{-# LANGUAGE FlexibleContexts #-}
module EditDistance (dist) where

import qualified Data.Sequence as Sequence
import qualified Data.Map as Map
import qualified Control.Monad.State as State

dist :: Eq a => [a] -> [a] -> Int
dist a b = State.evalState (d (pred $ length aSeq) . pred $ length bSeq) Map.empty
  where d :: Int -> Int -> State.State (Map.Map (Int, Int) Int) Int
        d i (-1) = return (succ i)
        d (-1) j = return (succ j)
        d i j = do m <- State.get
                   case Map.lookup (i, j) m of
                     Just res -> return res
                     Nothing
                       | aSeq `Sequence.index` i == bSeq `Sequence.index` j -> do res <- d (pred i) (pred j)
                                                                                  State.modify (Map.insert (i, j) res)
                                                                                  return res
                       | otherwise -> do left <- succ <$> d (pred i) j
                                         right <- succ <$> d i (pred j)
                                         middle <- succ <$> d (pred i) (pred j)
                                         let res = min (min left right) middle
                                         State.modify (Map.insert (i, j) res)
                                         return res
        aSeq = Sequence.fromList a
        bSeq = Sequence.fromList b