15 Longest Common Subsequence Top down(Memoization).cpp

#include <bits/stdc++.h>
using namespace std;


int dp[1001][1001];

int LCS(string X, string Y, int n, int m) {
	// base case
	if (n == 0 || m == 0)
		dp[n][m] = 0;

	if (dp[n][m] != -1) // when table is not having -1 then return the value which is preseent in that block
		return dp[n][m];

  // choice diagram 
	// when last character is same
	if (X[n - 1] == Y[m - 1])
		dp[n][m] = 1 + LCS(X, Y, n - 1, m - 1);// count the number and decreament the both's string length // store the value in particular block 
	// when last character is not same -> pick max
	else
		dp[n][m] = max(LCS(X, Y, n - 1, m), LCS(X, Y, n, m - 1)); // one take full and another by leaving last char and vice versa // store the value in particular block 

	return dp[n][m];
}

int main() {
	string X, Y; cin >> X >> Y;
	int n = X.length(), m = Y.length();

	memset(dp, -1, sizeof(dp)); // intialize the whole dp matrix with -1; // from memset we can initialise either -1 and zero;

	cout << LCS(X, Y, n, m) << endl;
	return 0;
}