/* A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
 *
 * a2 + b2 = c2
 *
 * For example, 32 + 42 = 9 + 16 = 25 = 52.
 *
 * There exists exactly one Pythagorean triplet for which a + b + c = 1000.
 *
 * Find the product abc.*/

#define _POSIX_C_SOURCE 199309L

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include "projecteuler.h"

int main(int argc, char **argv)
{
    int a, b, c, tmpa, tmpb, tmpc, i, m, n, found = 0;
    double elapsed;
    struct timespec start, end;

    clock_gettime(CLOCK_MONOTONIC, &start);

    /* Brute force approach: generate all the Pythagorean triplets using
     * Euclid's formula, until the one where a+b+c=1000 is found.*/
    for(m = 2; found == 0; m++)
    {
        for(n = 1; n < m && !found; n++)
        {
            if(gcd(m, n) == 1 && ((m % 2 == 0 && n % 2 != 0) || (m % 2 != 0 && n % 2 == 0)))
            {
                a = m * m - n * n;
                b = 2 * m * n;
                c = m * m + n * n;

                if(a + b + c == 1000)
                {
                    found = 1;
                    break;
                }

                i = 2;

                do
                {
                    tmpa = a * i;
                    tmpb = b * i;
                    tmpc = c * i;

                    if(tmpa + tmpb + tmpc == 1000)
                    {
                        a = tmpa;
                        b = tmpb;
                        c = tmpc;
                        found = 1;
                        break;
                    }

                    i++;
                } while(tmpa + tmpb + tmpc < 1000);
            }
        }
    }

    clock_gettime(CLOCK_MONOTONIC, &end);

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

    printf("Project Euler, Problem 9\n");
    printf("Answer: %d\n", a*b*c);

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

    return 0;
}