dynamic-programming-classics-the-longest-common-subsequence.cpp

#include <iostream>
#include <vector>
#include <algorithm>

std::vector<int> longestCommonSubsequence(const std::vector<int>& a, const std::vector<int>& b) {
    int n = a.size();
    int m = b.size();

    std::vector<std::vector<int>> dp(n + 1, std::vector<int>(m + 1, 0));

    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j <= m; ++j) {
            if (a[i - 1] == b[j - 1]) {
                dp[i][j] = dp[i - 1][j - 1] + 1;
            } else {
                dp[i][j] = std::max(dp[i - 1][j], dp[i][j - 1]);
            }
        }
    }

    std::vector<int> result;
    int i = n, j = m;
    while (i > 0 && j > 0) {
        if (a[i - 1] == b[j - 1]) {
            result.push_back(a[i - 1]);
            i--;
            j--;
        } else if (dp[i - 1][j] > dp[i][j - 1]) {
            i--;
        } else {
            j--;
        }
    }

    std::reverse(result.begin(), result.end());
    return result;
}

int main() {
    int n, m;
    std::cin >> n >> m;

    std::vector<int> a(n), b(m);
    for (int i = 0; i < n; ++i) {
        std::cin >> a[i];
    }
    for (int i = 0; i < m; ++i) {
        std::cin >> b[i];
    }

    std::vector<int> result = longestCommonSubsequence(a, b);

    for (int i = 0; i < result.size(); ++i) {
        std::cout << result[i] << " ";
    }
    std::cout << std::endl;

    return 0;
}