ManyPrizes.scala

object manyPrizes {
  def getMinWin(N: Int, P: Int): Int = {
    val lastTeam = BigInt(2).pow(N).toInt - 1
    (lastTeam to (lastTeam - P + 1) by -1).map(BigInt(_).bitCount).min
  }                                               //> getMinWin: (N: Int, P: Int)Int
  
  def defeatTeamNum(numWin: Int): Int = BigInt(2).pow(numWin).toInt - 1
                                                  //> defeatTeamNum: (numWin: Int)Int
                                                  
  def maxTeamNum(N: Int, defeatNum: Int): Int = BigInt(2).pow(N).toInt - 1 - defeatNum
                                                  //> maxTeamNum: (N: Int, defeatNum: Int)Int
  
  def getLuckyTeam(N: Int, P: Int): Int = maxTeamNum(N, defeatTeamNum(getMinWin(N, P)))
                                                  //> getLuckyTeam: (N: Int, P: Int)Int
  
  def getStrongTeam(N: Int, P: Int): Int = 0      //> getStrongTeam: (N: Int, P: Int)Int
  
  getMinWin(3, 4)                                 //> res0: Int = 1
  getMinWin(3, 5)                                 //> res1: Int = 1
  getMinWin(3, 3)                                 //> res2: Int = 2
  
  defeatTeamNum(1)                                //> res3: Int = 1
  defeatTeamNum(2)                                //> res4: Int = 3
  defeatTeamNum(3)                                //> res5: Int = 7
  defeatTeamNum(4)                                //> res6: Int = 15
  
  maxTeamNum(3, 1)                                //> res7: Int = 6
  maxTeamNum(3, 3)                                //> res8: Int = 4
  maxTeamNum(3, 7)                                //> res9: Int = 0
  
  getLuckyTeam(3, 4)                              //> res10: Int = 6
  getLuckyTeam(3, 5)                              //> res11: Int = 6
  getLuckyTeam(3, 3)                              //> res12: Int = 4
}