Data.Algorithms.KMP

This module implements the Knuth-Morris-Pratt algorithm. It can search a word in a text in O(m+n) time, where m and n are the length of the word and the text.

This module can apply on any list of instance of Eq.

Donald Knuth; James H. Morris, Jr, Vaughan Pratt (1977). Fast pattern matching in strings. SIAM Journal on Computing 6 (2): 323-350. doi:10.1137/0206024

Sample usage:

 let
   word = "abababcaba"
   text = "abababababcabababcababbb"
   kmpTable = build word
   result = match kmpTable text
   -- the result should be [4, 11]

Documentation

data Table a

The solid data type of KMP table

type MatchState = Int

build :: Eq a => [a] -> Table a

The build function eats a pattern (list of some Eq) and generates a KMP table.

The time and space complexities are both O(length of the pattern)

matchSingle :: Eq a => Table a -> MatchState -> a -> (Bool, MatchState)

The matchSingle function takes the KMP table, the current state of the matching and the next element in the sequence and returns whether it finished a matching sequence along with the new state. This is useful if your input doesn't come in a list or you need other flexibilities.

The matching state is just an integer representing how long of a pattern prefix has been matched already. Therefore the initial state should be 0 if you start with an empty sequence.

match :: Eq a => Table a -> [a] -> [Int]

The match function takes the KMP table and a list to be searched (might be infinite) and then generates the search results as a list of every matched begining (might be infinite).

The time complexity is O(length of the pattern + length of the searched list)