%  Copyright (C) 2002 David Roundy
%  Copyright (C) 2005 Benedikt Schmidt
%
%  This program is free software; you can redistribute it and/or modify
%  it under the terms of the GNU General Public License as published by
%  the Free Software Foundation; either version 2, or (at your option)
%  any later version.
%
%  This program is distributed in the hope that it will be useful,
%  but WITHOUT ANY WARRANTY; without even the implied warranty of
%  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%  GNU General Public License for more details.
%
%  You should have received a copy of the GNU General Public License
%  along with this program; see the file COPYING.  If not, write to
%  the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
%  Boston, MA 02110-1301, USA.

\chapter{LCS}

\section{Introduction}
``LCS'' stands for ``Longest Common Subsequence,'' and it is a relatively
challenging problem to find an LCS efficiently.  This module implements
the algorithm described in:
   "An O(ND) Difference Algorithm and its Variations", Eugene Myers,
   Algorithmica Vol. 1 No. 2, 1986, pp. 251-266;
especially the variation described in section 4.2 and most refinements
implemented in GNU diff (D is the edit-distance).
There is currently no heuristic to reduce the running time and produce
suboptimal output for large inputs with many differences. It behaves like
GNU diff with the -d option in this regard.

\begin{code}
{-# OPTIONS_GHC -cpp #-}
module Lcs ( getChanges, aLen,
             BArray, PArray, BSTArray,
             shiftBoundaries ) where

import Control.Monad
import Data.Int
import Control.Monad.ST
import Data.Maybe
import FastPackedString
import Data.Array.Base
import Data.Array.Unboxed
import qualified Data.Map as Map ( lookup, empty, insertWith )
#include "impossible.h"

\end{code}

In the first step, a hash value for every line is calculated and collisions
are marked with a special value. This reduces a string comparison to an
int comparison for line tuples where at least one of the hash values is
not equal to the special value. After that, lines which only exists in one
of the files are removed and marked as changed which reduces the running
time of the following difference algorithm. GNU diff additionally removes
lines that appear very often in the other file in some cases.
The last step tries to create longer changed regions and line up deletions
in the first file to insertions in the second by shifting changed lines
forward and backward.  

\begin{code}
-- | create a list of changes between a and b, each change has the form
--   (starta, lima, startb, limb) which means that a[starta, lima)
--   has to be replaced by b[startb, limb)
getChanges ::  [PackedString] -> [PackedString]
           -> [(Int,[PackedString],[PackedString])]
getChanges a b = dropStart (initP a) (initP b) 1

dropStart ::  PArray -> PArray -> Int
           -> [(Int,[PackedString],[PackedString])]
dropStart a b off
  | off > (aLen a) = [(off - 1, [], getSlice b off (aLen b))]
  | off > (aLen b) = [(off - 1, getSlice a off (aLen a), [])]
  | a!off == b!off = dropStart a b (off + 1)
  | otherwise      = dropEnd a b off 0

dropEnd ::  PArray -> PArray -> Int -> Int
        -> [(Int,[PackedString],[PackedString])]
dropEnd a b off end
    | off > alast        = [(off - 1, [], getSlice b off blast)]
    | off > blast        = [(off - 1, getSlice a off alast, [])]
    | a!alast == b!blast = dropEnd a b off (end + 1)
    | otherwise          = getChanges' (a, (off, alast)) (b, (off, blast))
  where alast = aLen a - end
        blast = aLen b - end

getSlice :: PArray -> Int -> Int -> [PackedString]
getSlice a from to
  | from > to = []
  | otherwise = (a!(from)):(getSlice a (from + 1) to)

getChanges' :: (PArray, (Int, Int)) -> (PArray, (Int, Int))
            -> [(Int,[PackedString],[PackedString])]
getChanges' (a, abounds) (b, bbounds) =
    map (convertPatch 0 a b) $ createPatch c_a c_b
  where toHash x bnds = listArray bnds [ hashPS $ x!i | i <- range bnds]
        ah = toHash a abounds :: HArray
        mkAMap m (i:is) =
            let ins (_,_,_,new) (collision,_,_,old) =
                    (collision || not (new == old), True, False, old)
                m' = Map.insertWith ins (ah!i) (False, True, False, a!i) m
            in mkAMap m' is
        mkAMap m _ = m
        hm_a = mkAMap Map.empty (range abounds)
        --
        bh = toHash b bbounds :: HArray
        mkBMap m (i:is) =
            let ins (_,_,_,new) (collision,in_a,_,old) =
                    (collision || not (new == old), in_a, True, old)
                m' = Map.insertWith ins (bh!i) (False, False, True, b!i) m
            in mkBMap m' is
        mkBMap m _ = m
        hm = mkBMap hm_a (range bbounds)
        -- take care of collisions, if there are different lines with the
        -- same hash in both files, then set the hash to markColl,
        -- PackedStrings are compared for two lines with the hash markColl
        get (i, h) = case Map.lookup h hm of
                      Just (_,False,_,_) -> Nothing
                      Just (_,_,False,_) -> Nothing
                      Just (False,True,True,_) -> Just (i, h)
                      Just (True,True,True,_) -> Just (i, markColl)
                      Nothing -> impossible

        a' = catMaybes $ map get [(i, ah!i) | i <- range (bounds ah)]
        b' = catMaybes $ map get [(i, bh!i) | i <- range (bounds bh)]

        (c_a, c_b) = diffArr a' b' (a, abounds) (b, bbounds)

-- | mark hash value where collision occured
markColl :: Int32
markColl = 2345677

-- | return arrays with changes in a and b (1 indexed), offsets start with 0
diffArr :: [(Int,Int32)] -> [(Int,Int32)]
        -> (PArray, (Int, Int)) -> (PArray, (Int, Int))
        -> (BArray, BArray)
diffArr a b (p_a, (off_a, l_a)) (p_b, (off_b, l_b)) = runST (
  do let h_a = initH (map snd a)
         h_b = initH (map snd b)
         m_a = initM (map fst a)
         m_b = initM (map fst b)
         end_a = (aLen p_a)
         end_b = (aLen p_b)
     c_a <- initVChanged end_a
     c_b <- initVChanged end_b
     mapM_ (\ (l,_) -> writeArray c_a l False) $ a
     mapM_ (\ (l,_) -> writeArray c_b l False) $ b
     _ <- cmpseq h_a h_b p_a p_b m_a m_b c_a c_b 0 0 (aLen h_a) (aLen h_b)
     let unchanged ar = do {xs <- getElems ar; return $ (length $ filter not $ xs) -1}
     err <- liftM2 (/=) (unchanged c_a) (unchanged c_b)
     when (err) impossible
     -- Mark common lines at beginning and end
     mapM_ (\ i -> writeArray c_a i False ) $ [1..(off_a - 1)]
     mapM_ (\ i -> writeArray c_b i False ) $ [1..(off_b - 1)]
     mapM_ (\ i -> writeArray c_a i False ) $ [(l_a + 1) .. (end_a)]
     mapM_ (\ i -> writeArray c_b i False ) $ [(l_b + 1) .. (end_b)]
     shiftBoundaries c_a c_b p_a 1 1
     shiftBoundaries c_b c_a p_b 1 1
     err1 <- liftM2 (/=) (unchanged c_a) (unchanged c_b)
     when (err1) impossible
     c_a' <- unsafeFreeze c_a
     c_b' <- unsafeFreeze c_b
     return (c_a', c_b'))

-- | set changes array for a and b and return number of changed lines
cmpseq :: HArray -> HArray -> PArray -> PArray -> MapArray -> MapArray
       -> BSTArray s -> BSTArray s -> Int -> Int -> Int -> Int -> ST s Int
cmpseq _ _ _ _ _ _ _ _ _ _ 0 0 = do return 0
cmpseq h_a h_b p_a p_b m_a m_b c_a c_b off_a off_b l_a l_b = do
  let lim_a = off_a+l_a
      lim_b = off_b+l_b
      off_a' = findSnake h_a h_b p_a p_b m_a m_b off_a off_b l_a l_b off_a off_b
      off_b' = off_b+off_a'-off_a
      lim_a' = findSnakeRev h_a h_b p_a p_b m_a m_b lim_a lim_b off_a' off_b'
      lim_b' = lim_b+lim_a'-lim_a
      l_a' = lim_a'-off_a'
      l_b' = lim_b'-off_b'
  if l_a' == 0 || l_b' == 0
     then if l_a' == 0
             then do when (l_b' > 0) $
                          mapM_ (\i -> writeArray c_b (m_b!i) True)
                                [(off_b' + 1) .. lim_b']
                     return l_b'
             else do when (l_a' > 0) $
                          mapM_ (\i -> writeArray c_a (m_a!i) True)
                                [(off_a' + 1) .. lim_a']
                     return l_a'
     else do let m = l_a' + l_b'
                 del = l_a' - l_b'
                 dodd = odd $ del
             v <- initV m
             vrev <- initVRev m l_a'
             writeArray vrev 0 l_a'
             writeArray v 0 0
             (xmid, ymid, _) <- findDiag 1 h_a h_b p_a p_b m_a m_b v vrev
                                off_a' off_b' l_a' l_b' del dodd
             when ((xmid == 0 && ymid == 0) || (xmid == l_a' && ymid == l_b')
                   || (xmid < 0 || ymid < 0 || xmid > l_a' || ymid > l_b')) 
                     impossible
             c1 <- cmpseq h_a h_b p_a p_b m_a m_b c_a c_b
                          off_a' off_b' xmid ymid
             c2 <- cmpseq h_a h_b p_a p_b m_a m_b c_a c_b
                          (off_a' + xmid) (off_b' + ymid)
                          (l_a' - xmid) (l_b' - ymid)
             return $ c1 + c2

-- | return (xmid, ymid, cost) for the two substrings
--   a[off_a+1..off_a+1+l_a] and b
findDiag :: Int -> HArray -> HArray -> PArray -> PArray -> MapArray -> MapArray
         -> VSTArray s -> VSTArray s -> Int -> Int -> Int -> Int -> Int -> Bool
         -> ST s (Int, Int, Int)
findDiag c h_a h_b p_a p_b m_a m_b v vrev off_a off_b l_a l_b del dodd = do
  if c > l_a + l_b then error "findDiag failed" else return ()
  r <- findF
  case r of
    Just (xmid, ymid) -> return (xmid, ymid, (c*2 - 1))
    Nothing ->
      do r' <- findR
         case r' of
           Just (xmid, ymid) -> return (xmid, ymid, c*2)
           Nothing -> findDiag (c + 1) h_a h_b p_a p_b m_a m_b v vrev
                      off_a off_b l_a l_b del dodd
 where fdmax = if c <= l_a then c else l_a - ((l_a + c) `mod` 2)
       rdmax = if c <= l_b then c else l_b - ((l_b + c) `mod` 2)
       lastrdmax = if (c-1) <= l_b then c-1 else l_b-((l_b + (c-1) `mod` 2))
       lastrdmin = -(if (c-1) <= l_a then c-1 else l_a-((l_a + (c-1)) `mod` 2))
       fdmin = -rdmax
       rdmin = -fdmax
       findF = findF' fdmax
       findR = findR' rdmax
       findF' d = do x <- findOne h_a h_b p_a p_b m_a m_b v d off_a off_b l_a l_b
                     if dodd && d - del >= lastrdmin && d - del <= lastrdmax
                        then do xr <- readArray vrev (d - del)
                                if xr <= x then return $ Just (x, x - d)
                                           else if d <= fdmin then return Nothing
                                                              else findF' (d-2)
                        else if d <= fdmin then return Nothing else findF' (d-2)
       findR' d = do x <- findOneRev h_a h_b p_a p_b m_a m_b vrev d del off_a off_b
                     if not dodd && (d + del >= fdmin) && (d + del <= fdmax)
                        then do xf <- readArray v (d + del)
                                if x <= xf then return $ Just (x,x-del-d)
                                           else if d <= rdmin then return Nothing
                                                              else findR' (d-2)
                        else if d <= rdmin then return Nothing else findR' (d-2)

-- | find position on diag d with one more insert/delete going forward
findOne  :: HArray -> HArray -> PArray -> PArray -> MapArray -> MapArray
         -> VSTArray s -> Int -> Int -> Int -> Int -> Int -> ST s Int 
findOne h_a h_b p_a p_b m_a m_b v d off_a off_b l_a l_b = do
  x0 <- do xbelow <- readArray v (d - 1)
           xover <- readArray v (d + 1)
           return $ if xover > xbelow then xover else xbelow + 1
  let y0 = x0 - d
      x = findSnake h_a h_b p_a p_b  m_a m_b (x0+off_a) (y0+off_b)
            l_a l_b off_a off_b
  writeArray v d (x - off_a)
  return (x-off_a)

-- | follow snake from northwest to southeast, x and y are absolute positions
findSnake :: HArray -> HArray -> PArray -> PArray -> MapArray -> MapArray
          -> Int -> Int -> Int -> Int -> Int -> Int -> Int
findSnake h_a h_b p_a p_b  m_a m_b x y l_a l_b off_a off_b =
  if x < l_a + off_a && y < l_b + off_b && h_a!(x+1) == h_b!(y+1)
       && (h_a!(x+1) /= markColl || p_a!(m_a!(x+1)) == p_b!(m_b!(y+1)))
     then findSnake h_a h_b p_a p_b m_a m_b (x + 1) (y + 1) l_a l_b off_a off_b
     else x

-- | find position on diag d with one more insert/delete going backward
findOneRev :: HArray -> HArray -> PArray -> PArray -> MapArray -> MapArray
           -> VSTArray s -> Int -> Int -> Int -> Int -> ST s Int 
findOneRev h_a h_b p_a p_b m_a m_b v d del off_a off_b = do
  x0 <- do xbelow <- readArray v (d - 1)
           xover <- readArray v (d + 1)
           return $ if xbelow < xover then xbelow else xover-1
  let y0 = x0 - del - d
      x = findSnakeRev h_a h_b p_a p_b m_a m_b (x0+off_a) (y0+off_b)
            off_a off_b
  writeArray v d (x-off_a)
  return (x-off_a)

-- | follow snake from southeast to northwest, x and y are absolute positions
findSnakeRev :: HArray -> HArray -> PArray -> PArray -> MapArray -> MapArray
             -> Int -> Int -> Int -> Int -> Int
findSnakeRev h_a h_b p_a p_b m_a m_b x y off_a off_b =
  if x > off_a && y > off_b && h_a!x == h_b!y
       && (h_a!x /= markColl || p_a!(m_a!x) == p_b!(m_b!y))
     then findSnakeRev h_a h_b p_a p_b m_a m_b (x - 1) (y - 1) off_a off_b
     else x
\end{code}

\begin{code}

-- | try to create nicer diffs by shifting around regions of changed lines
shiftBoundaries :: BSTArray s -> BSTArray s -> PArray -> Int -> Int -> ST s ()
shiftBoundaries c_a c_b p_a i_ j_ =
  do x <- nextChanged c_a i_
     case x of
       Just start ->
             do let skipped = start - i_
                j1 <- nextUnchangedN c_b skipped j_
                end <- nextUnchanged c_a start
                j2 <- nextUnchanged c_b j1
                (i3,j3) <- expand start end j2
                shiftBoundaries c_a c_b p_a i3 j3
       Nothing -> return () -- no change up to end of file
 where noline = (aLen p_a) + 1
       expand start i j =
         do let len = i - start
            (start0,i0,j0) <- shiftBackward start i j
            b <- if j0 > 1 then readArray c_b (j0-1) else return False
            let corr = if b then i0 else noline
            let blank = if p_a!(i0-1) == nilPS then i0
                                               else noline
            (start1,i1,j1,corr1,blank1) <- shiftForward start0 i0 j0 corr blank
            -- prefer corresponding to ending with blank line
            let newi = if corr1 == noline then blank1
                                          else corr1
            (start2,i2,j2) <- moveCorr start1 i1 j1 newi
            if len /= i2 - start2
                then expand start2 i2 j2
                else return (i2, j2)
       shiftBackward start i j =
         if start > 1 && p_a!(i-1) == p_a!(start-1)
            then do when (i == start) impossible
                    b1 <- readArray c_a (i-1)
                    b2 <- readArray c_a (start-1)
                    when ((not b1) || b2) impossible
                    writeArray c_a (i-1) False
                    writeArray c_a (start-1) True
                    b <- if start > 2 then readArray c_a (start-2)
                                      else return False
                    start' <- if b then liftM (1+) (prevUnchanged c_a (start-2))
                                   else return (start-1)
                    j' <- prevUnchanged c_b (j-1)
                    shiftBackward start' (i-1) j'
            else do return (start,i,j)
       shiftForward start i j corr blank =
         if i <= aLen p_a && p_a!i == p_a!start &&
             -- nilPS at the end of file marks empty line after final newline
             not ((i == aLen p_a) && (p_a!i == nilPS))
            then do when (i == start) impossible
                    b1 <- readArray c_a i
                    b2 <- readArray c_a start
                    when ((not b2) ||  b1) impossible
                    writeArray c_a i True
                    writeArray c_a start False
                    i0 <- nextUnchanged c_a (i+1)
                    j0 <- nextUnchanged c_b (j+1)
                    let corr0 = if i0 > (i+1) then noline
                                              else if j0-j > 2 then i0 else corr
                    let blank0 = if i0 > i+1 then noline
                                 else if p_a!(i0-1) == nilPS then i0
                                                             else blank
                    shiftForward (start+1) i0 j0 corr0 blank0
            else do return (start,i,j,corr,blank)
       moveCorr start i j corr =
         if corr >= i
            then return (start,i,j)
            else do b1 <- readArray c_a (i-1)
                    b2 <- readArray c_a (start-1)
                    when ((not b1) || b2) impossible
                    when (p_a!(i-1) /= p_a!(start-1)) impossible
                    writeArray c_a (i-1) False
                    writeArray c_a (start-1) True       
                    j' <- prevUnchanged c_b (j-1)
                    moveCorr (start-1) (i-1) j' corr

-- | goto next unchanged line, return the given line if unchanged
nextUnchanged :: BSTArray s -> Int -> ST s Int
nextUnchanged c i = do
  len <- aLenM c
  if i == len + 1 then return i
     else do b <- readArray c i
             if b then nextUnchanged c (i+1)
                  else return i

-- | skip at least one unchanged line, if there is none advance
--   behind the last line
skipOneUnChanged :: BSTArray s -> Int -> ST s Int
skipOneUnChanged c i = do
  len <- aLenM c
  if i == len + 1
     then return i
     else do b <- readArray c i
             if not b then return (i+1)
                      else skipOneUnChanged c (i+1)

-- | goto n-th next unchanged line
nextUnchangedN :: BSTArray s -> Int -> Int -> ST s Int
nextUnchangedN c n i = do
  if n == 0 then return i
            else do i' <- skipOneUnChanged c i
                    nextUnchangedN c (n-1) i'

-- | goto next changed line, return the given line if changed
nextChanged :: BSTArray s -> Int -> ST s (Maybe Int)
nextChanged c i = do
  len <- aLenM c
  if i <= len
    then do b <- readArray c i
            if not b then nextChanged c (i+1)
                     else return $ Just i
    else return Nothing

-- | goto previous unchanged line, return the given line if unchanged
prevUnchanged :: BSTArray s -> Int -> ST s Int
prevUnchanged c i = do
  b <- readArray c i
  if b then prevUnchanged c (i-1)
       else return i
\end{code}

\begin{code}
type HArray = UArray Int Int32
type BArray = UArray Int Bool
type PArray = Array Int PackedString
type MapArray = UArray Int Int
type VSTArray s = STUArray s Int Int
type BSTArray s = STUArray s Int Bool

initV :: Int -> ST s (VSTArray s)
initV dmax = do
  newArray (-(dmax + 1), dmax + 1) (-1)

initVRev :: Int -> Int -> ST s (VSTArray s)
initVRev dmax xmax = do
  newArray (-(dmax + 1), dmax + 1) (xmax + 1)

-- 1 indexed, v[0] is used as a guard element
initVChanged :: Int -> ST s (BSTArray s)
initVChanged l = do
  a <- newArray (0, l) True
  writeArray a 0 False
  return a
  -- set to false for all lines which have a mapping later
  -- other lines are only present in one of the files

initH :: [Int32] -> HArray
initH a = listArray (0, length a) (0:a)

initM :: [Int] -> MapArray
initM a = listArray (0, length a) (0:a)

initP :: [PackedString] -> PArray
initP a = listArray (0, length a) (nilPS:a)

#if __GLASGOW_HASKELL__ > 604
aLen :: (IArray a e) => a Int e -> Int
aLen a = snd $ bounds a
aLenM :: (MArray a e m) => a Int e -> m Int
aLenM a = getBounds a >>= return . snd
#else
aLen :: HasBounds a => a Int e -> Int
aLen a = snd $ bounds a
aLenM :: (HasBounds a, Monad m) => a Int e -> m Int
aLenM = return . snd . bounds
#endif
\end{code}

\begin{code}
convertPatch :: Int -> PArray -> PArray -> (Int, Int, Int, Int)
             -> (Int,[PackedString],[PackedString])
convertPatch off a b (a0,a1,b0,b1)
 | b0 == b1 = (b0+off,getDelete a a0 a1,[])
 | a0 == a1 = (b0+off,[],getInsert b b0 b1)
 | otherwise = (b0+off,getDelete a a0 a1,getInsert b b0 b1)

getInsert :: PArray -> Int -> Int -> [PackedString]
getInsert b from to
  | from >= to = []
  | otherwise = (b!(from+1)):(getInsert b (from+1) to)
getDelete :: PArray -> Int -> Int -> [PackedString]
getDelete a from to
  | from >= to = []
  | otherwise = (a!(from+1)):(getDelete a (from+1) to)

createPatch :: BArray -> BArray -> [(Int, Int, Int, Int)]
createPatch c_a c_b =
  reverse $ createP c_a c_b (aLen c_a) (aLen c_b)

createP :: BArray -> BArray -> Int -> Int -> [(Int, Int, Int, Int)]
createP _ _ 0 0 = []
createP c_a c_b ia ib =
  if c_a!ia || c_b!ib
     then let ia' = skipChangedRev c_a ia
              ib' = skipChangedRev c_b ib
          in (ia',ia,ib',ib):(createP c_a c_b ia' ib')
     else createP c_a c_b (ia-1) (ib-1)

skipChangedRev :: BArray -> Int -> Int
skipChangedRev c i = if i >= 0 && c!i then skipChangedRev c (i-1) else i
\end{code}