179 lines
3.4 KiB
C++
179 lines
3.4 KiB
C++
#include<cstdio>
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#include<cstring>
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#include<cstdlib>
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#include<cmath>
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#include<vector>
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#include<algorithm>
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using std::vector;
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using std::swap;
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struct Point
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{
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double x,y;
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Point(double x=0,double y=0):x(x),y(y){}
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};
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typedef Point Vector;
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inline Point read_point()
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{
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Point A;
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scanf("%lf%lf",&A.x,&A.y);
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return A;
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}
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inline Vector operator+(const Vector &A,const Vector &B)
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{ return Vector(A.x+B.x,A.y+B.y); }
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inline Vector operator-(const Point &a,const Point &b)
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{ return Vector(a.x-b.x,a.y-b.y); }
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inline Vector operator*(const Vector &A,double p)
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{ return Vector(A.x*p,A.y*p); }
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inline Vector operator/(const Vector &A,double p)
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{ return Vector(A.x/p,A.y/p); }
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inline bool operator<(const Point &a,const Point &b)
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{ return a.x<b.x||(a.x==b.x&&a.y<b.y); }
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const double eps=1e-10;
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inline int dcmp(double x)
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{ return (x>0?x:-x)<=eps?0:(x>0?1:-1); }
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inline bool operator==(const Point &a,const Point &b)
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{ return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0; }
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inline double Dot(const Vector &A,const Vector &B)
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{ return A.x*B.x+A.y*B.y; }
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inline double Length(const Vector &A)
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{ return sqrt(Dot(A,A)); }
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inline double Cross(const Vector &A,const Vector &B)
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{ return A.x*B.y-A.y*B.x; }
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inline Vector Normal(const Vector &A)
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{
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double L=Length(A);
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return Vector(-A.y/L,A.x/L);
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}
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inline Vector Format(const Vector &A)
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{
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double L=Length(A);
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return Vector(A.x/L,A.y/L);
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}
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using namespace std;
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const char* rslts[]={"Square","Rectangle","Rhombus","Parallelogram","Trapezium","Ordinary Quadrilateral"};
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int T,res;
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Point p[4];
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inline bool PingXing
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(const Point &A1,const Point &B1,const Point &A2,const Point &B2)
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{ return dcmp(Cross(B1-A1,B2-A2))==0; }
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bool is_Square()
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{
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sort(p,p+4);
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do
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{
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for(int i=0;i<4;i++)
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{
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Vector v1=p[(i+1)%4]-p[i],v2=p[(i+2)%4]-p[(i+1)%4];
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v1=Vector(-v1.y,v1.x);
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if(!(v1==v2)) goto next;
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}
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return true;
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next:
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continue;
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}
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while(next_permutation(p,p+4));
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return false;
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}
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bool is_JuXin()
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{
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sort(p,p+4);
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do
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{
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for(int i=0;i<4;i++)
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{
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Vector v1=p[(i+1)%4]-p[i],v2=p[(i+2)%4]-p[(i+1)%4];
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if(!(Normal(v1)==Format(v2))) goto next;
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}
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return true;
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next:
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continue;
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}
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while(next_permutation(p,p+4));
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return false;
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}
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bool is_LinXin()
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{
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sort(p,p+4);
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do
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{
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for(int i=0;i<4;i++)
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{
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Vector v1=p[(i+1)%4]-p[i],v2=p[(i+2)%4]-p[(i+1)%4];
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if(!(PingXing(p[i],p[(i+1)%4],p[(i+2)%4],p[(i+3)%4])
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&&Length(v1)==Length(v2))) goto next;
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}
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return true;
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next:
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continue;
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}
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while(next_permutation(p,p+4));
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return false;
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}
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bool is_PingXingSiBianXin()
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{
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sort(p,p+4);
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do
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{
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for(int i=0;i<4;i++)
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{
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Vector v1=p[(i+1)%4]-p[i],v2=p[(i+2)%4]-p[(i+1)%4];
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if(!(PingXing(p[i],p[(i+1)%4],p[(i+2)%4],p[(i+3)%4]))) goto next;
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}
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return true;
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next:
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continue;
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}
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while(next_permutation(p,p+4));
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return false;
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}
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bool is_TiXin()
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{
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sort(p,p+4);
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do
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{
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for(int i=0;i<4;i++)
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{
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Vector v1=p[(i+1)%4]-p[i],v2=p[(i+2)%4]-p[(i+1)%4];
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if(PingXing(p[i],p[(i+1)%4],p[(i+2)%4],p[(i+3)%4])) return true;
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}
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}
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while(next_permutation(p,p+4));
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return false;
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}
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int solve()
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{
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if(is_Square()) return 0;
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else if(is_JuXin()) return 1;
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else if(is_LinXin()) return 2;
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else if(is_PingXingSiBianXin()) return 3;
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else if(is_TiXin()) return 4;
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return 5;
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}
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int main()
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{
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#ifdef local
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freopen("pro.in","r",stdin);
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#endif
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scanf("%d",&T);
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for(int kase=1;kase<=T;kase++)
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{
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for(int i=0;i<4;i++) p[i]=read_point();
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printf("Case %d: %s\n",kase,rslts[solve()]);
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}
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return 0;
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}
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