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to Collatz Conjecture in the Elm Track

Published at Jun 29 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.

Elm Installation

Refer to the Installing Elm page for information about installing elm.

Writing the Code

The first time you start an exercise, you'll need to ensure you have the appropriate dependencies installed. Thankfully, Elm makes that easy for you and will install dependencies when you try to run tests or build the code.

Execute the tests with:

$ elm-test

Automatically run tests again when you save changes:

$ elm-test --watch

As you work your way through the test suite, be sure to remove the skip <| calls from each test until you get them all passing!

Source

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

Submitting Incomplete Solutions

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

Tests.elm

module Tests exposing (tests)

import CollatzConjecture exposing (collatz)
import Expect
import Test exposing (..)


tests : Test
tests =
    describe "CollatzConjecture tests"
        [ test "zero steps for one" <|
            \() ->
                Expect.equal (Ok 0) (collatz 1)

        -- Once you get the first test passing, remove the
        -- `skip <|` (just leave the comma) on the next
        -- lines to continue!
        , skip <|
            test "divide if even" <|
                \() ->
                    Expect.equal (Ok 4) (collatz 16)
        , skip <|
            test "even and odd step" <|
                \() ->
                    Expect.equal (Ok 9) (collatz 12)
        , skip <|
            test "Large number of even and odd step" <|
                \() ->
                    Expect.equal (Ok 152) (collatz 1000000)
        , skip <|
            test "zero is an error" <|
                \() ->
                    Expect.equal (Err "Only positive numbers are allowed") (collatz 0)
        , skip <|
            test "negative values is an error" <|
                \() ->
                    Expect.equal (Err "Only positive numbers are allowed") (collatz -15)
        ]
module CollatzConjecture exposing (collatz)


collatz : Int -> Result String Int
collatz start =
    if start > 0 then
        Ok (calculate 0 start)

    else
        Err "Only positive numbers are allowed"



-- PRIVATE


calculate : Int -> Int -> Int
calculate steps int =
    if isTerminatingNumber int then
        steps

    else if isEven int then
        int
            |> nDivTwo
            |> calculate (steps + 1)

    else
        int
            |> threeNPlusOne
            |> calculate (steps + 1)


isTerminatingNumber : Int -> Bool
isTerminatingNumber int =
    int == 1


isEven : Int -> Bool
isEven int =
    modBy 2 int == 0


nDivTwo : Int -> Int
nDivTwo n =
    n // 2


threeNPlusOne : Int -> Int
threeNPlusOne n =
    3 * n + 1

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