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hendrikniemann's solution

to All Your Base in the PureScript Track

Published at Nov 04 2018 · 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
  , toNumber
  ) where

import Prelude

import Data.Array (any, head, mapWithIndex, reverse, snoc)
import Data.Foldable (sum)
import Data.Int (pow, quot, rem)
import Data.Maybe (Maybe(..))

rebase :: Int -> Int -> Array Int -> Maybe (Array Int)
rebase curr goal numbers
  | curr <= 1 || goal <= 1  = Nothing
  | numbers == []           = Nothing
  | head numbers == Just 0  = Nothing
  | any (_ < 0) numbers     = Nothing
  | any (_ >= curr) numbers = Nothing
  | otherwise               = pure $ fromNumber goal $ toNumber curr numbers

-- | Converts an integer value into the specific numeral system
fromNumber :: Int -> Int -> Array Int
fromNumber system number = let init = quot number system in if init == 0
  then [number]
  else snoc (fromNumber system init) $ rem number system

-- | Converts a numeral system pair into an integer
toNumber :: Int -> Array Int -> Int
toNumber system =
  reverse >>>
  mapWithIndex (\index num -> num * (pow system index)) >>>
  sum

Community comments

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hendrikniemann's Reflection

This exercise was very fun but not very hard once you understand the maths underneath. Converting it first to integer and then to then target system makes things a lot easier. I am sure there is a solution where you would convert the systems directly. I don't think it will be easier to build and understand though. The verification part is very annoying. Is there a better way to do this?