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349 lines
16 KiB
Elm
349 lines
16 KiB
Elm
module Levenshtein exposing (distance)
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{-| Levenshtein distance is a metric for measuring the difference between two strings.
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@docs distance
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Copied from
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-}
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import Array exposing (Array)
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{-| Computes the Levenshtein distance between two strings.
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-}
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distance : String -> String -> Int
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distance str1 str2 =
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if str1 == str2 then
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0
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else
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distanceHelper
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(Array.fromList (String.toList str1))
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(Array.fromList (String.toList str2))
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distanceHelper : Array Char -> Array Char -> Int
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distanceHelper arr1 arr2 =
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let
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calculateEditDistanceForChars : Table -> ( Int, Int ) -> ( Table, Int )
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calculateEditDistanceForChars table ( i, j ) =
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case ( Array.get (i - 1) arr1, Array.get (j - 1) arr2 ) of
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( Just chr1, Just chr2 ) ->
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let
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( table1, dist1 ) =
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tableFetch ( i - 1, j ) calculateEditDistanceForChars table
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( table2, dist2 ) =
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tableFetch ( i, j - 1 ) calculateEditDistanceForChars table1
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( table3, dist3 ) =
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tableFetch ( i - 1, j - 1 ) calculateEditDistanceForChars table2
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in
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( table3
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-- Find the smallest of (dist1 + 1), (dist2 + 1), and (dist3 + distanceIndicator)
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, if dist3 < dist1 then
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if dist3 < dist2 then
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if chr1 /= chr2 then
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dist3 + 1
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else
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dist3
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else
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dist1 + 1
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else if dist1 > dist2 then
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dist2 + 1
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else
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dist1 + 1
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)
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_ ->
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( table, max i j )
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indecesForLastChars =
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( Array.length arr1, Array.length arr2 )
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in
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calculateEditDistanceForChars (tableEmpty indecesForLastChars) indecesForLastChars
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|> Tuple.second
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--- tableElm
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{-
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The algorithm goes across the various combinations of characters in the two strings to be compared.
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The result of every combination can be looked at like a grid:
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- K I T T E N
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- (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (6,0)
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S (0,1) (1,1) (2,1) (3,1) (4,1) (5,1) (6,1)
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I (0,2) (1,2) (2,2) (3,2) (4,2) (5,2) (6,2)
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T (0,3) (1,3) (2,3) (3,3) (4,3) (5,3) (6,3)
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T (0,4) (1,4) (2,4) (3,4) (4,4) (5,4) (6,4)
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I (0,5) (1,5) (2,5) (3,5) (4,5) (5,5) (6,5)
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N (0,6) (1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
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G (0,7) (1,7) (2,7) (3,7) (4,7) (5,7) (6,7)
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Note that each row and column have room for one more element than the length of the string they represent.
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To store the result for each comparison efficiently, we use a flat array, where the data looks like this:
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[ (0,0), (1,0), (2,0), (3,0), (4,0), (5,0), (6,0), (0,1), (1,1), (2,1), (3,1), etc.]
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Where the index to read from can be calculated from the key and the "width" of the grid.
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-}
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type Table
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= Table Int (Array Int)
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tableEmpty : ( Int, Int ) -> Table
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tableEmpty ( sizeA, sizeB ) =
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let
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dimension =
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sizeB + 1
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arraySize =
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(sizeA + 1) * dimension - 1
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in
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Table dimension (Array.repeat arraySize -1)
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tableFetch : ( Int, Int ) -> (Table -> ( Int, Int ) -> ( Table, Int )) -> Table -> ( Table, Int )
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tableFetch (( iKey, jKey ) as key) builder ((Table dimension distanceStore) as table) =
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let
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index =
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iKey * dimension + jKey
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in
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case Array.get index distanceStore of
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Just editDistance ->
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if editDistance == -1 then
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let
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( Table _ newStore, actualEditDistance ) =
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builder table key
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in
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( Table dimension (Array.set index actualEditDistance newStore), actualEditDistance )
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else
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( table, editDistance )
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Nothing ->
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-- Would only occur if we are out of bounds on the array. This should never happen
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( table, -1 )
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{- LICENSE
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The code was copied from https://github.com/dasch/levenshtein
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and including the change in https://github.com/dasch/levenshtein/pull/10
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from https://github.com/KasMA1990/levenshtein
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Apache License
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-}
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