hdu-1115（计算多边形重心）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1115

思路：带公式：http://www.cnblogs.com/jbelial/archive/2011/08/08/2131165.html

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;
struct Node{
    double x,y;
};
double Area(Node p1,Node p2,Node p3)
{
    return ((p1.x*p2.y+p2.x*p3.y+p3.x*p1.y)-(p1.y*p2.x+p2.y*p3.x+p3.y*p1.x))/2.0;
}
int main(void)
{
    Node p1,p2,p3;
    int t,n,i;
    double area,area_x,area_y;
    scanf("%d",&t);
    while(t--)
    {
        area=0,area_x=0,area_y=0;
        scanf("%d",&n);
        scanf("%lf%lf",&p1.x,&p1.y);
        scanf("%lf%lf",&p2.x,&p2.y);
        for(i=2;i<n;i++)
        {
            scanf("%lf%lf",&p3.x,&p3.y);
            double tmp=Area(p1,p2,p3);
            area+=tmp;
            area_x+=(p1.x+p2.x+p3.x)*tmp;
            area_y+=(p1.y+p2.y+p3.y)*tmp;
            p2=p3;
        }
        printf("%.2f %.2f\n",area_x/(area*3.0),area_y/(area*3.0));
    }
    return 0;
}