15 Lattice Paths
Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.
How many such routes are there through a 20×20 grid?
#include <iostream>
#include <limits>
#include <vector>
using namespace std;
void pause() { cin.ignore(numeric_limits<streamsize>::max(), '\n'); }
#define GRID 20
int main()
{
long long int combinations = 1;
for (int i = 0; i < GRID; i++)
{
combinations *= 2 * GRID - i;
combinations /= i + 1;
}
cout << combinations;
pause();
}
Solution: 137846528820
Last modified 3yr ago