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POJ 3335
/*半平面交求核心的增量法:假设前N-1个半平面交,对于第N个半平面,只需用它来交前N-1个平面交出的多边形。算法开始时,调整点的方向为顺时针方向,对于是否为顺时针,只需求出其面积,若为正,必为逆时针的。对于每相邻两点求出一条直线,用该直线去交其半平面,并求出交点及判断原多边形点的方位。*/ #include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>using namespace std;const int MAXN=110;const double eps=1e-8;struct point { double x,y;};point pts[MAXN],p[MAXN],q[MAXN];int n,cCnt,curCnt;int DB(double d){ if(d>eps) return 1; if(d<-eps) return -1; return 0;}double getArea(point *tmp, int n){ double ans=0; for(int i=1;i<=n;i++) ans+=(tmp[i].x*tmp[i+1].y-tmp[i].y*tmp[i+1].x); return ans/2;}void Adjust(point *ps,int n){ for(int i = 1; i < (n+1)/2; i ++) swap(ps[i], ps[n-i]);}void initial(){ double area=getArea(pts,n); if(DB(area)==1) Adjust(pts,n); for(int i=1;i<=n;i++) p[i]=pts[i]; p[n+1]=p[1]; p[0]=p[n]; cCnt=n;}void getline(point x,point y,double &a,double &b,double &c){ a = y.y - x.y; b = x.x - y.x; c = y.x * x.y - x.x * y.y;}point intersect(point x,point y,double a,double b,double c){ double u = fabs(a * x.x + b * x.y + c); double v = fabs(a * y.x + b * y.y + c); point pt; pt.x=(x.x * v + y.x * u) / (u + v); pt.y=(x.y * v + y.y * u) / (u + v); return pt;}void cut(double a,double b,double c){ curCnt=0; for(int i=1;i<=cCnt;i++){ if(DB(a*p[i].x+b*p[i].y+c)>=0) q[++curCnt] = p[i]; else { if(DB(a*p[i-1].x + b*p[i-1].y + c )>0){ q[++curCnt] = intersect(p[i],p[i-1],a,b,c); } if(DB(a*p[i+1].x + b*p[i+1].y + c )> 0){ q[++curCnt] = intersect(p[i],p[i+1],a,b,c); } } } for(int i = 1; i <= curCnt; ++i)p[i] = q[i]; p[curCnt+1] = q[1];p[0] = p[curCnt]; cCnt = curCnt;}void slove(){ initial(); for(int i=1;i<=n;i++){ double a,b,c; getline(pts[i],pts[i+1],a,b,c); cut(a,b,c); }}int main(){ int t; scanf("%d",&t); while(t--){ scanf("%d",&n); for(int i=1;i<=n;i++) scanf("%lf%lf",&pts[i].x,&pts[i].y); pts[n+1]=pts[1]; slove(); if(cCnt>=1) printf("YES\n"); else printf("NO\n"); } return 0;}
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