Copyright  (C) 2015 mniip 

License  BSD3 
Maintainer  mniip <mniip@mniip.com> 
Stability  experimental 
Portability  portable 
Safe Haskell  Safe 
Language  Haskell2010 
Implementation of the prefixfunction on conscells.
prefixfunction 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 tyingtheknot data passing
structure, however no complicated laziness mechanisms are used: a KmpState
only depends on previous KmpState
s and therefore this algorithm can be
safely implemented in a strict language using pointers.
 data KmpState a = KmpState {}
 data GenericKmpState i a = GenericKmpState {
 gKmpTail :: [a]
 gKmpLength :: Maybe i
 gKmpPrev :: [GenericKmpState i a]
 kmpTraverse :: Eq a => [a] > [KmpState a]
 kmpTraverseBy :: (a > a > Bool) > [a] > [KmpState a]
 gKmpTraverse :: (Num i, Eq a) => [a] > [GenericKmpState i a]
 gKmpTraverseBy :: Num i => (a > a > Bool) > [a] > [GenericKmpState i a]
Documentation
data GenericKmpState i a Source
KmpState
generalized over the number type. Nothing
represents zero and
is used to avoid the Eq
constraint
GenericKmpState  

kmpTraverse :: Eq a => [a] > [KmpState a] Source
O(N). Compute the list of prefixfunction states for a given input.
kmpTraverseBy :: (a > a > Bool) > [a] > [KmpState a] Source
O(N) and O(N) calls to the predicate. Compute the list of prefixfunction
states using a given equality predicate. See prefixFunBy
for a detailed explanation of what predicates are allowed.
gKmpTraverse :: (Num i, Eq a) => [a] > [GenericKmpState i a] Source
O(N) and O(N) plus1's. Compute the list of prefixfunction states using a given number type.
gKmpTraverseBy :: Num i => (a > a > Bool) > [a] > [GenericKmpState i a] Source
O(N), O(N) calls to the predicate, and O(N) plus1's. Compute the list of prefixfunction states using a given number type and a given equality predicate.