-----------------------------------------------------------------------------
-- |
-- Module : Codec.Gray
-- Copyright : (c) Amy de Buitléir 2011-2012
-- License : BSD-style
-- Maintainer : amy@nualeargais.ie
-- Stability : experimental
-- Portability : portable
--
-- Gray encoding schemes. A Gray code is a list of values such that two
-- successive values differ in only one digit. Usually the term /Gray code/
-- refers to the Binary Reflected Gray code (BRGC), but non-binary Gray codes
-- have also been discovered. Some Gray codes are also /cyclic/: the last and
-- first values differ in only one digit.
--
-----------------------------------------------------------------------------
{-# LANGUAGE UnicodeSyntax #-}
module Codec.Gray
(
grayCodes,
naryGrayCodes
) where
import Data.List (foldl')
-- | @'grayCodes' k@ generates the list of Binary Reflected Gray Code (BRGC)
-- numbers of length k. This code is cyclic.
grayCodes ∷ Int → [[Bool]]
grayCodes 0 = [[]]
grayCodes k =
let xs = grayCodes (k-1) in map (False:) xs ++ map (True:) (reverse xs)
-- | @'naryGrayCodes' xs k@ generates a non-Boolean (or n-ary) Gray code of
-- length @k@ using the elements of @x@ as "digits". This code is cyclic.
--
-- Ex: @'naryGrayCodes' "012" 4@ generates a ternary Gray code that is
-- four digits long.
naryGrayCodes ∷ [a] → Int → [[a]]
naryGrayCodes xs 1 = map (\x → [x]) xs
naryGrayCodes xs k = snd $ foldl' prefixAndShift (ys,[]) xs'
where ys = naryGrayCodes xs 1
xs' = naryGrayCodes xs (k-1)
-- | Shift elements right.
shift ∷ [a] → [a]
shift as = last as : init as
prefixAndShift ∷ ([[a]],[[a]]) → [a] → ([[a]],[[a]])
prefixAndShift (ys,zs) xs = (shift ys, zs ++ (map (xs++) ys))