LA 3263 That Nice Euler Circuit 欧拉定理 -

题目地址：https://vjudge.net/problem/UVALive-3263

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <complex>
using namespace std;
#define REP(i,a,b) for(int i=a;i<=(int)(b);++i)
#define REPD(i,a,b) for(int i=a;i>=(int)(b);--i)

/*Point模板部分*/
typedef complex<double> Point;
typedef Point Vector;
const double eps = 1e-10;
int dcmp(double x){
if(fabs(x) < eps) return 0;
else return x < 0 ? -1: 1;
}
double Dot(Vector A, Vector B) { return real(conj(A)*B); }
double Cross(Vector A, Vector B) { return imag(conj(A)*B); }
Vector Rotate(Vector A, double rad) { return A*exp(Point(0,rad)); }
double Length(Vector A) { return sqrt(Dot(A,A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B)/Length(A)/Length(B)); } //叉积
double Area2(Point A, Point B, Point C) { return Cross(B-A,C-A); } //有向面积
/*Point模板部分*/

Point GetLineIntersection(Point P, Vector v, Point Q, Vector w){ //两直线的交点，前提是Cross(v,w)!=0
Vector u=P-Q;
double t=Cross(w,u)/Cross(v,w);
return P+v*t;
}
double DistanceToLine(Point P, Point A, Point B){ //P到直线A-B距离
Vector v1=B-A, v2=P-A;
return fabs(Cross(v1,v2) / Length(v1));
}
double DistanceToSegment(Point P, Point A, Point B){ //P到线段A-B距离
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);
}
Point GetLineProjection(Point P, Point A, Point B){ //求P到直线A-B垂点
Vector v=B-A;
return A+v*(Dot(v,P-A)) / Dot(v,v);
}
bool SegmentProPerIntersection(Point a1, Point a2, Point b1,Point b2){ //两线是否规范相交
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;
}
bool OnSegment(Point p, Point a1, Point a2){ //p点是否在a1,a2线段上(不在a1,a2点上)
return dcmp(Cross(a1-p,a2-p))==0 && dcmp(Dot(a1-p,a2-p)) < 0;
}
Point ReadPoint(){
double a,b;
scanf("%lf%lf",&a,&b);
return Point(a,b);
}
const int maxn=300+5;
Point p[maxn],v[maxn*maxn];
bool cmp(const Point& a, const Point& b){
return real(a) < real(b) || (real(a) == real(b) && imag(a) < imag(b));
}
int main(int argc, char const *argv[])
{
int n,kase=0;
// freopen("input.in","r",stdin);
while(scanf("%d",&n)==1&&n){
REP(i,0,n-1) { p[i]=ReadPoint(); v[i]=p[i]; }
n--; //最后一个点重复了
int c=n,e=n;
REP(i,0,n-1) REP(j,i+1,n-1) //枚举所有两个的线段，如果规范相交，则存在新的交点，加入v[]中
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,cmp);
c=unique(v,v+c)-v; //去除重复的交点
REP(i,0,c-1) REP(j,0,n-1)
if(OnSegment(v[i],p[j],p[j+1])) e++; //一个点在线段上说明肯定多了一条边

printf("Case %d: There are %d pieces.\n", ++kase,e+2-c);
}
return 0;
}