hdu 1115 Lifting the Stone

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题目地址

题目大意：给定n个点的坐标，求n边形的重心

解题思路：选定任意一点作为定点（坐标原点）为每个三角形的一个顶点，将n边形分成n个三角形，n边形的重心=（每个三角形的重心*每个三角形的面积）/面积和

#include <iostream>#include <cstdio>#include <cmath>#include <algorithm>#include <cstring>#include <queue>#include <string>#include <map>#include <stack>#include <list>#include <set>using namespace std;const int maxn = 1e6+100;struct Point{    double x;    double y;}p[maxn],gra;int main(){    int n,t;    scanf("%d",&t);    while(t--)    {        scanf("%d",&n);        for(int i = 0; i < n; i++)            scanf("%lf%lf",&p[i].x,&p[i].y);        double area = 0.;        gra.x = gra.y = 0.;        p[n] = p[0];        for(int i = 0; i < n; i++)        {            area += (p[i].x*p[i+1].y-p[i].y*p[i+1].x);            gra.x += (p[i].x*p[i+1].y-p[i].y*p[i+1].x)*(p[i].x+p[i+1].x);            gra.y += (p[i].x*p[i+1].y-p[i].y*p[i+1].x)*(p[i].y+p[i+1].y);        }        gra.x /= 3*area;        gra.y /= 3*area;        printf("%.2lf %.2lf\n",gra.x,gra.y);    }    return 0;}

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