// Part 1 about the 3n+1 conjecture

//==================================

object CW6a {

def collatz(n: Long): Long =

  if (n == 1) 1 else

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

      1 + collatz(3 * n + 1)

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

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

  val max = all.max

  (max, all.indexOf(max) + 1)

}

// some testing harness...5 Mio pushes the envelope

val bnds = List(2, 10, 100, 1000, 10000, 100000, 

		77000, 90000, 1000000, 5000000)

for (bnd <- bnds) {

  val (steps, max) = collatz_max(bnd)

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

}

}