100 Prisoners problem simulation

IBSim.scala

import scala.collection.immutable.TreeMap
import scala.util.Random

/* 100 prisoners problem - simulation of various strategies
 * Decription at:
 *     - http://en.m.wikipedia.org/wiki/100_prisoners_problem
 *     - https://www.youtube.com/watch?v=eivGlBKlK6M
 */

object IBSim {
  /* Configuration */
  val n = 100
  val pickCount = (n / 2.0).toInt
  /* ------------- */
  val nums = (1 to n).toList

  def main(args: Array[String]) {
    val trialsCount = 10000
    testStrategy("Cheat", CheatStrategy.apply, 10)
    testStrategy("Random Pick", RandomPickStrategy.apply, trialsCount)
    testStrategy("Correlated Pick", CorrelatedPickStrategy.apply, trialsCount)
    testStrategy("Traverse Pick", TraversePickStrategy.apply, trialsCount)
  }

  def testStrategy(strategyName: String, strategy: (Map[Int, Int] => Boolean), trialsCount: Int) = {
    var wins = 0
    for (_ <- 1 to trialsCount) {
      val boxes = TreeMap.empty[Int, Int] ++ nums.zip(Random shuffle nums)
      if (strategy(boxes)) wins += 1
    }

    val proc = (wins / trialsCount.toDouble) * 100
    println(s"$strategyName Strategy\nWins = $wins\nEfficiency = $proc%\n")
  }

  object CheatStrategy {
    def apply(boxes: Map[Int, Int]) = {
      val isFoundOwnNumber = nums map {
        num =>
          val pickedBoxed = Random shuffle nums
          (pickedBoxed map boxes) contains num
      }
      isFoundOwnNumber forall (_ == true)
    }
  }

  object RandomPickStrategy {
    def apply(boxes: Map[Int, Int]) = {
      val isFoundOwnNumber = nums map {
        num =>
          val pickedBoxed = (Random shuffle nums) take pickCount
          (pickedBoxed map boxes) contains num
      }
      isFoundOwnNumber forall (_ == true)
    }
  }

  object CorrelatedPickStrategy {
    def apply(boxes: Map[Int, Int]) = {
      val isFoundOwnNumber = nums map {
        num =>
          val pickedBoxed = (nums ++ nums).drop(num - 1).take(pickCount)
          (pickedBoxed map boxes) contains num
      }
      isFoundOwnNumber forall (_ == true)
    }
  }

  object TraversePickStrategy {
    def apply(boxes: Map[Int, Int]) = {
      val isFoundOwnNumber = nums map {
        num =>
          var picks = List.empty[Int]
          var next = num
          for (i <- 1 to pickCount) {
            val pick = boxes(next)
            picks = pick :: picks
            next = pick
          }
          picks.contains(num)
      }
      isFoundOwnNumber forall (_ == true)
    }
  }

}