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CraigTreptow's solution

to Collatz Conjecture in the Scala Track

Published at Apr 16 2020 · 0 comments
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:

  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.

Please see the learning and installation pages if you need any help.

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(num: Double): Option[Int] = {
    collatz(num, 0)
  }

  def collatz(n: Double, steps: Int): Option[Int] = {
    if (n == 1) { return Some(steps) }

    try {
      if (isEven(n)) {
        collatz(n / 2, steps + 1)
      } else {
        collatz((n * 3) + 1, steps + 1)
      }
    } catch {
      case _: Throwable => return None
    }
  }

  def isEven(number: Double): Boolean = { number % 2 == 0 }
}

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CraigTreptow's Reflection

I like that I know a little more about the Option type! I considered doing more of a guard clause at the top to prevent blowing up with a divide by zero, but ultimately went with the try/catch because I _think_ it is more idiomatic Scala?