/* It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
 *
 * 9 = 7 + 2×1^2
 * 15 = 7 + 2×2^2
 * 21 = 3 + 2×3^2
 * 25 = 7 + 2×3^2
 * 27 = 19 + 2×2^2
 * 33 = 31 + 2×1^2
 *
 * It turns out that the conjecture was false.
 *
 * What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?*/

#define _POSIX_C_SOURCE 199309L

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

#define N 10000

int goldbach(int n);

int *primes;

int main(int argc, char **argv)
{
    int i, found = 0;
    double elapsed;
    struct timespec start, end;

    clock_gettime(CLOCK_MONOTONIC, &start);

    if((primes = sieve(N)) == NULL)
    {
        fprintf(stderr, "Error! Sieve function returned NULL\n");
        return 1;
    }

    /* For every odd number, check if it's prime, if it is check
     * if it satisfies the Goldbach property. Continue until the
     * first number that doesn't is found.*/
    for(i = 3; !found && i < N; i += 2)
    {
        if(!primes[i])
        {
            if(!goldbach(i))
            {
                found = 1;
            }
        }
    }

    free(primes);

    clock_gettime(CLOCK_MONOTONIC, &end);

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

    printf("Project Euler, Problem 46\n");
    printf("Answer: %d\n", i-2);

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

    return 0;
}

int goldbach(int n)
{
    int i, j, tmp;

    /* Check every prime smaller than n.*/
    for(i = 3; i < n; i += 2)
    {
        if(primes[i])
        {
            j = 1;

            /* Check if summing twice a square to the prime number
             * gives n. Return 1 when succeeding.*/
            do
            {
                tmp = i + 2 * j * j;

                if(tmp == n)
                {
                    return 1;
                }

                j++;
            } while(tmp < n);
        }
    }

    /* Return 0 if no solution is found.*/
    return 0;
}