Problem:
Score : 600 points

Problem Statement

Given are N points (x_i, y_i) in a two-dimensional plane.

Find the minimum radius of a circle such that all the points are inside or on it.

Constraints

2 \leq N \leq 50

0 \leq x_i \leq 1000

0 \leq y_i \leq 1000

The given N points are all different.

The values in input are all integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the minimum radius of a circle such that all the N points are inside or on it.

Your output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

Both points are contained in the circle centered at (0.5,0) with a radius of 0.5.

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

Sample Output 3

6.726812023536805158

If the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define ll long long int

using namespace std;

const ll mod=1000000007;
const ll inf=1e18;

int main(){

  ll n;
  cin >> n;

  double x[n],y[n];
  for(ll i=0;i<n;i++)cin >> x[i] >> y[i];

  double a[4],b[4];
  a[0]=0;
  b[0]=0;
  a[1]=1000;
  b[1]=0;
  a[2]=1000;
  b[2]=1000;
  a[3]=0;
  b[3]=1000;

  ll c=0;

  while(abs(a[0]-a[1])>0.0000000001){
    double d[4]={};
    for(ll i=0;i<4;i++){
      for(ll j=0;j<n;j++){
        d[i]=max(d[i],(a[i]-x[j])*(a[i]-x[j])+(b[i]-y[j])*(b[i]-y[j]));
      }
    }

    double e=min(d[0],min(d[1],min(d[2],d[3])));

    //if(a[1]<=1 && a[1]>=0.2)cout << a[1] <<" "<< b[1] << " " << e << " " << d[1] << endl;

    //cout <<c<<" "<< a[0] <<" "<< b[0] << " " << a[2] << " "<<b[2] << endl;

    double q,r;
    q=100;
    r=99;

    if(e==d[0]){
      ll p=0;
      for(ll i=0;i<4;i++){
        a[i]=(r*a[i]+a[p])/q;
        b[i]=(r*b[i]+b[p])/q;
      }
    }
    else if(e==d[1]){
      ll p=1;
      for(ll i=0;i<4;i++){
        a[i]=(r*a[i]+a[p])/q;
        b[i]=(r*b[i]+b[p])/q;
      }
    }
    else if(e==d[2]){
      ll p=2;
      for(ll i=0;i<4;i++){
        a[i]=(r*a[i]+a[p])/q;
        b[i]=(r*b[i]+b[p])/q;
      }
    }
    else{
      ll p=3;
      for(ll i=0;i<4;i++){
        a[i]=(r*a[i]+a[p])/q;
        b[i]=(r*b[i]+b[p])/q;
      }
    }
    c++;

  }

  //cout << a[0]<< " " <<b[0] << endl;

  double d;
  for(ll i=0;i<n;i++){
    d=max(d,sqrt((a[1]-x[i])*(a[1]-x[i])+(b[1]-y[i])*(b[1]-y[i])));
  }

  printf("%.12f",d);

}