p15_dp

#include <bits/stdc++.h>
#include <chrono>

using namespace std;

const int gridsize = 20;

long long grid[gridsize+2][gridsize+2];

int main() {

    // YOU COULD DO THIS OR JUST USE MATH :)
    // 40! / ((20!)^2)

    grid[1][1] = 1;

    auto start = std::chrono::steady_clock::now();

    for (int i = 1; i <= gridsize+1; i++) {
        for (int j = 1; j <= gridsize+1; j++) {
            grid[i][j] += grid[i][j-1] + grid[i-1][j];
        }
    }

    auto stop = std::chrono::steady_clock::now();

    auto duration = std::chrono::duration_cast<std::chrono::nanoseconds>((stop - start) / 1000);

    cout << "Time taken by function: " << duration.count() << " nanoseconds" << endl;

    cout << grid[gridsize+1][gridsize+1] << "\n";
}