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:
Resulting in 9 steps. So for input n = 12, the return value would be 9.
Refer to the Installing Elm page for information about installing elm.
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:
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
calls from each test until you get them all passing!
An unsolved problem in mathematics named after mathematician Lothar Collatz https://en.wikipedia.org/wiki/3x_%2B_1_problem
It is possible to submit an incomplete solution so you can see how others have completed the exercise.
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
A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.
Here are some questions to help you reflect on this solution and learn the most from it.