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

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)

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)