🎉 Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io 🎉
Avatar of aimorris

aimorris's solution

to All Your Base in the PureScript Track

Published at Jan 21 2020 · 0 comments
Instructions
Test suite
Solution

Convert a number, represented as a sequence of digits in one base, to any other base.

Implement general base conversion. Given a number in base a, represented as a sequence of digits, convert it to base b.

Note

  • Try to implement the conversion yourself. Do not use something else to perform the conversion for you.

About Positional Notation

In positional notation, a number in base b can be understood as a linear combination of powers of b.

The number 42, in base 10, means:

(4 * 10^1) + (2 * 10^0)

The number 101010, in base 2, means:

(1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0)

The number 1120, in base 3, means:

(1 * 3^3) + (1 * 3^2) + (2 * 3^1) + (0 * 3^0)

I think you got the idea!

Yes. Those three numbers above are exactly the same. Congratulations!

Submitting Incomplete Solutions

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

Main.purs

module Test.Main where

import Prelude

import Effect (Effect)
import Data.Maybe (Maybe(..))
import Test.Unit.Assert as Assert
import Test.Unit (TestSuite, suite, test)
import Test.Unit.Main (runTest)
import AllYourBase (rebase)

main :: Effect Unit
main = runTest suites

suites :: TestSuite
suites = do
  suite "AllYourBase.rebase" do

    test "single bit one to decimal" $
      Assert.equal (Just [1])
                   (rebase 2 10 [1])

    test "binary to single decimal" $
      Assert.equal (Just [5])
                   (rebase 2 10 [1,0,1])

    test "single decimal to binary" $
      Assert.equal (Just [1,0,1])
                   (rebase 10 2 [5])

    test "binary to multiple decimal" $
      Assert.equal (Just [4,2])
                   (rebase 2 10 [1,0,1,0,1,0])

    test "decimal to binary" $
      Assert.equal (Just [1,0,1,0,1,0])
                   (rebase 10 2 [4,2])

    test "trinary to hexadecimal" $
      Assert.equal (Just [2,10])
                   (rebase 3 16 [1,1,2,0])

    test "hexadecimal to trinary" $
      Assert.equal (Just [1,1,2,0])
                   (rebase 16 3 [2,10])

    test "15-bit integer" $
      Assert.equal (Just [6,10,45])
                   (rebase 97 73 [3,46,60])

    test "empty list" $
      Assert.equal Nothing
                   (rebase 2 10 [])

    test "single zero" $
      Assert.equal Nothing
                   (rebase 10 2 [0])

    test "multiple zeros" $
      Assert.equal Nothing
                   (rebase 10 2 [0,0,0])

    test "leading zeros" $
      Assert.equal Nothing
                   (rebase 7 10 [0,6,0])

    test "negative digit" $
      Assert.equal Nothing
                   (rebase 2 10 [1,-1,1,0,1,0])

    test "invalid positive digit" $
      Assert.equal Nothing
                   (rebase 2 10 [1,2,1,0,1,0])

    test "first base is one" $
      Assert.equal Nothing
                   (rebase 1 10 [])

    test "second base is one" $
      Assert.equal Nothing
                   (rebase 2 1 [1,0,1,0,1,0])

    test "first base is zero" $
      Assert.equal Nothing
                   (rebase 0 10 [])

    test "second base is zero" $
      Assert.equal Nothing
                   (rebase 10 0 [7])

    test "first base is negative" $
      Assert.equal Nothing
                   (rebase (-2) 10 [1])

    test "second base is negative" $
      Assert.equal Nothing
                   (rebase 2 (-7) [1])

    test "both bases are negative" $
      Assert.equal Nothing
                   (rebase (-2) (-7) [1])
module AllYourBase (rebase) where

import Data.Maybe (Maybe (..))
import Data.Array (head, mapWithIndex, reverse, snoc)
import Prelude (otherwise, pure, ($), (*), (<), (<<<), (==), (>=), (||))
import Data.Foldable (any, sum)
import Data.Int (pow, quot, rem)

type Base = Int

rebase :: Base -> Base -> Array Int -> Maybe (Array Int)
rebase b1 b2 num
  | b1 < 2 || b2 < 2 = Nothing
  | num == [] = Nothing
  | head num == Just 0 = Nothing
  | any (_ < 0) num = Nothing
  | any (_ >= b1) num = Nothing
  | otherwise = pure $ fromInt b2 $ toInt b1 num

toInt :: Base -> Array Int -> Int
toInt b = sum <<< mapWithIndex power <<< reverse
  where power i x = (pow b i) * x

fromInt :: Base -> Int -> Array Int
fromInt b num =
  let
    quotNum = quot num b
  in
    if quotNum == 0
      then [num]
      else snoc (fromInt b quotNum) (rem num b)

Community comments

Find this solution interesting? Ask the author a question to learn more.

What can you learn from this solution?

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?