uva 11800 - Determine the Shape

題意：給定平面上4個點，沒有3點共線；判斷這4個點能組成怎樣的四邊形。

正方形：Square

矩形：Rectangle

菱形：Rhombus

平行四邊形：Parallelogram

梯形：Trapezium

普通四邊形：Ordinary Quadrilateral

#include<iostream>
#include<algorithm>

using namespace std;

typedef struct points
{
    double x,y;
    points(double xx=0,double yy=0):x(xx),y(yy){}
}vectors;
points p[4],ch[4];

bool operator < (points a,points b)
{
    return a.x<b.x || (a.x==b.x && a.y<b.y);
}
vectors operator - (points a,points b)
{
    return vectors(a.x-b.x,a.y-b.y);
}
double dot(vectors a,vectors b)
{
    return a.x*b.x+a.y*b.y;
}
double len(vectors a)
{
    return dot(a,a);
}
double cross(vectors a,vectors b)
{
    return a.x*b.y-a.y*b.x;
}
bool convex()
{
    sort(p,p+4);
    int m=0;
    for(int i=0;i<4;i++)
    {
        while(m>1 && cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;
        ch[m++]=p[i];
    }
    int k=m;
    for(int i=2;i>=0;i--)
    {
        while(m>k && cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;
        ch[m++]=p[i];
    }
    return m==5;
}

int main()
{
    int i,t;
    cin>>t;
    for(i=1;i<=t;i++)
    {
        for(int j=0;j<4;j++) cin>>p[j].x>>p[j].y;
        cout<<"Case "<<i<<": ";
        if(convex())
        {
            vectors u=ch[1]-ch[0],v=ch[3]-ch[2];
            vectors w=ch[2]-ch[1],r=ch[0]-ch[3];
            if(cross(u,v))
            {
                if(cross(w,r)) cout<<"Ordinary Quadrilateral"<<endl;
                else cout<<"Trapezium"<<endl;
            }
            else
            {
                if(cross(w,r)) cout<<"Trapezium"<<endl;
                else
                {
                    if(dot(u,w))
                    {
                        if(len(u)==len(w)) cout<<"Rhombus"<<endl;
                        else cout<<"Parallelogram"<<endl;
                    }
                    else
                    {
                        if(len(u)==len(w)) cout<<"Square"<<endl;
                        else cout<<"Rectangle"<<endl;
                    }
                }
            }
        }
        else cout<<"Ordinary Quadrilateral"<<endl;
    }
    return 0;
}