/* The 5-digit number, 16807=7^5, is also a fifth power. Similarly, the 9-digit number, 134217728=8^9, is a ninth power.
 *
 * How many n-digit positive integers exist which are also an nth power?*/

#define _POSIX_C_SOURCE 199309L

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

int count_digits(mpz_t n);

int main(int argc, char **argv)
{
    int i, j, count = 0, finished = 0;
    double elapsed;
    struct timespec start, end;
    mpz_t p;

    mpz_init(p);

    clock_gettime(CLOCK_MONOTONIC, &start);

    i = 1;

    while(!finished)
    {
        /* When j=10, j^i will have i+1 digits (e.g if i=3, 10^3=1000).*/
        for(j = 1; j < 10; j++)
        {
            mpz_ui_pow_ui(p, j, i);

            if(count_digits(p) == i)
            {
                count++;
            }
        }

        /* When 9^i has less than i digits, all the numbers have been found.*/
        if(count_digits(p) < i)
        {
            finished = 1;
        }

        i++;
    }

    mpz_clear(p);

    clock_gettime(CLOCK_MONOTONIC, &end);

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

    printf("Project Euler, Problem 63\n");
    printf("Answer: %d\n", count);

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

    return 0;
}

int count_digits(mpz_t n)
{
    int count = 0;
    mpz_t tmp;

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

    mpz_init_set(tmp, n);

    while(mpz_cmp_ui(tmp, 0))
    {
        mpz_tdiv_q_ui(tmp, tmp, 10);
        count++;
    }

    return count;
}