/* A spider, S, sits in one corner of a cuboid room, measuring 6 by 5 by 3, and a fly, F, sits in the opposite corner.
 * By travelling on the surfaces of the room the shortest "straight line" distance from S to F is 10 and the path is shown on the diagram.
 *
 * However, there are up to three "shortest" path candidates for any given cuboid and the shortest route doesn't always have integer length.
 *
 * It can be shown that there are exactly 2060 distinct cuboids, ignoring rotations, with integer dimensions,
 * up to a maximum size of M by M by M, for which the shortest route has integer length when M = 100.
 * This is the least value of M for which the number of solutions first exceeds two thousand; the number of solutions when M = 99 is 1975.
 *
 * Find the least value of M such that the number of solutions first exceeds one million.*/

#define _POSIX_C_SOURCE 199309L

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>

int main(int argc, char **argv)
{
    int a, b, c, count = 0;
    double d, elapsed;
    struct timespec start, end;

    clock_gettime(CLOCK_MONOTONIC, &start);

    a = 0;

    while(count <= 1000000)
    {
        a++;

        for(b = 1; b <= a; b++)
        {
            for(c = 1; c <= b; c++)
            {
                /* Unfolding the cuboid, it's obvious that the shortest path
                 * is the hypotenuse of a triangle, and the catheti are the
                 * longest side of the cubois and the sum of the other two sides.*/
                d = sqrt(a*a+(b+c)*(b+c));

                if(d == (int)d)
                    count++;
            }
        }
    }

    clock_gettime(CLOCK_MONOTONIC, &end);

    elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;

    printf("Project Euler, Problem 86\n");
    printf("Answer: %d\n", a);

    printf("Elapsed time: %.9lf seconds\n", elapsed);

    return 0;
}