lcs.cpp

/* Dynamic Programming C/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() 
{ 
	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; 
}