1.质量集中在顶点上。n个顶点坐标为(xi,yi),质量为mi,则重心(∑( xi×mi ) / ∑mi, ∑( yi×mi ) / ∑mi)
2.质量分布均匀。这个题就是这一类型,算法和上面的不同。
特殊地,质量均匀的三角形重心:(( x0 + x1 + x2 ) / 3,Y = ( y0 + y1 + y2 ) / 3)
以(0,0)为顶点三角剖分之后求三角形重心,把重心连起来转换成质量集中在顶点上的情况求解即可

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;
const int N=1000005;
int T,n;
double am;
struct dian
{
	double x,y,v;
	dian(double X=0,double Y=0)
	{
		x=X,y=Y;
	}
	dian operator + (const dian &a) const
	{
		return dian(x+a.x,y+a.y);
	}
	dian operator - (const dian &a) const
	{
		return dian(x-a.x,y-a.y);
	}
	dian operator * (const double &a) const
	{
		return dian(x*a,y*a);
	}
	dian operator / (const double &a) const
	{
		return dian(x/a,y/a);
	}
}p[N],a;
int read()
{
	int r=0,f=1;
	char p=getchar();
	while(p>'9'||p<'0')
	{
		if(p=='-')
			f=-1;
		p=getchar();
	}
	while(p>='0'&&p<='9')
	{
		r=r*10+p-48;
		p=getchar();
	}
	return r*f;
}
double cj(dian a,dian b)
{
	return a.x*b.y-a.y*b.x;
}
int main()
{
	T=read();
	while(T--)
	{
		n=read();am=0,a.x=0,a.y=0;
		for(int i=1;i<=n;i++)
			p[i].x=read(),p[i].y=read();
		p[n+1]=p[1];
		for(int i=2;i<=n+1;i++)
		{
			double mj=cj(p[i-1],p[i]);
			am+=mj,a=a+(p[i-1]+p[i])*mj;
		}
		printf("%.2f %.2f\n",a.x/am/3,a.y/am/3);
	}
	return 0;
}