lcs.cpp

#include <bits/stdc++.h>
using namespace std;
void lcs(string X, string Y, int m, int n)
{
    int L[m + 1][n + 1];

    for (int i = 0; i <= m; i++)
    {
        for (int 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]);
            }
        }
    }

    int index = L[m][n];
    char lcs[index + 1];
    lcs[index] = '\0';

    int i = m, j = n;
    while (i > 0 && j > 0)
    {
        if (X[i - 1] == Y[j - 1])
        {
            lcs[index - 1] = X[i - 1];
            i--, j--, index--;
        }
        else if (L[i - 1][j] > L[i][j - 1])
        {
            i--;
        }
        else
        {
            j--;
        }
    }
    cout << lcs << endl;
}
int main()
{
    string X, Y;
    cin >> X >> Y;
    int m = X.length();
    int n = Y.length();
    lcs(X, Y, m, n);
    return 0;
}

/*
Time Complexity : O(n^2)
Space Complexity : O(n^2)
The user is expected to enter the two string whose longest common 
subsequence is to be found.
Input : AGGTAB
        GXTXAYB
Output : GTAB