Data.List.Zalgo.Internal

Implementation of the prefix-function on cons-cells.

prefix-function has a simple implementation using arrays, the challenge, however was to implement it on haskell lists (which are cons cells) without losing any complexity. The following code uses a tying-the-knot data passing structure, however no complicated laziness mechanisms are used: a ZState only depends on previous ZStates and therefore this algorithm can be safely implemented in a strict language with pointers.

Documentation

data ZState a

A state of the Z-function computation. zTail points to the tail of the input at the state's position, zLength is the value of the prefix-function, and zPrev is a reference to the list of ZStates starting from position described by zLength.

Constructors

ZState

Fields

zTail :: [a]

zLength :: !Int

zPrev :: [ZState a]

data GenericZState i a

ZState generalized of the number type. Nothing represents zero and is used to avoid the Eq constraint

Constructors

GenericZState

Fields

gzTail :: [a]

gzLength :: Maybe i

gzPrev :: [GenericZState i a]

zTraverse :: Eq a => [a] -> [ZState a]

O(N). Compute the list of prefix-function states for a given input.

zTraverseBy :: (a -> a -> Bool) -> [a] -> [ZState a]

O(N) and O(N) calls to the predicate. Compute the list of prefix-function states using a given equality predicate. See "Data.List.Zalgo.prefixFunBy" for a detailed explanation of what predicates are allowed.

gzTraverse :: (Num i, Eq a) => [a] -> [GenericZState i a]

O(N) and O(N) plus-1's. Compute the list of prefix-function states using a given number type.

gzTraverseBy :: Num i => (a -> a -> Bool) -> [a] -> [GenericZState i a]

O(N), O(N) calls to the predicate, and O(N) plus-1's. Compute the list of prefix-function states using a given number type and a given equality predicate.