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

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

object C1 {

// ADD YOUR CODE BELOW

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

// test1 7 Nov

// test2

// test3

// test4

//(1) 

def collatz(n: Long) : Long = 

  if (n == 1) 0 else

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

      1 + collatz(3 * n + 1)

//(2) 

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

//  val all = for (i <- (1L to bnd)) yield (collatz(i), i)

//  all.maxBy(_._1)

//}

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

  val all = for (i <- (1L to bnd)) yield (collatz(i), i)

  all.maxBy(_._1)

}

//(3)

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

def is_hard(n: Long) : Boolean = is_pow_of_two(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)

}

// This template code is subject to copyright 

// by King's College London, 2022. Do not 

// make the template code public in any shape 

// or form, and do not exchange it with other 

// students under any circumstance.