src/algorithms/math/karatsuba-multiplication/README.md

@@ -0,0 +1,41 @@
+# Karatsuba Multiplication
+
+Karatsuba is a fast multiplication algorithm discovered by Anatoly Karatsuba in 1960. Given two n-digit numbers, the "grade-school" method of long multiplication has a time complexity of O(n<sup>2</sup>), whereas the karatsuba algorithm has a time complexity of O(n<sup>1.59</sup>).
+
+## Recursive Formula
+
+```
+x = 1234
+y = 5678
+
+karatsuba(x, y)
+```
+
+1. Split each number into numbers with half as many digits
+```
+a = 12
+b = 34
+
+c = 56
+d = 78
+```
+
+2. Compute 3 subexpressions from the smaller numbers
+  - `ac = a * c`
+  - `bd = b * d`
+  - `abcd = (a + b) * (c + d)`
+
+3. Combine subexpressions to calculate the product
+```
+A = ac * 10000
+B = (abcd - ac - bd) * 100
+C = bd
+
+x * y = A + B + C
+```
+
+_**Note:**_ *The karatsuba algorithm can be applied recursively to calculate each product in the subexpressions.* (`a * c = karatsuba(a, c)`*). When the numbers get smaller than some arbitrary threshold, they are multiplied in the traditional way.*
+
+## References
+[Stanford Algorithms (YouTube)](https://www.youtube.com/watch?v=JCbZayFr9RE)
+[Wikipedia](https://en.wikipedia.org/wiki/Karatsuba_algorithm)

src/algorithms/math/karatsuba-multiplication/__test__/karatsuba.test.js

@@ -0,0 +1,14 @@
+import karatsuba from '../karatsuba';
+
+describe('karatsuba multiplication', () => {
+  it('should multiply simple numbers correctly', () => {
+    expect(karatsuba(0, 37)).toEqual(0);
+    expect(karatsuba(1, 8)).toEqual(8);
+    expect(karatsuba(5, 6)).toEqual(30);
+  });
+
+  it('should multiply larger numbers correctly', () => {
+    expect(karatsuba(1234, 5678)).toEqual(7006652);
+    expect(karatsuba(9182734, 726354172)).toEqual(6669917151266248);
+  });
+});

src/algorithms/math/karatsuba-multiplication/karatsuba.js

@@ -0,0 +1,68 @@
+/**
+ *
+ * @param {number} x
+ * @param {number} y
+ * @return {number}
+ */
+export default function karatsuba(x, y) {
+  // BASE CASE:
+  // if numbers are sufficiently small,
+  // multiply them together in the traditional way
+  if (x < 10 || y < 10) {
+    return x * y;
+  }
+
+  // SCALE FACTOR:
+  // scaleFactor is used to split the numbers
+  // into smaller numbers for recursion.
+  // when combining the subexpressions back
+  // together, the scaleFactor is used to
+  // recreate the magnitude of the original numbers
+  const minDigits = Math.min(
+    String(x).length,
+    String(y).length,
+  );
+  const scaleFactor = 10 ** Math.floor(minDigits / 2);
+
+  // PARAMETER COMPONENTS:
+  // a b are the two components of x
+  // c d are the two components of y
+  //
+  // e.g.
+  // x = 1234 -> a = 12, b = 34
+  // y = 5678 -> c = 56, d = 78
+
+  // example of component computations:
+  // x = 1234, y = 5678
+  // scaleFactor = 100
+
+  // a = floor(1234 / 100) = floor(12.34) = 12
+  const a = Math.floor(x / scaleFactor);
+
+  // b = 1234 - (12 * 100) = 1234 - 1200 = 34
+  const b = x - (a * scaleFactor);
+
+  // c = floor(5678 / 100) = floor(56.78) = 56
+  const c = Math.floor(y / scaleFactor);
+
+  // d = 5678 - (56 * 100) = 5678 - 5600 = 78
+  const d = y - (c * scaleFactor);
+
+  // COMPUTE SUBEXPRESSIONS:
+  // since a + b is less than x, and c + d is less than y
+  // the recursion is guaranteed to reach the base case
+  const ac = karatsuba(a, c);
+  const bd = karatsuba(b, d);
+  const abcd = karatsuba(a + b, c + d);
+
+  // COMBINE SUBEXPRESSIONS:
+  // since the scaleFactor was used to
+  // reduce the size of the components,
+  // the scaleFactor must be applied in reverse
+  // to reconstruct the magnitude of the original components
+  const A = ac * (scaleFactor ** 2);
+  const B = (abcd - ac - bd) * scaleFactor;
+  const C = bd;
+
+  return A + B + C;
+}

src/algorithms/sorting/bubble-sort/BubbleSort.js

@@ -19,9 +19,7 @@ export default class BubbleSort extends Sort {
 
         // Swap elements if they are in wrong order.
         if (this.comparator.lessThan(array[j + 1], array[j])) {
-          const tmp = array[j + 1];
-          array[j + 1] = array[j];
-          array[j] = tmp;
+          [array[j], array[j + 1]] = [array[j + 1], array[j]];
 
           // Register the swap.
           swapped = true;

src/algorithms/sorting/counting-sort/__test__/CountingSort.test.js

@@ -27,14 +27,10 @@ describe('CountingSort', () => {
     const sorter = new CountingSort({ visitingCallback });
 
     // Detect biggest number in array in prior.
-    const biggestElement = notSortedArr.reduce((accumulator, element) => {
-      return element > accumulator ? element : accumulator;
-    }, 0);
+    const biggestElement = Math.max(...notSortedArr);
 
     // Detect smallest number in array in prior.
-    const smallestElement = notSortedArr.reduce((accumulator, element) => {
-      return element < accumulator ? element : accumulator;
-    }, 0);
+    const smallestElement = Math.min(...notSortedArr);
 
     const sortedArray = sorter.sort(notSortedArr, smallestElement, biggestElement);
 

src/data-structures/linked-list/README.zh-CN.md

@@ -28,7 +28,20 @@ Add(value)
   end if
 end Add
 ```
-
+
+```
+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
+```
+
 ### 搜索
 
 ```text
@@ -67,10 +80,10 @@ Remove(head, value)
     end if
     return true
   end if
-  while n.next = ø and n.next.value = value
+  while n.next != ø and n.next.value != value
     n ← n.next
   end while
-  if n.next = ø
+  if n.next != ø
     if n.next = tail
       tail ← n
     end if
@@ -88,7 +101,7 @@ Traverse(head)
   Pre: head is the head node in the list
   Post: the items in the list have been traversed
   n ← head
-  while n = 0
+  while n != 0
     yield n.value
     n ← n.next
   end while
@@ -101,11 +114,11 @@ end Traverse
 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
+  if tail != ø
     curr ← tail
-    while curr = head
+    while curr != head
       prev ← head
-      while prev.next = curr
+      while prev.next != curr
         prev ← prev.next
       end while
       yield curr.value

src/data-structures/tree/fenwick-tree/FenwickTree.js

@@ -60,7 +60,7 @@ export default class FenwickTree {
    */
   queryRange(leftIndex, rightIndex) {
     if (leftIndex > rightIndex) {
-      throw new Error('Left index can not be greater then right one');
+      throw new Error('Left index can not be greater than right one');
     }
 
     if (leftIndex === 1) {