements have the same
priority, they are served according to their order in the queue.
-While priority queues are often implemented with heaps, they are
-conceptually distinct from heaps. A priority queue is an abstract
+While priority queues are often implemented with heaps, they are
+conceptually distinct from heaps. A priority queue is an abstract
concept like "a list" or "a map"; just as a list can be implemented
with a linked list or an array, a priority queue can be implemented
-with a heap or a variety of other methods such as an unordered
+with a heap or a variety of other methods such as an unordered
array.
## References
diff --git a/src/data-structures/priority-queue/README.pt-BR.md b/src/data-structures/priority-queue/README.pt-BR.md
index 9e836bde7e..e6d84e263a 100644
--- a/src/data-structures/priority-queue/README.pt-BR.md
+++ b/src/data-structures/priority-queue/README.pt-BR.md
@@ -1,7 +1,7 @@
# Fila de Prioridade (Priority Queue)
-Na ciência da computação, uma **fila de prioridade** é um tipo de dados
-abastrato que é como uma fila regular (regular queue) ou estrutura de
+Na ciência da computação, uma **fila de prioridade** é um tipo de estrutura de
+dados abastrata que é como uma fila regular (regular queue) ou estrutura de
dados de pilha (stack), mas adicionalmente cada elemento possui uma
"prioridade" associada.
@@ -10,11 +10,11 @@ antes de um elemento com baixa prioridade. Caso dois elementos posusam a
mesma prioridade, eles serão servidos de acordo com sua ordem na fila.
Enquanto as filas de prioridade são frequentemente implementadas com
-pilhas (heaps), elas são conceitualmente distintas das pilhas (heaps).
+pilhas (stacks), elas são conceitualmente distintas das pilhas (stacks).
A fila de prioridade é um conceito abstrato como uma "lista" (list) ou
um "mapa" (map); assim como uma lista pode ser implementada com uma
lista encadeada (liked list) ou um array, a fila de prioridade pode ser
-implementada com uma pilha (heap) ou com uima variedade de outros métodos,
+implementada com uma pilha (stack) ou com uma variedade de outros métodos,
como um array não ordenado (unordered array).
## Referências
diff --git a/src/data-structures/priority-queue/README.uk-UA.md b/src/data-structures/priority-queue/README.uk-UA.md
new file mode 100644
index 0000000000..2f0454479e
--- /dev/null
+++ b/src/data-structures/priority-queue/README.uk-UA.md
@@ -0,0 +1,21 @@
+# Черга з пріоритетом
+
+Черга з пріоритетом (англ. priority queue) - абстрактний тип даних в інформатиці,
+для кожного елемента якого можна визначити його пріоритет.
+
+У черзі з пріоритетами елемент із високим пріоритетом обслуговується раніше
+елемент з низьким пріоритетом. Якщо два елементи мають однаковий пріоритет, вони
+обслуговуються відповідно до їх порядку в черзі.
+
+Черга з пріоритетом підтримує дві обов'язкові операції – додати елемент та
+витягти максимум (мінімум).
+
+Хоча пріоритетні черги часто реалізуються у вигляді куп (heaps), вони
+концептуально відрізняються від куп. Черга пріоритетів є абстрактною
+концепцією на кшталт «списку» чи «карти»; так само, як список може бути реалізований
+у вигляді зв'язкового списку або масиву, так і черга з пріоритетом може бути реалізована
+у вигляді купи або безліччю інших методів, наприклад, у вигляді невпорядкованого масиву.
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%A7%D0%B5%D1%80%D0%B3%D0%B0_%D0%B7_%D0%BF%D1%80%D1%96%D0%BE%D1%80%D0%B8%D1%82%D0%B5%D1%82%D0%BE%D0%BC)
diff --git a/src/data-structures/queue/Queue.js b/src/data-structures/queue/Queue.js
index f6ec6d2dad..64e646fc00 100644
--- a/src/data-structures/queue/Queue.js
+++ b/src/data-structures/queue/Queue.js
@@ -21,7 +21,7 @@ export default class Queue {
* @return {*}
*/
peek() {
- if (!this.linkedList.head) {
+ if (this.isEmpty()) {
return null;
}
diff --git a/src/data-structures/queue/README.fr-FR.md b/src/data-structures/queue/README.fr-FR.md
index 452e875bcf..33d327744f 100644
--- a/src/data-structures/queue/README.fr-FR.md
+++ b/src/data-structures/queue/README.fr-FR.md
@@ -20,7 +20,9 @@ structure de données linéaire, ou, plus abstraitement, une collection séquent
Représentation d'une file PEPS (premier entré, premier sorti)
-
+
+
+*Made with [okso.app](https://okso.app)*
## Références
diff --git a/src/data-structures/queue/README.ja-JP.md b/src/data-structures/queue/README.ja-JP.md
index 7b033b0938..1ffa9c1a68 100644
--- a/src/data-structures/queue/README.ja-JP.md
+++ b/src/data-structures/queue/README.ja-JP.md
@@ -4,7 +4,9 @@
FIFO(先入れ先出し)のキュー
-
+
+
+*Made with [okso.app](https://okso.app)*
## 参考
diff --git a/src/data-structures/queue/README.ko-KR.md b/src/data-structures/queue/README.ko-KR.md
new file mode 100644
index 0000000000..606c8ff35e
--- /dev/null
+++ b/src/data-structures/queue/README.ko-KR.md
@@ -0,0 +1,23 @@
+# Queue
+
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Français_](README.fr-FR.md),
+[_Português_](README.pt-BR.md)
+
+컴퓨터 공학에서 **큐**는 일종의 추상 데이터 타입이자 컬렉션입니다. 큐 내부의 엔터티들은 순서를 유지하며 컬렉션의 가장 뒷 부분에 엔터티를 추가하는 인큐(enqueue), 컬렉션의 가장 앞에 위치한 엔터티를 제거하는 디큐(dequeue) 작업을 수행합니다. 이것은 큐를 선입선출 자료 구조로 만듭니다. 선입선출 자료 구조에서는, 추가된 첫 번째 요소가 가장 먼저 제거되는 요소가 됩니다. 이는 새로운 요소가 추가되면 이전에 추가되었던 모든 요소들을 제거해야 새로운 요소를 제거할 수 있다는것과 같은 의미입니다. 또한 큐의 가장 앞에 위치한 요소를 반환하기 위한 작업이 입력되면 디큐 작업 없이 해당 요소를 반환합니다.
+
+큐는 선형 자료 구조의 예시이며, 더 추상적으로는 순차적인 컬렉션입니다.
+
+선입선출 자료 구조인 큐를 나타내면 다음과 같습니다.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## 참고
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Queue_(abstract_data_type))
+- [YouTube](https://www.youtube.com/watch?v=wjI1WNcIntg&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=3&)
diff --git a/src/data-structures/queue/README.md b/src/data-structures/queue/README.md
index e6c9bc2d23..d8e0288b42 100644
--- a/src/data-structures/queue/README.md
+++ b/src/data-structures/queue/README.md
@@ -5,27 +5,31 @@ _Read this in other languages:_
[_Русский_](README.ru-RU.md),
[_日本語_](README.ja-JP.md),
[_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
-In computer science, a **queue** is a particular kind of abstract data
-type or collection in which the entities in the collection are
-kept in order and the principle (or only) operations on the
-collection are the addition of entities to the rear terminal
-position, known as enqueue, and removal of entities from the
-front terminal position, known as dequeue. This makes the queue
-a First-In-First-Out (FIFO) data structure. In a FIFO data
-structure, the first element added to the queue will be the
-first one to be removed. This is equivalent to the requirement
-that once a new element is added, all elements that were added
-before have to be removed before the new element can be removed.
-Often a peek or front operation is also entered, returning the
-value of the front element without dequeuing it. A queue is an
-example of a linear data structure, or more abstractly a
+In computer science, a **queue** is a particular kind of abstract data
+type or collection in which the entities in the collection are
+kept in order and the principle (or only) operations on the
+collection are the addition of entities to the rear terminal
+position, known as enqueue, and removal of entities from the
+front terminal position, known as dequeue. This makes the queue
+a First-In-First-Out (FIFO) data structure. In a FIFO data
+structure, the first element added to the queue will be the
+first one to be removed. This is equivalent to the requirement
+that once a new element is added, all elements that were added
+before have to be removed before the new element can be removed.
+Often a peek or front operation is also entered, returning the
+value of the front element without dequeuing it. A queue is an
+example of a linear data structure, or more abstractly a
sequential collection.
Representation of a FIFO (first in, first out) queue
-
+
+
+*Made with [okso.app](https://okso.app)*
## References
diff --git a/src/data-structures/queue/README.pt-BR.md b/src/data-structures/queue/README.pt-BR.md
index b86c9713c9..9464864120 100644
--- a/src/data-structures/queue/README.pt-BR.md
+++ b/src/data-structures/queue/README.pt-BR.md
@@ -20,7 +20,9 @@ coleção seqüencial.
Representação de uma file FIFO (first in, first out)
-
+
+
+*Made with [okso.app](https://okso.app)*
## References
diff --git a/src/data-structures/queue/README.ru-RU.md b/src/data-structures/queue/README.ru-RU.md
index 539272475d..1f9e5ff6f1 100644
--- a/src/data-structures/queue/README.ru-RU.md
+++ b/src/data-structures/queue/README.ru-RU.md
@@ -2,8 +2,8 @@
Очередь (англ. queue) - структура данных в информатике, в которой элементы
хранятся в порядке их добавления. Добавление новых элементов(enqueue)
-осуществляется в начало списка. А удаление элементов (dequeue)
-осуществляется с конца. Таким образом очередь реализует принцип
+осуществляется в конец списка. А удаление элементов (dequeue)
+осуществляется с начала. Таким образом очередь реализует принцип
"первым вошёл - первым вышел" (FIFO). Часто реализуется операция чтения
головного элемента (peek), которая возвращает первый в очереди элемент,
при этом не удаляя его. Очередь является примером линейной структуры
@@ -11,7 +11,9 @@
Иллюстрация работы с очередью.
-
+
+
+*Made with [okso.app](https://okso.app)*
## References
diff --git a/src/data-structures/queue/README.uk-UA.md b/src/data-structures/queue/README.uk-UA.md
new file mode 100644
index 0000000000..7934c7571a
--- /dev/null
+++ b/src/data-structures/queue/README.uk-UA.md
@@ -0,0 +1,21 @@
+# Черга
+
+Черга (англ. queue) – структура даних в інформатиці, в якій елементи
+зберігаються у порядку їх додавання. Додавання нових елементів(enqueue)
+здійснюється на кінець списку. А видалення елементів (dequeue)
+здійснюється із початку. Таким чином черга реалізує принцип
+"першим увійшов – першим вийшов" (FIFO). Часто реалізується операція читання
+головного елемента (peek), яка повертає перший у черзі елемент,
+при цьому не видаляючи його. Черга є прикладом лінійної структури
+даних чи послідовної колекції.
+
+Ілюстрація роботи з чергою.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## Список літератури
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%A7%D0%B5%D1%80%D0%B3%D0%B0_(%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0_%D0%B4%D0%B0%D0%BD%D0%B8%D1%85))
+- [YouTube](https://www.youtube.com/watch?v=ll4QLNSPn60)
diff --git a/src/data-structures/queue/README.vi-VN.md b/src/data-structures/queue/README.vi-VN.md
new file mode 100644
index 0000000000..84b3bdbfa6
--- /dev/null
+++ b/src/data-structures/queue/README.vi-VN.md
@@ -0,0 +1,22 @@
+# Hàng đợi (Queue)
+
+_Đọc bằng ngôn ngữ khác:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
+
+Trong khoa học máy tính, một **hàng đợi** là một loại cụ thể của kiểu dữ liệu trừu tượng hoặc bộ sưu tập trong đó các phần tử trong bộ sưu tập được giữ theo thứ tự và nguyên tắc (hoặc chỉ) các hoạt động trên bộ sưu tập là thêm các phần tử vào vị trí cuối cùng, được gọi là đưa vào hàng đợi (enqueue), và loại bỏ các phần tử từ vị trí đầu tiên, được gọi là đưa ra khỏi hàng đợi (dequeue). Điều này khiến cho hàng đợi trở thành một cấu trúc dữ liệu First-In-First-Out (FIFO). Trong cấu trúc dữ liệu FIFO, phần tử đầu tiên được thêm vào hàng đợi sẽ là phần tử đầu tiên được loại bỏ. Điều này tương đương với yêu cầu rằng sau khi một phần tử mới được thêm vào, tất cả các phần tử đã được thêm vào trước đó phải được loại bỏ trước khi có thể loại bỏ phần tử mới. Thường thì cũng có thêm một hoạt động nhìn hay lấy phần đầu, trả về giá trị của phần tử đầu tiên mà không loại bỏ nó. Hàng đợi là một ví dụ về cấu trúc dữ liệu tuyến tính, hoặc trừu tượng hơn là một bộ sưu tập tuần tự.
+
+Hàng đợi FIFO (First-In-First-Out) có thể được biểu diễn như sau:
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## Tham Khảo
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Queue_(abstract_data_type))
+- [YouTube](https://www.youtube.com/watch?v=wjI1WNcIntg&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=3&)
diff --git a/src/data-structures/queue/README.zh-CN.md b/src/data-structures/queue/README.zh-CN.md
index d61a2c7dac..af608107d3 100644
--- a/src/data-structures/queue/README.zh-CN.md
+++ b/src/data-structures/queue/README.zh-CN.md
@@ -7,7 +7,9 @@
队列中元素先进先出 FIFO (first in, first out)的示意
-
+
+
+*Made with [okso.app](https://okso.app)*
## 参考
diff --git a/src/data-structures/queue/images/queue.jpeg b/src/data-structures/queue/images/queue.jpeg
new file mode 100644
index 0000000000..579f4d8c83
Binary files /dev/null and b/src/data-structures/queue/images/queue.jpeg differ
diff --git a/src/data-structures/stack/README.fr-FR.md b/src/data-structures/stack/README.fr-FR.md
index 5e9a95c81c..0d6c388640 100644
--- a/src/data-structures/stack/README.fr-FR.md
+++ b/src/data-structures/stack/README.fr-FR.md
@@ -20,7 +20,9 @@ autres articles en premier.
Représentation simple de l'éxecution d'une pile avec des opérations empiler (push) et dépiler (pop).
-
+
+
+*Made with [okso.app](https://okso.app)*
## Références
diff --git a/src/data-structures/stack/README.ja-JP.md b/src/data-structures/stack/README.ja-JP.md
index 7f77828425..55ca25206c 100644
--- a/src/data-structures/stack/README.ja-JP.md
+++ b/src/data-structures/stack/README.ja-JP.md
@@ -9,7 +9,9 @@
プッシュとポップの例
-
+
+
+*Made with [okso.app](https://okso.app)*
## 参考
diff --git a/src/data-structures/stack/README.ko-KR.md b/src/data-structures/stack/README.ko-KR.md
new file mode 100644
index 0000000000..c36a472e66
--- /dev/null
+++ b/src/data-structures/stack/README.ko-KR.md
@@ -0,0 +1,26 @@
+# 스택
+
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Français_](README.fr-FR.md),
+[_Português_](README.pt-BR.md)
+
+컴퓨터 과학에서, **스택**은 아래의 두가지 연산을 가진 요소들의 집합인 추상 자료형입니다.
+
+* **push**는 집합에 요소를 추가하는 것이며,
+* **pop**은 아직 제거되지 않은 가장 최근에 추가된 요소를 제거하는 연산입니다.
+
+요소가 스택에서 나오는 과정은 LIFO (last in, first out)라는 이름으로 확인할 수 있습니다. 추가적으로, peek 연산은 스택을 수정하지 않고 최상단의 요소에 접근할 수 있게 해줍니다. 이런 자료구조의 "스택"이라는 이름은 실제 물건들이 다른 물건들의 위에 쌓이게 되는 것에서 유추되었습니다. 스택의 최상단의 물건은 빼내기 쉽지만 깊이 있는 물건을 빼내려면 다른 물건들을 먼저 빼내야 하는게 필요합니다.
+
+다음은 push와 pop 연산을 실행하는 간단한 스택의 실행입니다.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## 참조
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Stack_(abstract_data_type))
+- [YouTube](https://www.youtube.com/watch?v=wjI1WNcIntg&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=3&)
diff --git a/src/data-structures/stack/README.md b/src/data-structures/stack/README.md
index dc4f311b01..612f926736 100644
--- a/src/data-structures/stack/README.md
+++ b/src/data-structures/stack/README.md
@@ -5,26 +5,30 @@ _Read this in other languages:_
[_Русский_](README.ru-RU.md),
[_日本語_](README.ja-JP.md),
[_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
-In computer science, a **stack** is an abstract data type that serves
+In computer science, a **stack** is an abstract data type that serves
as a collection of elements, with two principal operations:
* **push**, which adds an element to the collection, and
* **pop**, which removes the most recently added element that was not yet removed.
-The order in which elements come off a stack gives rise to its
-alternative name, LIFO (last in, first out). Additionally, a
-peek operation may give access to the top without modifying
-the stack. The name "stack" for this type of structure comes
-from the analogy to a set of physical items stacked on top of
-each other, which makes it easy to take an item off the top
-of the stack, while getting to an item deeper in the stack
+The order in which elements come off a stack gives rise to its
+alternative name, LIFO (last in, first out). Additionally, a
+peek operation may give access to the top without modifying
+the stack. The name "stack" for this type of structure comes
+from the analogy to a set of physical items stacked on top of
+each other, which makes it easy to take an item off the top
+of the stack, while getting to an item deeper in the stack
may require taking off multiple other items first.
Simple representation of a stack runtime with push and pop operations.
-
+
+
+*Made with [okso.app](https://okso.app)*
## References
diff --git a/src/data-structures/stack/README.pt-BR.md b/src/data-structures/stack/README.pt-BR.md
index 9390ea5155..ee862fe43a 100644
--- a/src/data-structures/stack/README.pt-BR.md
+++ b/src/data-structures/stack/README.pt-BR.md
@@ -1,14 +1,14 @@
-# Stack
+# Pilha (Stack)
-Na ciência da computação, um **stack** é uma estrutura de dados abstrata
+Na ciência da computação, uma **pilha** é uma estrutura de dados abstrata
que serve como uma coleção de elementos com duas operações principais:
* **push**, pela qual adiciona um elemento à coleção, e
* **pop**, pela qual remove o último elemento adicionado.
A ordem em que os elementos saem de um _stack_ dá origem ao seu
-nome alternativo, LIFO (last in, first out). Adicionalmente, uma
-espiar a operação pode dar acesso ao topo sem modificar o _stack_.
+nome alternativo, LIFO (last in, first out). Adicionalmente, uma operação
+de espiada (peek) pode dar acesso ao topo sem modificar o _stack_.
O nome "stack" para este tipo de estrutura vem da analogia de
um conjunto de itens físicos empilhados uns sobre os outros,
o que facilita retirar um item do topo da pilha, enquanto para chegar a
@@ -18,7 +18,9 @@ vários outros itens primeiro.
Representação simples de um tempo de execução de pilha com operações
_push_ e _pop_.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Referências
diff --git a/src/data-structures/stack/README.ru-RU.md b/src/data-structures/stack/README.ru-RU.md
index 136cd6f4d2..3e33c87119 100644
--- a/src/data-structures/stack/README.ru-RU.md
+++ b/src/data-structures/stack/README.ru-RU.md
@@ -8,14 +8,16 @@
* **удаление (pop)**, последнего добавленного элемента.
Дополнительная операция чтения головного элемента (peek) даёт доступ
-к последнему элементу стека без изменения самого стека.
+к последнему элементу стека без изменения самого стека.
Чаще всего принцип работы стека сравнивают со стопкой тарелок: чтобы взять вторую
сверху, нужно снять верхнюю.
Иллюстрация работы со стеком.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Ссылки
diff --git a/src/data-structures/stack/README.uk-UA.md b/src/data-structures/stack/README.uk-UA.md
new file mode 100644
index 0000000000..f71d2274eb
--- /dev/null
+++ b/src/data-structures/stack/README.uk-UA.md
@@ -0,0 +1,25 @@
+# Стек
+
+Стек (англ. stack - стопка) - абстрактний тип даних, що представляє собою
+список елементів, організованих за принципом LIFO (останнім прийшов – першим вийшов).
+
+Стек має дві ключові операції:
+* **додавання (push)** елемента в кінець стеку, та
+* **видалення (pop)**, останнього доданого елемента.
+
+Додаткова операція для читання головного елемента (peek) дає доступ
+до останнього елементу стека без зміни самого стека.
+
+Найчастіше принцип роботи стека порівнюють із стопкою тарілок: щоб узяти другу
+зверху потрібно спочатку зняти верхню.
+
+Ілюстрація роботи зі стеком.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D0%BA)
+- [YouTube](https://www.youtube.com/watch?v=4jh1e1YCbYc)
diff --git a/src/data-structures/stack/README.vi-VN.md b/src/data-structures/stack/README.vi-VN.md
new file mode 100644
index 0000000000..f051f3201f
--- /dev/null
+++ b/src/data-structures/stack/README.vi-VN.md
@@ -0,0 +1,27 @@
+# Ngăn xếp (stack)
+
+_Đọc bằng ngôn ngữ khác:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Español_](README.es-ES.md),
+[_Українська_](README.uk-UA.md)
+
+Trong khoa học máy tính, một ngăn xếp (stack) là một kiểu dữ liệu trừu tượng phục vụ như một bộ sưu tập các phần tử, với hai hoạt động chính:
+
+đẩy (push), thêm một phần tử vào bộ sưu tập, và
+lấy (pop), loại bỏ phần tử được thêm gần nhất mà chưa được loại bỏ.
+Thứ tự mà các phần tử được lấy ra khỏi ngăn xếp dẫn đến tên gọi thay thế của nó, là LIFO (last in, first out). Ngoài ra, một hoạt động nhìn có thể cung cấp quyền truy cập vào phần trên mà không làm thay đổi ngăn xếp. Tên "ngăn xếp" cho loại cấu trúc này đến từ sự tương tự với một bộ sưu tập các vật phẩm vật lý được xếp chồng lên nhau, điều này làm cho việc lấy một vật phẩm ra khỏi đỉnh của ngăn xếp dễ dàng, trong khi để đến được một vật phẩm sâu hơn trong ngăn xếp có thể đòi hỏi việc lấy ra nhiều vật phẩm khác trước đó.
+
+Biểu diễn đơn giản về thời gian chạy của một ngăn xếp với các hoạt động đẩy và lấy.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+## Tham Khảo
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
+- [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/stack/README.zh-CN.md b/src/data-structures/stack/README.zh-CN.md
index bd9bce4b2a..f00e3eab00 100644
--- a/src/data-structures/stack/README.zh-CN.md
+++ b/src/data-structures/stack/README.zh-CN.md
@@ -13,7 +13,9 @@
栈的 push 和 pop 操作的示意
-
+
+
+*Made with [okso.app](https://okso.app)*
## 参考
diff --git a/src/data-structures/stack/images/stack.jpeg b/src/data-structures/stack/images/stack.jpeg
new file mode 100644
index 0000000000..6a3bf599c4
Binary files /dev/null and b/src/data-structures/stack/images/stack.jpeg differ
diff --git a/src/data-structures/stack/images/stack.jpg b/src/data-structures/stack/images/stack.jpg
new file mode 100644
index 0000000000..8c966f276f
Binary files /dev/null and b/src/data-structures/stack/images/stack.jpg differ
diff --git a/src/data-structures/tree/README.md b/src/data-structures/tree/README.md
index d2d338f434..e492257d33 100644
--- a/src/data-structures/tree/README.md
+++ b/src/data-structures/tree/README.md
@@ -10,24 +10,26 @@ _Read this in other languages:_
* [Segment Tree](segment-tree) - with min/max/sum range queries examples
* [Fenwick Tree](fenwick-tree) (Binary Indexed Tree)
-In computer science, a **tree** is a widely used abstract data
-type (ADT) — or data structure implementing this ADT—that
-simulates a hierarchical tree structure, with a root value
-and subtrees of children with a parent node, represented as
+In computer science, a **tree** is a widely used abstract data
+type (ADT) — or data structure implementing this ADT—that
+simulates a hierarchical tree structure, with a root value
+and subtrees of children with a parent node, represented as
a set of linked nodes.
-A tree data structure can be defined recursively (locally)
-as a collection of nodes (starting at a root node), where
-each node is a data structure consisting of a value,
-together with a list of references to nodes (the "children"),
-with the constraints that no reference is duplicated, and none
+A tree data structure can be defined recursively (locally)
+as a collection of nodes (starting at a root node), where
+each node is a data structure consisting of a value,
+together with a list of references to nodes (the "children"),
+with the constraints that no reference is duplicated, and none
points to the root.
-A simple unordered tree; in this diagram, the node labeled 7 has
+A simple unordered tree; in this diagram, the node labeled 3 has
two children, labeled 2 and 6, and one parent, labeled 2. The
root node, at the top, has no parent.
-
+
+
+*Made with [okso.app](https://okso.app)*
## References
diff --git a/src/data-structures/tree/README.pt-BR.md b/src/data-structures/tree/README.pt-BR.md
index 905c419c19..7aade88caa 100644
--- a/src/data-structures/tree/README.pt-BR.md
+++ b/src/data-structures/tree/README.pt-BR.md
@@ -8,7 +8,7 @@
Na ciência da computação, uma **árvore** é uma estrutura de dados
abstrada (ADT) amplamente utilizada - ou uma estrutura de dados
-implementando este ADT que simula uma estrutura hierarquica de árvore,
+implementando este ADT que simula uma estrutura hierárquica de árvore,
com valor raíz e sub-árvores de filhos com um nó pai, representado
como um conjunto de nós conectados.
@@ -22,7 +22,9 @@ Uma árvore não ordenada simples; neste diagrama, o nó rotulado como `7`
possui dois filhos, rotulados como `2` e `6`, e um pai, rotulado como `2`.
O nó raíz, no topo, não possui nenhum pai.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Referências
diff --git a/src/data-structures/tree/README.zh-CN.md b/src/data-structures/tree/README.zh-CN.md
index 3188c2b0e2..2f4df983d4 100644
--- a/src/data-structures/tree/README.zh-CN.md
+++ b/src/data-structures/tree/README.zh-CN.md
@@ -13,10 +13,12 @@
一棵简单的无序树; 在下图中:
-标记为7的节点具有两个子节点, 标记为2和6;
+标记为7的节点具有两个子节点, 标记为2和6;
一个父节点,标记为2,作为根节点, 在顶部,没有父节点。
-
+
+
+*Made with [okso.app](https://okso.app)*
## 参考
diff --git a/src/data-structures/tree/binary-search-tree/README.md b/src/data-structures/tree/binary-search-tree/README.md
index f3e448a995..d05a891545 100644
--- a/src/data-structures/tree/binary-search-tree/README.md
+++ b/src/data-structures/tree/binary-search-tree/README.md
@@ -3,32 +3,34 @@
_Read this in other languages:_
[_Português_](README.pt-BR.md)
-In computer science, **binary search trees** (BST), sometimes called
-ordered or sorted binary trees, are a particular type of container:
-data structures that store "items" (such as numbers, names etc.)
-in memory. They allow fast lookup, addition and removal of
-items, and can be used to implement either dynamic sets of
-items, or lookup tables that allow finding an item by its key
+In computer science, **binary search trees** (BST), sometimes called
+ordered or sorted binary trees, are a particular type of container:
+data structures that store "items" (such as numbers, names etc.)
+in memory. They allow fast lookup, addition and removal of
+items, and can be used to implement either dynamic sets of
+items, or lookup tables that allow finding an item by its key
(e.g., finding the phone number of a person by name).
-Binary search trees keep their keys in sorted order, so that lookup
-and other operations can use the principle of binary search:
-when looking for a key in a tree (or a place to insert a new key),
-they traverse the tree from root to leaf, making comparisons to
-keys stored in the nodes of the tree and deciding, on the basis
-of the comparison, to continue searching in the left or right
-subtrees. On average, this means that each comparison allows
-the operations to skip about half of the tree, so that each
-lookup, insertion or deletion takes time proportional to the
-logarithm of the number of items stored in the tree. This is
-much better than the linear time required to find items by key
-in an (unsorted) array, but slower than the corresponding
+Binary search trees keep their keys in sorted order, so that lookup
+and other operations can use the principle of binary search:
+when looking for a key in a tree (or a place to insert a new key),
+they traverse the tree from root to leaf, making comparisons to
+keys stored in the nodes of the tree and deciding, on the basis
+of the comparison, to continue searching in the left or right
+subtrees. On average, this means that each comparison allows
+the operations to skip about half of the tree, so that each
+lookup, insertion or deletion takes time proportional to the
+logarithm of the number of items stored in the tree. This is
+much better than the linear time required to find items by key
+in an (unsorted) array, but slower than the corresponding
operations on hash tables.
A binary search tree of size 9 and depth 3, with 8 at the root.
The leaves are not drawn.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Pseudocode for Basic Operations
@@ -45,7 +47,7 @@ insert(value)
end if
end insert
```
-
+
```text
insertNode(current, value)
Pre: current is the node to start from
@@ -84,8 +86,8 @@ contains(root, value)
end if
end contains
```
-
-
+
+
### Deletion
```text
@@ -186,7 +188,7 @@ findNode(root, value)
end if
end findNode
```
-
+
### Find Minimum
```text
@@ -200,7 +202,7 @@ findMin(root)
findMin(root.left)
end findMin
```
-
+
### Find Maximum
```text
@@ -214,7 +216,7 @@ findMax(root)
findMax(root.right)
end findMax
```
-
+
### Traversal
#### InOrder Traversal
@@ -244,7 +246,7 @@ preorder(root)
end if
end preorder
```
-
+
#### PostOrder Traversal
```text
@@ -258,7 +260,7 @@ postorder(root)
end if
end postorder
```
-
+
## Complexities
### Time Complexity
diff --git a/src/data-structures/tree/binary-search-tree/README.pt-BR.md b/src/data-structures/tree/binary-search-tree/README.pt-BR.md
index 4565538a7b..1e71714104 100644
--- a/src/data-structures/tree/binary-search-tree/README.pt-BR.md
+++ b/src/data-structures/tree/binary-search-tree/README.pt-BR.md
@@ -26,8 +26,9 @@ Uma pesquisa de árvore binária de tamanho 9 e profundidade 3, com valor 8
na raíz.
As folhas não foram desenhadas.
+
-
+*Made with [okso.app](https://okso.app)*
## Pseudocódigo para Operações Básicas
@@ -44,7 +45,7 @@ insert(value)
end if
end insert
```
-
+
```text
insertNode(current, value)
Pre: current is the node to start from
@@ -83,8 +84,8 @@ contains(root, value)
end if
end contains
```
-
-
+
+
### Remoção
```text
@@ -185,7 +186,7 @@ findNode(root, value)
end if
end findNode
```
-
+
### Encontrar Mínimo
```text
@@ -199,7 +200,7 @@ findMin(root)
findMin(root.left)
end findMin
```
-
+
### Encontrar Máximo
```text
@@ -213,7 +214,7 @@ findMax(root)
findMax(root.right)
end findMax
```
-
+
### Traversal
#### Na Ordem Traversal (InOrder Traversal)
@@ -243,7 +244,7 @@ preorder(root)
end if
end preorder
```
-
+
#### Pós Ordem Traversal (PostOrder Traversal)
```text
@@ -257,7 +258,7 @@ postorder(root)
end if
end postorder
```
-
+
## Complexidades
### Complexidade de Tempo
diff --git a/src/data-structures/tree/binary-search-tree/images/binary-search-tree.jpg b/src/data-structures/tree/binary-search-tree/images/binary-search-tree.jpg
new file mode 100644
index 0000000000..1309e4ee4d
Binary files /dev/null and b/src/data-structures/tree/binary-search-tree/images/binary-search-tree.jpg differ
diff --git a/src/data-structures/tree/images/tree.jpeg b/src/data-structures/tree/images/tree.jpeg
new file mode 100644
index 0000000000..c888843d6c
Binary files /dev/null and b/src/data-structures/tree/images/tree.jpeg differ
diff --git a/src/data-structures/trie/README.ko-KO.md b/src/data-structures/trie/README.ko-KO.md
new file mode 100644
index 0000000000..e57142ece4
--- /dev/null
+++ b/src/data-structures/trie/README.ko-KO.md
@@ -0,0 +1,19 @@
+# Trie
+
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_Português_](README.pt-BR.md),
+[_Українська_](README.uk-UA.md),
+[_한국어_](README.ko-KO.md)
+
+컴퓨터 과학에서 **트라이**는 디지털 트리라고도 불리며 때로는 기수 트리 또는 접두사 트리(접두사로 검색할 수 있기 때문에)라고도 불리며 일종의 검색 트리입니다. 키가 보통 문자열인 동적 집합 또는 연관 배열을 저장하는 데 사용되는 순서가 지정된 트리 데이터 구조입니다. 이진 검색 트리와 달리 트리의 어떤 노드도 해당 노드와 연결된 키를 저장하지 않으며 대신 트리의 위치가 해당 노드와 연결된 키를 정의합니다. 노드의 모든 하위 항목은 해당 노드와 연결된 문자열의 공통 접두사를 가지며 루트는 빈 문자열과 연결됩니다. 값은 모든 노드와 반드시 연결되지는 않습니다. 오히려 값은 나뭇잎과 관심 있는 키에 해당하는 일부 내부 노드에만 연결되는 경향이 있습니다. 접두사 트리의 공간에 최적화된 표현은 콤팩트 접두사 트리를 참조하십시오.
+
+
+
+_Made with [okso.app](https://okso.app)_
+
+## 참조
+
+- [Wikipedia](<https://ko.wikipedia.org/wiki/%ED%8A%B8%EB%9D%BC%EC%9D%B4_(%EC%BB%B4%ED%93%A8%ED%8C%85)>)
+- [YouTube](https://www.youtube.com/watch?v=zIjfhVPRZCg&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=7&t=0s)
diff --git a/src/data-structures/trie/README.md b/src/data-structures/trie/README.md
index d07c69feb1..b3bba5de1e 100644
--- a/src/data-structures/trie/README.md
+++ b/src/data-structures/trie/README.md
@@ -3,24 +3,28 @@
_Read this in other languages:_
[_简体中文_](README.zh-CN.md),
[_Русский_](README.ru-RU.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Українська_](README.uk-UA.md),
+[_한국어_](README.ko-KO.md)
-In computer science, a **trie**, also called digital tree and sometimes
-radix tree or prefix tree (as they can be searched by prefixes),
-is a kind of search tree—an ordered tree data structure that is
-used to store a dynamic set or associative array where the keys
-are usually strings. Unlike a binary search tree, no node in the
-tree stores the key associated with that node; instead, its
+In computer science, a **trie**, also called digital tree and sometimes
+radix tree or prefix tree (as they can be searched by prefixes),
+is a kind of search tree—an ordered tree data structure that is
+used to store a dynamic set or associative array where the keys
+are usually strings. Unlike a binary search tree, no node in the
+tree stores the key associated with that node; instead, its
position in the tree defines the key with which it is associated.
All the descendants of a node have a common prefix of the string
-associated with that node, and the root is associated with the
-empty string. Values are not necessarily associated with every
-node. Rather, values tend only to be associated with leaves,
-and with some inner nodes that correspond to keys of interest.
-For the space-optimized presentation of prefix tree, see compact
+associated with that node, and the root is associated with the
+empty string. Values are not necessarily associated with every
+node. Rather, values tend only to be associated with leaves,
+and with some inner nodes that correspond to keys of interest.
+For the space-optimized presentation of prefix tree, see compact
prefix tree.
-
+
+
+*Made with [okso.app](https://okso.app)*
## References
diff --git a/src/data-structures/trie/README.pt-BR.md b/src/data-structures/trie/README.pt-BR.md
index 7a1415814d..50a294b77c 100644
--- a/src/data-structures/trie/README.pt-BR.md
+++ b/src/data-structures/trie/README.pt-BR.md
@@ -1,9 +1,9 @@
-# Trie
+# Árvore de Prefixos (Trie)
Na ciência da computação, uma **trie**, também chamada de árvore digital (digital tree)
e algumas vezes de _radix tree_ ou _prefix tree_ (tendo em vista que eles
-podem ser pesquisados por prefixos), é um tipo de árvore de pesquisa, uma
-uma estrutura de dados de árvore ordenada que é usado para armazenar um
+podem ser pesquisados por prefixos), é um tipo de árvore de pesquisa, uma
+estrutura de dados de árvore ordenada que é usado para armazenar um
conjunto dinâmico ou matriz associativa onde as chaves são geralmente _strings_.
Ao contrário de uma árvore de pesquisa binária (binary search tree),
nenhum nó na árvore armazena a chave associada a esse nó; em vez disso,
@@ -17,7 +17,9 @@ internos que correspondem a chaves de interesse.
Para a apresentação otimizada do espaço da árvore de prefixo (_prefix tree_),
veja árvore de prefixo compacto.
-
+
+
+*Made with [okso.app](https://okso.app)*
## Referências
diff --git a/src/data-structures/trie/README.ru-RU.md b/src/data-structures/trie/README.ru-RU.md
index f447f8eb0e..30a4536383 100644
--- a/src/data-structures/trie/README.ru-RU.md
+++ b/src/data-structures/trie/README.ru-RU.md
@@ -16,7 +16,9 @@
дополнительную информацию, связанную с ключом, и обычно выделенными являются только листья и, возможно, некоторые
внутренние узлы.
-
+
+
+*Made with [okso.app](https://okso.app)*
На рисунке представлено префиксное дерево, содержащее ключи «A», «to», «tea», «ted», «ten», «i», «in», «inn».
diff --git a/src/data-structures/trie/README.uk-UA.md b/src/data-structures/trie/README.uk-UA.md
new file mode 100644
index 0000000000..3b1f01f0aa
--- /dev/null
+++ b/src/data-structures/trie/README.uk-UA.md
@@ -0,0 +1,27 @@
+# Префіксне дерево
+
+**Префіксне дерево** (Також промінь, навантажене або суфіксне дерево) в інформатиці - впорядкована деревоподібна
+структура даних, яка використовується для зберігання динамічних множин або асоціативних масивів, де
+ключем зазвичай виступають рядки. Дерево називається префіксним, тому що пошук здійснюється за префіксами.
+
+На відміну від бінарного дерева, вузли не містять ключів, що відповідають вузлу. Являє собою кореневе дерево, кожне
+ребро якого позначено якимось символом так, що для будь-якого вузла всі ребра, що з'єднують цей вузол з його синами,
+позначені різними символами. Деякі вузли префіксного дерева виділені (на малюнку вони підписані цифрами) і вважається,
+що префіксне дерево містить цей рядок-ключ тоді і тільки тоді, коли цей рядок можна прочитати на шляху з
+кореня до певного виділеного вузла.
+
+Таким чином, на відміну від бінарних дерев пошуку, ключ, що ідентифікує конкретний вузол дерева, не явно зберігається в
+цьому вузлі, а неявно задається положенням цього вузла в дереві. Отримати ключ можна виписуванням поспіль символів,
+помічають ребра по дорозі від кореня до вузла. Ключ кореня дерева - порожній рядок. Часто у виділених вузлах зберігають
+додаткову інформацію, пов'язану з ключем, і зазвичай виділеними є тільки листя і, можливо, деякі
+внутрішні вузли.
+
+
+
+*Made with [okso.app](https://okso.app)*
+
+На малюнку представлено префіксне дерево, що містить ключі. «A», «to», «tea», «ted», «ten», «i», «in», «inn».
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D1%84%D1%96%D0%BA%D1%81%D0%BD%D0%B5_%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D0%BE)
diff --git a/src/data-structures/trie/README.zh-CN.md b/src/data-structures/trie/README.zh-CN.md
index bad277d4bd..e812f57523 100644
--- a/src/data-structures/trie/README.zh-CN.md
+++ b/src/data-structures/trie/README.zh-CN.md
@@ -2,13 +2,15 @@
在计算机科学中, **字典树(trie,中文又被称为”单词查找树“或 ”键树“)**, 也称为数字树,有时候也被称为基数树或前缀树（因为它们可以通过前缀搜索）,它是一种搜索树--一种已排序的数据结构,通常用于存储动态集或键为字符串的关联数组。
-与二叉搜索树不同, 树上没有节点存储与该节点关联的键; 相反,节点在树上的位置定义了与之关联的键。一个节点的全部后代节点都有一个与该节点关联的通用的字符串前缀, 与根节点关联的是空字符串。
+与二叉搜索树不同, 树上没有节点存储与该节点关联的键; 相反,节点在树上的位置定义了与之关联的键。一个节点的全部后代节点都有一个与该节点关联的通用的字符串前缀, 与根节点关联的是空字符串。
值对于字典树中关联的节点来说,不是必需的,相反,值往往和相关的叶子相关,以及与一些键相关的内部节点相关。
有关字典树的空间优化示意,请参阅紧凑前缀树
-
+
+
+*Made with [okso.app](https://okso.app)*
## 参考
diff --git a/src/data-structures/trie/images/trie.jpg b/src/data-structures/trie/images/trie.jpg
new file mode 100644
index 0000000000..001b04f2e7
Binary files /dev/null and b/src/data-structures/trie/images/trie.jpg differ
diff --git a/src/playground/__test__/playground.test.js b/src/playground/__test__/playground.test.js
index 501a87a728..84a3e8301f 100644
--- a/src/playground/__test__/playground.test.js
+++ b/src/playground/__test__/playground.test.js
@@ -1,5 +1,8 @@
+import playground from '../playground';
+
describe('playground', () => {
- it('should perform playground tasks', () => {
- // Place your playground tests here.
+ it('should return correct results', () => {
+ // Replace the next dummy test with your playground function tests.
+ expect(playground()).toBe(120);
});
});
diff --git a/src/playground/playground.js b/src/playground/playground.js
index 7872c9e3b8..b8c5b210bc 100644
--- a/src/playground/playground.js
+++ b/src/playground/playground.js
@@ -1 +1,12 @@
-// Place your playground code here.
+// Import any algorithmic dependencies you need for your playground code here.
+import factorial from '../algorithms/math/factorial/factorial';
+
+// Write your playground code inside the playground() function.
+// Test your code from __tests__/playground.test.js
+// Launch playground tests by running: npm test -- 'playground'
+function playground() {
+ // Replace the next line with your playground code.
+ return factorial(5);
+}
+
+export default playground;
diff --git a/src/utils/comparator/Comparator.js b/src/utils/comparator/Comparator.js
index 12957d2d73..f5c41b5c18 100644
--- a/src/utils/comparator/Comparator.js
+++ b/src/utils/comparator/Comparator.js
@@ -1,5 +1,6 @@
export default class Comparator {
/**
+ * Constructor.
* @param {function(a: *, b: *)} [compareFunction] - It may be custom compare function that, let's
* say may compare custom objects together.
*/