diff --git a/BSD3 b/BSD3 new file mode 100644 --- /dev/null +++ b/BSD3 @@ -0,0 +1,26 @@ +Copyright (c) Ian Lynagh. +All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions +are met: +1. Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. +2. Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in the + documentation and/or other materials provided with the distribution. +3. The names of the author may not be used to endorse or promote + products derived from this software without specific prior written + permission. + +THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +SUCH DAMAGE. diff --git a/COPYING b/COPYING new file mode 100644 --- /dev/null +++ b/COPYING @@ -0,0 +1,6 @@ + +Copyright (c) Ian Lynagh, 2005, 2008. + +This package can be used under either the GPL v2, as in ./GPL-2, or the +3-clause BSD, as in ./BSD3, license. + diff --git a/Data/List/LCS.hs b/Data/List/LCS.hs new file mode 100644 --- /dev/null +++ b/Data/List/LCS.hs @@ -0,0 +1,19 @@ + +----------------------------------------------------------------------------- +-- | +-- Module : Data.List.LCS +-- Copyright : (c) Ian Lynagh 2005, 2008 +-- License : BSD or GPL v2 +-- +-- Maintainer : igloo@earth.li +-- Stability : provisional +-- Portability : non-portable (HuntSzymanski implementation is non-portable) +-- +-- Provides a function lcs that takes two lists and returns a longest common +-- sublist. For example, lcs "abcd" "acbd" is either "abd" or "acd". +----------------------------------------------------------------------------- + +module Data.List.LCS (lcs) where + +import Data.List.LCS.HuntSzymanski (lcs) + diff --git a/Data/List/LCS/HuntSzymanski.hs b/Data/List/LCS/HuntSzymanski.hs new file mode 100644 --- /dev/null +++ b/Data/List/LCS/HuntSzymanski.hs @@ -0,0 +1,213 @@ + +----------------------------------------------------------------------------- +-- | +-- Module : Data.List.LCS.HuntSzymanski +-- Copyright : (c) Ian Lynagh 2005 +-- License : BSD or GPL v2 +-- +-- Maintainer : igloo@earth.li +-- Stability : provisional +-- Portability : non-portable (uses STUArray) +-- +-- This is an implementation of the Hunt-Szymanski LCS algorithm. +-- Derived from the description in \"String searching algorithms\" by +-- Graham A Stephen, ISBN 981021829X. +----------------------------------------------------------------------------- + +module Data.List.LCS.HuntSzymanski ( + -- * Algorithm + -- $algorithm + + -- * LCS + lcs + ) where + +import System.Environment (getArgs) +import Data.Array (listArray, (!)) +import Data.Array.MArray (MArray, newArray, newArray_) +import Data.Array.Base (unsafeRead, unsafeWrite) +import Data.Array.ST (STArray, STUArray) +import Control.Monad (when) +import Control.Monad.ST (ST, runST) +import Data.List (groupBy, sort) + +{- $algorithm +We take two sequences, @xs@ and @ys@, of length @\#xs@ and @\#ys@. + +First we make an array + +> matchlist[i=0..(#xs-1)] + +such that + +> (matchlist[i] = js) => ((j `elem` js) <=> (xs !! i == ys !! j)) +> && sort js == reverse js + +i.e. @matchlist[i]@ is the indices of elements of @ys@ equal to the +ith element of @xs@, in descending order. + +Let @\#xys@ be the minimum of @\#xs@ and @\#ys@. Trivially this is the maximum +possible length of the LCS of @xs@ and @ys@. Then we can imagine an array + +> k[i=0..#xs][l=0..#xys] + +such that @k[i][l] = j@ where @j@ is the smallest value such that the +LCS of @xs[0..i]@ and @ys[0..j]@ has length @l@. We use @\#ys@ to +mean there is no such @j@. + +We will not need to whole array at once, though. Instead we use an array + +> kk[l=0..#xys] + +representing a row of @kk@ for a particular @i@. Initially it is for +@i = -1@, so @kk[0] = -1@ and @kk[l] = \#ys@ otherwise. As the algorithm +progresses we will increase @i@ by one at the outer level and compute +the replacement values for @k@'s elements. + +But we want more than just the length of the LCS, we also want the LCS +itself. Another array + +> revres[l=0..#xys] + +stores the list of @xs@ indices an LCS of length @l@, if one is known, +at @revres[l]@. + +Now, suppose @kk@ contains @k[i-1]@. We consider each @j@ in @matchlist[i]@ +in turn. We find the @l@ such that @k[l-1] < j <= k[l]@. If @j < k[l]@ then +we updated @k[l]@ to be @j@ and set @revres[l]@ to be @i:revres[l-1]@. + +Finding @l@ is basically binary search, but there are some tricks we can +do. First, as the @j@s are decreasing the last @l@ we had for this @i@ is +an upper bound on this @l@. Second, we use another array + +> lastl[j=0..#ys-1] + +to store the @l@ we got last time for this @j@, initially all @1@. As the +values in @kk[j]@ monotonically decrease this is a lower bound for @l@. +We also test to see whether this old @l@ is still @l@ before we start the +binary search. +-} + +-- |The 'lcs' function takes two lists and returns a list with a longest +-- common subsequence of the two. +lcs :: Ord a => [a] -> [a] -> [a] +-- Start off by returning the common prefix +lcs [] _ = [] +lcs _ [] = [] +lcs (c1:c1s) (c2:c2s) + | c1 == c2 = c1 : lcs c1s c2s +-- Then reverse everything, get the backwards LCS and reverse it +lcs s1 s2 = lcs_tail [] (reverse s1) (reverse s2) + +-- To get the backwards LCS, we again start off by returning the common +-- prefix (or suffix, however you want to think of it :-) ) +lcs_tail :: Ord a => [a] -> [a] -> [a] -> [a] +lcs_tail acc (c1:c1s) (c2:c2s) + | c1 == c2 = lcs_tail (c1:acc) c1s c2s +lcs_tail acc [] _ = acc +lcs_tail acc _ [] = acc +-- Then we begin the real algorithm +lcs_tail acc s1 s2 = runST (lcs' acc s1 s2) + +lcs' :: Ord a => [a] -> [a] -> [a] -> ST s [a] +lcs' acc xs ys = + do let max_xs = length xs + max_ys = length ys + minmax = max_xs `min` max_ys + -- Initialise all the arrays + matchlist <- newArray_ (0, max_xs - 1) + mk_matchlist matchlist xs ys + kk <- newArray (0, minmax) max_ys + unsafeWrite kk 0 (-1) + lastl <- newArray (0, max_ys - 1) 1 + revres <- newArray_ (0, minmax) + unsafeWrite revres 0 [] + -- Pass the buck to lcs'' to finish the job off + is <- lcs'' matchlist lastl kk revres max_xs max_ys minmax + -- Convert the list of i indices into the result sequence + let axs = listArray (0, max_xs - 1) xs + return $ map (axs !) is ++ acc + +eqFst :: Eq a => (a, b) -> (a, b) -> Bool +eqFst (x, _) (y, _) = x == y + +-- mk_matchlist fills the matchlist array such that if +-- xs !! i == ys !! j then (j+1) `elem` matchlist ! i +-- and matchlist ! i is decreasing for all i +mk_matchlist :: Ord a => STArray s Int [Int] -> [a] -> [a] -> ST s () +mk_matchlist matchlist xs ys = + do let -- xs' is a list of (string, ids with that string in xs) + xs' = map (\sns -> (fst (head sns), map snd sns)) + $ groupBy eqFst $ sort $ zip xs [0..] + -- ys' is similar, only the ids are reversed + ys' = map (\sns -> (fst (head sns), reverse $ map snd sns)) + $ groupBy eqFst $ sort $ zip ys [0..] + -- add_to_matchlist does all the hardwork + add_to_matchlist all_xs@((sx, idsx):xs'') all_ys@((sy, idsy):ys'') + = case compare sx sy of + -- If we have the same string in xs'' and ys'' then all + -- the indices in xs'' must map to the indices in ys'' + EQ -> do sequence_ [ unsafeWrite matchlist i idsy + | i <- idsx ] + add_to_matchlist xs'' ys'' + -- If the string in xs'' is smaller then there are no + -- corresponding indices in ys so we assign all the xs'' + -- indices the empty list + LT -> do sequence_ [ unsafeWrite matchlist i [] + | i <- idsx ] + add_to_matchlist xs'' all_ys + -- Otherwise the string appears in ys only, so we ignore it + GT -> do add_to_matchlist all_xs ys'' + -- If we run out of ys'' altogether then just go through putting + -- in [] for the list of indices of each index remaining in xs'' + add_to_matchlist ((_, idsx):xs'') [] + = do sequence_ [ unsafeWrite matchlist i [] | i <- idsx ] + add_to_matchlist xs'' [] + -- When we run out of xs'' we are done + add_to_matchlist [] _ = return () + -- Finally, actually call add_to_matchlist to populate matchlist + add_to_matchlist xs' ys' + +lcs'' :: STArray s Int [Int] -- matchlist + -> STUArray s Int Int -- lastl + -> STUArray s Int Int -- kk + -> STArray s Int [Int] -- revres + -> Int -> Int -> Int -> ST s [Int] +lcs'' matchlist lastl kk revres max_xs max_ys minmax = + do let -- Out the outermost level we loop over the indices i of xs + loop_i = sequence_ [ loop_j i | i <- [0..max_xs - 1] ] + -- For each i we loop over the matching indices j of elements of ys + loop_j i = do js <- unsafeRead matchlist i + with_js i js minmax + -- Deal with this i and j + with_js i (j:js) max_bound = + do x0 <- unsafeRead lastl j + l <- find_l j x0 max_bound + unsafeWrite lastl j l + vl <- unsafeRead kk l + when (j < vl) $ do + unsafeWrite kk l j + rs <- unsafeRead revres (l - 1) + unsafeWrite revres l (i:rs) + with_js i js l + with_js _ [] _ = return () + -- find_l returns the l such that kk ! (l-1) < j <= kk ! l + find_l j x0 z0 + = let f x z + | x + 1 == z = return z + | otherwise = let y = (x + z) `div` 2 + in do vy <- unsafeRead kk y + if vy < j + then f y z + else f x y + in j `seq` do q1 <- unsafeRead kk x0 + if j <= q1 + then return x0 + else f x0 z0 + -- Do the hard work + loop_i + -- Find where the result starts + succ_l <- find_l max_ys 1 (minmax + 1) + -- Get the result + unsafeRead revres (succ_l - 1) + diff --git a/Data/List/LCS/Simple.hs b/Data/List/LCS/Simple.hs new file mode 100644 --- /dev/null +++ b/Data/List/LCS/Simple.hs @@ -0,0 +1,30 @@ + +----------------------------------------------------------------------------- +-- | +-- Module : Data.List.LCS.Simple +-- Copyright : (c) Ian Lynagh 2005 +-- License : BSD or GPL v2 +-- +-- Maintainer : igloo@earth.li +-- Stability : provisional +-- Portability : portable +-- +-- This is a simple, stupid and (most of all) slow implementation of the +-- Data.List.LCS interface. +----------------------------------------------------------------------------- + +module Data.List.LCS.Simple (lcs) where + +lcs :: Ord a => [a] -> [a] -> [a] +lcs xs ys = snd $ lcs' xs ys + +lcs' :: Ord a => [a] -> [a] -> (Int, [a]) +lcs' (x:xs) (y:ys) + | x == y = case lcs' xs ys of + (len, zs) -> (len + 1, x:zs) + | otherwise = let r1@(l1, _) = lcs' (x:xs) ys + r2@(l2, _) = lcs' xs (y:ys) + in if l1 >= l2 then r1 else r2 +lcs' [] _ = (0, []) +lcs' _ [] = (0, []) + diff --git a/GPL-2 b/GPL-2 new file mode 100644 --- /dev/null +++ b/GPL-2 @@ -0,0 +1,340 @@ + GNU GENERAL PUBLIC LICENSE + Version 2, June 1991 + + Copyright (C) 1989, 1991 Free Software Foundation, Inc. + 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The licenses for most software are designed to take away your +freedom to share and change it. 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Of course, the commands you use may +be called something other than `show w' and `show c'; they could even be +mouse-clicks or menu items--whatever suits your program. + +You should also get your employer (if you work as a programmer) or your +school, if any, to sign a "copyright disclaimer" for the program, if +necessary. Here is a sample; alter the names: + + Yoyodyne, Inc., hereby disclaims all copyright interest in the program + `Gnomovision' (which makes passes at compilers) written by James Hacker. + + , 1 April 1989 + Ty Coon, President of Vice + +This General Public License does not permit incorporating your program into +proprietary programs. If your program is a subroutine library, you may +consider it more useful to permit linking proprietary applications with the +library. If this is what you want to do, use the GNU Library General +Public License instead of this License. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,8 @@ + +module Main (main) where + +import Distribution.Simple + +main :: IO () +main = defaultMain + diff --git a/lcs.cabal b/lcs.cabal new file mode 100644 --- /dev/null +++ b/lcs.cabal @@ -0,0 +1,35 @@ +Name: lcs +Version: 0.2 +License: OtherLicense +License-File: COPYING +Extra-source-files: "BSD3", "GPL-2" +Copyright: Ian Lynagh, 2005 +Author: Ian Lynagh +Maintainer: igloo@earth.li +Stability: provisional +Homepage: http://urchin.earth.li/~ian/cabal/lcs/ +Synopsis: Find longest common sublist of two lists +Description: + Provides a function lcs that takes two lists and returns a longest + common sublist. For example, lcs "abcd" "acbd" is either "abd" or + "acd". + . + The package provides a simple, stupid and (most of all) slow + implementation that needs, for inputs of length m and n, O(m+n) + space and O((m+n)!) time in the worst case. + . + It also provides an implementation of the Hunt-Szymanski LCS + algorithm, based on that in "String searching algorithms" by + Graham A Stephen, ISBN 981021829X. + . + Given inputs xs and ys of length m and n respectively, where there + are r pairs (x, y) where x is in xs, y is in ys and x == y, + Hunt-Szymanski needs O(r+m+n) space and O((r+m+n)*log(m+n)) time. + Thus this is O((m+n)^2) space and O((m+n)^2*log(m+n)) time in the + worst case. +Category: List +Tested-With: GHC==6.8.2 +Build-Depends: base, array +Exposed-modules: + Data.List.LCS, Data.List.LCS.Simple, Data.List.LCS.HuntSzymanski +