/* Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
 *
 * 2^2=4, 2^3=8, 2^4=16, 2^5=32
 * 3^2=9, 3^3=27, 3^4=81, 3^5=243
 * 4^2=16, 4^3=64, 4^4=256, 4^5=1024
 * 5^2=25, 5^3=125, 5^4=625, 5^5=3125
 *
 * If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
 *
 * 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
 *
 * How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?*/

#define _POSIX_C_SOURCE 199309L

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

int compare(void *a, void *b);

int main(int argc, char **argv)
{
    mpz_t a;
    mpz_t **powers;
    int i, j, count;
    double elapsed;
    struct timespec start, end;

    clock_gettime(CLOCK_MONOTONIC, &start);

    if((powers = (mpz_t **)malloc(9801*sizeof(mpz_t *))) == NULL)
    {
        fprintf(stderr, "Error while allocating memory\n");
        return 1;
    }

    for(i = 0; i < 9801; i++)
    {
        if((powers[i] = (mpz_t *)malloc(sizeof(mpz_t))) == NULL)
        {
            fprintf(stderr, "Error while allocating memory\n");
            return 1;
        }
    }

    mpz_init(a);

    for(i = 0; i < 9801; i++)
    {
        mpz_init(*powers[i]);
    }

    /* Using the GMP Library to calculate all the powers.*/
    for(i = 2; i <= 100; i++)
    {
        mpz_set_ui(a, i);
        for(j = 2; j <= 100; j++)
        {
            mpz_pow_ui(*powers[(i-2)*99+j-2], a, j);
        }
    }

    mpz_clear(a);

    /* Sort the values and count the different values.*/
    quick_sort((void **)powers, 0, 9800, compare);
    count = 1;

    for(i = 1; i < 9801; i++)
    {
        if(mpz_cmp(*powers[i], *powers[i-1]))
        {
            count++;
        }
    }

    for(i = 0; i < 9801; i++)
    {
        mpz_clear(*powers[i]);
        free(powers[i]);
    }

    free(powers);

    clock_gettime(CLOCK_MONOTONIC, &end);

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

    printf("Project Euler, Problem 29\n");
    printf("Answer: %d\n", count);

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

    return 0;
}

int compare(void *a, void *b)
{
    mpz_t *n1, *n2;

    n1 = (mpz_t *)a;
    n2 = (mpz_t *)b;

    return mpz_cmp(*n1, *n2);
}