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。

 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\n";

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\n",ans.x,ans.y);

85     }

86     return 0;

87 }