uva 11800 - Determine the Shape

题意：给定平面上4个点，没有3点共线；判断这4个点能组成怎样的四边形。

正方形：Square

矩形：Rectangle

菱形：Rhombus

平行四边形：Parallelogram

梯形：Trapezium

普通四边形：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;

}