euler504.c


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#include <stdio.h>
#include <string.h>
#include <math.h>

int inside[101][101];

int __inside(int a, int b)
{
	int count = 0;
	/* y = -a/b * x + a */
	for (int i = 1; i < b; i++) {
		int t = a - (i * a) / b - 1;
		if (t > 0)
			count += t;
	}
	return count;
}

void init()
{
	for (int i = 1; i <= 100; i++) {
		for (int j = i; j <= 100; j++) {
			inside[i][j] = __inside(i, j);
		}
	}
}

int ninside(int a, int b)
{
	if (a <= b)
		return inside[a][b];
	else
		return inside[b][a];
}

int issqr(int x)
{
	int sx = sqrt(x);
	if (sx * sx == x)
		return 1;
	else
		return 0;
}

int main()
{
	int a, b, c, d;
	int m;
	int nsqr = 0;
	init();
	scanf("%d", &m);
	for (a = 1; a <= m; a++) {
		for (b = 1; b <= m; b++) {
			for (c = a; c <= m; c++) {
				for (d = b; d <= m; d++) {
					int count = ninside(a, b) + ninside(a, d)
						+ ninside(c, b) + ninside(c, d)
						+ a + b + c + d - 3;
					if (issqr(count)) {
						if (a == c && b == d) {
							nsqr++;
						} else if (a == c || b == d) {
							nsqr += 2;
						} else {
							nsqr += 4;
						}
					}
				}
			}
		}
	}
	printf("%d\n", nsqr);
}