// Basic Part about the 3n+1 conjecture

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

// generate jar with

//   > scala -d collatz.jar  collatz.scala

object CW6a { // for purposes of generating a jar

def collatz(n: Long): Long =

  if (n == 1) 0 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 <- (1L to bnd)) yield (collatz(i), i)

  all.maxBy(_._1)

}

//collatz_max(1000000)

//collatz_max(10000000)

//collatz_max(100000000)

/* some test cases

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

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}")

}

*/

def is_pow(n: Long) : Boolean = (n & (n - 1)) == 0

def is_hard(n: Long) : Boolean = is_pow(3 * n + 1)

def last_odd(n: Long) : Long = 

  if (is_hard(n)) n else

    if (n % 2 == 0) last_odd(n / 2) else 

      last_odd(3 * n + 1)

}