Add Levenshtein.

src/algorithms/string/levenshtein-distance/__test__/levenshteinDistance.test.js

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+import levenshteinDistance from '../levenshteinDistance';
+
+describe('levenshteinDistance', () => {
+  it('should calculate edit distance between two strings', () => {
+    expect(levenshteinDistance('', '')).toBe(0);
+    expect(levenshteinDistance('a', '')).toBe(1);
+    expect(levenshteinDistance('', 'a')).toBe(1);
+    expect(levenshteinDistance('abc', '')).toBe(3);
+    expect(levenshteinDistance('', 'abc')).toBe(3);
+
+    // Should just add I to the beginning.
+    expect(levenshteinDistance('islander', 'slander')).toBe(1);
+
+    // Needs to substitute M by K, T by M and add an A to the end
+    expect(levenshteinDistance('mart', 'karma')).toBe(3);
+
+    // Substitute K by S, E by I and insert G at the end.
+    expect(levenshteinDistance('kitten', 'sitting')).toBe(3);
+
+    // Should add 4 letters FOOT at the beginning.
+    expect(levenshteinDistance('ball', 'football')).toBe(4);
+
+    // Should delete 4 letters FOOT at the beginning.
+    expect(levenshteinDistance('football', 'foot')).toBe(4);
+
+    // Needs to substitute the first 5 chars: INTEN by EXECU
+    expect(levenshteinDistance('intention', 'execution')).toBe(5);
+  });
+});

src/algorithms/string/levenshtein-distance/levenshteinDistance.js

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+/**
+ * @param {string} a
+ * @param {string} b
+ * @return {number}
+ */
+export default function levenshteinDistance(a, b) {
+  // Create empty edit distance matrix for all possible modifications of
+  // substrings of a to substrings of b.
+  const distanceMatrix = Array(b.length + 1).fill(null).map(() => Array(a.length + 1).fill(null));
+
+  // Fill the first raw of the matrix.
+  // If this is first row then we're transforming empty string to a.
+  // In this case the number of transformations equals to size of a substring.
+  for (let i = 0; i <= a.length; i += 1) {
+    distanceMatrix[0][i] = i;
+  }
+
+  // Fill the first column of the matrix.
+  // If this is first column then we're transforming empty string to b.
+  // In this case the number of transformations equals to size of b substring.
+  for (let j = 0; j <= b.length; j += 1) {
+    distanceMatrix[j][0] = j;
+  }
+
+  for (let j = 1; j <= b.length; j += 1) {
+    for (let i = 1; i <= a.length; i += 1) {
+      const indicator = a[i - 1] === b[j - 1] ? 0 : 1;
+      distanceMatrix[j][i] = Math.min(
+        distanceMatrix[j][i - 1] + 1, // deletion
+        distanceMatrix[j - 1][i] + 1, // insertion
+        distanceMatrix[j - 1][i - 1] + indicator, // substitution
+      );
+    }
+  }
+
+  return distanceMatrix[b.length][a.length];
+}