Added dp problem edit distance

Edit_Distance.cpp

@@ -0,0 +1,145 @@
+
+
+/*
+*!Brute force Time complexity:O(3^n)
+*! DP SOLUTION: TIme:O(m*n) space:O(m*n)
+*!SPace optimized: Time:O(m*n) space:(m)
+
+*/
+//Brute force
+#include<bits/stdc++.h>
+using namespace std;
+int editDistance(string s1, string s2) 
+{
+
+    if(s1.empty())
+        return s2.size();
+    if(s2.empty())
+        return s1.size();
+
+    if(s1==s2)
+        return 0;
+
+ int answer=0;   
+ if(s1[0]!=s2[0])
+ {
+ int a=editDistance(s1.substr(1),s2);
+ int b=editDistance(s1,s2.substr(1));
+ int c=editDistance(s1.substr(1),s2.substr(1));
+ answer=min(a,min(b,c))+1;
+ }	 
+    else
+    {
+        answer= editDistance(s1.substr(1),s2.substr(1));    
+    }
+    return answer;
+
+}
+
+//Better brute force, is to avoid using substr method
+int min(int x, int y, int z) { return min(min(x, y), z); }
+
+int editDist(string str1, string str2, int m, int n)
+{
+    if (m == 0)
+        return n;
+
+
+    if (n == 0)
+        return m;
+
+    if (str1[m - 1] == str2[n - 1])
+        return editDist(str1, str2, m - 1, n - 1);
+
+
+    return 1
+           + min(editDist(str1, str2, m, n - 1), // Insert
+                 editDist(str1, str2, m - 1, n), // Remove
+                 editDist(str1, str2, m - 1,
+                          n - 1) // Replace
+             );
+}
+
+
+//*Memoization
+
+
+int helper(string s1,string s2,int **arr)
+{
+    int m=s1.size();
+    int n=s2.size();
+    if(s1.empty())
+        return s2.size();
+    if(s2.empty())
+        return s1.size();
+    if(s1==s2)
+        return 0;
+    if(arr[m][n]!=-1)
+        return arr[m][n];
+    if(s1[0]!=s2[0])
+    {
+        int a,b,c;
+        a=helper(s1.substr(1),s2,arr);
+        b=helper(s1,s2.substr(1),arr);
+        c=helper(s1.substr(1),s2.substr(1),arr);
+       arr[m][n]= min(a,min(b,c))+1;
+    }
+    else
+        arr[m][n]=helper(s1.substr(1),s2.substr(1),arr);
+    return arr[m][n];
+}
+
+
+int editDistance(string s1, string s2)
+{
+    int m=s1.size();
+    int n=s2.size();
+    int i,j;
+	int **arr=new int*[m+1];
+    for(i=0;i<=m;i++)
+        arr[i]=new int[n+1];
+    for(i=0;i<=m;i++)
+        for(j=0;j<=n;j++)
+            arr[i][j]=-1;
+    return helper(s1,s2,arr);
+
+}
+
+
+
+
+
+// * Solution through DP
+
+ int editDistance(string s, string t) {
+        int m,n,i,j;
+        m=s.size();
+        n=t.size();
+        vector<vector<int>> dp(m+1,vector<int>(n+1));
+
+
+        dp[0][0]=0;
+
+        for(i=1;i<=n;i++)
+        dp[0][i]=i;
+
+        for(i=1;i<=m;i++)
+        dp[i][0]=i;
+
+        for(i=1;i<=m;i++){
+            for(j=1;j<=n;j++){
+
+                if(s[i-1]==t[j-1])
+                dp[i][j]=dp[i-1][j-1];
+                else{
+                    int a = dp[i-1][j];
+                    int b = dp[i][j-1];
+                    int c = dp[i-1][j-1];
+                    dp[i][j]=min(a,min(b,c))+1;
+                }
+            }
+        }
+        return dp[m][n];
+    }
+
+