# Talk:Toy compression implementations

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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)