Talk:Toy compression implementations

From HaskellWiki
Revision as of 13:34, 9 March 2007 by MathematicalOrchid (talk | contribs) (I'm impressed...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

Much kudos for fixing the underflow error. The new LZW implementation is much smaller, but... how in the name of God does it actually work? o_O MathematicalOrchid 11:36, 9 March 2007 (UTC)

To understand it I rewrote it a bit:

encode_LZW :: (Eq t) => [t] -> [t] -> [Int]
encode_LZW alphabet = work (map (:[]) alphabet) where
  work table []  = []
  work table lst = index : work table' rest
    where (tok, rest) = last . takeWhile ((`elem` table) . fst) . tail $ zip (inits lst) (tails lst)
          index = fromJust (elemIndex tok table)
          table' = table ++ [tok']
          tok' = tok ++ [head rest]

The idea of the the table, which is the 1st argument to 'work', is that some prefix of the input is already in the table.

(encode_LZW chars) uses 'chars' to make the initial table for the 'work' function by turning the list of characters into a list of length 1 strings.

The where (tok,rst) definition can be read right to left:

  • The zip (inits lst) (tails lst) computes every possible way to split lst input into a prefix and suffix, in increasing length of prefix.
  • The tail function just drops the head because it doesn't want to consider the length 0 prefix
  • takeWhile applies the predicate (`elem` table) to the prefix. This will always succeed on the length 1 prefix, and may find longer prefixes in the table.
  • The last function take the last prefix in the table, which will always be the longest such prefix
  • tok is this prefix, and rest is the remaining suffix to process.

Wow... a most ingenious (and inefficient) approach! Well, now it makes sense anyway. MathematicalOrchid 13:34, 9 March 2007 (UTC)