Added Edit Distance Algorithm in Dynamic-Programming (#402)

* DP Edit Distance Algorithm

* Update EditDistance.js

Co-authored-by: vinayak <itssvinayak@gmail.com>

Dynamic-Programming/EditDistance.js

@@ -0,0 +1,61 @@
+/*
+Wikipedia -> https://en.wikipedia.org/wiki/Edit_distance
+
+Q. -> Given two strings `word1` and `word2`. You can perform these operations on any of the string to make both strings similar.
+    - Insert
+    - Remove
+    - Replace
+Find the minimum operation cost required to make both same. Each operation cost is 1.
+
+Algorithm details ->
+time complexity - O(n*m)
+space complexity - O(n*m)
+*/
+
+const minimumEditDistance = (word1, word2) => {
+  const n = word1.length
+  const m = word2.length
+  const dp = new Array(m + 1).fill(0).map(item => [])
+
+  /*
+    fill dp matrix with default values -
+        - first row is filled considering no elements in word2.
+        - first column filled considering no elements in word1.
+    */
+
+  for (let i = 0; i < n + 1; i++) {
+    dp[0][i] = i
+  }
+
+  for (let i = 0; i < m + 1; i++) {
+    dp[i][0] = i
+  }
+
+  /*
+        indexing is 1 based for dp matrix as we defined some known values at first row and first column/
+    */
+
+  for (let i = 1; i < m + 1; i++) {
+    for (let j = 1; j < n + 1; j++) {
+      const letter1 = word1[j - 1]
+      const letter2 = word2[i - 1]
+
+      if (letter1 === letter2) {
+        dp[i][j] = dp[i - 1][j - 1]
+      } else {
+        dp[i][j] = Math.min(dp[i - 1][j], dp[i - 1][j - 1], dp[i][j - 1]) + 1
+      }
+    }
+  }
+
+  return dp[m][n]
+}
+
+const main = () => {
+  console.log(minimumEditDistance('horse', 'ros'))
+  console.log(minimumEditDistance('cat', 'cut'))
+  console.log(minimumEditDistance('', 'abc'))
+  console.log(minimumEditDistance('google', 'glgool'))
+}
+
+main()