Longest_common_subsequence.cpp

/* DP Execrise */

#include <iostream>
#include <string>
#include <algorithm>

using namespace std;

const int MAX_M = 1000;
const int MAX_N = 1000;

int dp[MAX_M][MAX_N];

int main()
{
    string a, b;

    cin >> a >> b;

    const char *pa = a.c_str();
    const char *pb = b.c_str();


    /* if a[i] == b[j] then max_seq += 1 else max_seq = max(max_seq[i][j-1],max_seq[i-1][j])*/
    /* boundary: i == 0 || j == 0 */

    for (int i = 0; i < a.size(); ++i) {
        for (int j = 0; j < b.size(); ++j) {
            if (i == 0 || j == 0) {
                dp[i][j] = pa[i] == pb[j] ? 1 : 0;

            } else if (pa[i] == pb[j]) {
                dp[i][j] = dp[i - 1][j - 1] + 1;

            } else {

                dp[i][j] = max(dp[i][j - 1], dp[i - 1][j]);
            }
        }
    }
    
    cout << dp[a.size() - 1][b.size() - 1] << endl;
    return 0;
}