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

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

     3 

     4 // generate jar with

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

     6 

     7 object CW6a { // for purposes of generating a jar

     8 

     9 def collatz(n: Long): Long =

    10   if (n == 1) 0 else

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

    12       1 + collatz(3 * n + 1)

    13 

    14 

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

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

    17   all.maxBy(_._1)

    18 }

    19 

    20 //collatz_max(1000000)

    21 //collatz_max(10000000)

    22 //collatz_max(100000000)

    23 

    24 /* some test cases

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

    26 

    27 for (bnd <- bnds) {

    28   val (steps, max) = collatz_max(bnd)

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

    30 }

    31 

    32 */

    33 

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

    35 

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

    37 

    38 def last_odd(n: Long) : Long = 

    39   if (is_hard(n)) n else

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

    41       last_odd(3 * n + 1)

    42 

    43 

    44 //for (i <- 130 to 10000) println(s"$i: ${last_odd(i)}")

    45 for (i <- 1 to 100) println(s"$i: ${collatz(i)}")

    46 

    47 }

    48 

    49 

    50