HDU3685计算几何
下午和队友一起做了下杭州赛区的比赛题，结果被虐了，只过了三题，两个队友没一会儿就开始打酱油。。。。实在受不了。
这道题裸的计算几何，求出多边形的重心，求重凸包，然后直接判断重心到凸包各点的投影是否在线段上，注意这里不用求出投影直接用点积即可，队友看错题WA了一次，我看了下图发现90的时候是不稳的。。。。到此整题就理论AC了，只要代码稳，可以轻松拿下。
我的代码：
#include <cstdio> #include <cstring> #include <cstdlib> #include <cmath> #include <vector> #include <algorithm> using namespace std; const int MAX=50100; const double oo=1e10; const double eps=1e-8; struct Point{ double x,y; double angle,dis; Point(){ } Point(double x,double y):x(x),y(y){ } }; struct Line{ Point p1,p2; Line(){ } Line(Point p1,Point p2):p1(p1),p2(p2){ } }; typedef vector<Point> Polygon; typedef vector<Point> Points; bool ZERO(double x){ return fabs(x)<eps; } bool ZERO(Point p){ return ZERO(p.x)&&ZERO(p.y); } bool EQ(double x,double y){ return fabs(x-y)<eps; } bool NEQ(double x,double y){ return fabs(x-y)>=eps; } bool LT(double x,double y){ return NEQ(x,y)&&x<y; } bool GT(double x,double y){ return NEQ(x,y)&&x>y; } bool LEQ(double x,double y){ return EQ(x,y)||x<y; } bool GEQ(double x,double y){ return EQ(x,y)||x>y; } double sqr(double x){ return x*x; } bool operator==(const Point& p1,const Point& p2){ return EQ(p1.x,p2.x)&&EQ(p1.y,p2.y); } bool operator!=(const Point& p1,const Point& p2){ return NEQ(p1.x,p2.x)||NEQ(p1.y,p2.y); } bool operator<(const Point& p1,const Point& p2){ if(NEQ(p1.x,p2.x)){ return p1.x<p2.x; }else{ return p1.y<p2.y; } } Point operator+(const Point& p1,const Point& p2){ return Point(p1.x+p2.x,p1.y+p2.y); } Point operator-(const Point& p1,const Point& p2){ return Point(p1.x-p2.x,p1.y-p2.y); } double operator*(const Point& p1,const Point& p2){ return p1.x*p2.y-p1.y*p2.x; } double operator&(const Point& p1,const Point& p2){ return p1.x*p2.x+p1.y*p2.y; } double Norm(const Point& p){ return sqrt(sqr(p.x)+sqr(p.y)); } bool comp(const Point& left,const Point& right){ if(EQ(left.angle,right.angle)){ return left.dis<right.dis; }else{ return left.angle<right.angle; } } void Scan(Points& points,Polygon& result){ int i,k,n; Point p; n=points.size(); result.clear(); if(n<3){ result=points; return; } k=0; for(i=1;i<n;i++){ if(EQ(points[i].y,points[k].y)){ if(points[i].x<=points[k].x){ k=i; } }else if(points[i].y<points[k].y){ k=i; } } swap(points[0],points[k]); for(i=1;i<n;i++){ points[i].angle=atan2(points[i].y-points[0].y,points[i].x-points[0].x); points[i].dis=Norm(points[i]-points[0]); } sort(points.begin()+1,points.end(),comp); result.push_back(points[0]); for(i=1;i<n;i++){ if((i+1<n)&&EQ(points[i].angle,points[i+1].angle)){ continue; } if(result.size()>=3){ p=result[result.size()-2]; while(GEQ((points[i]-p)*(result.back()-p),0)){ result.pop_back(); p=result[result.size()-2]; } } result.push_back(points[i]); } } Point center(const Polygon& poly){ Point p,p0,p1,p2,p3; double m,m0; p1=poly[0]; p2=poly[1]; p.x=p.y=m=0; for(int i=2;i<(int)poly.size();i++){ p3=poly[i]; p0.x=(p1.x+p2.x+p3.x)/3.0; p0.y=(p1.y+p2.y+p3.y)/3.0; m0=p1.x*p2.y+p2.x*p3.y+p3.x*p1.y-p1.y*p2.x-p2.y*p3.x-p3.y*p1.x; if(ZERO(m+m0)){ m0+=eps; } p.x=(m*p.x+m0*p0.x)/(m+m0); p.y=(m*p.y+m0*p0.y)/(m+m0); m+=m0; p2=p3; } return p; } bool isconter(const Points pts){ double res=0.0; int n=pts.size(); for(int i=0;i<n;i++){ res+=(pts[i]*pts[(i+1)%n]); } return res>0; } bool check(const Point& p,const Line& l){ return LT((l.p1-p)&(l.p2-l.p1),0)&<((l.p2-p)&(l.p1-l.p2),0); } Points pts,poly; int main(){ int t; int n,ret; Point p; scanf("%d",&t); while(t--){ scanf("%d",&n); ret=0; pts.clear(); for(int i=0;i<n;i++){ scanf("%lf%lf",&p.x,&p.y); pts.push_back(p); } if(!isconter(pts)){ reverse(pts.begin(),pts.end()); } p=center(pts); Scan(pts,poly); n=poly.size(); poly.push_back(poly[0]); for(int i=0;i<n;i++){ if(check(p,Line(poly[i],poly[i+1]))){ ret++; } } printf("%d/n",ret); } return 0; }