/* By counting carefully it can be seen that a rectangular grid measuring 3 by 2 contains eighteen rectangles.
 *
 * Although there exists no rectangular grid that contains exactly two million rectangles, find the area of the grid with the nearest solution.*/

#define _POSIX_C_SOURCE 199309L

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

int main(int argc, char **argv)
{
    int i, j, n, diff, min_diff = INT_MAX, area;
    double elapsed;
    struct timespec start, end;

    clock_gettime(CLOCK_MONOTONIC, &start);

    for(i = 1; i < 100; i++)
    {
        for(j = 1; j <= i; j++)
        {
            /* In a 2x3 grid, we can take rectangles of height 2 in 3 ways
             * (two rectangles of height one and one of height 2). For the
             * width, can take 6 rectangles (3 of width 1, 2 of width 2 and
             * 1 of width 3). The total is 6x3=18 rectagles.
             * Extending to mxn, we can take (m+m-1+m-2+...+1)x(n+n-1+n-2+...+1)=
             * m(m+1)/2*n(n+1)/2=m(m+1)*n(n+1)/4 rectangles.*/
            n = ( i * (i + 1) * j * (j + 1)) / 4;
            diff = abs(2000000 - n);

            if(diff < min_diff)
            {
                min_diff = diff;
                area = i * j;
            }
        }
    }

    clock_gettime(CLOCK_MONOTONIC, &end);

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

    printf("Project Euler, Problem 85\n");
    printf("Answer: %d\n", area);

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

    return 0;
}