collatz.scala

// Part 1 about the 3n+1 conjecture
//=================================

object CW6a {

  //(1) Complete the collatz function below. It should
  //    recursively calculate the number of steps needed
  //    until the collatz series reaches the number 1.
  //    If needed, you can use an auxiliary function that
  //    performs the recursion. The function should expect
  //    arguments in the range of 1 to 1 Million.

  def collatz(n: Long) : Long = {

    if(n == 1)
      1
    else {

      if(n % 2 == 1) collatz(n*3 + 1) + 1

      else collatz(n/2) + 1
    }
  }



  //(2)  Complete the collatz-bound function below. It should
  //     calculate how many steps are needed for each number
  //     from 1 up to a bound and then calculate the maximum number of
  //     steps and the corresponding number that needs that many
  //     steps. Again, you should expect bounds in the range of 1
  //     up to 1 Million. The first component of the pair is
  //     the maximum number of steps and the second is the
  //     corresponding number.

  def collatz_max(bnd: Long) : (Long, Long) = {


    val listOfCollatz = for (i<- (1 to bnd.toInt).toList) yield collatz(i.toLong)

    val maxValue = listOfCollatz.max

    val idx = listOfCollatz.indexOf(maxValue) + 1

    (maxValue, idx)
  }


}