Files
OI-source/2.1342.cpp
2023-08-03 09:22:52 +08:00

154 lines
3.5 KiB
C++

#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<algorithm>
using namespace std;
struct Point
{
double x,y;
Point(double x=0,double y=0):x(x),y(y){}
};
typedef Point Vector;
inline Point read_point()
{
Point A;
scanf("%lf%lf",&A.x,&A.y);
return A;
}
inline Vector operator+(const Vector &A,const Vector &B)
{ return Vector(A.x+B.x,A.y+B.y); }
inline Vector operator-(const Point &a,const Point &b)
{ return Vector(a.x-b.x,a.y-b.y); }
inline Vector operator*(const Vector &A,double p)
{ return Vector(A.x*p,A.y*p); }
inline Vector operator/(const Vector &A,double p)
{ return Vector(A.x/p,A.y/p); }
inline bool operator<(const Point &a,const Point &b)
{ return a.x<b.x||(a.x==b.x&&a.y<b.y); }
const double ops=1e-10;
inline int dcmp(double x)
{ return (x>0?x:-x)<ops?0:(x>0?1:-1); }
inline bool operator==(const Point &a,const Point &b)
{ return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0; }
inline double Dot(const Vector &A,const Vector &B)
{ return A.x*B.x+A.y*B.y; }
inline double Length(const Vector &A)
{ return sqrt(Dot(A,A)); }
inline double Angle(const Vector &A,const Vector &B)
{ return acos(Dot(A,B)/Length(A)/Length(B)); }
const double Pi=atan(1)*4;
inline double PAG(const Vector &A)
{ return atan2(A.y,A.x); }
inline double R_to_D(double rad)
{ return 180/Pi*rad; }
inline double D_to_R(double D)
{ return Pi/180*D; }
inline double Cross(const Vector &A,const Vector &B)
{ return A.x*B.y-A.y*B.x; }
inline double Area2(const Point &a,const Point &b,const Point &c)
{ return Cross(b-a,c-a); }
inline Vector Rotate(const Vector &A,double rad)
{
double csr=cos(rad),sir=sin(rad);
return Vector(A.x*csr-A.y*sir,A.x*sir+A.y*csr);
}
inline Vector Normal(const Vector &A)
{
double L=Length(A);
return Vector(-A.y/L,A.x/L);
}
inline Point GetLineIntersection
(const Point &P,const Vector &v,const Point &Q,const Vector &w)
{
Vector u=P-Q;
double t=Cross(w,u)/Cross(v,w);
return P+v*t;
}
inline double DistanceToLine
(const Point &P,const Point &A,const Point &B)
{
Vector v1=B-A,v2=P-A;
return fabs(Cross(v1,v2))/Length(v1);
}
inline double DistanceToSegment
(const Point &P,const Point &A,const Point &B)
{
if(A==B) return Length(P-A);
Vector v1=B-A,v2=P-A,v3=P-B;
if(dcmp(Dot(v1,v2))<0) return Length(v2);
else if(dcmp(Dot(v1,v3))>0) return Length(v3);
else return fabs(Cross(v1,v2))/Length(v1);
}
inline Point GetLineProjection
(const Point &P,const Point &A,const Point &B)
{
Vector v=B-A;
return A+v*(Dot(v,P-A)/Dot(v,v));
}
inline bool SegmentProperIntersection
(const Point &a1,const Point &a2,const Point &b1,const Point &b2)
{
double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),
c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;
}
inline bool OnSegment
(const Point &p,const Point &a1,const Point &a2)
{ return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0; }
inline double PolygonArea(Point* p,int n)
{
double area=0;
for(int i=1;i<n-1;i++)
area+=Cross(p[i]-p[0],p[i+1]-p[0]);
return area/2;
}
const int maxn=310;
Point P[maxn],V[maxn*maxn];
int n,kase;
int main()
{
#ifdef local
freopen("pro.in","r",stdin);
#endif
while(scanf("%d",&n)==1&&n)
{
for(int i=0;i<n;i++) V[i]=P[i]=read_point();
n--;
int c=n,e=n;
for(int i=0;i<n;i++)
for(int j=i+1;j<n;j++)
if(SegmentProperIntersection(P[i],P[i+1],P[j],P[j+1]))
V[c++]=GetLineIntersection(P[i],P[i+1]-P[i],P[j],P[j+1]-P[j]);
sort(V,V+c);
c=unique(V,V+c)-V;
for(int i=0;i<c;i++)
for(int j=0;j<n;j++)
if(OnSegment(V[i],P[j],P[j+1])) e++;
printf("Case %d: There are %d pieces.\n",++kase,e+2-c);
}
return 0;
}