```-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Algorithm.Diff
-- Copyright   :  (c) Sterling Clover 2008-2011, Kevin Charter 2011
-- License     :  BSD 3 Clause
-- Maintainer  :  s.clover@gmail.com
-- Stability   :  experimental
-- Portability :  portable
--
-- This is an implementation of the O(ND) diff algorithm as described in
-- \"An O(ND) Difference Algorithm and Its Variations (1986)\"
-- <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.6927>. It is O(mn) in space.
-- The algorithm is the same one used by standared Unix diff.
-----------------------------------------------------------------------------

module Data.Algorithm.Diff
( Diff(..)
-- * Comparing lists for differences
, getDiff
, getDiffBy

-- * Finding chunks of differences
, getGroupedDiff
, getGroupedDiffBy
) where

import Prelude hiding (pi)

import Data.Array

data DI = F | S | B deriving (Show, Eq)

-- | A value is either from the 'First' list, the 'Second' or from 'Both'.
-- 'Both' contains both the left and right values, in case you are using a form
-- of equality that doesn't check all data (for example, if you are using a
-- newtype to only perform equality on side of a tuple).
data Diff a = First a | Second a | Both a a deriving (Show, Eq)

data DL = DL {poi :: !Int, poj :: !Int, path::[DI]} deriving (Show, Eq)

instance Ord DL where x <= y = poi x <= poi y

canDiag :: (a -> a -> Bool) -> [a] -> [a] -> Int -> Int -> Int -> Int -> Bool
canDiag eq as bs lena lenb i j =
if i < lena && j < lenb then (arAs ! i) `eq` (arBs ! j) else False
where arAs = listArray (0,lena - 1) as
arBs = listArray (0,lenb - 1) bs

dstep :: (Int -> Int -> Bool) -> [DL] -> [DL]
dstep cd dls = hd:pairMaxes rst
where (hd:rst) = nextDLs dls
nextDLs [] = []
nextDLs (dl:rest) = dl':dl'':nextDLs rest
where dl'  = addsnake cd \$ dl {poi=poi dl + 1, path=(F : pdl)}
dl'' = addsnake cd \$ dl {poj=poj dl + 1, path=(S : pdl)}
pdl = path dl
pairMaxes [] = []
pairMaxes [x] = [x]
pairMaxes (x:y:rest) = max x y:pairMaxes rest

addsnake :: (Int -> Int -> Bool) -> DL -> DL
| cd pi pj = addsnake cd \$
dl {poi = pi + 1, poj = pj + 1, path=(B : path dl)}
| otherwise   = dl
where pi = poi dl; pj = poj dl

lcs :: (a -> a -> Bool) -> [a] -> [a] -> [DI]
lcs eq as bs = path . head . dropWhile (\dl -> poi dl /= lena || poj dl /= lenb) .
concat . iterate (dstep cd) . (:[]) . addsnake cd \$
DL {poi=0,poj=0,path=[]}
where cd = canDiag eq as bs lena lenb
lena = length as; lenb = length bs

-- | Takes two lists and returns a list of differences between them. This is
-- 'getDiffBy' with '==' used as predicate.
getDiff :: (Eq t) => [t] -> [t] -> [Diff t]
getDiff = getDiffBy (==)

-- | Takes two lists and returns a list of differences between them, grouped
-- into chunks. This is 'getGroupedDiffBy' with '==' used as predicate.
getGroupedDiff :: (Eq t) => [t] -> [t] -> [Diff [t]]
getGroupedDiff = getGroupedDiffBy (==)

-- | A form of 'getDiff' with no 'Eq' constraint. Instead, an equality predicate
-- is taken as the first argument.
getDiffBy :: (t -> t -> Bool) -> [t] -> [t] -> [Diff t]
getDiffBy eq a b = markup a b . reverse \$ lcs eq a b
where markup (x:xs)   ys   (F:ds) = First x  : markup xs ys ds
markup   xs   (y:ys) (S:ds) = Second y : markup xs ys ds
markup (x:xs) (y:ys) (B:ds) = Both x y : markup xs ys ds
markup _ _ _ = []

getGroupedDiffBy :: (t -> t -> Bool) -> [t] -> [t] -> [Diff [t]]
getGroupedDiffBy eq a b = go \$ getDiffBy eq a b
where go (First x  : xs) = let (fs, rest) = goFirsts  xs in First  (x:fs)     : go rest
go (Second x : xs) = let (fs, rest) = goSeconds xs in Second (x:fs)     : go rest
go (Both x y : xs) = let (fs, rest) = goBoth    xs
(fxs, fys) = unzip fs
in Both (x:fxs) (y:fys) : go rest
go [] = []

goFirsts  (First x  : xs) = let (fs, rest) = goFirsts  xs in (x:fs, rest)
goFirsts  xs = ([],xs)

goSeconds (Second x : xs) = let (fs, rest) = goSeconds xs in (x:fs, rest)
goSeconds xs = ([],xs)

goBoth    (Both x y : xs) = let (fs, rest) = goBoth xs    in ((x,y):fs, rest)
goBoth    xs = ([],xs)
```