Edit Distance Algorithm

Dynamic Programming/Edit Distance.cpp

@@ -0,0 +1,87 @@
+/* Given two strings str1 & str2
+ * and below operations that can
+ * be performed on str1. Find
+ * minimum number of edits
+ * (operations) required to convert
+ * 'str1' into 'str2'/
+ * a. Insert
+ * b. Remove
+ * c. Replace
+ * All of the above operations are 
+ * of equal cost
+ */
+
+#include <iostream>
+#include <string>
+using namespace std;
+
+int min(int x, int y, int z){
+    return min(min(x,y), z);
+}
+
+/* A Naive recursive C++ program to find
+ * minimum number of operations to convert
+ * str1 to str2.
+ * O(3^m)
+ */
+int editDist(string str1, string str2, int m, int n) {
+        if(m == 0) return n;
+        if(n == 0) return m;
+    
+        //If last characters are same then continue
+        //for the rest of them.
+        if(str1[m-1] == str2[n-2])
+            return editDist(str1, str2, m-1, n-1);
+
+        //If last not same, then 3 possibilities
+        //a.Insert b.Remove c. Replace
+        //Get min of three and continue for rest.
+        return 1 + min ( editDist(str1, str2, m, n-1),
+                         editDist(str1, str2, m-1, n),
+                         editDist(str1, str2, m-1, n-1)
+                       );
+}
+
+/* A DP based program
+ * O(m x n)
+ */
+int editDistDP(string str1, string str2, int m, int n) {
+
+    //Create Table for SubProblems
+    int dp[m+1][n+1];
+
+    //Fill d[][] in bottom up manner
+    for(int i=0; i<=m; i++) {
+        for(int j=0; j<=n; j++) {
+            //If str1 empty. Then add all of str2
+            if(i==0) 
+                dp[i][j] = j;
+
+            //If str2 empty. Then add all of str1 
+            else if(j==0)
+                dp[i][j] = i;
+
+            //If character same. Recur for remaining 
+            else if(str1[i-1] == str2[j-1])
+                dp[i][j] == dp[i-1][j-1];
+
+            else
+                dp[i][j] = 1 + min(dp[i][j-1],//Insert
+                                   dp[i-1][j],//Remove
+                                   dp[i-1][j-1]//Replace
+                                  );
+        }
+    }
+
+    return dp[m][n];
+}
+
+int main() {
+    string str1 = "sunday";
+    string str2 = "saturday";
+    
+    cout << editDist(str1, str1, str1.length(), str2.length()) << endl;
+    cout << editDistDP(str1, str1, str1.length(), str2.length()) << endl;
+
+    return 0;
+}