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\n", ans);

49     }

50     

51     return 0;

52 }

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