Added Levenshtein Distance Algorithm (#263)

Dynamic-Programming/LevenshteinDistance.js

@@ -0,0 +1,49 @@
+/**
+ * A Dynamic Programming based solution for calculation of the Levenshtein Distance
+ * https://en.wikipedia.org/wiki/Levenshtein_distance
+ */
+
+function minimum (a, b, c) {
+  if (a < b && a < c) {
+    return a
+  } else if (b < a && b < c) {
+    return b
+  } else {
+    return c
+  }
+}
+
+function costOfSubstitution (x, y) {
+  return x === y ? 0 : 1
+}
+
+function calculate (x, y) {
+  const dp = new Array(x.length + 1)
+  for (let i = 0; i < x.length + 1; i++) {
+    dp[i] = new Array(y.length + 1)
+  }
+
+  for (let i = 0; i < x.length + 1; i++) {
+    for (let j = 0; j < y.length + 1; j++) {
+      if (i === 0) {
+        dp[i][j] = j
+      } else if (j === 0) {
+        dp[i][j] = i
+      } else {
+        dp[i][j] = minimum(dp[i - 1][j - 1] + costOfSubstitution(x.charAt(i - 1), y.charAt(j - 1)), dp[i - 1][j] + 1, dp[i][j - 1] + 1)
+      }
+    }
+  }
+
+  return dp[x.length][y.length]
+}
+
+function main () {
+  const x = '' // enter your string here
+  const y = '' // enter your string here
+
+  console.log('Levenshtein distance between ' + x + ' and ' + y + ' is: ')
+  console.log(calculate(x, y))
+}
+
+main()