skywalker

#include<stdio.h>
#include<math.h>

struct pointset
{
 double x,y;
};

const int MAXN=100;
const double precison=1.0e-8;
pointset maxcic, point[MAXN];;
double radius;
int curset[MAXN],posset[3];
int set_cnt,pos_cnt;

inline double dis_2(pointset& from,pointset& to)
{
 return ((from.x-to.x)*(from.x-to.x)+(from.y-to.y)*(from.y-to.y));
}

int in_cic(int pt)
{
 if(sqrt(dis_2(maxcic,point[pt]))<radius+precison) return 1;
 return 0;
}

int  cal_mincic()
{
 if(pos_cnt==1||pos_cnt==0)
  return 0;
 else if(pos_cnt==3) 
 {
  double A1,B1,C1,A2,B2,C2;
  int t0=posset[0],t1=posset[1],t2=posset[2];
  A1=2*(point[t1].x-point[t0].x);
  B1=2*(point[t1].y-point[t0].y);
  C1=point[t1].x*point[t1].x-point[t0].x*point[t0].x
   +point[t1].y*point[t1].y-point[t0].y*point[t0].y;
  A2=2*(point[t2].x-point[t0].x);
  B2=2*(point[t2].y-point[t0].y);
  C2=point[t2].x*point[t2].x-point[t0].x*point[t0].x
   +point[t2].y*point[t2].y-point[t0].y*point[t0].y;
  maxcic.y=(C1*A2-C2*A1)/(A2*B1-A1*B2);
  maxcic.x=(C1*B2-C2*B1)/(A1*B2-A2*B1);
  radius=sqrt(dis_2(maxcic,point[t0]));

 }
 else if(pos_cnt==2)
 {
  maxcic.x=(point[posset[0]].x+point[posset[1]].x)/2;
  maxcic.y=(point[posset[0]].y+point[posset[1]].y)/2;
  radius=sqrt(dis_2(point[posset[0]],point[posset[1]]))/2;
 }
 return 1;
}

int mindisk()
{
 if(set_cnt==0||pos_cnt==3) 
 {
  return cal_mincic();  
 }

 int tt=curset[--set_cnt];
 int res=mindisk();
 set_cnt++;

 if(!res||!in_cic(tt)) 
 {
  set_cnt--;
  posset[pos_cnt++]=curset[set_cnt];
  res=mindisk();
  pos_cnt--;
  curset[set_cnt++]=curset[0];
  curset[0]=tt;
 }

 return res;
}

int main()
{
 int n;

 while(scanf("%d",&n)!=EOF)
 {
  if(n==0)
   break;

  int i; 

  for(i=0;i<n;i++)
   scanf("%lf%lf",&point[i].x,&point[i].y);

  if(n==1)
  {
   maxcic.x=point[0].x;maxcic.y=point[0].y;
   radius=0;
   printf("%.2lf %.2lf %.2lf\n",maxcic.x,maxcic.y,radius);
   continue;
  }

  set_cnt=n;pos_cnt=0;
  for(i=0;i<n;i++) 
   curset[i]=i;

  mindisk();
  printf("%.2lf %.2lf %.2lf\n",maxcic.x,maxcic.y,radius);
 }

 return 0;
}