1 // Part 1 about the 3n+1 conceture

     2 //=================================

     3 

     4 

     5 //(1) Complete the collatz function below. It should

     6 //recursively calculates the number of steps needed 

     7 //number until a series ends with 1

     8 

     9 def collatz(n: Long): List[Long] = ...

    10 

    11 

    12 // an alternative that calculates the steps directly

    13 def collatz1(n: Long): Int =

    14   if (n == 1) 1 else

    15     if (n % 2 == 0) (1 + collatz1(n / 2)) else 

    16       (1 + collatz1(3 * n + 1))

    17 

    18 

    19 //(2)

    20 def collatz_max(bnd: Int): Int = {

    21   (for (i <- 1 to bnd) yield collatz(i).length).max

    22 }

    23 

    24 

    25 val bnds = List(10, 100, 1000, 10000, 100000, 1000000, 10000000)

    26 

    27 for (bnd <- bnds) {

    28   val max = collatz_max(bnd)

    29   println(s"In the range of 1 - ${bnd} the maximum steps are ${max}")

    30 }

    31