What is the longest common subsequence in C++?

Can you explain what the longest common subsequence is?

The longest common subsequence (LCS) is the longest sequence that can appear in the same order in both strings, but not necessarily consecutively.

How can I implement the LCS algorithm in C++?

You can use dynamic programming to implement the LCS algorithm. Would you like to see a code example?

Yes, please show me the code!

Here's a simple implementation of the LCS algorithm in C++:

#include <iostream>
#include <vector>
#include <string>
using namespace std;

int LCS(string X, string Y) {
    int m = X.length();
    int n = Y.length();
    vector<vector<int>> L(m + 1, vector<int>(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]);
        }
    }
    return L[m][n];
}

int main() {
    string X = "AGGTAB";
    string Y = "GXTXAYB";
    cout << "Length of LCS is " << LCS(X, Y) << endl;
    return 0;
}

This code calculates the length of the LCS between two strings.

What is the time complexity of this algorithm?

The time complexity of the LCS algorithm using dynamic programming is O(m * n), where m and n are the lengths of the two strings.