计算几何专项：UVa 11072

一道纯的模板，就是先求一个凸包，然后再判断点是否在凸包内。需要注意给定点与凸包顶点重合的情况（样例里就有这样的情况，恩，样例还是给了提示的）。

#include <iostream>#include <cstdio>#include <cmath>#include <algorithm>#include <vector>using namespace std;#define M 100010struct point{    int x,y;    point(int x=0,int y=0):x(x),y(y){}};point operator-(point a,point b){return point(a.x-b.x,a.y-b.y);}point operator+(point a,point b){return point(a.x+b.x,a.y+b.y);}bool operator<(const point& a,const point& b){    return a.x<b.x||(a.x==b.x&&a.y<b.y);}int cross(point a,point b){return a.x*b.y-a.y*b.x;}int dot(point a,point b){return a.x*b.x+a.y*b.y;}bool onseg(point p,point a1,point a2){    return cross(a1-p,a2-p)==0&&dot(a1-p,a2-p)<0;}vector<point> p,ch;int P,R;vector<point> convex(){    int n=p.size();    vector<point> CH(n+1);    sort(p.begin(),p.end());    int m=0;    for(int i=0;i<n;i++)    {        while(m>1&&cross(CH[m-1]-CH[m-2],p[i]-CH[m-2])<=0) m--;        CH[m++]=p[i];    }    int k=m;    for(int i=n-2;i>=0;i--)    {        while(m>k&&cross(CH[m-1]-CH[m-2],p[i]-CH[m-2])<=0) m--;        CH[m++]=p[i];    }    if(n>1) m--;    CH.resize(m);    return CH;}int isin(point p0){    int wn=0;    int n=ch.size();    for(int i=0;i<n;i++)    {        if(onseg(p0,ch[i],ch[(i+1)%n])) return 1;        if(p0.x==ch[i].x&&p0.y==ch[i].y) return 1;        int k=cross(ch[(i+1)%n]-ch[i],p0-ch[i]);        int d1=ch[i].y-p0.y;        int d2=ch[(i+1)%n].y-p0.y;        if(k>0&&d1<=0&&d2>0) wn++;        if(k<0&&d2<=0&&d1>0) wn--;    }    if(wn!=0) return 1;    return 0;}int main(){    freopen("in.txt","r",stdin);    while(cin>>P)    {        p.clear();ch.clear();        int x,y;        for(int i=0;i<P;i++)        {            cin>>x>>y;            p.push_back(point(x,y));        }        ch=convex();        cin>>R;        while(R--)        {            cin>>x>>y;            if(isin(point(x,y))) cout<<"inside"<<endl;            else cout<<"outside"<<endl;        }    }    return 0;}