nr-5's solution to Collatz Conjecture on the Scala track

Instructions

Test suite

Solution

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.

Examples

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

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.

Source

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

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

CollatzConjectureTest.scala

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") {
    pending
    CollatzConjecture.steps(16) should be (Some(4))
  }

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

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

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

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

object CollatzConjecture {

  def steps(number: Int): Option[Int] = {
    steps(number, 0)
  }


  def steps(number: Int, stepNr: Int): Option[Int] = {
    if (number == 1) Option(stepNr)
    else if (number <= 0) None
    else if (number % 2 == 0) steps(number / 2, stepNr + 1)
    else if (number % 3 == 0) steps(number * 3 + 1, stepNr + 1)
    else steps(number * 3 + 1, stepNr + 1)
  }

}

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to Collatz Conjecture in the Scala Track