TheAlgorithms-C-Plus-Plus/dynamic_programming/longest_common_subsequence.cpp

// Longest common subsequence - Dynamic Programming
#include <iostream>
using namespace std;

void Print(int trace[20][20], int m, int n, string a)
{
    if (m == 0 || n == 0)
    {
        return;
    }
    if (trace[m][n] == 1)
    {
        Print(trace, m - 1, n - 1, a);
        cout << a[m - 1];
    }
    else if (trace[m][n] == 2)
    {
        Print(trace, m - 1, n, a);
    }
    else if (trace[m][n] == 3)
    {
        Print(trace, m, n - 1, a);
    }
}

int lcs(string a, string b)
{
    int m = a.length(), n = b.length();
    int res[m + 1][n + 1];
    int trace[20][20];

    // fills up the arrays with zeros.
    for (int i = 0; i < m + 1; i++)
    {
        for (int j = 0; j < n + 1; j++)
        {
            res[i][j] = 0;
            trace[i][j] = 0;
        }
    }

    for (int i = 0; i < m + 1; ++i)
    {
        for (int j = 0; j < n + 1; ++j)
        {
            if (i == 0 || j == 0)
            {
                res[i][j] = 0;
                trace[i][j] = 0;
            }

            else if (a[i - 1] == b[j - 1])
            {
                res[i][j] = 1 + res[i - 1][j - 1];
                trace[i][j] = 1;  // 1 means trace the matrix in upper left
                                  // diagonal direction.
            }
            else
            {
                if (res[i - 1][j] > res[i][j - 1])
                {
                    res[i][j] = res[i - 1][j];
                    trace[i][j] =
                        2;  // 2 means trace the matrix in upwards direction.
                }
                else
                {
                    res[i][j] = res[i][j - 1];
                    trace[i][j] =
                        3;  //  means trace the matrix in left direction.
                }
            }
        }
    }
    Print(trace, m, n, a);
    return res[m][n];
}

int main()
{
    string a, b;
    cin >> a >> b;
    cout << lcs(a, b);
    return 0;
}