Add LCS.

Author: trekhleb

README.md

@@ -39,11 +39,11 @@
   * [Least Common Multiple](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple) (LCM)
   * [Fisher–Yates Shuffle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fisher-yates) - random permutation of a finite sequence
 * **String**
-  * [Levenshtein Distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences (DP approach)
+  * [Levenshtein Distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences (dynamic programming approach)
   * [Hamming Distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/hamming-distance) - number of positions at which the symbols are different
   * [Knuth–Morris–Pratt Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/knuth-morris-pratt) - substring search
   * [Rabin Karp Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/rabin-karp) - substring search
-  * Longest common subsequence
+  * [Longest Common Subsequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-subsequnce) (LCS)
   * longest common substring
 * **Search**
   * [Binary Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search)

src/algorithms/string/longest-common-subsequnce/README.md

@@ -0,0 +1,25 @@
+# Longest common subsequence problem
+
+The longest common subsequence (LCS) problem is the problem of finding 
+the longest subsequence common to all sequences in a set of sequences 
+(often just two sequences). It differs from the longest common substring
+problem: unlike substrings, subsequences are not required to occupy 
+consecutive positions within the original sequences. 
+
+## Application
+
+The longest common subsequence problem is a classic computer science 
+problem, the basis of data comparison programs such as the diff utility, 
+and has applications in bioinformatics. It is also widely used by 
+revision control systems such as Git for reconciling multiple changes 
+made to a revision-controlled collection of files.
+
+## Example
+
+- LCS for input Sequences `ABCDGH` and `AEDFHR` is `ADH` of length 3.
+- LCS for input Sequences `AGGTAB` and `GXTXAYB` is `GTAB` of length 4.
+
+## References
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem)
+- [YouTube](https://www.youtube.com/watch?v=NnD96abizww)

src/algorithms/string/longest-common-subsequnce/__test__/longestCommonSubsequnce.test.js

@@ -0,0 +1,13 @@
+import longestCommonSubsequnce from '../longestCommonSubsequnce';
+
+describe('longestCommonSubsequnce', () => {
+  it('should find longest common subsequence for two strings', () => {
+    expect(longestCommonSubsequnce('', '')).toBe('');
+    expect(longestCommonSubsequnce('', 'ABC')).toBe('');
+    expect(longestCommonSubsequnce('ABC', '')).toBe('');
+    expect(longestCommonSubsequnce('ABC', 'DEFG')).toBe('');
+    expect(longestCommonSubsequnce('ABCDGH', 'AEDFHR')).toBe('ADH');
+    expect(longestCommonSubsequnce('AGGTAB', 'GXTXAYB')).toBe('GTAB');
+    expect(longestCommonSubsequnce('ABCDAF', 'ACBCF')).toBe('ABCF');
+  });
+});

src/algorithms/string/longest-common-subsequnce/longestCommonSubsequnce.js

@@ -0,0 +1,60 @@
+/**
+ * @param {string} s1
+ * @param {string} s2
+ * @return {string}
+ */
+export default function longestCommonSubsequnce(s1, s2) {
+  // Init LCS matrix.
+  const lcsMatrix = Array(s2.length + 1).fill(null).map(() => Array(s1.length + 1).fill(null));
+
+  // Fill first row with zeros.
+  for (let columnIndex = 0; columnIndex <= s1.length; columnIndex += 1) {
+    lcsMatrix[0][columnIndex] = 0;
+  }
+
+  // Fill first column with zeros.
+  for (let rowIndex = 0; rowIndex <= s2.length; rowIndex += 1) {
+    lcsMatrix[rowIndex][0] = 0;
+  }
+
+  // Fill rest of the column that correspond to each of two strings.
+  for (let rowIndex = 1; rowIndex <= s2.length; rowIndex += 1) {
+    for (let columnIndex = 1; columnIndex <= s1.length; columnIndex += 1) {
+      if (s1[columnIndex - 1] === s2[rowIndex - 1]) {
+        lcsMatrix[rowIndex][columnIndex] = lcsMatrix[rowIndex - 1][columnIndex - 1] + 1;
+      } else {
+        lcsMatrix[rowIndex][columnIndex] = Math.max(
+          lcsMatrix[rowIndex - 1][columnIndex],
+          lcsMatrix[rowIndex][columnIndex - 1],
+        );
+      }
+    }
+  }
+
+  // Calculate LCS based on LCS matrix.
+  if (!lcsMatrix[s2.length][s1.length]) {
+    // If the length of largest common string is zero then return empty string.
+    return '';
+  }
+
+  let lcs = '';
+  let columnIndex = s1.length;
+  let rowIndex = s2.length;
+
+  while (columnIndex > 0 || rowIndex > 0) {
+    if (s1[columnIndex - 1] === s2[rowIndex - 1]) {
+      // Move by diagonal left-top.
+      lcs = s1[columnIndex - 1] + lcs;
+      columnIndex -= 1;
+      rowIndex -= 1;
+    } else if (lcsMatrix[rowIndex][columnIndex] === lcsMatrix[rowIndex][columnIndex - 1]) {
+      // Move left.
+      columnIndex -= 1;
+    } else {
+      // Move up.
+      rowIndex -= 1;
+    }
+  }
+
+  return lcs;
+}