TheAlgorithms-C/project_euler/Problem 15/sol1.c

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>


/**
 * At every node, there are 2 possible ways to move -> down or right.
 * Since it is a square grid, there are in all, 2N steps with N down 
 * and N right options, without preference for order. 
 * Hence, the path can be be traced in N out of 2N number of ways.
 * This is the same as binomial coeeficient.
 **/
unsigned long long number_of_paths(int N)
{
    unsigned long long path = 1;
    for (int i = 0; i < N; i++)
    {
        path *= (N << 1) - i;
        path /= i + 1;
    }
    
    return path;
}

int main(int argc, char **argv)
{
    int N = 20;

    if (argc == 2)
        N = atoi(argv[1]);

    printf("Number of ways to traverse diagonal of %dx%d grid = %llu\n", N, N, number_of_paths(N));

    return 0;
}