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 Scala (2.11.7) (judge verdict: Accepted)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}
import scala.collection.mutable.{Map, Stack, Queue, PriorityQueue, Set}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  val N = in.next().toInt
  val coords = new Array[(Double, Double)](N)
  for (i <- 0 until N) {
    val x, y = in.next().toDouble
    coords(i) = (x, y)
  }

  def getDist(p1: (Double, Double), p2: (Double, Double)): Double = {
    import Math.{pow, sqrt}
    sqrt(pow(p1._1 - p2._1, 2) + pow(p1._2 - p2._2, 2))
  }

  def getValue(s: Double, g: Double, d: Double): Double = {
    val move = (s-g).abs * d

    if (s > g)
      s - move
    else
      s + move
  }

  var now = (500.0, 500.0)
  var d = 1.0
  while (d > 1e-7) {
    val (nx, ny) =
      coords
        .map(pos => (getDist(now, pos), pos))
        .sorted.reverse
        .head._2

    now = (getValue(now._1, nx, d), getValue(now._2, ny, d))
    d *= 0.999
  }

  val ans =
    coords
      .map(pos => getDist(now, pos))
      .sorted.reverse
      .head

  println(ans)
}

object Sub {
  def print2DimArray[A](mat: Array[Array[A]]): Unit = {
    mat.foreach(lin => println(lin.toList))
  }
}

class InputReader(stream: InputStream) {
  private[this] val reader = new BufferedReader(new InputStreamReader(stream))
  private[this] var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}