lcs (empty) → 0.2
raw patch · 8 files changed
+677/−0 lines, 8 filesdep +arraydep +basebuild-type:Customsetup-changed
Dependencies added: array, base
Files
- BSD3 +26/−0
- COPYING +6/−0
- Data/List/LCS.hs +19/−0
- Data/List/LCS/HuntSzymanski.hs +213/−0
- Data/List/LCS/Simple.hs +30/−0
- GPL-2 +340/−0
- Setup.hs +8/−0
- lcs.cabal +35/−0
+ BSD3 view
@@ -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.
+ COPYING view
@@ -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.+
+ Data/List/LCS.hs view
@@ -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)+
+ Data/List/LCS/HuntSzymanski.hs view
@@ -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)+
+ Data/List/LCS/Simple.hs view
@@ -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, [])+
+ GPL-2 view
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+ Setup.hs view
@@ -0,0 +1,8 @@++module Main (main) where++import Distribution.Simple++main :: IO ()+main = defaultMain+
+ lcs.cabal view
@@ -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+