uva10002凸包重心

把每个三角形看成一个质点，坐标就是各自的重心，

#include<map>
#include<set>
#include<cmath>
#include<queue>
#include<stack>
#include<vector>
#include<cstdio>
#include<cassert>
#include<iomanip>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
#define pi acos(-1.0)
#define ll long long
#define mod 1000000007
#define ls l,m,rt<<1
#define rs m+1,r,rt<<1|1
#pragma comment(linker, "/STACK:1024000000,1024000000")

using namespace std;

const double g=10.0,eps=1e-7;
const int N=100+10,maxn=500+100,inf=0x3f3f3f;

struct point{
    double x,y;
   /* point(){};
    point(double _x,double _y):x(_x),y(_y){}
    point operator *(double p)
    {
        return point(x*p,y*p);
    }
    double operator *(point p)
    {
        return x*p.x+y*p.y;
    }
    point operator /(double p)
    {
        return point(x/p,y/p);
    }
    point operator +(point p)
    {
        return point(x+p.x,y+p.y);
    }
    point operator -(point p)
    {
        return point(x-p.x,y-p.y);
    }*/
};
point p[N],s[N];
int n;
inline bool zero(double x)
{
    return fabs(x)<eps;
}
double dir(point p1,point p2,point p3)
{
    return (p3.x-p1.x)*(p2.y-p1.y)-(p3.y-p1.y)*(p2.x-p1.x);
}
double dis(point p1,point p2)
{
    return sqrt((p2.x-p1.x)*(p2.x-p1.x)+(p2.y-p1.y)*(p2.y-p1.y));
}
bool comp(point p1,point p2)
{
    double te=dir(p[0],p1,p2);
    if(te<0)return 1;
    if(zero(te)&&dis(p[0],p1)<dis(p[0],p2))return 1;
    return 0;
}
void Graham()
{
    for(int i=1;i<n;i++)
        if(p[i].x<p[0].x||(p[i].x==p[0].x&&p[i].y<p[0].y))
           swap(p[0],p[i]);
    sort(p+1,p+n,comp);
    p[n]=p[0];
    s[0]=p[0],s[1]=p[1],s[2]=p[2];
    int top=2;
    for(int i=3;i<=n;i++)
    {
        while(top>=2&&dir(s[top-1],s[top],p[i])>=0)top--;
        s[++top]=p[i];
    }
  //  for(int i=0;i<top;i++)cout<<s[i].x<<" "<<s[i].y<<endl;
    point ans;
    ans.x=0.0;ans.y=0.0;
    double sum=0;
    for(int i=2;i<top;i++)
    {
        double te=dir(s[0],s[i],s[i-1]);
        sum+=te;
        ans.x+=(s[0].x+s[i].x+s[i-1].x)/3*te;
        ans.y+=(s[0].y+s[i].y+s[i-1].y)/3*te;
    }
    ans.x=ans.x/sum;ans.y=ans.y/sum;
    if(zero(ans.x))ans.x=0.0;if(zero(ans.y))ans.y=0.0;
    cout<<ans.x<<" "<<ans.y<<endl;
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout<<setiosflags(ios::fixed)<<setprecision(3);
    while(cin>>n){
        if(n<3)continue;
        for(int i=0;i<n;i++)cin>>p[i].x>>p[i].y;
        Graham();
    }
    return 0;
}
/*********************
4
0 1
1 1
0 0
1 0
3
1 2
1 0
0 0
7
-4 -4
-6 -3
-4 -10
-7 -12
-9 -8
-3 -6
-8 -3
1
*********************/