UVA 10002 Center of Masses

题目链接：http://acm.uva.es/local/online_judge/search_uva.html

Problem:Find out the center of masses of a convex polygon.

Input:A series of convex polygons, defined as a number n () stating the number of points of the polygon, followed by n different pairs of integers (in no particular order), denoting the x and y coordinates of each point. The input is finished by a fake ``polygon" with m (m < 3) points, which should not be processed.

Output:For each polygon, a single line with the coordinates x and y of the center of masses of that polygon, rounded to three decimal digits.

解法：求多边形的重心。先求出其凸包，然后求重心。

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<cstdlib>
 #include<cmath>
 #include<algorithm>
 #define inf 0x7fffffff
 #define exp 1e-10
 #define PI 3.141592654
 using namespace std;
 const int maxn=;
 struct Point
 {
     double x,y;
     Point (double x=,double y=):x(x),y(y){}
     bool friend operator < (Point a,Point b)
     {
         if (a.x!=b.x) return a.x<b.x;
         return a.y<b.y;
     }
 }an[maxn],bn[maxn];
 typedef Point Vector;
 Vector operator + (Vector A,Vector B) {return Vector(A.x+B.x , A.y+B.y); }
 Vector operator - (Vector A,Vector B) {return Vector(A.x-B.x , A.y-B.y); }
 Vector operator * (Vector A,double p) {return Vector(A.x*p , A.y*p); }
 int dcmp(double x)
 {
     if (fabs(x)<exp) return ;
     return x< ? - : ;
 }
 double cross(Vector A,Vector B)
 {
     return A.x*B.y-B.x*A.y;
 }
 Point PolyGravity(Point *p,int n)
 {
     Point tmp,g=Point(,);
     double sumArea=,area;
     for (int i= ;i<n ;i++)
     {
         area=cross(p[i-]-p[],p[i]-p[]);
         sumArea += area;
         tmp.x=p[].x+p[i-].x+p[i].x;
         tmp.y=p[].y+p[i-].y+p[i].y;
         g.x += tmp.x*area;
         g.y += tmp.y*area;
     }
     g.x /= (sumArea*3.0);
     g.y /= (sumArea*3.0);
     return g;
 }
 int ConvexHull(Point *p,int n,Point *ch)
 {
     sort(p,p+n);
     int m=;
     for (int i= ;i<n ;i++)
     {
         while (m> && dcmp(cross(ch[m-]-ch[m-],p[i]-ch[m-]))<) m--;
         ch[m++]=p[i];
     }
     int k=m;
     for (int i=n- ;i>= ;i--)
     {
         while (m>k && dcmp(cross(ch[m-]-ch[m-],p[i]-ch[m-]))<) m--;
         ch[m++]=p[i];
     }
     if (n>) m--;
     return m;
 }
 int main()
 {
     int n;
     while (scanf("%d",&n)!=EOF)
     {
         if (n<) break;
         for (int i= ;i<n ;i++)
         {
             scanf("%lf%lf",&an[i].x,&an[i].y);
         }
         int k=ConvexHull(an,n,bn);
         //cout<<"DEBUG\n";
         //for (int i=0 ;i<n ;i++) cout<<an[i].x<<" "<<an[i].y<<endl;
         Point ans=PolyGravity(bn,k);
         printf("%.3lf %.3lf\n",ans.x,ans.y);
     }
     return ;
 }