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。
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<cstdlib> 5 #include<cmath> 6 #include<algorithm> 7 #define inf 0x7fffffff 8 #define exp 1e-10 9 #define PI 3.141592654 10 using namespace std; 11 const int maxn=111; 12 struct Point 13 { 14 double x,y; 15 Point (double x=0,double y=0):x(x),y(y){} 16 bool friend operator < (Point a,Point b) 17 { 18 if (a.x!=b.x) return a.x<b.x; 19 return a.y<b.y; 20 } 21 }an[maxn],bn[maxn]; 22 typedef Point Vector; 23 Vector operator + (Vector A,Vector B) {return Vector(A.x+B.x , A.y+B.y); } 24 Vector operator - (Vector A,Vector B) {return Vector(A.x-B.x , A.y-B.y); } 25 Vector operator * (Vector A,double p) {return Vector(A.x*p , A.y*p); } 26 int dcmp(double x) 27 { 28 if (fabs(x)<exp) return 0; 29 return x<0 ? -1 : 1; 30 } 31 double cross(Vector A,Vector B) 32 { 33 return A.x*B.y-B.x*A.y; 34 } 35 Point PolyGravity(Point *p,int n) 36 { 37 Point tmp,g=Point(0,0); 38 double sumArea=0,area; 39 for (int i=2 ;i<n ;i++) 40 { 41 area=cross(p[i-1]-p[0],p[i]-p[0]); 42 sumArea += area; 43 tmp.x=p[0].x+p[i-1].x+p[i].x; 44 tmp.y=p[0].y+p[i-1].y+p[i].y; 45 g.x += tmp.x*area; 46 g.y += tmp.y*area; 47 } 48 g.x /= (sumArea*3.0); 49 g.y /= (sumArea*3.0); 50 return g; 51 } 52 int ConvexHull(Point *p,int n,Point *ch) 53 { 54 sort(p,p+n); 55 int m=0; 56 for (int i=0 ;i<n ;i++) 57 { 58 while (m>1 && dcmp(cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]))<0) m--; 59 ch[m++]=p[i]; 60 } 61 int k=m; 62 for (int i=n-2 ;i>=0 ;i--) 63 { 64 while (m>k && dcmp(cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]))<0) m--; 65 ch[m++]=p[i]; 66 } 67 if (n>1) m--; 68 return m; 69 } 70 int main() 71 { 72 int n; 73 while (scanf("%d",&n)!=EOF) 74 { 75 if (n<3) break; 76 for (int i=0 ;i<n ;i++) 77 { 78 scanf("%lf%lf",&an[i].x,&an[i].y); 79 } 80 int k=ConvexHull(an,n,bn); 81 //cout<<"DEBUG "; 82 //for (int i=0 ;i<n ;i++) cout<<an[i].x<<" "<<an[i].y<<endl; 83 Point ans=PolyGravity(bn,k); 84 printf("%.3lf %.3lf ",ans.x,ans.y); 85 } 86 return 0; 87 }