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JohnMToal's solution

to Collatz Conjecture in the Scala Track

Published at Sep 10 2019 · 0 comments
Test suite

The Collatz Conjecture or 3x+1 problem can be summarized as follows:

Take any positive integer n. If n is even, divide n by 2 to get n / 2. If n is odd, multiply n by 3 and add 1 to get 3n + 1. Repeat the process indefinitely. The conjecture states that no matter which number you start with, you will always reach 1 eventually.

Given a number n, return the number of steps required to reach 1.


Starting with n = 12, the steps would be as follows:

  1. 12
  2. 6
  3. 3
  4. 10
  5. 5
  6. 16
  7. 8
  8. 4
  9. 2
  10. 1

Resulting in 9 steps. So for input n = 12, the return value would be 9.

The Scala exercises assume an SBT project scheme. The exercise solution source should be placed within the exercise directory/src/main/scala. The exercise unit tests can be found within the exercise directory/src/test/scala.

To run the tests simply run the command sbt test in the exercise directory.

For more detailed info about the Scala track see the help page.


An unsolved problem in mathematics named after mathematician Lothar Collatz https://en.wikipedia.org/wiki/3x_%2B_1_problem

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import org.scalatest.{Matchers, FunSuite}

/** @version 1.2.0 */
class CollatzConjectureTest extends FunSuite with Matchers {

  test("zero steps for one") {
    CollatzConjecture.steps(1) should be (Some(0))

  test("divide if even") {
    CollatzConjecture.steps(16) should be (Some(4))

  test("even and odd steps") {
    CollatzConjecture.steps(12) should be (Some(9))

  test("Large number of even and odd steps") {
    CollatzConjecture.steps(1000000) should be (Some(152))

  test("zero is an error") {
    CollatzConjecture.steps(0) should be (None)

  test("negative value is an error") {
    CollatzConjecture.steps(-15) should be (None)
object CollatzConjecture {

  def steps(input: Int): Option[Int] = {
    input match {
      case input if(input > 1) => calcSteps(input, 0)
      case 1 => Some(0)
      case _ => None

  def calcSteps(input: Int, stepCount: Int): Option[Int] = {
    input match {
      case input if(input%2 == 0) => calcSteps(input/2, stepCount+1)
      case input if(input%2 != 0 && input > 1) => calcSteps((input*3)+1, stepCount+1)
      case _ => Some(stepCount)

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