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 ($n \le 100$) 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 }

 

posted @ 2014-08-22 00:29  huangxf  阅读(379)  评论(0)  编辑  收藏  举报