Copyright | (c) 2010 Daniel Fischer |
---|---|

License | BSD3 |

Maintainer | Daniel Fischer <daniel.is.fischer@googlemail.com> |

Stability | Provisional |

Portability | non-portable (BangPatterns) |

Safe Haskell | None |

Language | Haskell98 |

Simultaneous search for multiple patterns in a lazy `ByteString`

using the Karp-Rabin algorithm.

A description of the algorithm for a single pattern can be found at http://www-igm.univ-mlv.fr/~lecroq/string/node5.html#SECTION0050.

- indicesOfAny :: [ByteString] -> ByteString -> [(Int64, [Int])]

# Overview

The Karp-Rabin algorithm works by calculating a hash of the pattern and comparing that hash with the hash of a slice of the target string with the same length as the pattern. If the hashes are equal, the slice of the target is compared to the pattern character by character (since the hash function generally isn't injective).

For a single pattern, this tends to be more efficient than the naïve algorithm, but it cannot compete with algorithms like Knuth-Morris-Pratt or Boyer-Moore.

However, the algorithm can be generalised to search for multiple patterns
simultaneously. If the shortest pattern has length `k`

, hash the prefix of
length `k`

of all patterns and compare the hash of the target's slices of
length `k`

to them. If there's a match, check whether the slice is part
of an occurrence of the corresponding pattern.

With a hash-function that

- allows to compute the hash of one slice in constant time from the hash of the previous slice, the new and the dropped character, and
- produces few spurious matches,

searching for occurrences of any of `n`

patterns has a best-case complexity
of *O*(`targetLength`

* `lookup n`

). The worst-case complexity is
*O*(`targetLength`

* `lookup n`

* `sum patternLengths`

), the average is
not much worse than the best case.

The functions in this module store the hashes of the patterns in an
`IntMap`

, so the lookup is *O*(`log n`

). Re-hashing is done in constant
time and spurious matches of the hashes *should be* sufficiently rare.
The maximal length of the prefixes to be hashed is 32.

## Caution

Unfortunately, the constant factors are high, so these functions are slow.
Unless the number of patterns to search for is high (larger than 50 at
least), repeated search for single patterns using Boyer-Moore or DFA and
manual merging of the indices is faster. *Much* faster for less than 40
or so patterns.

`indicesOfAny`

has the advantage over multiple single-pattern searches that
it doesn't hold on to large parts of the string (which is likely to happen
for multiple searches), however, so in contrast to the strict version, it
may be useful for relatively few patterns already.

Nevertheless, this module seems more of an interesting curiosity than anything else.

# Function

:: [ByteString] | List of non-empty patterns |

-> ByteString | String to search |

-> [(Int64, [Int])] | List of matches |

finds all occurrences of any of several non-empty strict
patterns in a lazy target string. If no non-empty patterns are given,
the result is an empty list. Otherwise the result list contains
the pairs of all indices where any of the (non-empty) patterns start
and the list of all patterns starting at that index, the patterns being
represented by their (zero-based) position in the pattern list.
Empty patterns are filtered out before processing begins.`indicesOfAny`