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## to Collatz Conjecture in the Scala Track

Published at Aug 16 2019 · 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.

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)
}
}``````
``````import scala.annotation.tailrec

object CollatzConjecture {
@tailrec
def steps(number: Int, stepCount: Int = 0): Any =
number match {
case x if x < 1 => None
case 1 => Some(stepCount)
case x if x % 2 == 0 => steps(x / 2, stepCount + 1)
case x => steps(3 * x + 1, stepCount + 1)
}
}

// original https://exercism.io/tracks/scala/exercises/collatz-conjecture/solutions/8fc23cfec5684080b5abe04df2e41400
//object CollatzConjecture {
//  def steps(n: Int): Option[Int] = {
//    loop(n, 0)
//  }
//
//  @tailrec
//  private def loop(n: Int, count: Int): Option[Int] = n match {
//    case 1 => Some(count)
//    case NonPositive(_) => None
//    case Even(_) => loop(n / 2, count + 1)
//    case Odd(_) => loop(3 * n + 1, count + 1)
//  }
//}
//
//object Even {
//  def unapply(n: Int) = {
//    if (n % 2 == 0) Some(n) else None
//  }
//}
//
//object Odd {
//  def unapply(n: Int) = {
//    if (n % 2 == 1) Some(n) else None
//  }
//}
//
//object NonPositive {
//  def unapply(n: Int) = {
//    if (n < 1) Some(n) else None
//  }
//}

// my original first solution
//object CollatzConjecture {
//  def steps(num: Int): Option[Int] = {
//    def count(p: Int): Int = p match {
//      case 0 => 0
//      case 1 => 0
//      case `p` => 1 + count(next(p))
//    }
//
//    def next(p: Int): Int = p % 2 match {
//      case 1 =>
//        println(s"0 \$p")
//        p * 3 + 1
//      case 0 =>
//        println(s"0 \$p")
//        p / 2
//    }
//
//    num > 0 match {
//      case false => None
//      case true => Some(count(num))
//    }
//  }
//}``````