added LCS problem

Lcs.cpp

@@ -0,0 +1,51 @@
+* Dynamic Programming C implementation of LCS problem */
+#include<bits/stdc++.h> 
+
+int max(int a, int b); 
+
+/* Returns length of LCS for X[0..m-1], Y[0..n-1] */
+int lcs( char *X, char *Y, int m, int n ) 
+{ 
+   int L[m+1][n+1]; 
+   int i, j; 
+
+   /* Following steps build L[m+1][n+1] in bottom up fashion. Note  
+      that L[i][j] contains length of LCS of X[0..i-1] and Y[0..j-1] */
+   for (i=0; i<=m; i++) 
+   { 
+     for (j=0; j<=n; j++) 
+     { 
+       if (i == 0 || j == 0) 
+         L[i][j] = 0; 
+
+       else if (X[i-1] == Y[j-1]) 
+         L[i][j] = L[i-1][j-1] + 1; 
+
+       else
+         L[i][j] = max(L[i-1][j], L[i][j-1]); 
+     } 
+   } 
+
+   /* L[m][n] contains length of LCS for X[0..n-1] and Y[0..m-1] */
+   return L[m][n]; 
+} 
+
+/* Utility function to get max of 2 integers */
+int max(int a, int b) 
+{ 
+    return (a > b)? a : b; 
+} 
+
+/* Driver program to test above function */
+int main() 
+{ 
+
+   string X,Y;
+   cin>>X>>Y;
+  int m = strlen(X); 
+  int n = strlen(Y); 
+
+  printf("Length of LCS is %d", lcs( X, Y, m, n ) ); 
+
+  return 0; 
+}