uva 11186 Circum Triangle<叉积>

链接： http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2127

题意：圆心在原点，半径为 R 的圆，其边上有 N 个点，任意三点组成一个三角形，求三角形面积和~

思路：利用叉积求面积~暴力求三角形~

 1 #include <cstdio>
 2 #include <cmath>
 3 #include <iostream>
 4 #include <algorithm>
 5 #include <cstring>
 6 using namespace std;
 7 const double Pi=acos(-1);
 8 const double eps=1e-8; 
 9 struct Point
10 {
11     double x, y;
12     Point(){}
13     Point(double _x, double _y){
14         x=_x, y=_y;
15     }
16     inline Point operator - (const Point A)const {
17         return Point(x-A.x, y-A.y);    
18     }
19     inline double operator ^ (const Point A)const{
20         return x*A.y-y*A.x;     
21     }
22     inline double operator * (const Point A)const{
23         return x*A.x+y*A.y;    
24     }
25 }p[505];
26 double Area( Point A, Point B, Point C )
27 {
28     return  fabs(((A-B)^(A-C))/2.0);    
29 }
30 int N;
31 double r, a;
32 int main( )
33 {
34     while( scanf("%d%lf", &N, &r)!= EOF ){
35         if(N==0 && r==0)break;
36         for(int i=0; i<N; ++ i ){
37             scanf("%lf", &a);
38             p[i]=Point( r*cos(a/180.0*Pi), r*sin(a/180.0*Pi) );
39         }
40         double ans=0;
41         for( int i=0; i<N; ++ i ){
42             for( int j=i+1;j<=N; ++ j ){
43                 for( int k=j+1; k<N; ++ k ){
44                     ans+=Area( p[i], p[j], p[k] );
45                 }
46             }
47         }
48         printf("%.0lf
", ans);
49     }
50     
51     return 0;
52 }

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