edit distance using DP added

Dynamic Programming/edit-distance.cpp

@@ -0,0 +1,41 @@
+// Problem name: Edit Distance
+// Problem link: https://leetcode.com/problems/edit-distance/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+int editDistanceUtil(string& S1, string& S2, int i, int j, vector<vector<int>>& dp){
+
+    if(i<0)
+        return j+1;
+    if(j<0)
+        return i+1;
+
+    if(dp[i][j]!=-1) return dp[i][j];
+
+    if(S1[i]==S2[j])
+        return dp[i][j] =  0+editDistanceUtil(S1,S2,i-1,j-1,dp);
+
+    // Minimum of three choices
+    else return dp[i][j] = 1+min(editDistanceUtil(S1,S2,i-1,j-1,dp),
+    min(editDistanceUtil(S1,S2,i-1,j,dp),editDistanceUtil(S1,S2,i,j-1,dp)));
+
+}
+
+int editDistance(string& S1, string& S2){
+
+    int n = S1.size();
+    int m = S2.size();
+
+    vector<vector<int>> dp(n,vector<int>(m,-1));
+    return editDistanceUtil(S1,S2,n-1,m-1,dp);
+
+}
+
+int main() {
+
+  string s1 = "horse";
+  string s2 = "ros";
+
+  cout << "The minimum number of operations required is: "<<editDistance(s1,s2);
+}