zoj 1377 Grandpa‘s Estate

Graham算法求凸包问题

#include 
#include
using namespace std;
const int maxn = 1001;
struct node {
	node () {};
	node (int _x, int _y): x(_x), y(_y) {};
	int x, y;
	node operator -(node nd) {
		return node(x - nd.x, y - nd.y);
	}

	int operator *(node nd) {
		return x * nd.y - y * nd.x;
	}

} p[maxn], q[maxn];
int per[maxn], n, l;

inline int dis(node p1, node p2) {
	return (p2.x - p1.x) * (p2.x - p1.x) + (p2.y - p1.y) * (p2.y - p1.y);
}

inline bool cmp(int v1, int v2) {
	int det = (p[v1] - p[1]) * (p[v2] - p[1]);
	if (det != 0)return det > 0;
	return dis(p[1], p[v1]) < dis(p[1], p[v2]);
}

void Graham() {
	int i, id, k;
	id = 1;
	for (i = 2; i <= n; i++) {
		if (p[i].x < p[id].x || (p[i].x == p[id].x && p[i].y < p[id].y))id = i;
	}
	if (id != 1)swap(p[1], p[id]);
	for (i = 1; i <= n; i++) {
		per[i] = i;
	}
	sort(per + 2, per + n + 1, cmp);
	l = 0;
	q[++l] = p[1];
	for (i = 2; i <= n; i++) {
		k = per[i];
		while (l >= 2 && (q[l] - q[l - 1]) * (p[k] - q[l - 1]) <= 0)l--;
		q[++l] = p[k];
	}
}

bool judge() {
	if (l == 2)return 0;
	int sum;
	for (int i = 1; i <= l; i++) {
		sum = 0;
		for (int j = 1; j <= n; j++) {
			if ((p[j] - q[i]) * (q[i % l + 1] - p[j]) == 0)sum++;
		}
		if (sum < 3)return 0;
	}
	return 1;
}

int main() {
	int t, i;
	scanf("%d", &t);
	while (t--) {
		scanf("%d", &n);
		for (i = 1; i <= n; i++) {
			scanf("%d%d", &p[i].x, &p[i].y);
		}
		Graham();
		if (judge())puts("YES");
		else puts("NO");
	}
}
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