sol1.c

/**
 * \file
 * \brief [Problem 15](https://projecteuler.net/problem=15) solution
 * \author [Krishna Vedala](https://github.com/kvedala)
 */
#include <stdint.h>
#include <stdio.h>
#include <stdlib.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;
}

/** Main function */
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;
}