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70 lines
2.5 KiB
Idris
70 lines
2.5 KiB
Idris
module Text.Distance.Levenshtein
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import Data.List
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import Data.Maybe
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import Data.String
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import Data.IOMatrix
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import Data.List.Extra
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%default total
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||| Self-evidently correct but O(3 ^ (min mn)) complexity
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spec : String -> String -> Nat
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spec a b = loop (fastUnpack a) (fastUnpack b) where
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loop : List Char -> List Char -> Nat
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loop [] ys = length ys -- deletions
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loop xs [] = length xs -- insertions
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loop (x :: xs) (y :: ys)
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= if x == y then loop xs ys -- match
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else 1 + minimum [ loop (x :: xs) ys -- insert y
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, loop xs (y :: ys) -- delete x
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, loop xs ys -- substitute y for x
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]
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||| Dynamic programming
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export
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compute : HasIO io => String -> String -> io Nat
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compute a b = do
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let w = strLength a
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let h = strLength b
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-- In mat[i][j], we store the distance between
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-- * the suffix of a of size i
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-- * the suffix of b of size j
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-- So we need a matrix of size (|a|+1) * (|b|+1)
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mat <- new (w+1) (h+1)
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-- Whenever one of the two suffixes of interest is empty, the only
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-- winning move is to:
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-- * delete all of the first
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-- * insert all of the second
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-- i.e. the cost is the length of the non-zero suffix
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for_ [0..w] $ \ i => write mat i 0 i -- deletions
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for_ [0..h] $ \ j => write mat 0 j j -- insertions
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-- We introduce a specialised `read` for ease of use
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let get = \i, j => case !(read {io} mat i j) of
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Nothing => assert_total $
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idris_crash "INTERNAL ERROR: Badly initialised matrix"
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Just n => pure n
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-- We fill the matrix from the bottom up, using the same formula we used
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-- in the specification's `loop`.
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for_ [1..h] $ \ j => do
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for_ [1..w] $ \ i => do
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-- here we change Levenshtein slightly so that we may only substitute
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-- alpha / numerical characters for similar ones. This avoids suggesting
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-- "#" as a replacement for an out of scope "n".
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let cost = let c = assert_total $ strIndex a (i-1)
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d = assert_total $ strIndex b (j-1)
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in if c == d then 0 else
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if isAlpha c && isAlpha d then 1 else
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if isDigit c && isDigit d then 1 else 2
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write mat i j $
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minimum [ 1 + !(get i (j-1)) -- insert y
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, 1 + !(get (i-1) j) -- delete x
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, cost + !(get (i-1) (j-1)) -- equal or substitute y for x
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]
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-- Once the matrix is fully filled, we can simply read the top right corner
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integerToNat . cast <$> get w h
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