Published at Jun 29 2019
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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.

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

- 12
- 6
- 3
- 10
- 5
- 16
- 8
- 4
- 2
- 1

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:

```
$ 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!

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.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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