// Part 1

//(1)

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

  if (n == 1) List(1) else

    if (n % 2 == 0) (n::collatz(n / 2)) else 

      (n::collatz(3 * n + 1))

// an alternative that calculates the steps directly

def collatz1(n: Long): Int =

  if (n == 1) 1 else

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

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

//(2)

def collatz_max(bnd: Int): Int = {

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

}

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

for (bnd <- bnds) {

  val max = collatz_max(bnd)

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

}