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~

#include <cstdio>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
const double Pi=acos(-1);
const double eps=1e-8; 
struct Point
{
    double x, y;
    Point(){}
    Point(double _x, double _y){
        x=_x, y=_y;
    }
    inline Point operator - (const Point A)const {
        return Point(x-A.x, y-A.y);    
    }
    inline double operator ^ (const Point A)const{
        return x*A.y-y*A.x;     
    }
    inline double operator * (const Point A)const{
        return x*A.x+y*A.y;    
    }
}p[505];
double Area( Point A, Point B, Point C )
{
    return  fabs(((A-B)^(A-C))/2.0);    
}
int N;
double r, a;
int main( )
{
    while( scanf("%d%lf", &N, &r)!= EOF ){
        if(N==0 && r==0)break;
        for(int i=0; i<N; ++ i ){
            scanf("%lf", &a);
            p[i]=Point( r*cos(a/180.0*Pi), r*sin(a/180.0*Pi) );
        }
        double ans=0;
        for( int i=0; i<N; ++ i ){
            for( int j=i+1;j<=N; ++ j ){
                for( int k=j+1; k<N; ++ k ){
                    ans+=Area( p[i], p[j], p[k] );
                }
            }
        }
        printf("%.0lf
", ans);
    }
    
    return 0;
}