最小覆盖圆

给你n个点，求一个最小的圆把所有点覆盖。 hdu3007

----------摘自顾研的《浅谈随机化思想在几何问题中的应用》

const  int  maxn = 508 ;const  double  eps = 1e-8 ;int    dcmp(double x){       if(fabs(x) < eps)  return 0 ;       if(x > 0)  return 1 ;       return -1 ;}struct point{       double x , y ;       point(){}       point(double x , double y){            this->x = x ;            this->y = y ;       }       friend point operator - (const point &a , const point &b){            return  point(a.x-b.x , a.y-b.y) ;       }       double dist(){            return sqrt(x*x + y*y) ;       }};/*三角形（p0 , p1 , p2）外接圆圆心cp*/void  circle_center(point p0 , point p1 , point p2 , point &cp){      double a1 = p1.x-p0.x , b1 = p1.y-p0.y , c1 = (a1*a1+b1*b1)/2 ;      double a2 = p2.x-p0.x , b2 = p2.y-p0.y , c2 = (a2*a2+b2*b2)/2 ;      double d  = a1 * b2 - a2 * b1 ;      cp.x = p0.x + (c1*b2 - c2*b1) / d ;      cp.y = p0.y + (a1*c2 - a2*c1) / d ;}void  circle_center(point p0 , point p1 , point &cp){      cp.x = (p0.x + p1.x) / 2 ;      cp.y = (p0.y + p1.y) / 2 ;}point center ;double radius ;bool  point_in(const point &p){      return dcmp((p - center).dist() - radius) < 0 ;}int   n ; point a[maxn] ;void  min_circle_cover(){      std::random_shuffle(a , a+n) ; // 打乱顺序      radius = 0 ;      center = a[0] ;      for(int i = 1 ; i < n ; i++) if(! point_in(a[i])){           center = a[i] ; radius = 0 ;           for(int j = 0 ; j < i ; j++) if(! point_in(a[j])){               circle_center(a[i] , a[j] , center) ;               radius = (a[j] - center).dist() ;               for(int k = 0 ; k < j ; k++) if(! point_in(a[k])){                  circle_center(a[i] , a[j] , a[k] , center) ;                  radius = (a[k] - center).dist() ;               }           }      }}int  main(){     int i ;     while(cin>>n && n){          for(i = 0 ; i < n ; i++) scanf("%lf%lf" ,&a[i].x , &a[i].y) ;          min_circle_cover() ;          printf("%.2lf %.2lf %.2lf\n" , center.x , center.y , radius) ;     }     return 0 ;}洗牌函数 random_shuffle(p, p + n);