/* The prime factors of 13195 are 5, 7, 13 and 29.
 *
 * What is the largest prime factor of the number 600851475143?*/

#define _POSIX_C_SOURCE 199309L

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

long int max_prime_factor(long int num);

int main(int argc, char **argv)
{
    long int res;
    long int num = 600851475143;
    double elapsed;
    struct timespec start, end;

    clock_gettime(CLOCK_MONOTONIC, &start);

    /* Use a function to calculate the largest prime factor.*/
    res = max_prime_factor(num);

    clock_gettime(CLOCK_MONOTONIC, &end);

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

    printf("Project Euler, Problem 3\n");
    printf("Answer: %ld\n", res);

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

    return 0;
}

/* Recursive approach: if num is prime, return num, otherwise
 * recursively look for the largest prime factor of num divided
 * by its prime factors until only the largest remains.*/
long int max_prime_factor(long int num)
{
    long int i;

    /* Use function defined in projecteuler.c to check if a number is prime.*/
    if(is_prime(num))
    {
        return num;
    }

    /* If num is even, find the largest prime factor of num/2.*/
    if(num % 2 == 0)
    {
        return max_prime_factor(num/2);
    }
    else
    {
        i = 3;

        while(1)
        {
            /* If num is divisible by i and i is prime, find largest prime
             * factor of num/i.*/
            if(num % i == 0)
            {
                if(is_prime(i))
                {
                    return max_prime_factor(num/i);
                }
            }

            i += 2;
        }
    }

    /* Should never get here.*/
    return -1;
}