uva,132 Bumpy Objects (凸包，角度)

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题意：自己百度吧，有全翻译的。

分析：先求凸包，然后判断重心是否在凸多边形的边上面，也就是说边和重心组成的三角形，重心为顶点，下面两个底角不为钝角就是说明此时重心在线段上侧。然后遍历所有点，判断是否在该边上，找到该边上标号最大的点。

#include <iostream>#include<cstdio>#include<algorithm>#include<cmath>using namespace std;#define N 999999#define INF 0x7fffffff#define EPS 1e-6struct point{    double x,y;    int index;    point(double x,double y):x(x),y(y){}    point(){}    bool operator< (const point &s)const    {        return (x-s.x<-EPS)||(abs(x-s.x)<EPS&&y<s.y);    }    double det(point a)    {        return x*a.y-y*a.x;    }    double dot(point a)    {        return x*a.x+y*a.y;    }    point operator-(point a)    {        return point(x-a.x,y-a.y);    }    point operator +(point a)    {        return point(x+a.x,y+a.y);    }    point operator *(double s)    {        return point(x*s,y*s);    }    point operator /(double s)    {        return point(x/s,y/s);    }};point p[N],res[N];bool on_seg(point p1,point p2,point p3);void convex_hull();bool point_to_seg(point p1,point p2,point p3);double dist(point p1,point p2);int k,n;int main(){    string s;    point pc;    while(cin>>s&&s[0]!='#')    {        scanf("%lf%lf",&pc.x,&pc.y);        n=-1;        do        {            n++;            scanf("%lf%lf",&p[n].x,&p[n].y);            p[n].index=n+1;        }while(!(abs(p[n].x)<EPS&&abs(p[n].y)<EPS));        //cout<<n<<endl;        convex_hull();        int ans=INF;        for(int i=0;i<k-1;i++)        {            //cout<<res[i].x<<"  "<<res[i].y<<"  "<<res[i].index<<endl;            if(point_to_seg(res[i],res[i+1],pc))            {                int temp=max(res[i].index,res[i+1].index);                for(int j=0;j<n;j++)                {                    if(on_seg(res[i],res[i+1],p[j]))                    {                        temp=max(p[j].index,temp);                    }                }               // cout<<temp<<endl;                ans=min(ans,temp);            }        }        cout<<s<<" ";        printf("%d\n",ans);    }    return 0;}//p3是否在线段p1和p2之间的区域内。bool point_to_seg(point p1,point p2,point p3){    double A=dist(p1,p3);    double B=dist(p2,p3);    double C=dist(p1,p2);    return (A*A+C*C-B*B>-EPS&&B*B+C*C-A*A>-EPS);}//求凸包void convex_hull(){        sort(p,p+n);         k=0;        for(int i=0;i<n;i++)        {            while(k>1&&(res[k-1]-res[k-2]).det(p[i]-res[k-2])<=EPS)            k--;            res[k++]=p[i];        }          int t=k;         for(int i=n-2;i>=0;i--)          {            while(k>t&&(res[k-1]-res[k-2]).det(p[i]-res[k-2])<=EPS)            k--;            res[k++]=p[i];          }}//判断点是否在线段上bool on_seg(point p1,point p2,point p3){    return abs((p1-p3).det(p2-p3))<EPS;//&&(p1-p3).dot(p2-p3)<EPS;}//两点之间的距离double dist(point p1,point p2){    return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));}

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