#1040 : 矩形判断

#1040 : 矩形判断

时间限制:1000ms

单点时限:1000ms

内存限制:256MB

描述

给出平面上4条线段，判断这4条线段是否恰好围成一个面积大于0的矩形。

输入

输入第一行是一个整数T(1<=T<=100)，代表测试数据的数量。

每组数据包含4行，每行包含4个整数x1, y1, x2, y2 (0 <= x1, y1, x2, y2 <= 100000)；其中(x1, y1), (x2,y2)代表一条线段的两个端点。

输出

每组数据输出一行YES或者NO，表示输入的4条线段是否恰好围成矩形。

样例输入

3
0 0 0 1
1 0 1 1
0 1 1 1
1 0 0 0
0 1 2 3
1 0 3 2
3 2 2 3
1 0 0 1
0 1 1 0
1 0 2 0
2 0 1 1
1 1 0 1

样例输出

YES
YES
NO

#include <iostream>
#include <limits.h>
#include <set>
using namespace std;


struct Line {
	int x1, y1, x2, y2;
};


int main()
{
	int T;
	cin >> T;
	set<pair<int, int>> st;

	while (T--) {
		st.clear();

		Line line1, line2, line3, line4;

		cin >> line1.x1 >> line1.y1 >> line1.x2 >> line1.y2;
		st.insert(make_pair(line1.x1, line1.y1));
		st.insert(make_pair(line1.x2, line1.y2));


		cin >> line2.x1 >> line2.y1 >> line2.x2 >> line2.y2;
		st.insert(make_pair(line2.x1, line2.y1));
		st.insert(make_pair(line2.x2, line2.y2));

		cin >> line3.x1 >> line3.y1 >> line3.x2 >> line3.y2;
		st.insert(make_pair(line3.x1, line3.y1));
		st.insert(make_pair(line3.x2, line3.y2));

		cin >> line4.x1 >> line4.y1 >> line4.x2 >> line4.y2;
		st.insert(make_pair(line4.x1, line4.y1));
		st.insert(make_pair(line4.x2, line4.y2));

		if (st.size() != 4) {
			cout << "NO" << endl;
			continue;
		}

		double slope1, slope2, slope3, slope4;
		slope1 = (line1.x1 == line1.x2) ? INT_MAX : (double)(line1.y2 - line1.y1) / (line1.x2 - line1.x1);
		slope2 = (line2.x1 == line2.x2) ? INT_MAX : (double)(line2.y2 - line2.y1) / (line2.x2 - line2.x1);
		slope3 = (line3.x1 == line3.x2) ? INT_MAX : (double)(line3.y2 - line3.y1) / (line3.x2 - line3.x1);
		slope4 = (line4.x1 == line4.x2) ? INT_MAX : (double)(line4.y2 - line4.y1) / (line4.x2 - line4.x1);

		if (slope1 == slope2) {
			if (slope3 != slope4) {
				cout << "NO" << endl;
				continue;
			}
			//垂直
			if (((line1.y1 - line1.y2) * (line3.y1 - line3.y2) +
				(line1.x1 - line1.x2) * (line3.x1 - line3.x2)) == 0) {
				cout << "YES" << endl;
			}

			else {
				cout << "NO" << endl;
			}
		}
		///////////////////////////////////
		else if (slope1 == slope3) {
			if (slope2 != slope4) {
				cout << "NO" << endl;
				continue;
			}
			//垂直
			if (((line1.y1 - line1.y2) * (line2.y1 - line2.y2) +
				(line1.x1 - line1.x2) * (line2.x1 - line2.x2)) == 0) {
				cout << "YES" << endl;
			}

			else {
				cout << "NO" << endl;
			}
		}
		/////////////////////////////////
		else if(slope1 == slope4) {
			if (slope2 != slope3) {
				cout << "NO" << endl;
				continue;
			}
			//垂直
			if (((line1.y1 - line1.y2) * (line3.y1 - line3.y2) +
				(line1.x1 - line1.x2) * (line3.x1 - line3.x2)) == 0) {
				cout << "YES" << endl;
			}

			else {
				cout << "NO" << endl;
			}
		}
		/////////////////////////////
		else {
			cout << "NO" << endl;
		}
	}

	return 0;
}