[hdu3685]Rotational Painting 凸包 重心

大致题意：

　　给出一个多边形，问你有多少种放法可以使得多边形稳定得立在平面上。

　　先对多边形求重心，在求凸包，枚举凸包的边，如果重心没有在边的范围内，则不行

　　判断是否在范围内可用点积来判断

　　　

 #include<cstdio>
 #include<iostream>
 #include<cstring>
 #include<algorithm>
 #include<queue>
 #include<set>
 #include<map>
 #include<stack>
 #include<time.h>
 #include<cstdlib>
 #include<cmath>
 #include<list>
 using namespace std;
 #define MAXN 100100
 #define eps 1e-9
 #define For(i,a,b) for(int i=a;i<=b;i++)
 #define Fore(i,a,b) for(int i=a;i>=b;i--)
 #define lson l,mid,rt<<1
 #define rson mid+1,r,rt<<1|1
 #define mkp make_pair
 #define pb push_back
 #define cr clear()
 #define sz size()
 #define met(a,b) memset(a,b,sizeof(a))
 #define iossy ios::sync_with_stdio(false)
 #define fre freopen
 #define pi acos(-1.0)
 #define inf 1e6+7
 #define Vector Point
 const int Mod=1e9+;
 typedef unsigned long long ull;
 typedef long long ll;
 int dcmp(double x){
     if(fabs(x)<=eps) return ;
     return x<?-:;
 }
 struct Point{
     double x,y;
     Point(double x=,double y=):x(x),y(y) {}
     bool operator < (const Point &a)const{
         if(x==a.x) return y<a.y;
         return x<a.x;
     }
     Point operator - (const Point &a)const{
         return Point(x-a.x,y-a.y);
     }
     Point operator + (const Point &a)const{
         return Point(x+a.x,y+a.y);
     }
     Point operator * (const double &a)const{
         return Point(x*a,y*a);
     }
     Point operator / (const double &a)const{
         return Point(x/a,y/a);
     }
     void read(){
         scanf("%lf%lf",&x,&y);
     }
     void out(){
         cout<<"debug: "<<x<<" "<<y<<endl;
     }
     bool operator == (const Point &a)const{
         return dcmp(x-a.x)== && dcmp(y-a.y)==;
     }
 };
 double Dot(Vector a,Vector b) {
     return a.x*b.x+a.y*b.y;
 }
 double dis(Vector a) {
     return sqrt(Dot(a,a));
 }
 double Cross(Point a,Point b){
     return a.x*b.y-a.y*b.x;
 }
 int ConvexHull(Point *p,int n,Point *ch){
     int m=;
     For(i,,n-) {
         while(m> && Cross(ch[m-]-ch[m-],p[i]-ch[m-])<=) m--;
         ch[m++]=p[i];
     }
     int k=m;
     Fore(i,n-,){
         while(m>k && Cross(ch[m-]-ch[m-],p[i]-ch[m-])<=) m--;
         ch[m++]=p[i];
     }
     if(n>) m--;
     return m;
 }
 int n,m;
 Point p[];
 Point ch[];
 Point cp;
 void solve(){
     scanf("%d",&n);
     For(i,,n-) p[i].read();
     double tar=,ar;
     cp.x=;cp.y=;
     For(i,,n-){
         ar=Cross(p[i]-p[],p[i-]-p[])/;
         tar+=ar;
         cp=cp+(p[i]+p[i-]+p[])*ar;
     }
     cp=cp/tar/;
     sort(p,p+n);
     m=ConvexHull(p,n,ch);
     int ans=;
     For(i,,m-) {
         int nxt=(i+)%m;
         if(dcmp(Dot(ch[i]-ch[nxt],cp-ch[nxt]))> && dcmp(Dot(ch[nxt]-ch[i],cp-ch[i]))>) ans++;
     }
     printf("%d\n",ans);
 }
 int main(){
 //    fre("in.txt","r",stdin);
     int t=;
     cin>>t;
     For(i,,t) solve();
     return ;
 }