/* The first two consecutive numbers to have two distinct prime factors are:
 *
 * 14 = 2 × 7
 * 15 = 3 × 5
 *
 * The first three consecutive numbers to have three distinct prime factors are:
 *
 * 644 = 2² × 7 × 23
 * 645 = 3 × 5 × 43
 * 646 = 2 × 17 × 19.
 *
 * Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?*/

#define _POSIX_C_SOURCE 199309L

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

#define N 150000

int *count_factors(int n);

int main(int argc, char **argv)
{
    int i, count, res;
    int *factors;
    double elapsed;
    struct timespec start, end;

    clock_gettime(CLOCK_MONOTONIC, &start);

    if((factors = count_factors(N)) == NULL)
    {
        fprintf(stderr, "Error! Count_factors function returned NULL\n");
        return 1;
    }

    count = 0;

    for(i = 0; i < N; i++)
    {
        if(factors[i] == 4)
        {
            count++;
        }
        else
        {
            count = 0;
        }

        if(count == 4)
        {
            res = i - 3;
            break;
        }
    }

    clock_gettime(CLOCK_MONOTONIC, &end);

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

    printf("Project Euler, Problem 47\n");
    printf("Answer: %d\n", res);

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

    return 0;
}

/* Function using a modified sieve of Eratosthenes to count
 * the distinct prime factors of each number.*/
int *count_factors(int n)
{
    int i = 2, j;
    int *factors;

    if((factors = (int *)calloc(n, sizeof(int))) == NULL)
    {
        return NULL;
    }

    while(i < n / 2)
    {
        if(factors[i] == 0)
        {
            for(j = i; j < n; j += i)
            {
                factors[j]++;
            }
        }
        i++;
    }

    return factors;
}