学步园

题目意思为给你四个点的坐标，判断这四个点围成的形状是正方形、矩形、菱形、平行四边形、梯形还是普通的四边形。

按照边长是否平行和对角线是否垂直判断。

#include <iostream>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <algorithm>

using namespace std;

char shape[6][30] = {
	"Square",
	"Rectangle",
	"Rhombus",
	"Parallelogram",
	"Trapezium",
	"Ordinary Quadrilateral",
};

const double eps = 1e-8;

int sig(double argu)
{
	return (argu > eps) - (argu < -eps);
}

typedef struct Point
{
	double x, y;
	Point (double _x = 0.0, double _y = 0.0):
		x(_x), y(_y) {}
	Point operator +(const Point &argu) const
	{
		return Point(x + argu.x, y + argu.y);
	}
	Point operator -(const Point &argu) const
	{
		return Point(x - argu.x, y - argu.y);
	}
	Point operator *(const double k) const
	{
		return Point(x * k, y * k);
	}
	Point operator /(const double k) const
	{
		return Point(x / k, y / k);
	}
	double operator ^(const Point &argu) const
	{
		return (x * argu.y - y * argu.x);
	}
	double operator *(const Point &argu) const
	{
		return (x * argu.x + y * argu.y);
	}
	bool operator <(const Point &argu) const
	{
		if(sig(y - argu.y) == 0)
			return x < argu.x;
		else
			return y < argu.y;
	}
}Vector;

Point vert[4], minv;
Vector edge[4], diag[2];
double x, y;

bool cmp(Point m, Point n)
{
	double mang = atan2(m.y - minv.y, m.x - minv.x);
	double nang = atan2(n.y - minv.y, n.x - minv.x);
	if(sig(mang - nang) == 0)
		return m.x < n.x;
	else
		return mang < nang;
}

void CheckShape()
{
	if(sig(edge[0] ^ edge[2]) == 0 || sig(edge[1] ^ edge[3]) == 0)
	{
		if(sig(edge[0] ^ edge[2]) == 0 && sig(edge[1] ^ edge[3]) == 0)
		{
			if(sig(diag[0] * diag[1]) == 0)
			{
				if(sig(edge[0] * edge[1]) == 0)
					puts(shape[0]);
				else
					puts(shape[2]);
			}
			else if(sig(edge[0] * edge[1]) == 0)
				puts(shape[1]);
			else
				puts(shape[3]);
		}
		else
			puts(shape[4]);
	}
	else
		puts(shape[5]);
}

int main()
{
	//freopen("11800.in", "r", stdin);
	
	int n;
	scanf("%d", &n);
	for(int cas = 1; cas <= n; cas++)
	{
		printf("Case %d: ", cas);
		for(int i = 0; i < 4; i++)
		{
			scanf("%lf%lf", &x, &y);
			vert[i] = Point(x, y);
		}
		minv = vert[0];
		for(int i = 0; i < 4; i++)
			if(minv < vert[i])
				minv = vert[i];
		sort(vert, vert + 4, cmp);
		for(int i = 0; i < 4; i++)
			edge[i] = vert[i] - vert[(i + 1) % 4];
		diag[0] = vert[0] - vert[2];
		diag[1] = vert[1] - vert[3];
		CheckShape();
	}
	return 0;
}