Added Levenshtein distance (a.k.a edit distance) algorithm to strings directory

String/LevenshteinDistance.js

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+/* The Levenshtein distance (a.k.a edit distance) is a
+measure of similarity between two strings. It is
+defined as the minimum number of changes required to
+convert string a into string b (this is done by
+inserting, deleting or replacing a character in
+string a).
+The smaller the Levenshtein distance,
+the more similar the strings are. This is a very
+common problem in the application of Dynamic Programming.
+*/
+
+const levenshteinDistance = (a, b) => {
+  // Declaring array 'D' with rows = len(a) + 1 and columns = len(b) + 1:
+  const distanceMatrix = Array(b.length + 1)
+    .fill(null)
+    .map(() => Array(a.length + 1).fill(null))
+
+  // Initialising first column:
+  for (let i = 0; i <= a.length; i += 1) {
+    distanceMatrix[0][i] = i
+  }
+
+  // Initialising first row:
+  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
+      // choosing the minimum of all three, vis-a-vis:
+      distanceMatrix[j][i] = Math.min(
+        distanceMatrix[j][i - 1] + 1, // deletion
+        distanceMatrix[j - 1][i] + 1, // insertion
+        distanceMatrix[j - 1][i - 1] + indicator // substitution
+      )
+    }
+  }
+
+  console.log(
+    'Levenshtein Distance between ' +
+            a +
+            ' and ' +
+            b +
+            ' is = ' +
+            distanceMatrix[b.length][a.length]
+  )
+  return distanceMatrix[b.length][a.length]
+}
+
+export { levenshteinDistance }

String/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('igloo', 'gloo')).toBe(1)
+
+    // Should just substitute i with o, m with g and insert e at end
+    expect(levenshteinDistance('firm', 'forge')).toBe(3)
+
+    // Should just substitute i with s, g with i, h with t and delete f from front
+    expect(levenshteinDistance('fighting', 'sitting')).toBe(4)
+
+    // Should add 4 letters b, a, s and e at the beginning.
+    expect(levenshteinDistance('ball', 'baseball')).toBe(4)
+
+    // Should delete 4 letters b, a, s and e at the beginning.
+    expect(levenshteinDistance('baseball', 'foot')).toBe(4)
+  })
+})