【BZOJ1041】[HAOI2008]圆上的整点【数学】

【题目链接】

奇怪的姿势。

【csyzcyj的题解】

/* Footprints In The Blood Soaked Snow */
#include <cstdio>
#include <cmath>

typedef long long LL;

LL R;

inline int gcd(LL a, LL b) {
	for(; b; b ^= a ^= b ^= a %= b);
	return a;
}

inline bool check(LL x, double y) {
	if(y == (LL)y) {
		LL y1 = (LL)y;
		if(gcd(x * x, y1 * y1) == 1 && x != y1) return 1;
	}
	return 0;
}

int main() {
	scanf("%lld", &R);
	LL _2R = 2.0 * R, _sqrt2R = sqrt(_2R), ans = 0;
	for(int d = 1; d <= _sqrt2R; d++)
		if(_2R % d == 0) {
			LL upb = sqrt(_2R / (2 * d));
			for(int a = 1; a <= upb; a++) {
				double b = sqrt(_2R / d - a * a);
				if(check(a, b)) ans++;
			}
			if(d != _2R / d) {
				LL upb = sqrt(d / 2);
				for(int a = 1; a <= upb; a++) {
					double b = sqrt(d - a * a);
					if(check(a, b)) ans++;
				}
			}
		}
	printf("%lld\n", ans * 4 + 4);
	return 0;
}