/* We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital
 * and is also prime.
 *
 * What is the largest n-digit pandigital prime that exists?*/

#define _POSIX_C_SOURCE 199309L

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

int count_digits(int n);

int main(int argc, char **argv)
{
    /* 8- and 9-digit pandigital numbers can't be prime, because
     * 1+2+...+8=36, which is divisible by 3, and 36+9=45 which is
     * also divisible by 3, and therefore the whole number is divisible
     * by 3. So we can start from the largest 7-digit pandigital number,
     * until we find a prime.*/
    int i = 7654321;
    double elapsed;
    struct timespec start, end;

    clock_gettime(CLOCK_MONOTONIC, &start);

    while(i > 0)
    {
        if(is_pandigital(i, count_digits(i)) && is_prime(i))
        {
            break;
        }
        /*Skipping the even numbers.*/
        i -= 2;
    }

    clock_gettime(CLOCK_MONOTONIC, &end);

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

    printf("Project Euler, Problem 41\n");
    printf("Answer: %d\n", i);

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

    return 0;
}

int count_digits(int n)
{
    int i = 0;

    if(n == 0)
    {
        return 1;
    }

    while(n > 0)
    {
        i++;
        n /= 10;
    }

    return i;
}