多边形重心

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质量集中在顶点上。n个顶点坐标为(xi,yi)，质量为mi，则重心
　　X = ∑( xi×mi ) / ∑mi
　　Y = ∑( yi×mi ) / ∑mi
　　特殊地，若每个点的质量相同，则
　　X = ∑xi / n

　　Y = ∑yi / n

hdu1115，题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1115

#include <iostream>#include <cstdio>using namespace std;struct Point{      double x, y;};double cross(Point p0, Point p1, Point p2){      return (p1.x-p0.x)*(p2.y-p0.y)-(p1.y-p0.y)*(p2.x-p0.x);}int main(){      int ncase, n;      double sum_x, sum_y, area1, area;      Point p1, p2, p3;      scanf("%d", &ncase);      while (ncase--)      {            scanf("%d", &n);            scanf("%lf%lf", &p1.x, &p1.y);            scanf("%lf%lf", &p2.x, &p2.y);            sum_x = sum_y = area = 0;            for (int i=2; i<n; i++)            {                  scanf("%lf%lf", &p3.x, &p3.y);                  area1 = cross(p1, p2, p3)/2.0;                  area += area1;                  sum_x += (p1.x + p2.x + p3.x)*area1;                  sum_y += (p1.y + p2.y + p3.y)*area1;                  p2 = p3;            }            double x = sum_x/area/3, y = sum_y/area/3;            printf("%.3f %.3f\n", x, y);      }      return 0;}