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;}