ðŸŽ‰ Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io ðŸŽ‰

nicolemon's solution

to Collatz Conjecture in the Haskell Track

Published at Jul 28 2018 · 0 comments
Instructions
Test suite
Solution

Note:

This exercise has changed since this solution was written.

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.

Getting Started

For installation and learning resources, refer to the exercism help page.

Running the tests

To run the test suite, execute the following command:

``````stack test
``````

If you get an error message like this...

``````No .cabal file found in directory
``````

You are probably running an old stack version and need to upgrade it.

Otherwise, if you get an error message like this...

``````No compiler found, expected minor version match with...
Try running "stack setup" to install the correct GHC...
``````

Just do as it says and it will download and install the correct compiler version:

``````stack setup
``````

Running GHCi

If you want to play with your solution in GHCi, just run the command:

``````stack ghci
``````

Feedback, Issues, Pull Requests

The exercism/haskell repository on GitHub is the home for all of the Haskell exercises.

If you have feedback about an exercise, or want to help implementing a new one, head over there and create an issue. We'll do our best to help you!

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.

Tests.hs

``````{-# OPTIONS_GHC -fno-warn-type-defaults #-}
{-# LANGUAGE RecordWildCards #-}

import Data.Foldable     (for_)
import Test.Hspec        (Spec, describe, it, shouldBe)
import Test.Hspec.Runner (configFastFail, defaultConfig, hspecWith)

import CollatzConjecture (collatz)

main :: IO ()
main = hspecWith defaultConfig {configFastFail = True} specs

specs :: Spec
specs = describe "collatz" \$ for_ cases test
where

test Case{..} = it description assertion
where
assertion = collatz number `shouldBe` expected

data Case = Case { description :: String
, number      :: Integer
, expected    :: Maybe Integer
}

cases :: [Case]
cases = [ Case { description = "zero steps for one"
, number      = 1
, expected    = Just 0
}
, Case { description = "divide if even"
, number      = 16
, expected    = Just 4
}
, Case { description = "even and odd steps"
, number      = 12
, expected    = Just 9
}
, Case { description = "Large number of even and odd steps"
, number      = 1000000
, expected    = Just 152
}
, Case { description = "zero is an error"
, number      = 0
, expected    = Nothing
}
, Case { description = "negative value is an error"
, number      = -15
, expected    = Nothing
}
]``````
``````module CollatzConjecture (collatz) where

collatz :: Integer -> Maybe Integer
collatz n
| n <= 0    = Nothing
| otherwise = Just (collatz' n)

collatz' :: Integer -> Integer
collatz' 1 = 0
collatz' n
| even n = 1 + collatz' (div n 2)
| odd n = 1 + collatz' (3 * n + 1)``````