C++ Program for Longest Common Subsequence

A subsequence is a sequence with the same order of the set of elements. For the sequence “stuv”, the subsequences are “stu”, “tuv”, “suv”,.... etc.

For a string of length n, there can be 2n ways to create subsequence from the string.

Example

The longest common subsequence for the strings “ ABCDGH ” and “ AEDFHR ” is of length 3.

 Live Demo

#include <iostream>
#include <string.h>
using namespace std;
int max(int a, int b);
int lcs(char* X, char* Y, int m, int n){
   if (m == 0 || n == 0)
      return 0;
   if (X[m - 1] == Y[n - 1])
      return 1 + lcs(X, Y, m - 1, n - 1);
   else
      return max(lcs(X, Y, m, n - 1), lcs(X, Y, m - 1, n));
}
int max(int a, int b){
   return (a > b) ? a : b;
}
int main(){
   char X[] = "AGGTAB";
   char Y[] = "GXTXAYB";
   int m = strlen(X);
   int n = strlen(Y);
   printf("Length of LCS is %d\n", lcs(X, Y, m, n));
   return 0;
}

Output

Length of LCS is 4