hdu 3685 10 杭州 现场 F - Rotational Painting 重心

#include <iostream>
#include <cmath>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <vector>
#include <algorithm>

using namespace std;

const int maxn=60100;
const double eps=1e-10;

double add(double a,double b)
{
    if(abs(a+b)<eps*(abs(a)+abs(b))) return 0;
    return a+b;
}

struct point
{
	double x,y;
	point () {}
	point(double x,double y) : x(x),y(y){
	}
	point operator + (point p){
		return point(add(x,p.x),add(y,p.y));
	}
	point operator - (point p){
		return point(add(x,-p.x),add(y,-p.y));
	}
	point operator * (double d){
		return point(x*d,y*d);
	}
	double dot(point p){
		return add(x*p.x,y*p.y);
	}
	double det(point p){
		return add(x*p.y,-y*p.x);
	}

} pi[maxn];
int nn;

bool on_seg(point p1,point p2,point q)
{
	return (p1-q).det(p2-q)==0&&(p1-q).dot(p2-q)<=0;
}
point intersection(point p1,point p2,point q1,point q2)
{
	return p1+(p2-p1)*((q2-q1).det(q1-p1)/(q2-q1).det(p2-p1));
}
bool cmp_x(const point& p,const point& q)
{
	if(p.x!=q.x) return p.x<q.x;
	return p.y<q.y;
}

vector<point> convex_hull(point * ps,int n)
{
	sort(ps,ps+n,cmp_x);
	int k=0;	//凸包的顶点数
	vector<point> qs(n*2);
	for(int i=0;i<n;i++){
		while(k>1&&(qs[k-1]-qs[k-2]).det(ps[i]-qs[k-1])<=0) k--;
		qs[k++]=ps[i];
	}
	for(int i=n-2,t=k;i>=0;i--){
		while(k>t&&(qs[k-1]-qs[k-2]).det(ps[i]-qs[k-1])<=0) k--;
		qs[k++]=ps[i];
	}
	qs.resize(k-1);
	return qs;
}


point gravity(point *p,int n)
{
	double area=0;
	point center;
	center.x=0;
	center.y=0;

	for(int i=0;i<n-1;i++){
		area+=(p[i].x*p[i+1].y-p[i+1].x*p[i].y)/2;
		center.x+=(p[i].x*p[i+1].y-p[i+1].x*p[i].y)*(p[i].x+p[i+1].x);
		center.y+=(p[i].x*p[i+1].y-p[i+1].x*p[i].y)*(p[i].y+p[i+1].y);
	}

	area+=(p[n-1].x*p[0].y-p[0].x*p[n-1].y)/2;
	center.x+=(p[n-1].x*p[0].y-p[0].x*p[n-1].y)*(p[n-1].x+p[0].x);
	center.y+=(p[n-1].x*p[0].y-p[0].x*p[n-1].y)*(p[n-1].y+p[0].y);

	center.x/=6*area;
	center.y/=6*area;

	return center;
}
bool judge(point cen,point ind1,point ind2){
    point v=ind1-ind2;
    point w;w.x=v.y;w.y=-v.x;
    point u=ind2-cen;
    double t=w.det(u)/v.det(w);
  //  printf("%.8f\n",t);
    if(t<1&&t>0)return true;
    return false;
}
void solve()
{
    vector<point> pp;
    point cen;
	cen=gravity(pi,nn);
	pp=convex_hull(pi,nn);
	int ans=0;
	for(int i=0;i<pp.size();i++){
        if(judge(cen,pp[i],pp[(i+1)%pp.size()])){
            ans++;
        }
	}
	printf("%d\n",ans);
	return ;
}

int main()
{
	int T;
	scanf("%d",&T);
	while(T--){
		scanf("%d",&nn);
		for(int i=0;i<nn;i++) scanf("%lf%lf",&pi[i].x,&pi[i].y);
		solve();
	}
}