Levenshtein distance

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Task
Levenshtein distance
You are encouraged to solve this task according to the task description, using any language you may know.
This page uses content from Wikipedia. The original article was at Levenshtein distance. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)


In information theory and computer science, the Levenshtein distance is a metric for measuring the amount of difference between two sequences (i.e. an edit distance). The Levenshtein distance between two strings is defined as the minimum number of edits needed to transform one string into the other, with the allowable edit operations being insertion, deletion, or substitution of a single character.


Example

The Levenshtein distance between "kitten" and "sitting" is 3, since the following three edits change one into the other, and there isn't a way to do it with fewer than three edits:

  1.   kitten   sitten   (substitution of 'k' with 's')
  2.   sitten   sittin   (substitution of 'e' with 'i')
  3.   sittin   sitting   (insert 'g' at the end).


The Levenshtein distance between   "rosettacode",   "raisethysword"   is   8.

The distance between two strings is same as that when both strings are reversed.


Task

Implements a Levenshtein distance function, or uses a library function, to show the Levenshtein distance between   "kitten"   and   "sitting".


Related task


Other tasks related to string operations:
Metrics
Counting
Remove/replace
Anagrams/Derangements/shuffling
Find/Search/Determine
Formatting
Song lyrics/poems/Mad Libs/phrases
Tokenize
Sequences



11l[edit]

Translation of: Python
F minimumEditDistance(=s1, =s2)
   I s1.len > s2.len
      (s1, s2) = (s2, s1)

   V distances = Array(0 .. s1.len)

   L(char2) s2
      V newDistances = [L.index + 1]
      L(char1) s1
         I char1 == char2
            newDistances.append(distances[L.index])
         E
            newDistances.append(1 + min((distances[L.index], distances[L.index + 1], newDistances.last)))
      distances = newDistances
   R distances.last

print(minimumEditDistance(‘kitten’, ‘sitting’))
print(minimumEditDistance(‘rosettacode’, ‘raisethysword’))
Output:
3
8

360 Assembly[edit]

*        Levenshtein distance      - 22/04/2020
LEVENS   CSECT
         USING  LEVENS,R13         base register
         B      72(R15)            skip savearea
         DC     17F'0'             savearea
         SAVE   (14,12)            save previous context
         ST     R13,4(R15)         link backward
         ST     R15,8(R13)         link forward
         LR     R13,R15            set addressability
         LA     R8,1               ii=1 
       DO WHILE=(C,R8,LE,NN)       do ii=1 to nn
         LR     R1,R8                ii
         SLA    R1,5                 *32
         LA     R4,SS-32(R1)         @ss(ii,1)
         MVC    S1,0(R4)             s1=ss(ii,1)
         LR     R1,R8                ii
         SLA    R1,1                 *2
         LA     R1,1(R1)             +1
         SLA    R1,4                 *16
         LA     R4,SS-32(R1)         @ss(ii,2)
         MVC    S2,0(R4)             s2=ss(ii,2)
         LA     R1,S1                @s1
         BAL    R14,LENGTHST         call length
         AH     R0,=H'1'             +1 
         ST     R0,N1                n1=length(s1)+1
         LA     R1,S2                @s2
         BAL    R14,LENGTHST         call length
         AH     R0,=H'1'             +1 
         ST     R0,N2                n2=length(s2)+1
         L      R4,N1                n1
       IF     C,R4,EQ,=F'1' THEN     if n1=1 then
         L      R3,N2                  n2
         BCTR   R3,0                   lev=n2-1
         B      RET                    goto ret
       ENDIF    ,                    endif
         L      R4,N2                n2
       IF     C,R4,EQ,=F'1' THEN     if n2=1 then
         L      R3,N1                  n1
         BCTR   R3,0                   lev=n1-1
         B      RET                    goto ret
       ENDIF    ,                    endif
         LA     R6,1                 i=1 
       DO WHILE=(C,R6,LE,N1)         do i=1 to n1
         LR     R2,R6                  i
         BCTR   R2,0                   -1
         LR     R1,R6                  i
         SLA    R1,6                   *64
         ST     R2,D-64(R1)            d(i,1)=i-1
         LA     R6,1(R6)               i++ 
       ENDDO    ,                    enddo i
         LA     R7,1                 j=1 
       DO WHILE=(C,R7,LE,N2)         do j=1 to n2
         LR     R2,R7                  j
         BCTR   R2,0                   j-1
         LR     R1,R7                  j
         SLA    R1,2                   *4
         ST     R2,D-4(R1)             d(1,j)=j-1
         LA     R7,1(R7)               j++
       ENDDO    ,                    enddo j
         LA     R6,2                 i=2 
       DO WHILE=(C,R6,LE,N1)         do i=2 to n1
         LA     R4,S1-2                @s1-2
         AR     R4,R6                  +i
         MVC    C1(1),0(R4)            c1=substr(s1,i-1,1)
         LA     R7,2                   j=2 
       DO WHILE=(C,R7,LE,N2)           do j=2 to n2
         LA     R4,S2-2                  @s2-2
         AR     R4,R7                    +j
         MVC    C2(1),0(R4)              c2=substr(s2,j-1,1)
         LR     R1,R6                    i
         SH     R1,=H'2'                 -2
         SLA    R1,4                     *16
         AR     R1,R7                    +j
         SLA    R1,2                     *4
         L      R2,D-4(R1)               d(i-1,j)
         LA     R2,1(R2)                 +1
         ST     R2,D1                    d1=d(i-1,j)+1
         LR     R2,R7                    j
         BCTR   R2,0                     -1
         LR     R1,R6                    i
         BCTR   R1,0                     -1
         SLA    R1,4                     *16
         AR     R1,R2                    +(j-1)
         SLA    R1,2                     *4
         L      R2,D-4(R1)               d(i,j-1)
         LA     R2,1(R2)                 +1
         ST     R2,D2                    d2=d(i,j-1)+1
       IF   CLC,C1,NE,C2 THEN            if c1<>c2 then
         LA     R9,1                       x=1
       ELSE     ,                        else
         SR     R9,R9                      x=0
       ENDIF    ,                        endif
         LR     R1,R6                    i
         SH     R1,=H'2'                 i-2
         LR     R2,R7                    j
         BCTR   R2,0                     j-1
         SLA    R1,4                     *16
         AR     R1,R2                    +(j-1)
         SLA    R1,2                     *4
         L      R2,D-4(R1)               d(i-1,j-1)
         AR     R2,R9                    +x
         ST     R2,D3                    d3=d(i-1,j-1)+x
         L      R4,D1                    d1
       IF     C,R4,LT,D2 THEN            if d1<d2 then 
       IF     C,R4,LT,D3 THEN              if d1<d3 then
         L      R10,D1                       dd=d1
       ELSE     ,                          else
         L      R10,D3                       dd=d3
       ENDIF    ,                          endif
       ELSE     ,                        else
         L      R4,D2                      d2
       IF     C,R4,LT,D3 THEN              if d2<d3 then
         L      R10,D2                       dd=d2
       ELSE     ,                          else
         L      R10,D3                       dd=d3
       ENDIF    ,                          endif
       ENDIF    ,                        endif
         LR     R1,R6                    i
         BCTR   R1,0                     i-1
         SLA    R1,4                     *16
         AR     R1,R7                    +j
         SLA    R1,2                     *4
         ST     R10,D-4(R1)              d(i,j)=dd
         LA     R7,1(R7)                 j++
       ENDDO    ,                      enddo j
         LA     R6,1(R6)               i++ 
       ENDDO    ,                    enddo i
         L      R1,N1                n1
         BCTR   R1,0                 -1
         SLA    R1,4                 *16
         A      R1,N2                +n2
         SLA    R1,2                 *4
         L      R3,D-4(R1)           lev=d(n1,n2)
RET      MVC    PG,=CL80' '          clear buffer
         MVC    PG(16),S1            output s1
         MVC    PG+17(16),S2         output s2
         XDECO  R3,XDEC              edit lev
         MVC    PG+34(5),XDEC+7      output lev
         XPRNT  PG,L'PG              print bufffer
         LA     R8,1(R8)             ii++ 
       ENDDO    ,                  enddo ii
         L      R13,4(0,R13)       restore previous savearea pointer
         RETURN (14,12),RC=0       restore registers from calling save
LENGTHST CNOP   0,4                function lengthst(c)
         LA     R0,16              i=16
         LA     R1,15(R1)          @ci
LENGTHS1 LTR    R0,R0              while i>0
         BZ     LENGTHS2           ..
         CLI    0(R1),C' '           if Mid(c,i,1)=" "
         BNE    LENGTHS2             then  exit while
         BCTR   R1,0                 @ci--
         BCTR   R0,0                 i--
         B      LENGTHS1           endwhile
LENGTHS2 BR     R14                return to caller
SS       DC     CL16'kitten',CL16'sitting'
         DC     CL16'rosettacode',CL16'raisethysword'
         DC     CL16'saturday',CL16'sunday'
         DC     CL16'sleep',CL16'fleeting'
NN       DC     A((NN-SS)/(2*L'SS))
N1       DS     F                  n1
N2       DS     F                  n2
S1       DS     CL16               s1
S2       DS     CL16               s2
D        DS     256F               d(16,16)
D1       DS     F                  d1
D2       DS     F                  d2
D3       DS     F                  d3
C1       DS     CL1                c1
C2       DS     CL1                c2
PG       DS     CL80               buffer
XDEC     DS     CL12               temp fo xdeco
         REGEQU
         END    LEVENS
Output:
kitten           sitting              3
rosettacode      raisethysword        8
saturday         sunday               3
sleep            fleeting             5


Action![edit]

This example is in need of improvement:
The output shown does not appear to match the PrintF calls in the code
DEFINE STRING="CHAR ARRAY" ; sys.act
DEFINE width="15" ; max characters 14
DEFINE MatrixSize="225" ; 15*15

PROC Set2Dm(INT ARRAY matrix, INT x,y, val)
  matrix(x+y*width)=val
RETURN

INT FUNC Get2Dm(INT ARRAY matrix, INT x,y)
  INT res
  res=matrix(x+y*width)
RETURN(res)

INT FUNC DamerauLevenshteinDistance(STRING str1, str2)
  INT ARRAY matrix(MatrixSize)
  BYTE Result, tmp, Min, K, L, I, J, M, N

  Result=0
  M=str1(0)
  N=str2(0)

  FOR I=0 TO MatrixSize-1 DO matrix(I)=0 OD
  FOR I=0 TO M DO Set2Dm(matrix, I,0, I) OD
  FOR J=0 TO N DO Set2Dm(matrix, 0,J, J) OD
  
  FOR J=1 TO N DO
    FOR I=1 TO M DO
      IF str1(I) = str2(J) THEN
        tmp=Get2Dm(matrix, I-1, J-1)
        Set2Dm(matrix, I,J, tmp) ; no operation required
      ELSE
        Min = Get2Dm(matrix, I-1,J)+1  ; REM delete
        K = Get2Dm(matrix, I,J-1)+1    ; REM insert
        L = Get2Dm(matrix, I-1, J-1)+1 ; REM substitution
        IF K < Min THEN Min=K FI
        IF L < Min THEN Min=L FI
        Set2Dm(matrix, I,J, Min)

        ;transposition for Damerau Levenshtein Distance
        ;IF I>1 AND J>1 THEN
        ;  IF str1(I) = str2(J-1) AND str1(I-1) = str2(J) THEN
        ;    Min=Get2Dm(matrix, I,J)
        ;    tmp=Get2Dm(matrix, I-2,J-2)+1
        ;    IF Min>tmp THEN Min=tmp FI
        ;    Set2Dm(matrix, I,J, Min) ; REM transposition
        ;  FI
        ;FI

      FI
    OD
  OD
  Result=Get2Dm(matrix, M,N)
RETURN(Result)

PROC MAIN()
  INT result
  STRING Word_1(15), Word_2(15)
  PUT(125)
  PUTE()

  SCopy(Word_1,"kitten") SCopy(Word_2,"sitting")
  PrintF("%S - %S%E",Word_1,Word_2)
  result=DamerauLevenshteinDistance(Word_1,Word_2)
  PrintF("Levenshtein Distance=%U%E%E",result)
  ;PrintF("Damerau Levenshtein Distance=%U%E%E",result)

  SCopy(Word_1,"rosettacode") SCopy(Word_2,"raisethysword")
  PrintF("%S - %S%E",Word_1,Word_2)
  result=DamerauLevenshteinDistance(Word_1,Word_2)
  PrintF("Levenshtein Distance=%U%E%E",result)
  ;PrintF("Damerau Levenshtein Distance=%U%E%E",result)

  SCopy(Word_1,"qwerty") SCopy(Word_2,"qweryt")
  PrintF("%S - %S%E",Word_1,Word_2)
  result=DamerauLevenshteinDistance(Word_1,Word_2)
  PrintF("Levenshtein Distance=%U%E%E",result)
  ;PrintF("Damerau Levenshtein Distance=%U%E%E",result)
RETURN
Output:
kitten, sitting: 3
rosettacode, raisethysword: 8

Ada[edit]

with Ada.Text_IO;

procedure Main is
   function Levenshtein_Distance (S, T : String) return Natural is
      D : array (0 .. S'Length, 0 .. T'Length) of Natural;
   begin
      for I in D'Range (1) loop
         D (I, 0) := I;
      end loop;
      for I in D'Range (2) loop
         D (0, I) := I;
      end loop;
      for J in T'Range loop
         for I in S'Range loop
            if S (I) = T (J) then
               D (I, J) := D (I - 1, J - 1);
            else
               D (I, J) :=
                  Natural'Min
                    (Natural'Min (D (I - 1, J) + 1, D (I, J - 1) + 1),
                     D (I - 1, J - 1) + 1);
            end if;
         end loop;
      end loop;
      return D (S'Length, T'Length);
   end Levenshtein_Distance;
begin
   Ada.Text_IO.Put_Line
     ("kitten -> sitting:" &
      Integer'Image (Levenshtein_Distance ("kitten", "sitting")));
   Ada.Text_IO.Put_Line
     ("rosettacode -> raisethysword:" &
      Integer'Image (Levenshtein_Distance ("rosettacode", "raisethysword")));
end Main;
Output:
kitten -> sitting: 3
rosettacode -> raisethysword: 8

Aime[edit]

Translation of: C
integer
dist(data s, t, integer i, j, list d)
{
    integer x;

    x = d[i * (~t + 1) + j];
    if (x == -1) {
        if (i == ~s) {
            x = ~t - j;
        } elif (j == ~t) {
            x = ~s - i;
        } elif (s[i] == t[j]) {
            x = dist(s, t, i + 1, j + 1, d);
        } else {
            x = dist(s, t, i + 1, j + 1, d)
                .min(dist(s, t, i, j + 1, d))
                .min(dist(s, t, i + 1, j, d));
            x += 1;
        }

        d[i * (~t + 1) + j] = x;
    }

    x;
}

levenshtein(data s, t)
{
    list d;

    d.pn_integer(0, (~s + 1) * (~t + 1), -1);
    dist(s, t, 0, 0, d);
}

main(void)
{
    text s1, s2;

    o_form("`~' to `~' is ~\n", s1 = "rosettacode", s2 = "raisethysword",
           levenshtein(s1, s2));
    o_form("`~' to `~' is ~\n", s1 = "kitten", s2 = "sitting",
           levenshtein(s1, s2));

    0;
}
Output:
`rosettacode' to `raisethysword' is 8
`kitten' to `sitting' is 3

ALGOL 68[edit]

Translation of: Action!

...largely to highlight the syntactic similarities.
Non-recursive algorithm - although Algol 68 supports recursion, Action! doesn't.

# Calculate Levenshtein distance between strings - translated from the Action! sample #
BEGIN

  PROC levenshtein distance = (STRING str1, str2)INT:
  BEGIN

    INT m=UPB str1;
    INT n=UPB str2;

    (0:m,0:n)INT matrix;
 
    FOR i FROM 0 TO m DO FOR j FROM 0 TO n DO matrix(i,j):=0 OD OD;
    FOR i TO m DO matrix(i,1):=i OD;
    FOR j TO n DO matrix(1,j):=j OD;
 
    FOR j FROM 1 TO n DO
      FOR i FROM 1 TO m DO
        IF str1(i) = str2(j) THEN
          matrix(i,j):=matrix(i-1, j-1) # no operation required #
        ELSE
          INT min := matrix(i-1,j)+1    ; # deletion            #
          INT k    = matrix(i,j-1)+1    ; # insertion           #
          INT l    = matrix(i-1, j-1)+1 ; # substitution        #
          IF k < min THEN min:=k FI;
          IF l < min THEN min:=l FI;
          matrix(i,j):=min
        FI
      OD
    OD;
    matrix(m,n)
  END;

  STRING word 1, word 2;
 
  word 1 :="kitten"; word 2 := "sitting";
  print((word 1," -> ",word 2,": "));
  print(("Levenshtein Distance: ",whole(levenshtein distance(word 1,word 2),0),newline));
 
  word 1 := "rosettacode"; word 2 := "raisethysword";
  print((word 1," -> ",word 2,": "));
  print(("Levenshtein Distance: ",whole(levenshtein distance(word 1,word 2),0),newline));
 
  word 1 := "qwerty"; word 2 := "qweryt";
  print((word 1," -> ",word 2,": "));
  print(("Levenshtein Distance: ",whole(levenshtein distance(word 1,word 2),0),newline));

  word 1 := "Action!"; word 2 := "Algol 68";
  print((word 1," -> ",word 2,": "));
  print(("Levenshtein Distance: ",whole(levenshtein distance(word 1,word 2),0),newline))
END
Output:
kitten -> sitting: Levenshtein Distance: 3
rosettacode -> raisethysword: Levenshtein Distance: 8
qwerty -> qweryt: Levenshtein Distance: 2
Action! -> Algol 68: Levenshtein Distance: 7

AppleScript[edit]

Iteration[edit]

Translation of the "fast" C-version

set dist to findLevenshteinDistance for "sunday" against "saturday"
to findLevenshteinDistance for s1 against s2
    script o
        property l : s1
        property m : s2
    end script
    if s1 = s2 then return 0
    set ll to length of s1
    set lm to length of s2
    if ll = 0 then return lm
    if lm = 0 then return ll
    
    set v0 to {}
    
    repeat with i from 1 to (lm + 1)
        set end of v0 to (i - 1)
    end repeat
    set item -1 of v0 to 0
    copy v0 to v1
    
    repeat with i from 1 to ll
        -- calculate v1 (current row distances) from the previous row v0
        
        -- first element of v1 is A[i+1][0]
        --   edit distance is delete (i+1) chars from s to match empty t
        set item 1 of v1 to i
        --  use formula to fill in the rest of the row
        repeat with j from 1 to lm
            if item i of o's l = item j of o's m then
                set cost to 0
            else
                set cost to 1
            end if
            set item (j + 1) of v1 to min3 for ((item j of v1) + 1) against ((item (j + 1) of v0) + 1) by ((item j of v0) + cost)
        end repeat
        copy v1 to v0
    end repeat
    return item (lm + 1) of v1
end findLevenshteinDistance

to min3 for anInt against anOther by theThird
    if anInt < anOther then
        if theThird < anInt then
            return theThird
        else
            return anInt
        end if
    else
        if theThird < anOther then
            return theThird
        else
            return anOther
        end if
    end if
end min3

Composition of generic functions[edit]

Translation of: JavaScript

(ES6 version)

In the ancient tradition of "Use library functions whenever feasible." (for better productivity), and also in the even older functional tradition of composing values (for better reliability) rather than sequencing actions:

-- levenshtein :: String -> String -> Int
on levenshtein(sa, sb)
    set {s1, s2} to {characters of sa, characters of sb}
    
    script
        on |λ|(ns, c)
            script minPath
                on |λ|(z, c1xy)
                    set {c1, x, y} to c1xy
                    minimum({y + 1, z + 1, x + fromEnum(c1 is not c)})
                end |λ|
            end script
            
            set {n, ns1} to {item 1 of ns, rest of ns}
            scanl(minPath, n + 1, zip3(s1, ns, ns1))
        end |λ|
    end script
    
    last item of foldl(result, enumFromTo(0, length of s1), s2)
end levenshtein

--------------------------- TEST ---------------------------
on run
    script test
        on |λ|(tuple)
            set {sa, sb} to tuple
            
            levenshtein(sa, sb)
        end |λ|
    end script
    
    map(test, [["kitten", "sitting"], ["sitting", "kitten"], ¬
        ["rosettacode", "raisethysword"], ["raisethysword", "rosettacode"]])
    
    --> {3, 3, 8, 8}
end run


-------------------- GENERIC FUNCTIONS ---------------------

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
    if m  n then
        set lst to {}
        repeat with i from m to n
            set end of lst to i
        end repeat
        lst
    else
        {}
    end if
end enumFromTo


-- fromEnum :: Enum a => a -> Int
on fromEnum(x)
    set c to class of x
    if c is boolean then
        if x then
            1
        else
            0
        end if
    else if c is text then
        if x  "" then
            id of x
        else
            missing value
        end if
    else
        x as integer
    end if
end fromEnum


-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
    tell mReturn(f)
        set v to startValue
        set lng to length of xs
        repeat with i from 1 to lng
            set v to |λ|(v, item i of xs, i, xs)
        end repeat
        return v
    end tell
end foldl


-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
    -- The list obtained by applying f
    -- to each element of xs.
    tell mReturn(f)
        set lng to length of xs
        set lst to {}
        repeat with i from 1 to lng
            set end of lst to |λ|(item i of xs, i, xs)
        end repeat
        return lst
    end tell
end map


-- minimum :: Ord a => [a] -> a
on minimum(xs)
    set lng to length of xs
    if lng < 1 then return missing value
    set m to item 1 of xs
    repeat with x in xs
        set v to contents of x
        if v < m then set m to v
    end repeat
    return m
end minimum


-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
    -- 2nd class handler function lifted into 1st class script wrapper. 
    if script is class of f then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn


-- scanl :: (b -> a -> b) -> b -> [a] -> [b]
on scanl(f, startValue, xs)
    tell mReturn(f)
        set v to startValue
        set lng to length of xs
        set lst to {startValue}
        repeat with i from 1 to lng
            set v to |λ|(v, item i of xs, i, xs)
            set end of lst to v
        end repeat
        return lst
    end tell
end scanl


-- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
on zip3(xs, ys, zs)
    script
        on |λ|(x, i)
            {x, item i of ys, item i of zs}
        end |λ|
    end script
    map(result, items 1 thru ¬
        minimum({length of xs, length of ys, length of zs}) of xs)
end zip3
Output:
{3, 3, 8, 8}

Arc[edit]

Waterhouse Arc[edit]

O(n * m) time, linear space, using lists instead of vectors

(def levenshtein (str1 str2)
  (withs l1  len.str1
         l2  len.str2
         row range0:inc.l1

    (times j l2
      (let next list.j
        (times i l1
          (push
            (inc:min
              car.next
              ((if (is str1.i str2.j) dec id) car.row)
              (car:zap cdr row))
            next))
        (= row nrev.next)))
    row.l1))

Arturo[edit]

print levenshtein "kitten" "sitting"
Output:
3

AutoHotkey[edit]

Translation of: Go
levenshtein(s, t){
	If s =
		return StrLen(t)
	If t =
		return strLen(s)
	If SubStr(s, 1, 1) = SubStr(t, 1, 1)
		return levenshtein(SubStr(s, 2), SubStr(t, 2))
	a := Levenshtein(SubStr(s, 2), SubStr(t, 2))
	b := Levenshtein(s,            SubStr(t, 2))
	c := Levenshtein(SubStr(s, 2), t           )
	If (a > b)
		a := b
	if (a > c)
		a := c
	return a + 1
}
s1 := "kitten"
s2 := "sitting"
MsgBox % "distance between " s1 " and " s2 ": " levenshtein(s1, s2)
It correctly outputs '3'

AWK[edit]

Slavishly copied from the very clear AutoHotKey example.

#!/usr/bin/awk -f

BEGIN {
    a = "kitten";
    b = "sitting";
    d = levenshteinDistance(a, b);
    p = d == 1 ? "" : "s";
    printf("%s -> %s after %d edit%s\n", a, b, d, p);
    exit;
}

function levenshteinDistance(s1, s2,
    s1First, s2First, s1Rest, s2Rest,
    distA, distB, distC, minDist) {

    # If either string is empty,
    # then distance is insertion of the other's characters.
    if (length(s1) == 0) return length(s2);
    if (length(s2) == 0) return length(s1);

    # Rest of process uses first characters 
    # and remainder of each string.
    s1First = substr(s1, 1, 1);
    s2First = substr(s2, 1, 1);
    s1Rest = substr(s1, 2, length(s1));
    s2Rest = substr(s2, 2, length(s2));

    # If leading characters are the same, 
    # then distance is that between the rest of the strings.
    if (s1First == s2First) {
        return levenshteinDistance(s1Rest, s2Rest);
    }

    # Find the distances between sub strings.
    distA = levenshteinDistance(s1Rest, s2);
    distB = levenshteinDistance(s1, s2Rest);
    distC = levenshteinDistance(s1Rest, s2Rest);

    # Return the minimum distance between substrings.    
    minDist = distA;
    if (distB < minDist) minDist = distB;
    if (distC < minDist) minDist = distC;
    return minDist + 1; # Include change for the first character.
}

Example output:

kitten -> sitting after 3 edits


Alternative, much faster but also less readable lazy-evaluation version from http://awk.freeshell.org/LevenshteinEditDistance (where the above takes e.g. 0m44.904s in gawk 4.1.3 for 5 edits (length 10 and 14 strings), this takes user 0m0.004s):

#!/usr/bin/awk -f

function levdist(str1, str2,	l1, l2, tog, arr, i, j, a, b, c) {
	if (str1 == str2) {
		return 0
	} else if (str1 == "" || str2 == "") {
		return length(str1 str2)
	} else if (substr(str1, 1, 1) == substr(str2, 1, 1)) {
		a = 2
		while (substr(str1, a, 1) == substr(str2, a, 1)) a++
		return levdist(substr(str1, a), substr(str2, a))
	} else if (substr(str1, l1=length(str1), 1) == substr(str2, l2=length(str2), 1)) {
		b = 1
		while (substr(str1, l1-b, 1) == substr(str2, l2-b, 1)) b++
		return levdist(substr(str1, 1, l1-b), substr(str2, 1, l2-b))
	}
	for (i = 0; i <= l2; i++) arr[0, i] = i
	for (i = 1; i <= l1; i++) {
		arr[tog = ! tog, 0] = i
		for (j = 1; j <= l2; j++) {
			a = arr[! tog, j  ] + 1
			b = arr[  tog, j-1] + 1
			c = arr[! tog, j-1] + (substr(str1, i, 1) != substr(str2, j, 1))
			arr[tog, j] = (((a<=b)&&(a<=c)) ? a : ((b<=a)&&(b<=c)) ? b : c)
		}
	}
	return arr[tog, j-1]
}

BBC BASIC[edit]

      PRINT "'kitten' -> 'sitting' has distance " ;
      PRINT ; FNlevenshtein("kitten", "sitting")
      PRINT "'rosettacode' -> 'raisethysword' has distance " ;
      PRINT ; FNlevenshtein("rosettacode", "raisethysword")
      END
      
      DEF FNlevenshtein(s$, t$)
      LOCAL i%, j%, m%, d%()
      DIM d%(LENs$, LENt$)
      FOR i% = 0 TO DIM(d%(),1)
        d%(i%,0) = i%
      NEXT
      FOR j% = 0 TO DIM(d%(),2)
        d%(0,j%) = j%
      NEXT
      FOR j% = 1 TO DIM(d%(),2)
        FOR i% = 1 TO DIM(d%(),1)
          IF MID$(s$,i%,1) = MID$(t$,j%,1) THEN
            d%(i%,j%) = d%(i%-1,j%-1)
          ELSE
            m% = d%(i%-1,j%-1)
            IF d%(i%,j%-1) < m% m% = d%(i%,j%-1)
            IF d%(i%-1,j%) < m% m% = d%(i%-1,j%)
            d%(i%,j%) = m% + 1
          ENDIF
        NEXT
      NEXT j%
      = d%(i%-1,j%-1)

Output:

'kitten' -> 'sitting' has distance 3
'rosettacode' -> 'raisethysword' has distance 8

BQN[edit]

Recursive slow version:

Levenshtein ← {
  𝕨 𝕊"": ≠𝕨;
  ""𝕊 𝕩: ≠𝕩;
  𝕨 𝕊 𝕩:
    Tail←1⊸↓
    𝕨 =○⊑◶⟨1+·⌊´ 𝕊○Tail ∾ Tail⊸𝕊 ∾ 𝕊⟜Tail, 𝕊○Tail⟩ 𝕩
}

Fast version:

Levenshtein ← @⊸∾⊸{¯1⊑(↕≠𝕨)𝕨{(1⊸+⊸⌊`1⊸+⌊⊑⊸»+𝕨≠𝕗˙)𝕩}´⌽𝕩}
Example use:
   "kitten" Levenshtein "sitting"
3
   "Saturday" Levenshtein "Sunday"
3
   "rosettacode" Levenshtein "raisethysword"
8

Bracmat[edit]

Translation of: C

Recursive method, but with memoization.

(levenshtein=
  lev cache
.   ( lev
    =   s s0 s1 t t0 t1 L a b c val key
      .     (cache..find)$(str$!arg:?key):(?.?val)
          & !val
        |   !arg:(?s,?t)
          & ( !s:&@(!t:? [?L)
            | !t:&@(!s:? [?L)
            )
          & (cache..insert)$(!key.!L)
          & !L
        |   !arg:(@(?:%?s0 ?s1),@(?:%?t0 ?t1))
          & !s0:!t0
          & lev$(!s1,!t1)
        |   lev$(!s1,!t1):?a
          & lev$(!s,!t1):?b
          & lev$(!s1,!t):?c
          & (!b:<!a:?a|)
          & (!c:<!a:?a|)
          & (cache..insert)$(!key.1+!a)
          & 1+!a
    )
  & new$hash:?cache
  & lev$!arg);
Demonstrating:
 levenshtein$(kitten,sitting)
 3
 levenshtein$(rosettacode,raisethysword)
 8

C[edit]

Recursive method. Deliberately left in an inefficient state to show the recursive nature of the algorithm; notice how it would have become the Wikipedia algorithm if we memoized the function against parameters ls and lt.

#include <stdio.h>
#include <string.h>

/* s, t: two strings; ls, lt: their respective length */
int levenshtein(const char *s, int ls, const char *t, int lt)
{
        int a, b, c;

        /* if either string is empty, difference is inserting all chars 
         * from the other
         */
        if (!ls) return lt;
        if (!lt) return ls;

        /* if last letters are the same, the difference is whatever is
         * required to edit the rest of the strings
         */
        if (s[ls - 1] == t[lt - 1])
                return levenshtein(s, ls - 1, t, lt - 1);

        /* else try:
         *      changing last letter of s to that of t; or
         *      remove last letter of s; or
         *      remove last letter of t,
         * any of which is 1 edit plus editing the rest of the strings
         */
        a = levenshtein(s, ls - 1, t, lt - 1);
        b = levenshtein(s, ls,     t, lt - 1);
        c = levenshtein(s, ls - 1, t, lt    );

        if (a > b) a = b;
        if (a > c) a = c;

        return a + 1;
}

int main()
{
        const char *s1 = "rosettacode";
        const char *s2 = "raisethysword";
        printf("distance between `%s' and `%s': %d\n", s1, s2,
                levenshtein(s1, strlen(s1), s2, strlen(s2)));

        return 0;
}

Take the above and add caching, we get (in C99):

#include <stdio.h>
#include <string.h>

int levenshtein(const char *s, const char *t)
{
	int ls = strlen(s), lt = strlen(t);
	int d[ls + 1][lt + 1];

	for (int i = 0; i <= ls; i++)
		for (int j = 0; j <= lt; j++)
			d[i][j] = -1;

	int dist(int i, int j) {
		if (d[i][j] >= 0) return d[i][j];

		int x;
		if (i == ls)
			x = lt - j;
		else if (j == lt)
			x = ls - i;
		else if (s[i] == t[j])
			x = dist(i + 1, j + 1);
		else {
			x = dist(i + 1, j + 1);

			int y;
			if ((y = dist(i, j + 1)) < x) x = y;
			if ((y = dist(i + 1, j)) < x) x = y;
			x++;
		}
		return d[i][j] = x;
	}
	return dist(0, 0);
}

int main(void)
{
	const char *s1 = "rosettacode";
	const char *s2 = "raisethysword";
	printf("distance between `%s' and `%s': %d\n", s1, s2,
		levenshtein(s1, s2));
 
        return 0;
}

C#[edit]

This is a straightforward translation of the Wikipedia pseudocode.

using System;

namespace LevenshteinDistance
{
    class Program
    {
        static int LevenshteinDistance(string s, string t)
        {
            int n = s.Length;
            int m = t.Length;
            int[,] d = new int[n + 1, m + 1];
		
	    if (n == 0)
	    {
		return m;
	    }
	
	    if (m == 0)
	    {
		return n;
	    }

            for (int i = 0; i <= n; i++)
                d[i, 0] = i;
            for (int j = 0; j <= m; j++)
                d[0, j] = j;
			
            for (int j = 1; j <= m; j++)
                for (int i = 1; i <= n; i++)
                    if (s[i - 1] == t[j - 1])
                        d[i, j] = d[i - 1, j - 1];  //no operation
                    else
                        d[i, j] = Math.Min(Math.Min(
                            d[i - 1, j] + 1,    //a deletion
                            d[i, j - 1] + 1),   //an insertion
                            d[i - 1, j - 1] + 1 //a substitution
                            );
            return d[n, m];
        }

        static void Main(string[] args)
        {
            if (args.Length == 2)
                Console.WriteLine("{0} -> {1} = {2}",
                    args[0], args[1], LevenshteinDistance(args[0], args[1]));
            else
                Console.WriteLine("Usage:-\n\nLevenshteinDistance <string1> <string2>");
        }
    }
}
Example output:
> LevenshteinDistance kitten sitting
kitten -> sitting = 3

> LevenshteinDistance rosettacode raisethysword
rosettacode -> raisethysword = 8

C++[edit]

#include <string>
#include <iostream>
using namespace std;

// Compute Levenshtein Distance
// Martin Ettl, 2012-10-05

size_t uiLevenshteinDistance(const string &s1, const string &s2)
{
  const size_t
    m(s1.size()),
    n(s2.size());

  if( m==0 ) return n;
  if( n==0 ) return m;

  // allocation below is not ISO-compliant,
  // it won't work with -pedantic-errors.
  size_t costs[n + 1];

  for( size_t k=0; k<=n; k++ ) costs[k] = k;

  size_t i { 0 };
  for (char const &c1 : s1) 
  {
    costs[0] = i+1;
    size_t corner { i },
           j      { 0 };
    for (char const &c2 : s2)
    {
      size_t upper { costs[j+1] };
      if( c1 == c2 ) costs[j+1] = corner;
      else {
        size_t t(upper<corner? upper: corner);
        costs[j+1] = (costs[j]<t?costs[j]:t)+1;
      }

      corner = upper;
      j++;
    }
    i++;
  }

  return costs[n];
}

int main()
{
  string s0 { "rosettacode" },
         s1 { "raisethysword" };
  cout << "distance between " << s0 << " and " << s1 << " : " 
    << uiLevenshteinDistance(s0,s1) << endl;

  return 0;
}
Example output:
$ ./a.out rosettacode raisethysword
distance between rosettacode and raisethysword : 8

Generic ISO C++ version[edit]

#include <algorithm>
#include <iostream>
#include <numeric>
#include <string>
#include <vector>
 
template <typename StringType>
size_t levenshtein_distance(const StringType& s1, const StringType& s2) {
    const size_t m = s1.size();
    const size_t n = s2.size();
    if (m == 0)
        return n;
    if (n == 0)
        return m;
    std::vector<size_t> costs(n + 1);
    std::iota(costs.begin(), costs.end(), 0);
    size_t i = 0;
    for (auto c1 : s1) {
        costs[0] = i + 1;
        size_t corner = i;
        size_t j = 0;
        for (auto c2 : s2) {
            size_t upper = costs[j + 1];
            costs[j + 1] = (c1 == c2) ? corner
                : 1 + std::min(std::min(upper, corner), costs[j]);
            corner = upper;
            ++j;
        }
        ++i;
    }
    return costs[n];
}
 
int main() {
    std::wstring s0 = L"rosettacode";
    std::wstring s1 = L"raisethysword";
    std::wcout << L"distance between " << s0 << L" and " << s1 << L": "
        << levenshtein_distance(s0, s1) << std::endl;
    return 0;
}
Output:
distance between rosettacode and raisethysword: 8

Clojure[edit]

Recursive Version[edit]

(defn levenshtein [str1 str2]
  (let [len1 (count str1)
        len2 (count str2)]
    (cond (zero? len1) len2
          (zero? len2) len1
          :else
          (let [cost (if (= (first str1) (first str2)) 0 1)]
            (min (inc (levenshtein (rest str1) str2))
                 (inc (levenshtein str1 (rest str2)))
                 (+ cost
                    (levenshtein (rest str1) (rest str2))))))))

(println (levenshtein "rosettacode" "raisethysword"))
Output:
8

Iterative version[edit]

(defn levenshtein [w1 w2]
  (letfn [(cell-value [same-char? prev-row cur-row col-idx]
            (min (inc (nth prev-row col-idx))
                 (inc (last cur-row))
                 (+ (nth prev-row (dec col-idx)) (if same-char?
                                                   0
                                                   1))))]
    (loop [row-idx  1
           max-rows (inc (count w2))
           prev-row (range (inc (count w1)))]
      (if (= row-idx max-rows)
        (last prev-row)
        (let [ch2           (nth w2 (dec row-idx))
              next-prev-row (reduce (fn [cur-row i]
                                      (let [same-char? (= (nth w1 (dec i)) ch2)]
                                        (conj cur-row (cell-value same-char?
                                                                  prev-row
                                                                  cur-row
                                                                  i))))
                                    [row-idx] (range 1 (count prev-row)))]
          (recur (inc row-idx) max-rows next-prev-row))))))

CLU[edit]

min = proc [T: type] (a, b: T) returns (T) 
      where T has lt: proctype (T,T) returns (bool)
    if a<b 
        then return(a) 
        else return(b)
    end
end min

levenshtein = proc (s, t: string) returns (int)
    ai = array[int]
    aai = array[array[int]]
    m: int := string$size(s)
    n: int := string$size(t)
    
    d: aai := aai$fill_copy(0, m+1, ai$fill(0, n+1, 0))
    
    for i: int in int$from_to(1, m) do d[i][0] := i end
    for j: int in int$from_to(1, n) do d[0][j] := j end
    
    for j: int in int$from_to(1, n) do
        for i: int in int$from_to(1, m) do  
            cost: int
            if s[i] = t[j]
                then cost := 0
                else cost := 1
            end
            d[i][j] := min[int]( d[i-1][j]+1,
                       min[int]( d[i][j-1]+1,
                                 d[i-1][j-1]+cost ))
        end
    end
    
    return (d[m][n])
end levenshtein

show = proc (s, t: string)
    po: stream := stream$primary_output()
    stream$putl(po, s || " => " || t || ": " || int$unparse(levenshtein(s,t)))
end show

start_up = proc ()
    show("kitten", "sitting")
    show("rosettacode", "raisethysword")
end start_up
Output:
kitten => sitting: 3
rosettacode => raisethysword: 8

COBOL[edit]

GnuCobol 2.2

       identification division.
       program-id. Levenshtein.
 
       environment division.
       configuration section.
       repository.
           function all intrinsic.
 
       data division.
       working-storage section.
       77  string-a               pic x(255).
       77  string-b               pic x(255).
       77  length-a               pic 9(3).
       77  length-b               pic 9(3).
       77  distance               pic z(3).
       77  i                      pic 9(3).
       77  j                      pic 9(3).
       01  tab.
           05 filler              occurs 256.
              10 filler           occurs 256.
                 15 costs         pic 9(3).

       procedure division.
       main.
           move "kitten" to string-a
           move "sitting" to string-b
           perform levenshtein-dist

           move "rosettacode" to string-a
           move "raisethysword" to string-b
           perform levenshtein-dist
           stop run
           .
       levenshtein-dist.
           move length(trim(string-a)) to length-a
           move length(trim(string-b)) to length-b

           initialize tab
           
           perform varying i from 0 by 1 until i > length-a
              move i to costs(i + 1, 1)
           end-perform

           perform varying j from 0 by 1 until j > length-b
              move j to costs(1, j + 1)
           end-perform
           
           perform with test after varying i from 2 by 1 until i > length-a
              perform with test after varying j from 2 by 1 until j > length-b
                 if string-a(i - 1:1) = string-b(j - 1:1)
                    move costs(i - 1, j - 1) to costs(i, j)
                 else
                    move min(min(costs(i - 1, j) + 1,     *> a deletion
                                 costs(i, j - 1) + 1),    *> an insertion
                             costs(i - 1, j - 1) + 1)     *> a substitution
                       to costs(i, j)
                 end-if
              end-perform
           end-perform
           move costs(length-a + 1, length-b + 1) to distance
           display trim(string-a) " -> " trim(string-b) " = " trim(distance)
           .
Output:
> ./Levenshtein
kitten -> sitting = 3
rosettacode -> raisethysword = 8

CoffeeScript[edit]

levenshtein = (str1, str2) ->
  # more of less ported simple algorithm from JS
  m = str1.length
  n = str2.length
  d = []

  return n  unless m
  return m  unless n

  d[i] = [i] for i in [0..m]
  d[0][j] = j for j in [1..n]  
    
  for i in [1..m]
    for j in [1..n]
      if str1[i-1] is str2[j-1]
        d[i][j] = d[i-1][j-1]
      else
        d[i][j] = Math.min(
          d[i-1][j]
          d[i][j-1]
          d[i-1][j-1]
        ) + 1

  d[m][n]

console.log levenshtein("kitten", "sitting")
console.log levenshtein("rosettacode", "raisethysword")
console.log levenshtein("stop", "tops")
console.log levenshtein("yo", "")
console.log levenshtein("", "yo")

Common Lisp[edit]

(defun levenshtein (a b)
  (let* ((la  (length a))
         (lb  (length b))
         (rec (make-array (list (1+ la) (1+ lb)) :initial-element nil)))
    (labels ((leven (x y)
               (cond
                 ((zerop x) y)
                 ((zerop y) x)
                 ((aref rec x y) (aref rec x y))
                 (t (setf (aref rec x y)
                          (+ (if (char= (char a (- la x)) (char b (- lb y))) 0 1)
                             (min (leven (1- x) y)
                                  (leven x (1- y))
                                  (leven (1- x) (1- y)))))))))
      (leven la lb))))

(print (levenshtein "rosettacode" "raisethysword"))
Output:
8

Crystal[edit]

The standard library includes levenshtein module

require "levenshtein"
puts Levenshtein.distance("kitten", "sitting")
puts Levenshtein.distance("rosettacode", "raisethysword")
Output:
3
8
Translation of: Ruby 1st version
module Levenshtein
 
  def self.distance(a, b)
    a, b = a.downcase, b.downcase
    costs = (0..b.size).to_a
    (1..a.size).each do |i|
      costs[0], nw = i, i - 1  # j == 0; nw is lev(i-1, j)
      (1..b.size).each do |j|
        costs[j], nw = [costs[j] + 1, costs[j-1] + 1, a[i-1] == b[j-1] ? nw : nw + 1].min, costs[j]
      end
    end
    costs[b.size]
  end
 
  def self.test
    %w{kitten sitting saturday sunday rosettacode raisethysword}.each_slice(2) do |(a, b)| #or do |pair| a, b = pair
      puts "distance(#{a}, #{b}) = #{distance(a, b)}"
    end
  end
 
end
 
Levenshtein.test
Output:
distance(kitten, sitting) = 3
distance(saturday, sunday) = 3
distance(rosettacode, raisethysword) = 8
Translation of: Ruby 2nd version
def levenshtein_distance(str1, str2)
  n, m = str1.size, str2.size
  max = n / 2
  
  return 0 if n == 0 || m == 0
  return n if (n - m).abs > max
 
  d = (0..m).to_a
  x = 0
 
  str1.each_char_with_index do |char1, i|
    e = i + 1
 
    str2.each_char_with_index do |char2, j|
      cost = (char1 == char2) ? 0 : 1
      x = [ d[j+1] + 1, # insertion
            e + 1,      # deletion
            d[j] + cost # substitution
          ].min
      d[j] = e
      e = x
    end
 
    d[m] = x
  end
  x
end

%w{kitten sitting saturday sunday rosettacode raisethysword}.each_slice(2) do |(a, b)| #or do |pair| a, b = pair
  puts "distance(#{a}, #{b}) = #{levenshtein_distance(a, b)}"
end
Output:
distance(kitten, sitting) = 3
distance(saturday, sunday) = 3
distance(rosettacode, raisethysword) = 8

D[edit]

Standard Version[edit]

The standard library std.algorithm module includes a Levenshtein distance function:

void main() {
    import std.stdio, std.algorithm;

    levenshteinDistance("kitten", "sitting").writeln;
}
Output:
3

Iterative Version[edit]

Translation of: Java
import std.stdio, std.algorithm;

int distance(in string s1, in string s2) pure nothrow {
  auto costs = new int[s2.length + 1];

  foreach (immutable i; 0 .. s1.length + 1) {
    int lastValue = i;
    foreach (immutable j; 0 .. s2.length + 1) {
      if (i == 0)
        costs[j] = j;
      else {
        if (j > 0) {
          int newValue = costs[j - 1];
          if (s1[i - 1] != s2[j - 1])
            newValue = min(newValue, lastValue, costs[j]) + 1;
          costs[j - 1] = lastValue;
          lastValue = newValue;
        }
      }
    }

    if (i > 0)
      costs[$ - 1] = lastValue;
  }

  return costs[$ - 1];
}

void main() {
  foreach (p; [["kitten", "sitting"], ["rosettacode", "raisethysword"]])
    writefln("distance(%s, %s): %d", p[0], p[1], distance(p[0], p[1]));
}

Memoized Recursive Version[edit]

Translation of: Python
import std.stdio, std.array, std.algorithm, std.functional;

uint lDist(T)(in const(T)[] s, in const(T)[] t) nothrow {
    alias mlDist = memoize!lDist;
    if (s.empty || t.empty) return max(t.length, s.length);
    if (s[0] == t[0]) return mlDist(s[1 .. $], t[1 .. $]);
    return min(mlDist(s, t[1 .. $]),
               mlDist(s[1 .. $], t),
               mlDist(s[1 .. $], t[1 .. $])) + 1;
}

void main() {
    lDist("kitten", "sitting").writeln;
    lDist("rosettacode", "raisethysword").writeln;
}

Delphi[edit]

Translation of: C#
program Levenshtein_distanceTest;

{$APPTYPE CONSOLE}

{$R *.res}

uses
  System.SysUtils,
  Math;

function Levenshtein_distance(s, t: string): integer;
var
  d: array of array of integer;
  i, j, cost: integer;
begin
  SetLength(d, Length(s) + 1);
  for i := Low(d) to High(d) do
  begin
    SetLength(d[i], Length(t) + 1);
  end;

  for i := Low(d) to High(d) do
  begin
    d[i, 0] := i;
    for j := Low(d[i]) to High(d[i]) do
    begin
      d[0, j] := j;
    end;
  end;

  for i := Low(d) + 1 to High(d) do
  begin
    for j := Low(d[i]) + 1 to High(d[i]) do
    begin
      if s[i] = t[j] then
      begin
        cost := 0;
      end
      else
      begin
        cost := 1;
      end;

      d[i, j] := Min(Min(d[i - 1, j] + 1,      //deletion
        d[i, j - 1] + 1),     //insertion
        d[i - 1, j - 1] + cost  //substitution
      );
    end;
  end;
  Result := d[Length(s), Length(t)];
end;

procedure Println(s, t: string);
begin
  Writeln('> LevenshteinDistance "', s, '" "', t, '"');
  Writeln(s, ' -> ', t, ' = ', Levenshtein_distance(s, t), #10);
end;

begin
  Println('kitten', 'sitting');
  Println('rosettacode', 'raisethysword');
  readln;
end.


DWScript[edit]

Based on Wikipedia version

function LevenshteinDistance(s, t : String) : Integer;
var
   i, j : Integer;
begin
   var d:=new Integer[Length(s)+1, Length(t)+1];
   for i:=0 to Length(s) do
      d[i, 0] := i;
   for j:=0 to Length(t) do
      d[0, j] := j;
   
   for j:=1 to Length(t) do
      for i:=1 to Length(s) do
         if s[i]=t[j] then
            d[i, j] := d[i-1, j-1] // no operation
         else d[i,j]:=MinInt(MinInt(
               d[i-1, j] +1 ,    // a deletion
               d[i, j-1] +1 ),   // an insertion
               d[i- 1,j-1] +1    // a substitution
               );
   Result:=d[Length(s), Length(t)];
end;

PrintLn(LevenshteinDistance('kitten', 'sitting'));

Dyalect[edit]

func levenshtein(s, t) {
    var n = s.Length()
    var m = t.Length()
    var d = Array.Empty(n + 1, () => Array.Empty(m + 1))
 
    if n == 0 {
        return m
    }
 
    if (m == 0) {
        return n
    }
 
    for i in 0..n {
        d[i][0] = i
    }
 
    for j in 0..m {
        d[0][j] = j
    }
 
    for j in 1..m {
        for i in 1..n {
            if s[i - 1] == t[j - 1] {
                d[i][j] = d[i - 1][j - 1] //no operation
            }
            else {
                d[i][j] = min(min(
                    d[i - 1][j] + 1,    //a deletion
                    d[i][j - 1] + 1),   //an insertion
                    d[i - 1][j - 1] + 1 //a substitution
                    )
            }
        }
    }
 
    d[n][m]
}
 
func run(x, y) {
    print("\(x) -> \(y) = \(levenshtein(x, y))")
}
 
run("rosettacode", "raisethysword")
Output:
rosettacode -> raisethysword = 8

EchoLisp[edit]

;; Recursive version adapted from Clojure
;; Added necessary memoization

(define (levenshtein str1 str2 (cost 0) (rest1 0) (rest2 0) (key null))
(set! key (string-append str1 "|" str2))
(if (get 'mem key) ;; memoized ?
    (get 'mem key)
;; else memoize
(putprop 'mem 
  (let [(len1 (string-length str1))
        (len2 (string-length str2))]
    (cond ((zero? len1) len2)
          ((zero? len2) len1)
          (else
          (set! cost (if (= (string-first str1) (string-first str2)) 0 1))
          (set! rest1 (string-rest str1))
          (set! rest2 (string-rest str2))
            (min (1+ (levenshtein rest1 str2))
                 (1+ (levenshtein str1 rest2))
                 (+ cost
                    (levenshtein rest1 rest2 ))))))
    key)))

;; 😛 127 calls with memoization
;; 😰 29737 calls without memoization
(levenshtein "kitten" "sitting")  3

(levenshtein "rosettacode" "raisethysword")  8

Ela[edit]

This code is translated from Haskell version.

open list

levenshtein s1 s2 = last <| foldl transform [0 .. length s1] s2  
            where transform (n::ns')@ns c = scanl calc (n+1) <| zip3 s1 ns ns'
                        where calc z (c', x, y) = minimum [y+1, z+1, x + toInt (c' <> c)]

Executing:

(levenshtein "kitten" "sitting", levenshtein "rosettacode" "raisethysword")
Output:
(3, 8)

Elixir[edit]

Translation of: Ruby
defmodule Levenshtein do
  def distance(a, b) do
    ta = String.downcase(a) |> to_charlist |> List.to_tuple
    tb = String.downcase(b) |> to_charlist |> List.to_tuple
    m = tuple_size(ta)
    n = tuple_size(tb)
    costs = Enum.reduce(0..m, %{},   fn i,acc -> Map.put(acc, {i,0}, i) end)
    costs = Enum.reduce(0..n, costs, fn j,acc -> Map.put(acc, {0,j}, j) end)
    Enum.reduce(0..n-1, costs, fn j, acc ->
      Enum.reduce(0..m-1, acc, fn i, map ->
        d = if elem(ta, i) == elem(tb, j) do
              map[ {i,j} ]
            else
              Enum.min([ map[ {i  , j+1} ] + 1,         # deletion
                         map[ {i+1, j  } ] + 1,         # insertion
                         map[ {i  , j  } ] + 1 ])       # substitution
            end
        Map.put(map, {i+1, j+1}, d)
      end)
    end)
    |> Map.get({m,n})
  end
end

words = ~w(kitten sitting saturday sunday rosettacode raisethysword)
Enum.each(Enum.chunk(words, 2), fn [a,b] ->
  IO.puts "distance(#{a}, #{b}) = #{Levenshtein.distance(a,b)}"
end)
Output:
distance(kitten, sitting) = 3
distance(saturday, sunday) = 3
distance(rosettacode, raisethysword) = 8

Erlang[edit]

Here are two implementations. The first is the naive version, the second is a memoized version using Erlang's dictionary datatype.

-module(levenshtein).
-compile(export_all).

distance_cached(S,T) ->
    {L,_} = ld(S,T,dict:new()),
    L.

distance(S,T) ->
    ld(S,T).

ld([],T) ->
    length(T);
ld(S,[]) ->
    length(S);
ld([X|S],[X|T]) ->
    ld(S,T);
ld([_SH|ST]=S,[_TH|TT]=T) ->
    1 + lists:min([ld(S,TT),ld(ST,T),ld(ST,TT)]).

ld([]=S,T,Cache) ->
    {length(T),dict:store({S,T},length(T),Cache)};
ld(S,[]=T,Cache) ->
    {length(S),dict:store({S,T},length(S),Cache)};
ld([X|S],[X|T],Cache) ->
    ld(S,T,Cache);
ld([_SH|ST]=S,[_TH|TT]=T,Cache) ->
    case dict:is_key({S,T},Cache) of
        true -> {dict:fetch({S,T},Cache),Cache};
        false ->
            {L1,C1} = ld(S,TT,Cache),
            {L2,C2} = ld(ST,T,C1),
            {L3,C3} = ld(ST,TT,C2),
            L = 1+lists:min([L1,L2,L3]),
            {L,dict:store({S,T},L,C3)}
    end.

Below is a comparison of the runtimes, measured in microseconds, between the two implementations.

68> timer:tc(levenshtein,distance,["rosettacode","raisethysword"]).
{774799,8} % {Time, Result}
69> timer:tc(levenshtein,distance_cached,["rosettacode","raisethysword"]).
{659,8}
70> timer:tc(levenshtein,distance,["kitten","sitting"]).
{216,3}
71> timer:tc(levenshtein,distance_cached,["kitten","sitting"]).
{213,3}

ERRE[edit]

PROGRAM LEVENSHTEIN

!$DYNAMIC
  DIM D%[0,0]

PROCEDURE LEVENSHTEIN(S$,T$->RES%)
      LOCAL I%,J%,M%
      FOR I%=0 TO LEN(S$) DO
        D%[I%,0]=I%
      END FOR
      FOR J%=0 TO LEN(T$) DO
        D%[0,J%]=J%
      END FOR
      FOR J%=1 TO LEN(T$) DO
        FOR I%=1 TO LEN(S$) DO
          IF MID$(S$,I%,1)=MID$(T$,J%,1) THEN
            D%[I%,J%]=D%[I%-1,J%-1]
          ELSE
            M%=D%[I%-1,J%-1]
            IF D%[I%,J%-1]<M% THEN M%=D%[I%,J%-1] END IF
            IF D%[I%-1,J%]<M% THEN M%=D%[I%-1,J%] END IF
            D%[I%,J%]=M%+1
          END IF
        END FOR
      END FOR
      RES%=D%[I%-1,J%-1]
END PROCEDURE

BEGIN
   S$="kitten"  T$="sitting"
   PRINT("'";S$;"' -> '";T$;"' has distance ";)
   !$DIM D%[LEN(S$),LEN(T$)]
   LEVENSHTEIN(S$,T$->RES%)
   PRINT(RES%)
   !$ERASE D%

   S$="rosettacode" T$="raisethysword"
   PRINT("'";S$;"' -> '";T$;"' has distance ";)
   !$DIM D%[LEN(S$),LEN(T$)]
   LEVENSHTEIN(S$,T$->RES%)
   PRINT(RES%)
   !$ERASE D%
END PROGRAM
Output:

'kitten' -> 'sitting' has distance 3 'rosettacode' -> 'raisethysword' has distance 8

Euphoria[edit]

Code by Jeremy Cowgar from the Euphoria File Archive.

function min(sequence s)
    atom m
    m = s[1]
    for i = 2 to length(s) do
        if s[i] < m then
            m = s[i]
        end if
    end for
    return m
end function

function levenshtein(sequence s1, sequence s2)
    integer n, m
    sequence d
    n = length(s1) + 1
    m = length(s2) + 1

    if n = 1  then
        return m-1
    elsif m = 1 then
        return n-1
    end if

    d = repeat(repeat(0, m), n)
    for i = 1 to n do
        d[i][1] = i-1
    end for

    for j = 1 to m do
        d[1][j] = j-1
    end for

    for i = 2 to n do
        for j = 2 to m do
            d[i][j] = min({
                d[i-1][j] + 1,
                d[i][j-1] + 1,
                d[i-1][j-1] + (s1[i-1] != s2[j-1])
            })
        end for
    end for

    return d[n][m]
end function

? levenshtein("kitten", "sitting")
? levenshtein("rosettacode", "raisethysword")
Output:
3
8

F#[edit]

Standard version[edit]

open System

let getInput (name : string) =
    Console.Write ("String {0}: ", name)
    Console.ReadLine ()

let levDist (strOne : string) (strTwo : string) =
    let strOne = strOne.ToCharArray ()
    let strTwo = strTwo.ToCharArray ()

    let (distArray : int[,]) = Array2D.zeroCreate (strOne.Length + 1) (strTwo.Length + 1)

    for i = 0 to strOne.Length do distArray.[i, 0] <- i
    for j = 0 to strTwo.Length do distArray.[0, j] <- j

    for j = 1 to strTwo.Length do
        for i = 1 to strOne.Length do
            if strOne.[i - 1] = strTwo.[j - 1] then distArray.[i, j] <- distArray.[i - 1, j - 1]
            else
                distArray.[i, j] <- List.min (
                    [distArray.[i-1, j] + 1; 
                    distArray.[i, j-1] + 1; 
                    distArray.[i-1, j-1] + 1]
                )
    distArray.[strOne.Length, strTwo.Length]


let stringOne = getInput "One"
let stringTwo = getInput "Two"
printf "%A" (levDist stringOne stringTwo)

Console.ReadKey () |> ignore

Recursive Version[edit]

open System

let levenshtein (s1:string) (s2:string) : int =

    let s1' = s1.ToCharArray()
    let s2' = s2.ToCharArray()

    let rec dist l1 l2 =
        match (l1,l2) with
        | (l1, 0) -> l1
        | (0, l2) -> l2
        | (l1, l2) ->
            if s1'.[l1-1] = s2'.[l2-1] then dist (l1-1) (l2-1)
            else 
                let d1 = dist (l1 - 1) l2
                let d2 = dist l1 (l2 - 1)
                let d3 = dist (l1 - 1) (l2 - 1)
                1 + Math.Min(d1,(Math.Min(d2,d3)))

    dist s1.Length s2.Length
  
printfn "dist(kitten, sitting) = %i" (levenshtein "kitten" "sitting")

Factor[edit]

USING: lcs prettyprint ;
"kitten" "sitting" levenshtein .
Output:
3

Forth[edit]

Translation of: C
: levenshtein                          ( a1 n1 a2 n2 -- n3)
  dup                                  \ if either string is empty, difference
  if                                   \ is inserting all chars from the other
    2>r dup
    if
      2dup 1- chars + c@ 2r@ 1- chars + c@ =
      if
        1- 2r> 1- recurse exit
      else                             \ else try:
        2dup 1- 2r@ 1- recurse -rot    \   changing first letter of s to t;
        2dup    2r@ 1- recurse -rot    \   remove first letter of s;
        1- 2r> recurse min min 1+      \   remove first letter of t,
      then                             \ any of which is 1 edit plus 
    else                               \ editing the rest of the strings
      2drop 2r> nip
    then
  else
    2drop nip
  then
;

s" kitten"      s" sitting"       levenshtein . cr
s" rosettacode" s" raisethysword" levenshtein . cr

Fortran[edit]

program demo_edit_distance
character(len=:),allocatable :: sources(:),targets(:)
integer,allocatable          :: answers(:),expected(:)

sources=[character(len=20)   :: "kitten",  "rosettacode",   "Saturday", "sleep",    "qwerty", "Fortran" ]
targets=[character(len=20)   :: "sitting", "raisethysword", "Sunday",   "fleeting", "qweryt", "Fortran" ]
expected=[                       3,         8,               3,          5,          2,        0        ]
! calculate answers
answers=edit_distance(sources,targets)
! print inputs, answers, and confirmation
do i=1, size(sources)
   write(*,'(*(g0,1x))') sources(i), targets(i), answers(i), answers(i) == expected(i)
enddo
! a longer test
write(*,*)edit_distance("here's a bunch of words", "to wring out this code")==18

contains

pure elemental integer function edit_distance (source,target)
!! The Levenshtein distance function returns how many edits (deletions,
!! insertions, transposition) are required to turn one string into another.
character(len=*), intent(in) :: source, target
integer                      :: len_source, len_target, i, j, cost
integer                      :: matrix(0:len_trim(source), 0:len_trim(target))
   len_source = len_trim(source)
   len_target = len_trim(target)
   matrix(:,0) = [(i,i=0,len_source)]
   matrix(0,:) = [(j,j=0,len_target)]
   do i = 1, len_source
      do j = 1, len_target
         cost=merge(0,1,source(i:i)==target(j:j))
         matrix(i,j) = min(matrix(i-1,j)+1, matrix(i,j-1)+1, matrix(i-1,j-1)+cost)
      enddo
   enddo
   edit_distance = matrix(len_source,len_target)
end function edit_distance

end program demo_edit_distance
Output:
kitten               sitting              3 T
rosettacode          raisethysword        8 T
Saturday             Sunday               3 T
sleep                fleeting             5 T
qwerty               qweryt               2 T
Fortran              Fortran              0 T
 T

FreeBASIC[edit]

' FB 1.05.0 Win64

' Uses the "iterative with two matrix rows" algorithm 
' referred to in the Wikipedia article.

Function min(x As Integer, y As Integer) As Integer
   Return IIf(x < y, x, y)
End Function
 
Function levenshtein(s As String, t As String) As Integer
    ' degenerate cases
    If s = t Then Return 0
    If s = "" Then Return Len(t)
    If t = "" Then Return Len(s)

    ' create two integer arrays of distances
    Dim v0(0 To Len(t)) As Integer  '' previous
    Dim v1(0 To Len(t)) As Integer  '' current

    ' initialize v0
    For i As Integer = 0 To Len(t)
      v0(i) = i
    Next

    Dim cost As Integer
    For i As Integer = 0 To Len(s) - 1
      ' calculate v1 from v0
      v1(0) = i + 1
      
      For j As Integer = 0 To Len(t) - 1
        cost = IIf(s[i] = t[j], 0, 1)
        v1(j + 1) = min(v1(j) + 1, min(v0(j + 1) + 1, v0(j) + cost))
      Next j

      ' copy v1 to v0 for next iteration
      For j As Integer = 0 To Len(t)
        v0(j) = v1(j)
      Next  j
    Next i 

    Return v1(Len(t))
End Function

Print "'kitten' to 'sitting'            => "; levenshtein("kitten", "sitting")
Print "'rosettacode' to 'raisethysword' => "; levenshtein("rosettacode", "raisethysword") 
Print "'sleep' to 'fleeting'            => "; levenshtein("sleep", "fleeting")
Print
Print "Press any key to quit"
Sleep
Output:
'kitten' to 'sitting'            =>  3
'rosettacode' to 'raisethysword' =>  8
'sleep' to 'fleeting'            =>  5

Frink[edit]

Frink has a built-in function to calculate the Levenshtein edit distance between two strings:

println[editDistance["kitten","sitting"]]

It also has a function to calculate the Levenshtein-Damerau edit distance, editDistanceDamerau[str1,str2]. This is similar to the editDistance function but also allows swaps between two adjoining characters, which count as an edit distance of 1. This may make distances between some strings shorter, by say, treating transposition errors in a word as a less expensive operation than in the pure Levenshtein algorithm, and is generally more useful in more circumstances.

FutureBasic[edit]

Recursive version.

local fn LevenshteinDistance( s1 as CFStringRef, s2 as CFStringRef ) as NSInteger
  NSInteger result
  
  // If strings are equal, Levenshtein distance is 0
  if ( fn StringIsEqual( s1, s2 ) ) then result = 0 : exit fn
  
  // If either string is empty, then distance is the length of the other string.
  if ( len(s1) == 0) then result = len(s2) : exit fn
  if ( len(s2) == 0) then result = len(s1) : exit fn
  
  // The remaining recursive process uses first characters and remainder of each string.
  CFStringRef s1First = fn StringSubstringToIndex( s1, 1 )
  CFStringRef s2First = fn StringSubstringToIndex( s2, 1 )
  CFStringRef s1Rest  = mid( s1, 1, len(s1) -1 )
  CFStringRef s2Rest  = mid( s2, 1, len(s2) -1 )
  
  // If leading characters are the same, then distance is that between the rest of the strings.
  if fn StringIsEqual( s1First, s2First ) then result = fn LevenshteinDistance( s1Rest, s2Rest ) : exit fn
  
  // Find the distances between sub strings.
  NSInteger distA = fn LevenshteinDistance( s1Rest,     s2 )
  NSInteger distB = fn LevenshteinDistance( s1,     s2Rest )
  NSInteger distC = fn LevenshteinDistance( s1Rest, s2Rest )
  
  // Return the minimum distance between substrings.
  NSInteger minDist = distA
  if ( distB < minDist ) then minDist = distB
  if ( distC < minDist ) then minDist = distC
  result = minDist + 1 // Include change for the first character.
end fn = result


NSInteger  i
CFStringRef testStr( 6, 2 )

testStr( 0, 0 ) = @"kitten"      : testStr( 0, 1 ) = @"sitting"
testStr( 1, 0 ) = @"rosettacode" : testStr( 1, 1 ) = @"raisethysword"
testStr( 2, 0 ) = @"Saturday"    : testStr( 2, 1 ) = @"Sunday"
testStr( 3, 0 ) = @"FutureBasic" : testStr( 3, 1 ) = @"FutureBasic"
testStr( 4, 0 ) = @"rave"        : testStr( 4, 1 ) = @"ravel"
testStr( 5, 0 ) = @"black"       : testStr( 5, 1 ) = @"slack"
testStr( 6, 0 ) = @"rave"        : testStr( 6, 1 ) = @"grave"

for i = 0 to 6
  print @"1st string = "; testStr( i, 0 )
  print @"2nd string = "; testStr( i, 1 )
  print @"Levenshtein distance = "; fn LevenshteinDistance( testStr( i, 0 ), testStr( i, 1 ) )
  print
next

HandleEvents
Output:
1st string = kitten
2nd string = sitting
Levenshtein distance = 3

1st string = rosettacode
2nd string = raisethysword
Levenshtein distance = 8

1st string = Saturday
2nd string = Sunday
Levenshtein distance = 3

1st string = FutureBasic
2nd string = FutureBasic
Levenshtein distance = 0

1st string = rave
2nd string = ravel
Levenshtein distance = 1

1st string = black
2nd string = slack
Levenshtein distance = 1

1st string = rave
2nd string = grave
Levenshtein distance = 1

Go[edit]

WP algorithm:

package main

import "fmt"

func main() {
    fmt.Println(ld("kitten", "sitting"))
}

func ld(s, t string) int {
    d := make([][]int, len(s)+1)
    for i := range d {
        d[i] = make([]int, len(t)+1)
    }
    for i := range d {
        d[i][0] = i
    }
    for j := range d[0] {
        d[0][j] = j
    }
    for j := 1; j <= len(t); j++ {
        for i := 1; i <= len(s); i++ {
            if s[i-1] == t[j-1] {
                d[i][j] = d[i-1][j-1]
            } else {
                min := d[i-1][j]
                if d[i][j-1] < min {
                    min = d[i][j-1]
                }
                if d[i-1][j-1] < min {
                    min = d[i-1][j-1]
                }
                d[i][j] = min + 1
            }
        }

    }
    return d[len(s)][len(t)]
}
Output:
3
Translation of: C
package main

import "fmt"

func levenshtein(s, t string) int {
    if s == "" { return len(t) }
    if t == "" { return len(s) }
    if s[0] == t[0] {
        return levenshtein(s[1:], t[1:])
    }
    a := levenshtein(s[1:], t[1:])
    b := levenshtein(s,     t[1:])
    c := levenshtein(s[1:], t)
    if a > b { a = b }
    if a > c { a = c }
    return a + 1
}

func main() {
    s1 := "rosettacode"
    s2 := "raisethysword"
    fmt.Printf("distance between %s and %s: %d\n", s1, s2,
        levenshtein(s1, s2))
}
Output:
distance between rosettacode and raisethysword: 8

Groovy[edit]

def distance(String str1, String str2) {
    def dist = new int[str1.size() + 1][str2.size() + 1]
    (0..str1.size()).each { dist[it][0] = it }
    (0..str2.size()).each { dist[0][it] = it }

    (1..str1.size()).each { i ->
        (1..str2.size()).each { j ->
            dist[i][j] = [dist[i - 1][j] + 1, dist[i][j - 1] + 1, dist[i - 1][j - 1] + ((str1[i - 1] == str2[j - 1]) ? 0 : 1)].min()
        }
    }
    return dist[str1.size()][str2.size()]
}

[ ['kitten', 'sitting']: 3,
  ['rosettacode', 'raisethysword']: 8,
  ['edocattesor', 'drowsyhtesiar']: 8 ].each { key, dist ->
    println "Checking distance(${key[0]}, ${key[1]}) == $dist"
    assert distance(key[0], key[1]) == dist
}
Output:
Checking distance(kitten, sitting) == 3
Checking distance(rosettacode, raisethysword) == 8
Checking distance(edocattesor, drowsyhtesiar) == 8

Haskell[edit]

Implementation 1[edit]

levenshtein :: Eq a => [a] -> [a] -> Int
levenshtein s1 s2 = last $ foldl transform [0 .. length s1] s2
  where
    transform ns@(n:ns1) c = scanl calc (n + 1) $ zip3 s1 ns ns1
      where
        calc z (c1, x, y) = minimum [y + 1, z + 1, x + fromEnum (c1 /= c)]

main :: IO ()
main = print (levenshtein "kitten" "sitting")
Output:
3

Implementation 2[edit]

levenshtein :: Eq a => [a] -> [a] -> Int
levenshtein s1 [] = length s1
levenshtein [] s2 = length s2
levenshtein s1@(s1Head:s1Tail) s2@(s2Head:s2Tail)
    | s1Head == s2Head = levenshtein s1Tail s2Tail
    | otherwise        = 1 + minimum [score1, score2, score3]
        where score1 = levenshtein s1Tail s2Tail
              score2 = levenshtein s1 s2Tail
              score3 = levenshtein s1Tail s2

main :: IO ()
main = print (levenshtein "kitten" "sitting")
Output:
3

Icon and Unicon[edit]

procedure main()
    every process(!&input)
end
 
procedure process(s)
    s ? (s1 := tab(upto(' \t')), s2 := (tab(many(' \t')), tab(0))) | fail
    write("'",s1,"' -> '",s2,"' = ", levenshtein(s1,s2))
end
 
procedure levenshtein(s, t)
    if (n := *s+1) = 1 then return *t
    if (m := *t+1) = 1 then return *s
 
    every !(d := list(n,0)) := list(m, 0)
    every i := 1 to max(n,m) do d[i,1] := d[1,i] := i
    every d[1(i := 2 to n, s_i := s[iM1 := i-1]), j := 2 to m] :=
             min(d[iM1,j], d[i,jM1:=j-1],
                 d[iM1,jM1] + if s_i == t[jM1] then -1 else 0) + 1

    return d[n,m]-1
end
Example:
->leven
kitten  sitting
'kitten' -> 'sitting' = 3
->

Io[edit]

A levenshtein method is available on strings when the standard Range addon is loaded.

Io 20110905
Io> Range ; "kitten" levenshtein("sitting")
==> 3
Io> "rosettacode" levenshtein("raisethysword")
==> 8
Io>

J[edit]

One approach would be a literal transcription of the wikipedia implementation:

levenshtein=:4 :0
  D=. x +/&i.&>:&# y
  for_i.1+i.#x do.
    for_j.1+i.#y do.
      if. ((<:i){x)=(<:j){y do.
        D=.(D {~<<:i,j) (<i,j)} D
      else.
        min=. 1+<./D{~(i,j) <@:-"1#:1 2 3
        D=. min (<i,j)} D
      end.
    end.
  end.
  {:{:D
)

First, we setup up an matrix of costs, with 0 or 1 for unexplored cells (1 being where the character pair corresponding to that cell position has two different characters). Note that the "cost to reach the empty string" cells go on the bottom and the right, instead of the top and the left, because this works better with J's "insert" operation (which we will call "reduce" in the next paragraph here. It could also be thought of as a right fold which has been constrained such the initial value is the identity value for the operation. Or, just think of it as inserting its operation between each item of its argument...).

Then we reduce the rows of that matrix using an operation that treats those two rows as columns and reduces the rows of this derived matrix with an operation that gives the (unexplored cell + the minumum of the other cells) followed by (the cell adjacent to the previously unexplored cell.

However, this is a rather slow and bulky approach.

We can also do the usual optimization where we only represent one row of the distance matrix at a time:

levdist =:4 :0
  'a b'=. (x;y) /: (#x),(#y)
  D=. >: iz =. i.#b
  for_j. a do.
    D=. <./\&.(-&iz) (>: D) <. (j ~: b) + |.!.j_index D
  end.
  {:D
)
Example use:
   'kitten' levenshtein 'sitting'
3
   'kitten' levdist 'sitting'
3

Time and space use:

   timespacex '''kitten'' levenshtein ''sitting'''    
0.000113 6016
   timespacex '''kitten'' levdist ''sitting'''    
1.5e_5 4416

So the levdist implementation is about 7 times faster for this example (which approximately corresponds to the length of the shortest string) See the Levenshtein distance essay on the Jwiki for additional solutions.

Java[edit]

Based on the definition for Levenshtein distance given in the Wikipedia article:

public class Levenshtein {

    public static int distance(String a, String b) {
        a = a.toLowerCase();
        b = b.toLowerCase();
        // i == 0
        int [] costs = new int [b.length() + 1];
        for (int j = 0; j < costs.length; j++)
            costs[j] = j;
        for (int i = 1; i <= a.length(); i++) {
            // j == 0; nw = lev(i - 1, j)
            costs[0] = i;
            int nw = i - 1;
            for (int j = 1; j <= b.length(); j++) {
                int cj = Math.min(1 + Math.min(costs[j], costs[j - 1]), a.charAt(i - 1) == b.charAt(j - 1) ? nw : nw + 1);
                nw = costs[j];
                costs[j] = cj;
            }
        }
        return costs[b.length()];
    }

    public static void main(String [] args) {
        String [] data = { "kitten", "sitting", "saturday", "sunday", "rosettacode", "raisethysword" };
        for (int i = 0; i < data.length; i += 2)
            System.out.println("distance(" + data[i] + ", " + data[i+1] + ") = " + distance(data[i], data[i+1]));
    }
}
Output:
distance(kitten, sitting) = 3
distance(saturday, sunday) = 3
distance(rosettacode, raisethysword) = 8
Translation of: C
public class Levenshtein{
    public static int levenshtein(String s, String t){
        /* if either string is empty, difference is inserting all chars 
         * from the other
         */
        if(s.length() == 0) return t.length();
        if(t.length() == 0) return s.length();

        /* if first letters are the same, the difference is whatever is
         * required to edit the rest of the strings
         */
        if(s.charAt(0) == t.charAt(0))
            return levenshtein(s.substring(1), t.substring(1));

        /* else try:
         *      changing first letter of s to that of t,
         *      remove first letter of s, or
         *      remove first letter of t
         */
        int a = levenshtein(s.substring(1), t.substring(1));
        int b = levenshtein(s, t.substring(1));
        int c = levenshtein(s.substring(1), t);

        if(a > b) a = b;
        if(a > c) a = c;

        //any of which is 1 edit plus editing the rest of the strings
        return a + 1;
    }

    public static void main(String[] args) {
        String s1 = "kitten";
        String s2 = "sitting";
        System.out.println("distance between '" + s1 + "' and '"
                + s2 + "': " + levenshtein(s1, s2));
        s1 = "rosettacode";
        s2 = "raisethysword";
        System.out.println("distance between '" + s1 + "' and '"
                + s2 + "': " + levenshtein(s1, s2));
        StringBuilder sb1 = new StringBuilder(s1);
        StringBuilder sb2 = new StringBuilder(s2);
        System.out.println("distance between '" + sb1.reverse() + "' and '"
                + sb2.reverse() + "': "
                + levenshtein(sb1.reverse().toString(), sb2.reverse().toString()));
    }
}
Output:
distance between 'kitten' and 'sitting': 3
distance between 'rosettacode' and 'raisethysword': 8
distance between 'edocattesor' and 'drowsyhtesiar': 8

Iterative space optimized (even bounded)[edit]

Translation of: Python
import static java.lang.Math.abs;
import static java.lang.Math.max;

public class Levenshtein {

	public static int ld(String a, String b) { 
		return distance(a, b, -1);
	}
	public static boolean ld(String a, String b, int max) {
		return distance(a, b, max) <= max;
	}
	
	private static int distance(String a, String b, int max) {
		if (a == b) return 0;
		int la = a.length();
		int lb = b.length();
		if (max >= 0 && abs(la - lb) > max) return max+1;
		if (la == 0) return lb;
		if (lb == 0) return la;
		if (la < lb) {
			int tl = la; la = lb; lb = tl;
			String ts = a;  a = b; b = ts;
		}
		
		int[] cost = new int[lb+1];
		for (int i=0; i<=lb; i+=1) {
			cost[i] = i;
		}

		for (int i=1; i<=la; i+=1) {
			cost[0] = i;
			int prv = i-1;
			int min = prv;
			for (int j=1; j<=lb; j+=1) {
				int act = prv + (a.charAt(i-1) == b.charAt(j-1) ? 0 : 1);
				cost[j] = min(1+(prv=cost[j]), 1+cost[j-1], act);
				if (prv < min) min = prv;
			}
			if (max >= 0 && min > max) return max+1;
		}
		if (max >= 0 && cost[lb] > max) return max+1;
		return cost[lb];	
	}
	
	private static int min(int ... a) {
		int min = Integer.MAX_VALUE;
		for (int i: a) if (i<min) min = i;
		return min;
	}
	
	public static void main(String[] args) {
		System.out.println(
			ld("kitten","kitten") + " " + // 0
			ld("kitten","sitten") + " " + // 1
			ld("kitten","sittes") + " " + // 2
			ld("kitten","sityteng") + " " + // 3
			ld("kitten","sittYing") + " " + // 4
			ld("rosettacode","raisethysword") + " " + // 8 
			ld("kitten","kittenaaaaaaaaaaaaaaaaa") + " " + // 17
			ld("kittenaaaaaaaaaaaaaaaaa","kitten") // 17
		);
		System.out.println(
			ld("kitten","kitten", 3) + " " + // true
			ld("kitten","sitten", 3) + " " + // true
			ld("kitten","sittes", 3) + " " + // true
			ld("kitten","sityteng", 3) + " " + // true
			ld("kitten","sittYing", 3) + " " + // false
			ld("rosettacode","raisethysword", 3) + " " + // false 
			ld("kitten","kittenaaaaaaaaaaaaaaaaa", 3) + " " + // false
			ld("kittenaaaaaaaaaaaaaaaaa","kitten", 3) // false
		);
	}
}
Output:
0 1 2 3 4 8 17 17
true true true true false false false false

JavaScript[edit]

ES5[edit]

Iterative:

function levenshtein(a, b) {
  var t = [], u, i, j, m = a.length, n = b.length;
  if (!m) { return n; }
  if (!n) { return m; }
  for (j = 0; j <= n; j++) { t[j] = j; }
  for (i = 1; i <= m; i++) {
    for (u = [i], j = 1; j <= n; j++) {
      u[j] = a[i - 1] === b[j - 1] ? t[j - 1] : Math.min(t[j - 1], t[j], u[j - 1]) + 1;
    } t = u;
  } return u[n];
}

// tests
[ ['', '', 0],
  ['yo', '', 2],
  ['', 'yo', 2],
  ['yo', 'yo', 0],
  ['tier', 'tor', 2],
  ['saturday', 'sunday', 3],
  ['mist', 'dist', 1],
  ['tier', 'tor', 2],
  ['kitten', 'sitting', 3],
  ['stop', 'tops', 2],
  ['rosettacode', 'raisethysword', 8],
  ['mississippi', 'swiss miss', 8]
].forEach(function(v) {
  var a = v[0], b = v[1], t = v[2], d = levenshtein(a, b);
  if (d !== t) {
    console.log('levenstein("' + a + '","' + b + '") was ' + d + ' should be ' + t);
  }
});

ES6[edit]

Translation of: Haskell

By composition of generic functions:

(() => {
    'use strict';

    // levenshtein :: String -> String -> Int
    const levenshtein = sa => sb => {
        const cs = chars(sa);
        const go = (ns, c) => {
            const calc = z => tpl => {
                const [c1, x, y] = Array.from(tpl);
                return minimum([
                    succ(y),
                    succ(z),
                    x + (c !== c1 ? 1 : 0)
                ]);
            };
            const [n, ns1] = [ns[0], ns.slice(1)];
            return scanl(calc)(succ(n))(
                zip3(cs)(ns)(ns1)
            );
        };
        return last(
            chars(sb).reduce(
                go,
                enumFromTo(0)(cs.length)
            )
        );
    };

    // ----------------------- TEST ------------------------
    const main = () => [
        ["kitten", "sitting"],
        ["sitting", "kitten"],
        ["rosettacode", "raisethysword"],
        ["raisethysword", "rosettacode"]
    ].map(uncurry(levenshtein));


    // ----------------- GENERIC FUNCTIONS -----------------

    // Tuple (,) :: a -> b -> (a, b)
    const Tuple = a =>
        b => ({
            type: 'Tuple',
            '0': a,
            '1': b,
            length: 2
        });


    // TupleN :: a -> b ...  -> (a, b ... )
    function TupleN() {
        const
            args = Array.from(arguments),
            n = args.length;
        return 2 < n ? Object.assign(
            args.reduce((a, x, i) => Object.assign(a, {
                [i]: x
            }), {
                type: 'Tuple' + n.toString(),
                length: n
            })
        ) : args.reduce((f, x) => f(x), Tuple);
    };


    // chars :: String -> [Char]
    const chars = s =>
        s.split('');


    // enumFromTo :: Int -> Int -> [Int]
    const enumFromTo = m =>
        n => Array.from({
            length: 1 + n - m
        }, (_, i) => m + i);


    // last :: [a] -> a
    const last = xs => (
        // The last item of a list.
        ys => 0 < ys.length ? (
            ys.slice(-1)[0]
        ) : undefined
    )(xs);


    // minimum :: Ord a => [a] -> a
    const minimum = xs => (
        // The least value of xs.
        ys => 0 < ys.length ? (
            ys.slice(1)
            .reduce((a, y) => y < a ? y : a, ys[0])
        ) : undefined
    )(xs);


    // length :: [a] -> Int
    const length = xs =>
        // Returns Infinity over objects without finite
        // length. This enables zip and zipWith to choose
        // the shorter argument when one is non-finite,
        // like cycle, repeat etc
        'GeneratorFunction' !== xs.constructor.constructor.name ? (
            xs.length
        ) : Infinity;


    // scanl :: (b -> a -> b) -> b -> [a] -> [b]
    const scanl = f => startValue => xs =>
        xs.reduce((a, x) => {
            const v = f(a[0])(x);
            return Tuple(v)(a[1].concat(v));
        }, Tuple(startValue)([startValue]))[1];


    // succ :: Enum a => a -> a
    const succ = x =>
        1 + x;


    // uncurry :: (a -> b -> c) -> ((a, b) -> c)
    const uncurry = f =>
        // A function over a pair, derived
        // from a curried function.
        function () {
            const
                args = arguments,
                xy = Boolean(args.length % 2) ? (
                    args[0]
                ) : args;
            return f(xy[0])(xy[1]);
        };


    // zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
    const zip3 = xs =>
        ys => zs => xs
        .slice(0, Math.min(...[xs, ys, zs].map(length)))
        .map((x, i) => TupleN(x, ys[i], zs[i]));

    // MAIN ---
    return JSON.stringify(main())
})();
Output:
[3, 3, 8, 8]

jq[edit]

Works with: jq

Works with gojq, the Go implementation of jq

The main point of interest about the following implementation is that it shows how the naive recursive algorithm can be tweaked within a completely functional framework to yield an efficient implementation.

Performance: Here is a breakdown of the run-times on a 2.53GHz machine:

  9ms overhead (invoking jq and compiling the program)
 17ms for kitten/sitting
 67ms for rosettacode/raisethysword
 71ms for edocattesor/drowsyhtesiar
# lookup the distance between s and t in the nested cache,
# which uses basic properties of the Levenshtein distance to save space:
def lookup(s;t):
  if (s == t) then 0
  elif (s|length) == 0 then (t|length)
  elif (t|length) == 0 then (s|length)
  elif (s|length) > (t|length) then 
       .[t] as $t | if $t then $t[s] else null end
  else .[s] as $s | if $s then $s[t] else null end
  end ;

# output is the updated cache;
# basic properties of the Levenshtein distance are used to save space:
def store(s;t;value):
  if (s == t) then .
  else (s|length) as $s | (t|length) as $t
    | if $s == 0 or $t == 0 then .
      elif $s < $t then .[s][t] = value
      elif $t < $s then .[t][s] = value
      else (.[s][t] = value) | (.[t][s] = value)
      end
  end ;

# Input is a cache of nested objects; output is [distance, cache]
def ld(s1; s2):

  # emit [distance, cache]
  # input: cache
  def cached_ld(s;t):
    lookup(s;t) as $check
    | if $check then [ $check, . ]
      else ld(s;t)
      end
  ;

  # If either string is empty,
  # then distance is insertion of the other's characters.
  if   (s1|length) == 0 then [(s2|length), .]
  elif (s2|length) == 0 then [(s1|length), .]
  elif (s1[0:1] == s2[0:1]) then
    cached_ld(s1[1:]; s2[1:])
  else
    cached_ld(s1[1:]; s2) as $a
    | ($a[1] | cached_ld(s1; s2[1:])) as $b
    | ($b[1] | cached_ld(s1[1:]; s2[1:])) as $c
    | [$a[0], $b[0], $c[0]] | (min + 1) as $d
    | [$d, ($c[1] | store(s1;s2;$d)) ]
  end ;

def levenshteinDistance(s;t):
  s as $s | t as $t | {} | ld($s;$t) | .[0];

Task

def demo:
 "levenshteinDistance between \(.[0]) and \(.[1]) is \( levenshteinDistance(.[0]; .[1]) )";
 
(["kitten", "sitting"] | demo),
(["rosettacode","raisethysword"] | demo),
(["edocattesor", "drowsyhtesiar"] | demo),
(["this_algorithm_is_similar_to",
  "Damerau-Levenshtein_distance"] | demo)
Output:
levenshteinDistance between kitten and sitting is 3
levenshteinDistance between rosettacode and raisethysword is 8
levenshteinDistance between edocattesor and drowsyhtesiar is 8
levenshteinDistance between this_algorithm_is_similar_to and Damerau-Levenshtein_distance is 24

Jsish[edit]

From Javascript, ES5 entry.

/* Levenshtein Distance, in Jsish */

function levenshtein(a, b) {
  var t = [], u, i, j, m = a.length, n = b.length;
  if (!m) { return n; }
  if (!n) { return m; }
  for (j = 0; j <= n; j++) { t[j] = j; }
  for (i = 1; i <= m; i++) {
    for (u = [i], j = 1; j <= n; j++) {
      u[j] = a[i - 1] === b[j - 1] ? t[j - 1] : Math.min(t[j - 1], t[j], u[j - 1]) + 1;
    } t = u;
  } return u[n];
}

provide('levenshtein', 1);

;levenshtein('', '');
;levenshtein('yo', '');
;levenshtein('', 'yo');
;levenshtein('yo', 'yo');
;levenshtein('tier', 'tor');
;levenshtein('saturday', 'sunday');
;levenshtein('mist', 'dist');
;levenshtein('tier', 'tor');
;levenshtein('kitten', 'sitting');
;levenshtein('stop', 'tops');
;levenshtein('rosettacode', 'raisethysword');
;levenshtein('mississippi', 'swiss miss');

/*
=!EXPECTSTART!=
levenshtein('', '') ==> 0
levenshtein('yo', '') ==> 2
levenshtein('', 'yo') ==> 2
levenshtein('yo', 'yo') ==> 0
levenshtein('tier', 'tor') ==> 2
levenshtein('saturday', 'sunday') ==> 3
levenshtein('mist', 'dist') ==> 1
levenshtein('tier', 'tor') ==> 2
levenshtein('kitten', 'sitting') ==> 3
levenshtein('stop', 'tops') ==> 2
levenshtein('rosettacode', 'raisethysword') ==> 8
levenshtein('mississippi', 'swiss miss') ==> 8
=!EXPECTEND!=
*/
Output:
prompt$ jsish -u levenshtein.jsi
[PASS] levenshtein.jsi

Julia[edit]

Recursive:

Works with: Julia version 1.0
function levendist(s::AbstractString, t::AbstractString)
    ls, lt = length.((s, t))
    ls == 0 && return lt
    lt == 0 && return ls

    s₁, t₁ = s[2:end], t[2:end]
    ld₁ = levendist(s₁, t₁)
    s[1] == t[1] ? ld₁ : 1 + min(ld₁, levendist(s, t₁), levendist(s₁, t))
end

@show levendist("kitten", "sitting") # 3
@show levendist("rosettacode", "raisethysword") # 8

Iterative:

Works with: Julia version 0.6
function levendist1(s::AbstractString, t::AbstractString)
    ls, lt = length(s), length(t)
    if ls > lt
        s, t = t, s
        ls, lt = lt, ls
    end
    dist = collect(0:ls)
    for (ind2, chr2) in enumerate(t)
        newdist = Vector{Int}(ls+1)
        newdist[1] = ind2
        for (ind1, chr1) in enumerate(s)
            if chr1 == chr2
                newdist[ind1+1] = dist[ind1]
            else
                newdist[ind1+1] = 1 + min(dist[ind1], dist[ind1+1], newdist[end])
            end
        end
        dist = newdist
    end
    return dist[end]
end

Let's see some benchmark:

using BenchmarkTools
println("\n# levendist(kitten, sitting)")
s, t = "kitten", "sitting"
println(" - Recursive:")
@btime levendist(s, t)
println(" - Iterative:")
@btime levendist1(s, t)
println("\n# levendist(rosettacode, raisethysword)")
s, t = "rosettacode", "raisethysword"
println(" - Recursive:")
@btime levendist(s, t)
println(" - Iterative:")
@btime levendist1(s, t)
Output:
# levendist(kitten, sitting)
 - Recursive:
  78.788 μs (1103 allocations: 34.47 KiB)
 - Iterative:
  494.376 ns (9 allocations: 1.16 KiB)

# levendist(rosettacode, raisethysword)
 - Recursive:
  317.817 ms (3468524 allocations: 105.85 MiB)
 - Iterative:
  1.168 μs (15 allocations: 2.44 KiB)

Kotlin[edit]

Standard Version[edit]

// version 1.0.6

// Uses the "iterative with two matrix rows" algorithm referred to in the Wikipedia article.

fun levenshtein(s: String, t: String): Int {
    // degenerate cases
    if (s == t)  return 0
    if (s == "") return t.length
    if (t == "") return s.length

    // create two integer arrays of distances and initialize the first one
    val v0 = IntArray(t.length + 1) { it }  // previous
    val v1 = IntArray(t.length + 1)         // current

    var cost: Int
    for (i in 0 until s.length) {
        // calculate v1 from v0
        v1[0] = i + 1
        for (j in 0 until t.length) {
            cost = if (s[i] == t[j]) 0 else 1
            v1[j + 1] = Math.min(v1[j] + 1, Math.min(v0[j + 1] + 1, v0[j] + cost))  
        }
        // copy v1 to v0 for next iteration
        for (j in 0 .. t.length) v0[j] = v1[j]
    }
    return v1[t.length]
}

fun main(args: Array<String>) {
    println("'kitten' to 'sitting'            => ${levenshtein("kitten", "sitting")}")
    println("'rosettacode' to 'raisethysword' => ${levenshtein("rosettacode", "raisethysword")}") 
    println("'sleep' to 'fleeting'            => ${levenshtein("sleep", "fleeting")}")
}
Output:
'kitten' to 'sitting'            => 3
'rosettacode' to 'raisethysword' => 8
'sleep' to 'fleeting'            => 5

Functional/Folding Version[edit]

fun levenshtein(s: String, t: String,
                charScore : (Char, Char) -> Int = { c1, c2 -> if (c1 == c2) 0 else 1}) : Int {

    // Special cases
    if (s == t)  return 0
    if (s == "") return t.length
    if (t == "") return s.length

    val initialRow : List<Int> = (0 until t.length + 1).map { it }.toList()
    return (0 until s.length).fold(initialRow, { previous, u ->
        (0 until t.length).fold( mutableListOf(u+1), {
            row, v -> row.add(minOf(row.last() + 1,
                    previous[v+1] + 1,
                    previous[v] + charScore(s[u],t[v])))
            row
        })
    }).last()

}
Output:
'kitten' to 'sitting'            => 3
'rosettacode' to 'raisethysword' => 8
'sleep' to 'fleeting'            => 5

LFE[edit]

Simple Implementation[edit]

Suitable for short strings:

(defun levenshtein-simple
  (('() str)
    (length str))
  ((str '())
    (length str))
  (((cons a str1) (cons b str2)) (when (== a b))
    (levenshtein-simple str1 str2))
  (((= (cons _ str1-tail) str1) (= (cons _ str2-tail) str2))
    (+ 1 (lists:min
          (list
           (levenshtein-simple str1 str2-tail)
           (levenshtein-simple str1-tail str2)
           (levenshtein-simple str1-tail str2-tail))))))

You can copy and paste that function into an LFE REPL and run it like so:

> (levenshtein-simple "a" "a")
0
> (levenshtein-simple "a" "")
1
> (levenshtein-simple "" "a")
1
> (levenshtein-simple "kitten" "sitting")
3

It is not recommended to test strings longer than the last example using this implementation, as performance quickly degrades.

Cached Implementation[edit]

(defun levenshtein-distance (str1 str2)
  (let (((tuple distance _) (levenshtein-distance
                               str1 str2 (dict:new))))
    distance))

(defun levenshtein-distance
  (((= '() str1) str2 cache)
    (tuple (length str2)
           (dict:store (tuple str1 str2)
                       (length str2)
                       cache)))
  ((str1 (= '() str2) cache)
    (tuple (length str1)
           (dict:store (tuple str1 str2)
                       (length str1)
                       cache)))
  (((cons a str1) (cons b str2) cache) (when (== a b))
    (levenshtein-distance str1 str2 cache))
  (((= (cons _ str1-tail) str1) (= (cons _ str2-tail) str2) cache)
     (case (dict:is_key (tuple str1 str2) cache)
       ('true (tuple (dict:fetch (tuple str1 str2) cache) cache))
       ('false (let* (((tuple l1 c1) (levenshtein-distance str1 str2-tail cache))
                      ((tuple l2 c2) (levenshtein-distance str1-tail str2 c1))
                      ((tuple l3 c3) (levenshtein-distance str1-tail str2-tail c2))
                      (len (+ 1 (lists:min (list l1 l2 l3)))))
                 (tuple len (dict:store (tuple str1 str2) len c3)))))))

As before, here's some usage in the REPL. Note that longer strings are now possible to compare without incurring long execution times:

> (levenshtein-distance "a" "a")
0
> (levenshtein-distance "a" "")
1
> (levenshtein-distance "" "a")
1
> (levenshtein-distance "kitten" "sitting")
3
> (levenshtein-distance "rosettacode" "raisethysword")
8

Liberty BASIC[edit]

'Levenshtein Distance translated by Brandon Parker
'08/19/10
'from http://www.merriampark.com/ld.htm#VB
'No credit was given to the Visual Basic Author on the site :-(

Print LevenshteinDistance("kitten", "sitting")
End

'Get the minum of three values
Function Minimum(a, b, c)
    Minimum = Min(a, Min(b, c))
End Function

'Compute the Levenshtein Distance
Function LevenshteinDistance(string1$, string2$)
    n = Len(string1$)
    m = Len(string2$)
    If n = 0 Then
        LevenshteinDistance = m
        Exit Function
    End If
    If m = 0 Then
        LevenshteinDistance = n
        Exit Function
    End If
    Dim d(n, m)
    For i = 0 To n
        d(i, 0) = i
    Next i
    For i = 0 To m
        d(0, i) = i
    Next i
    For i = 1 To n
        si$ = Mid$(string1$, i, 1)
        For ii = 1 To m
            tj$ = Mid$(string2$, ii, 1)
            If si$ = tj$ Then
                cost = 0
            Else
                cost = 1
            End If
            d(i, ii) = Minimum((d(i - 1, ii) + 1), (d(i, ii - 1) + 1), (d(i - 1, ii - 1) + cost))
        Next ii
    Next i
    LevenshteinDistance = d(n, m)
End Function

Limbo[edit]

Translation of: Go
implement Levenshtein;

include "sys.m"; sys: Sys;
	print: import sys;
include "draw.m";


Levenshtein: module {
	init: fn(nil: ref Draw->Context, args: list of string);
	# Export distance so that this module can be used as either a
	# standalone program or as a library:
	distance: fn(s, t: string): int;
};

init(nil: ref Draw->Context, args: list of string)
{
	sys = load Sys Sys->PATH;
	if(!(len args % 2)) {
		sys->fprint(sys->fildes(2), "Provide an even number of arguments!\n");
		raise "fail:usage";
	}
	args = tl args;

	while(args != nil) {
		(s, t) := (hd args, hd tl args);
		args = tl tl args;
		print("%s <-> %s => %d\n", s, t, distance(s, t));
	}
}

distance(s, t: string): int
{
	if(s == "")
		return len t;
	if(t == "")
		return len s;
	if(s[0] == t[0])
		return distance(s[1:], t[1:]);
	a := distance(s[1:], t);
	b := distance(s, t[1:]);
	c := distance(s[1:], t[1:]);
	if(a > b)
		a = b;
	if(a > c)
		a = c;
	return a + 1;
}
Output:
 % levenshtein kitten sitting rosettacode raisethysword
 kitten <-> sitting => 3
 rosettacode <-> raisethysword => 8

LiveCode[edit]

Translation of: Go
//Code By Neurox66
function Levenshtein pString1 pString2 
   put 0 into tPosChar1
   repeat for each char tChar1 in pString1 
      add 1 to tPosChar1
      put tPosChar1 into tDistance[tPosChar1][0]  
      put 0 into tPosChar2
      repeat for each char tChar2 in pString2 
         add 1 to tPosChar2
         put tPosChar2 into tDistance[0][tPosChar2]  
         put 1 into tCost
         if tChar1 = tChar2 then 
            put 0 into tCost 
         end if
         put min((tDistance[tPosChar1-1][tPosChar2] + 1),(tDistance[tPosChar1][tPosChar2-1] + 1),(tDistance[tPosChar1-1][tPosChar2-1] + tCost)) into tDistance[tPosChar1][tPosChar2] 
      end repeat  
   end repeat  
   return tDistance[tPosChar1][tPosChar2]  
end Levenshtein


put Levenshtein("kitten","sitting") 
put Levenshtein("rosettacode","raisethysword")
Output:
3
8

Lobster[edit]

Translation of: C
def levenshtein(s: string, t: string) -> int:

    def makeNxM(n: int, m: int, v: int) -> [[int]]:
        let d:[[int]] = vector_reserve(typeof return, n)
        for(n) i:
            push(d, vector_reserve(typeof return, m))
            for(m) j:
                push(d[i], v)
        return d

    let ls = s.length
    let lt = t.length
    let d = makeNxM(ls + 1, lt + 1, -1)

    def dist (i: int, j: int) -> int:
        if d[i][j] >= 0: 
            return d[i][j]
        var x = 0
        if i == ls:
            x = lt - j
        else: if j == lt:
            x = ls - i
        else: if s[i] == t[j]:
            x = dist(i + 1, j + 1)
        else:
            x = dist(i + 1, j + 1)
            x = min(x, dist(i, j + 1))
            x = min(x, dist(i + 1, j))
            x += 1
        d[i][j] = x
        return x

    return dist(0,0)

assert 3 == levenshtein("kitten", "sitting")
assert 8 == levenshtein("rosettacode", "raisethysword")

Lua[edit]

function leven(s,t)
    if s == '' then return t:len() end
    if t == '' then return s:len() end

    local s1 = s:sub(2, -1)
    local t1 = t:sub(2, -1)

    if s:sub(0, 1) == t:sub(0, 1) then
        return leven(s1, t1)
    end

    return 1 + math.min(
        leven(s1, t1),
        leven(s,  t1),
        leven(s1, t )
      )
end

print(leven("kitten", "sitting"))
print(leven("rosettacode", "raisethysword"))
Output:
3
8

M2000 Interpreter[edit]

Module Checkit {
	\\ Iterative with two matrix rows
	function LevenshteinDistance(s$,t$) { 
		if len(s$)<len(t$) then swap s$, t$
		n=len(t$)
		m=len(s$)
		dim base 0, v0(n+1), v1(n+1)
Rem		dim sw()  ' we can use stack of values to make the swap.
		for i=0 to n : v0(i)=i:next
		for i=0 to m-1
			v1(0)=i+1
			for j=0 to n-1
				deletioncost=v0(j+1)+1
				insertioncost=v1(j)+1
				if mid$(s$,i+1,1)=mid$(t$,j+1,1) then
					substitutionCost=v0(j)
				else
					substitutionCost=v0(j)+1
				end if
				v1(j+1)=min.data(deletionCost, insertionCost, substitutionCost)
			next
Rem			sw()=v0():v0()=v1():v1()=sw()
			\\ when we push arrays, we only push a pointer to 
			\\ when we read array (identifier with parenthesis) then we get a copy
			\\ between Push and Read any change on arrays included in copies
			Push v0(),v1(): Read v0(),v1()
		next
		=v0(n)	
	}
	Print LevenshteinDistance("kitten","sitting")=3  ' true
	Print LevenshteinDistance("Sunday","Saturday")=3  ' true
	Print LevenshteinDistance("rosettacode","raisethysword")=8  ' true
}
Checkit

Module Checkit2 {
	\\ Iterative with two matrix rows, using pointers to arrays
	function LevenshteinDistance(s$,t$) { 
		if len(s$)<len(t$) then swap s$, t$
		n=len(t$)
		m=len(s$)
		dim base 0, v0(n+1), v1(n+1)
		v0=v0()  ' v0 is pointer to v0()
		v1=v1() ' v1 is pointer to v1()
		for i=0 to n : v0(i)=i:next
		for i=0 to m-1
			return v1, 0:=i+1
			for j=0 to n-1
				deletioncost=Array(v0,j+1)+1
				insertioncost=Array(v1,j)+1
				if mid$(s$,i+1,1)=mid$(t$,j+1,1) then
					substitutionCost=Array(v0,j)
				else
					substitutionCost=Array(v0,j)+1
				end if
				return v1, j+1:=min.data(deletionCost, insertionCost, substitutionCost)
			next
			swap v0, v1  ' just swap pointers
		next
		=Array(v0,n)	
	}
	Print LevenshteinDistance("kitten","sitting")=3
	Print LevenshteinDistance("Sunday","Saturday")=3
	Print LevenshteinDistance("rosettacode","raisethysword")=8
}
Checkit2

Maple[edit]

> with(StringTools):
> Levenshtein("kitten","sitting");
                                   3

> Levenshtein("rosettacode","raisethysword");
                                   8

Mathematica/Wolfram Language[edit]

EditDistance["kitten","sitting"]
EditDistance["rosettacode","raisethysword"]
Output:
3
7

MATLAB[edit]

function score = levenshtein(s1, s2)
% score = levenshtein(s1, s2)
%
% Calculates the area under the ROC for a given set
% of posterior predictions and labels. Currently limited to two classes.
%
% s1: string
% s2: string
% score: levenshtein distance
%
% Author: Ben Hamner (ben@benhamner.com)
if length(s1) < length(s2)
score = levenshtein(s2, s1);
elseif isempty(s2)
score = length(s1);
else
previous_row = 0:length(s2);
for i=1:length(s1)
current_row = 0*previous_row;
current_row(1) = i;
for j=1:length(s2)
insertions = previous_row(j+1) + 1;
deletions = current_row(j) + 1;
substitutions = previous_row(j) + (s1(i) ~= s2(j));
current_row(j+1) = min([insertions, deletions, substitutions]);
end
previous_row = current_row;
end
score = current_row(end);
end

Source : [1]

MiniScript[edit]

In the Mini Micro environment, this function is part of the stringUtil library module, and can be used like so:

import "stringUtil"
print "kitten".editDistance("sitting")

In environments where the stringUtil module is not available, you'd have to define it yourself:

string.editDistance = function(s2)
	n = self.len
	m = s2.len
	if n == 0 then return m
	if m == 0 then return n
	
	s1chars = self.split("")
	s2chars = s2.split("")
	d = range(0, m)	
	lastCost = 0
	
	for i in range(1, n)
		s1char = s1chars[i-1]
		lastCost = i
		jMinus1 = 0
		for j in range(1, m)
			if s1char == s2chars[jMinus1] then cost = 0 else cost = 1
			
			// set nextCost to the minimum of the following three possibilities:
			a = d[j] + 1
			b = lastCost + 1
			c = cost + d[jMinus1]
			
			if a < b then
				if c < a then nextCost = c else nextCost = a
			else
				if c < b then nextCost = c else nextCost = b
			end if
			
			d[jMinus1] = lastCost
			lastCost = nextCost
			jMinus1 = j
		end for
		d[m] = lastCost
	end for
	
	return nextCost
end function

print "kitten".editDistance("sitting")
Output:
3

Modula-2[edit]

MODULE LevenshteinDistance;
FROM InOut IMPORT WriteString, WriteCard, WriteLn;
FROM Strings IMPORT Length;

PROCEDURE levenshtein(s, t: ARRAY OF CHAR): CARDINAL;
    CONST MaxLen = 15;
    VAR d: ARRAY [0..MaxLen],[0..MaxLen] OF CARDINAL;
        lenS, lenT, i, j: CARDINAL;
        
    PROCEDURE min(a, b: CARDINAL): CARDINAL;
    BEGIN
        IF a<b THEN RETURN a;
        ELSE RETURN b;
        END;
    END min;
BEGIN
    lenS := Length(s);
    lenT := Length(t);
    
    IF lenS = 0 THEN RETURN lenT;
    ELSIF lenT = 0 THEN RETURN lenS;
    ELSE
        FOR i := 0 TO lenS DO d[i,0] := i; END;
        FOR j := 0 TO lenT DO d[0,j] := j; END;
        FOR i := 1 TO lenS DO
            FOR j := 1 TO lenT DO
                IF s[i-1] = t[j-1] THEN 
                    d[i,j] := d[i-1,j-1];
                ELSE
                    d[i,j] := 
                      min(d[i-1,j] + 1,
                      min(d[i,j-1] + 1, d[i-1,j-1]+1));
                END;
            END;
        END;
        RETURN d[lenS,lenT];
    END;
END levenshtein;

PROCEDURE ShowDistance(s, t: ARRAY OF CHAR);
BEGIN
    WriteString(s);
    WriteString(" -> ");
    WriteString(t);
    WriteString(": ");
    WriteCard(levenshtein(s, t), 0);
    WriteLn();
END ShowDistance;

BEGIN
    ShowDistance("kitten", "sitting");
    ShowDistance("rosettacode", "raisethysword");
END LevenshteinDistance.
Output:
kitten -> sitting: 3
rosettacode -> raisethysword: 8

NetRexx[edit]

Translation of: ooRexx
/* NetRexx */
options replace format comments java crossref symbols nobinary

n = 0
w = ''
n = n + 1; w[0] = n; w[n] = "kitten sitting"
n = n + 1; w[0] = n; w[n] = "rosettacode raisethysword"

loop n = 1 to w[0]
  say w[n].word(1) "->" w[n].word(2)":" levenshteinDistance(w[n].word(1), w[n].word(2))
  end n
return

method levenshteinDistance(s, t) private static
  s = s.lower
  t = t.lower

  m = s.length
  n = t.length

  -- for all i and j, d[i,j] will hold the Levenshtein distance between
  -- the first i characters of s and the first j characters of t;
  -- note that d has (m+1)x(n+1) values
  d = 0

  -- source prefixes can be transformed into empty string by
  -- dropping all characters (Note, ooRexx arrays are 1-based)
  loop i = 2 to m + 1
    d[i, 1] = 1
  end i

  -- target prefixes can be reached from empty source prefix
  -- by inserting every characters
  loop j = 2 to n + 1
    d[1, j] = 1
  end j

  loop j = 2 to n + 1
    loop i = 2 to m + 1
      if s.substr(i - 1, 1) == t.substr(j - 1, 1) then do
        d[i, j] = d[i - 1, j - 1]   -- no operation required
        end
      else do
        d[i, j] =                 -
          (d[i - 1, j] + 1).min(  - -- a deletion
          (d[i, j - 1] + 1)).min( - -- an insertion
          (d[i - 1, j - 1] + 1))    -- a substitution
        end
    end i
  end j

  return d[m + 1, n + 1]

Output:

kitten -> sitting: 3 
rosettacode -> raisethysword: 8 

Nim[edit]

Nim provides a function in module "std/editdistance" to compute the Levenshtein distance between two strings containing ASCII characters only or containing UTF-8 encoded Unicode runes.

import std/editdistance

echo editDistanceAscii("kitten", "sitting")
echo editDistanceAscii("rosettacode", "raisethysword")
Output:
3
8
Translation of: Python

Here is a translation of the Python version.

import sequtils

func min(a, b, c: int): int {.inline.} = min(a, min(b, c))

proc levenshteinDistance(s1, s2: string): int =
  var (s1, s2) = (s1, s2)

  if s1.len > s2.len:
    swap s1, s2

  var distances = toSeq(0..s1.len)

  for i2, c2 in s2:
    var newDistances = @[i2+1]
    for i1, c1 in s1:
      if c1 == c2:
        newDistances.add(distances[i1])
      else:
        newDistances.add(1 + min(distances[i1], distances[i1+1], newDistances[newDistances.high]))

    distances = newDistances
  result = distances[distances.high]

echo levenshteinDistance("kitten","sitting")
echo levenshteinDistance("rosettacode","raisethysword")

Objeck[edit]

Translation of: C#
class Levenshtein {
  function : Main(args : String[]) ~ Nil {
    if(args->Size() = 2) {
      s := args[0]; t := args[1]; d := Distance(s,t);
      "{$s} -> {$t} = {$d}"->PrintLine();
    };
  }
  
  function : native : Distance(s : String,t : String) ~ Int {
    d := Int->New[s->Size() + 1, t->Size() + 1];
    for(i := 0; i <= s->Size(); i += 1;) {
      d[i,0] := i;
    };
    
    for(j := 0; j <= t->Size(); j += 1;) {
      d[0,j] := j;
    };
    
    for(j := 1; j <= t->Size(); j += 1;) {
      for(i := 1; i <= s->Size(); i += 1;) {
        if(s->Get(i - 1) = t->Get(j - 1)) {
          d[i,j] := d[i - 1, j - 1];
        }
        else {
          d[i,j] := (d[i - 1, j] + 1)
            ->Min(d[i, j - 1] + 1)
            ->Min(d[i - 1, j - 1] + 1);
        };
      };
    };
    
    return d[s->Size(), t->Size()];
  }
}

Objective-C[edit]

Translation of the C# code into a NSString category

@interface NSString (levenshteinDistance)
- (NSUInteger)levenshteinDistanceToString:(NSString *)string;
@end

@implementation NSString (levenshteinDistance)
- (NSUInteger)levenshteinDistanceToString:(NSString *)string {
    NSUInteger sl = [self length];
    NSUInteger tl = [string length];
    NSUInteger *d = calloc(sizeof(*d), (sl+1) * (tl+1));
    
#define d(i, j) d[((j) * sl) + (i)]
    for (NSUInteger i = 0; i <= sl; i++) {
        d(i, 0) = i;
    }
    for (NSUInteger j = 0; j <= tl; j++) {
        d(0, j) = j;
    }
    for (NSUInteger j = 1; j <= tl; j++) {
        for (NSUInteger i = 1; i <= sl; i++) {
            if ([self characterAtIndex:i-1] == [string characterAtIndex:j-1]) {
                d(i, j) = d(i-1, j-1);
            } else {
                d(i, j) = MIN(d(i-1, j), MIN(d(i, j-1), d(i-1, j-1))) + 1;
            }
        }
    }
    
    NSUInteger r = d(sl, tl);
#undef d
    
    free(d);
    
    return r;
}
@end

OCaml[edit]

Translation of the pseudo-code of the Wikipedia article:

let minimum a b c =
  min a (min b c)

let levenshtein_distance s t =
  let m = String.length s
  and n = String.length t in
  (* for all i and j, d.(i).(j) will hold the Levenshtein distance between
     the first i characters of s and the first j characters of t *)
  let d = Array.make_matrix (m+1) (n+1) 0 in

  for i = 0 to m do
    d.(i).(0) <- i  (* the distance of any first string to an empty second string *)
  done;
  for j = 0 to n do
    d.(0).(j) <- j  (* the distance of any second string to an empty first string *)
  done;

  for j = 1 to n do
    for i = 1 to m do

      if s.[i-1] = t.[j-1] then
        d.(i).(j) <- d.(i-1).(j-1)  (* no operation required *)
      else
        d.(i).(j) <- minimum
                       (d.(i-1).(j) + 1)   (* a deletion *)
                       (d.(i).(j-1) + 1)   (* an insertion *)
                       (d.(i-1).(j-1) + 1) (* a substitution *)
    done;
  done;

  d.(m).(n)
;;

let test s t =
  Printf.printf " %s -> %s = %d\n" s t (levenshtein_distance s t);
;;

let () =
  test "kitten" "sitting";
  test "rosettacode" "raisethysword";
;;

A recursive functional version[edit]

This could be made faster with memoization

let levenshtein s t =
   let rec dist i j = match (i,j) with
      | (i,0) -> i
      | (0,j) -> j
      | (i,j) ->
         if s.[i-1] = t.[j-1] then dist (i-1) (j-1)
         else let d1, d2, d3 = dist (i-1) j, dist i (j-1), dist (i-1) (j-1) in
         1 + min d1 (min d2 d3)
   in
   dist (String.length s) (String.length t)

let test s t =
  Printf.printf " %s -> %s = %d\n" s t (levenshtein s t)

let () =
  test "kitten" "sitting";
  test "rosettacode" "raisethysword";
Output:
 kitten -> sitting = 3
 rosettacode -> raisethysword = 8

ooRexx[edit]

say "kitten -> sitting:" levenshteinDistance("kitten", "sitting")
say "rosettacode -> raisethysword:" levenshteinDistance("rosettacode", "raisethysword")

::routine levenshteinDistance
  use arg s, t
  s = s~lower
  t = t~lower

  m = s~length
  n = t~length

  -- for all i and j, d[i,j] will hold the Levenshtein distance between
  -- the first i characters of s and the first j characters of t;
  -- note that d has (m+1)x(n+1) values
  d = .array~new(m + 1, n + 1)

  -- clear all elements in d
  loop i = 1 to d~dimension(1)
      loop j = 1 to d~dimension(2)
          d[i, j] = 0
      end
  end

  -- source prefixes can be transformed into empty string by
  -- dropping all characters (Note, ooRexx arrays are 1-based)
  loop i = 2 to m + 1
      d[i, 1] = 1
  end

  -- target prefixes can be reached from empty source prefix
  -- by inserting every characters
  loop j = 2 to n + 1
      d[1, j] = 1
  end

  loop j = 2 to n + 1
      loop i = 2 to m + 1
          if s~subchar(i - 1) == t~subchar(j - 1) then
              d[i, j] = d[i - 1, j - 1]   -- no operation required
          else d[i, j] = min(d[i - 1, j] + 1,    - -- a deletion
                             d[i, j-1] + 1,      - -- an insertion
                             d[i - 1, j - 1] + 1)  -- a substitution
      end
  end

  return d[m + 1, n + 1 ]

Output:

kitten -> sitting: 3
rosettacode -> raisethysword: 8

PARI/GP[edit]

Translation of: JavaScript
Works with: PARI/GP version 2.7.4 and above
\\ Levenshtein distance between two words
\\ 6/21/16 aev
levensDist(s1,s2)={
my(n1=#s1,n2=#s2,v1=Vecsmall(s1),v2=Vecsmall(s2),c,
   n11=n1+1,n21=n2+1,t=vector(n21,z,z-1),u0=vector(n21),u=u0);
if(s1==s2, return(0)); if(!n1, return(n2)); if(!n2, return(n1));
for(i=2,n11, u=u0; u[1]=i-1;
  for(j=2,n21,
    if(v1[i-1]==v2[j-1], c=t[j-1], c=vecmin([t[j-1],t[j],u[j-1]])+1);
    u[j]=c;
  );\\fend j
  t=u;
);\\fend i 
print(" *** Levenshtein distance = ",t[n21]," for strings: ",s1,", ",s2);
return(t[n21]);
}
{ \\ Testing:
levensDist("kitten","sitting"); 
levensDist("rosettacode","raisethysword");
levensDist("Saturday","Sunday");
levensDist("oX","X");
levensDist("X","oX");
}
Output:
 *** Levenshtein distance = 3 for strings: kitten, sitting
 *** Levenshtein distance = 8 for strings: rosettacode, raisethysword
 *** Levenshtein distance = 3 for strings: Saturday, Sunday
 *** Levenshtein distance = 1 for strings: oX, X
 *** Levenshtein distance = 1 for strings: X, oX

Pascal[edit]

A fairly direct translation of the wikipedia pseudo code:

Program LevenshteinDistanceDemo(output);

uses
  Math;

function LevenshteinDistance(s, t: string): longint;
  var
    d: array of array of integer;
    i, j, n, m: integer;
  begin
    n := length(t);
    m := length(s);
    setlength(d, m+1, n+1);
    
    for i := 0 to m do
      d[i,0] := i;
    for j := 0 to n do
      d[0,j] := j;
    for j := 1 to n do
      for i := 1 to m do
        if s[i] = t[j] then  
          d[i,j] := d[i-1,j-1]
        else
          d[i,j] := min(d[i-1,j] + 1, min(d[i,j-1] + 1, d[i-1,j-1] + 1));
    LevenshteinDistance := d[m,n];
  end;
  
var
  s1, s2: string;

begin
  s1 := 'kitten';
  s2 := 'sitting';
  writeln('The Levenshtein distance between "', s1, '" and "', s2, '" is: ', LevenshteinDistance(s1, s2));
  s1 := 'rosettacode';
  s2 := 'raisethysword';
  writeln('The Levenshtein distance between "', s1, '" and "', s2, '" is: ', LevenshteinDistance(s1, s2));
end.
Output:
The Levenshtein distance between "kitten" and "sitting" is: 3
The Levenshtein distance between "rosettacode" and "raisethysword" is: 8

Perl[edit]

Recursive algorithm, as in the C sample. You are invited to comment out the line where it says so, and see the speed difference. By the way, there's the Memoize standard module, but it requires setting quite a few parameters to work right for this example, so I'm just showing the simple minded caching scheme here.

use List::Util qw(min);

my %cache;

sub leven {
    my ($s, $t) = @_;

    return length($t) if $s eq '';
    return length($s) if $t eq '';

    $cache{$s}{$t} //=    # try commenting out this line
      do {
        my ($s1, $t1) = (substr($s, 1), substr($t, 1));

        (substr($s, 0, 1) eq substr($t, 0, 1))
          ? leven($s1, $t1)
          : 1 + min(
                    leven($s1, $t1),
                    leven($s,  $t1),
                    leven($s1, $t ),
            );
      };
}

print leven('rosettacode', 'raisethysword'), "\n";

Iterative solution:

use List::Util qw(min);

sub leven {
    my ($s, $t) = @_;

    my $tl = length($t);
    my $sl = length($s);

    my @d = ([0 .. $tl], map { [$_] } 1 .. $sl);

    foreach my $i (0 .. $sl - 1) {
        foreach my $j (0 .. $tl - 1) {
            $d[$i + 1][$j + 1] =
              substr($s, $i, 1) eq substr($t, $j, 1)
              ? $d[$i][$j]
              : 1 + min($d[$i][$j + 1], $d[$i + 1][$j], $d[$i][$j]);
        }
    }

    $d[-1][-1];
}

print leven('rosettacode', 'raisethysword'), "\n";

Phix[edit]

with javascript_semantics

requires("0.8.2") -- (just the use of papply() at the end)

function levenshtein(string a, b)
    integer n = length(a),
            m = length(b)
    if n=0 then return m end if
    if m=0 then return n end if
    sequence d = repeat(repeat(0, m+1), n+1)
    for i=1 to n do
        d[i+1][1] = i
        for j=1 to m do
            d[1][j+1] = j
            --   next  := min({ prev  +substitution,  deletion, or insertion }):
            d[i+1][j+1] = min({d[i][j]+(a[i]!=b[j]), d[i][j+1]+1, d[i+1][j]+1})
        end for
    end for
    return d[$][$]
end function

procedure test(string s1, s2, integer expected)
    integer actual = levenshtein(s1,s2)
    if actual!=expected
    or actual!=levenshtein(s2,s1)
    or actual!=levenshtein(reverse(s1),reverse(s2))
    or actual!=levenshtein(reverse(s2),reverse(s1)) then
        crash("oh dear...")
    end if
    printf(1,"%14q <== %d ==> %q\n",{s1,actual,s2})
end procedure

constant tests = {{"kitten", "sitting", 3},
                  {"rosettacode", "raisethysword", 8},
                  {"abcdefgh", "defghabc", 6},
                  {"saturday", "sunday", 3},
                  {"sleep", "fleeting", 5},
                  {"", "four", 4},
                  {"", "", 0}}
papply(false,test,tests)
Output:
      "kitten" <== 3 ==> "sitting"
 "rosettacode" <== 8 ==> "raisethysword"
    "abcdefgh" <== 6 ==> "defghabc"
    "saturday" <== 3 ==> "sunday"
       "sleep" <== 5 ==> "fleeting"
            "" <== 4 ==> "four"
            "" <== 0 ==> ""

alternative[edit]

Modelled after the Processing code, uses a single/smaller array, passes the same tests as above.

function levenshtein(string a, b)
    sequence costs = tagset(length(b)+1,0)
    for i=1 to length(a) do
        costs[1] = i
        integer newcost = i-1, pj = i, cj
        for j=1 to length(b) do
            cj = costs[j+1]
            pj = min({pj+1, cj+1, newcost+(a[i]!=b[j])})
            costs[j+1] = pj
            newcost = cj
        end for
    end for
    return costs[$-1]
end function

PHP[edit]

echo levenshtein('kitten','sitting');
echo levenshtein('rosettacode', 'raisethysword');
Output:
3
8

Picat[edit]

Iterative[edit]

Based on the iterative algorithm at Wikipedia. Picat is 1-based so some adjustments are needed.

levenshtein(S,T) = Dist =>
  M = 1+S.length,
  N = 1+T.length,
  
  D = new_array(M,N),

  foreach(I in 1..M)
    D[I,1] := I-1
  end,
  
  foreach(J in 1..N) 
    D[1,J] := J-1
  end,
  
  foreach(J in 2..N, I in 2..M)
    if S[I-1] == T[J-1] then
      D[I,J] := D[I-1,J-1]            % no operation required
    else 
      D[I,J] := min([D[I-1,J  ] + 1,  % a deletion
                     D[I  ,J-1] + 1,  % an insertion
                     D[I-1,J-1] + 1]  % a substitution
                    )
    end
  end,

  Dist = D[M,N].

Tabled recursive version[edit]

table
levenshtein_rec(S,T) = Dist =>
  Dist1 = 0,
  if S.length = 0     then Dist1 := T.length
  elseif T.length = 0 then Dist1 := S.length
  elseif S[1] = T[1]  then Dist1 := levenshtein_rec(S.tail(), T.tail())
  else
    A = levenshtein_rec(S.tail(), T.tail()),
    B = levenshtein_rec(S       , T.tail()),
    C = levenshtein_rec(S.tail(), T),
    if A > B then
       A := B
    elseif A > C then
       A := C
    end,
    Dist1 := A + 1
  end,
  Dist = Dist1.

Mode-directed tabling[edit]

Translation of: Prolog
levenshtein_mode(S,T) = Dist => 
  lev(S, T, Dist).
  
table (+,+,min)
lev([], [], 0).
lev([X|L], [X|R], D) :- !, lev(L, R, D).
lev([_|L], [_|R], D) :- lev(L, R, H), D is H+1.
lev([_|L], R, D) :- lev(L, R, H), D is H+1.
lev(L, [_|R], D) :- lev(L, R, H), D is H+1.


Test[edit]

go =>
  
  S = [
       ["kitten","sitting"],
       ["rosettacode","raisethysword"],
       ["levenshtein","levenstein"],       
       ["saturday", "sunday"],
       ["stop", "tops"],
       ["saturday", "sunday"]
  ],
  foreach([W1,W2] in S)
    % clear the table cache 
    initialize_table,
    println(iter=[W1,W2,levenshtein(W1,W2)]),
    println(recu=[W1,W2,levenshtein_rec(W1,W2)]),
    println(mode=[W1,W2,levenshtein_mode(W1,W2)]),    
    nl
  end,
  nl.
Output:
goal = go
iter = [kitten,sitting,3]
recu = [kitten,sitting,3]
mode = [kitten,sitting,3]

iter = [rosettacode,raisethysword,8]
recu = [rosettacode,raisethysword,8]
mode = [rosettacode,raisethysword,8]

iter = [levenshtein,levenstein,1]
recu = [levenshtein,levenstein,1]
mode = [levenshtein,levenstein,1]

iter = [saturday,sunday,3]
recu = [saturday,sunday,3]
mode = [saturday,sunday,3]

iter = [stop,tops,2]
recu = [stop,tops,2]
mode = [stop,tops,2]

iter = [saturday,sunday,3]
recu = [saturday,sunday,3]
mode = [saturday,sunday,3]


Benchmark on larger strings[edit]

Benchmarking the methods with larger strings of random lengths (between 1 and 2000).

go2 =>
  _ = random2(),
  Len = 2000,
  S1 = generate_string(Len),
  S2 = generate_string(Len),
  println(len_s1=S1.len),
  println(len_s2=S2.len),
  nl,
  println("iter:"),
  time(L1 = levenshtein(S1,S2)),
  println("rec:"),
  time(L2 = levenshtein_rec(S1,S2)),
  println("mode:"),
  time(L3 = levenshtein_mode(S1,S2)),  
  println(distances=[iter=L1,rec=L2,mode=L3]),
  nl.

%
% Generate a random string of max length MaxLen
% 
generate_string(MaxLen) = S => 
  Alpha = "abcdefghijklmnopqrstuvxyz",
  Len = Alpha.length,
  S := [Alpha[random(1,Len)] : _ in 1..random(1,MaxLen)].

Here is sample run. The version using mode-directed tabling is clearly the fastest.

Output:
len_s1 = 1968
len_s2 = 1529

iter:
CPU time 9.039 seconds.

rec:
CPU time 10.439 seconds.

mode:
CPU time 1.402 seconds.

distances=[iter = 1607,rec = 1607,mode = 1607]

PicoLisp[edit]

Translation of the pseudo-code in the Wikipedia article:

(de levenshtein (A B)
   (let D
      (cons
         (range 0 (length A))
         (mapcar
            '((I) (cons I (copy A)))
            (range 1 (length B)) ) )
      (for (J . Y) B
         (for (I . X) A
            (set
               (nth D (inc J) (inc I))
               (if (= X Y)
                  (get D J I)
                  (inc
                     (min
                        (get D J (inc I))
                        (get D (inc J) I)
                        (get D J I) ) ) ) ) ) ) ) )

or, using 'map' to avoid list indexing:

(de levenshtein (A B)
   (let D
      (cons
         (range 0 (length A))
         (mapcar
            '((I) (cons I (copy A)))
            (range 1 (length B)) ) )
      (map
         '((B Y)
            (map
               '((A X P)
                  (set (cdr P)
                     (if (= (car A) (car B))
                        (car X)
                        (inc (min (cadr X) (car P) (car X))) ) ) )
               A
               (car Y)
               (cadr Y) ) )
         B
         D ) ) )
Output (both cases):
: (levenshtein (chop "kitten") (chop "sitting"))
-> 3

PL/I[edit]

version 1[edit]

*process source xref attributes or(!);
 lsht: Proc Options(main);
 Call test('kitten'      ,'sitting');
 Call test('rosettacode' ,'raisethysword');
 Call test('Sunday'      ,'Saturday');
 Call test('Vladimir_Levenshtein[1965]',
           'Vladimir_Levenshtein[1965]');
 Call test('this_algorithm_is_similar_to',
            'Damerau-Levenshtein_distance');
 Call test('','abc');

 test: Proc(s,t);
 Dcl (s,t) Char(*) Var;
 Put Edit('          1st string  = >'!!s!!'<')(Skip,a);
 Put Edit('          2nd string  = >'!!t!!'<')(Skip,a);
 Put Edit('Levenshtein distance  =',LevenshteinDistance(s,t))
         (Skip,a,f(3));
 Put Edit('')(Skip,a);
 End;

 LevenshteinDistance: Proc(s,t) Returns(Bin Fixed(31));
 Dcl (s,t) Char(*) Var;
 Dcl (sl,tl) Bin Fixed(31);
 Dcl ld      Bin Fixed(31);
 /* for all i and j, d[i,j] will hold the Levenshtein distance between
 *  the first i characters of s and the first j characters of t;
 *  note that d has (m+1)*(n+1) values                               */
 sl=length(s);
 tl=length(t);
 Begin;
   Dcl d(0:sl,0:tl) Bin Fixed(31);
   Dcl (i,j,ii,jj)  Bin Fixed(31);
   d=0;
   Do i=1 To sl;  /* source prefixes can be transformed into         */
     d(i,0)=i;    /* empty string by dropping all characters         */
     End;
   Do j=1 To tl;  /* target prefixes can be reached from             */
     d(0,j)=j;    /* empty source prefix by inserting every character*/
     End;
   Do j=1 To tl;
     jj=j-1;
     Do i=1 To sl;
       ii=i-1;
       If substr(s,i,1)=substr(t,j,1) Then
         d(i,j)=d(ii,jj);                  /* no operation required  */
       Else
         d(i,j)=1+min(d(ii,j),             /* a deletion             */
                      d(i,jj),             /* an insertion           */
                      d(ii,jj));           /* a substitution         */
       End;
     End;
   ld=d(sl,tl);
   End;
 Return(ld);
 End;
 End;
Output:
          1st string  = >kitten<
          2nd string  = >sitting<
Levenshtein distance  =  3

          1st string  = >rosettacode<
          2nd string  = >raisethysword<
Levenshtein distance  =  8

          1st string  = >Sunday<
          2nd string  = >Saturday<
Levenshtein distance  =  3

          1st string  = >Vladimir_Levenshtein[1965]<
          2nd string  = >Vladimir_Levenshtein[1965]<
Levenshtein distance  =  0

          1st string  = >this_algorithm_is_similar_to<
          2nd string  = >Damerau-Levenshtein_distance<
Levenshtein distance  = 24

          1st string  = ><
          2nd string  = >abc<
Levenshtein distance  =  3

version 2 recursive with memoization[edit]

*process source attributes xref or(!);
 ld3: Proc Options(main);
 Dcl ld(0:30,0:30) Bin Fixed(31);
 call test('kitten'      ,'sitting');
 call test('rosettacode' ,'raisethysword');
 call test('Sunday'      ,'Saturday');
 call test('Vladimir_Levenshtein[1965]',
           'Vladimir_Levenshtein[1965]');
 call test('this_algorithm_is_similar_to',
           'Damerau-Levenshtein_distance');
 call test('','abc');

 test: Proc(s,t);
 Dcl (s,t) Char(*);
 ld=-1;
 Put Edit('          1st string  = >'!!s!!'<')(Skip,a);
 Put Edit('          2nd string  = >'!!t!!'<')(Skip,a);
 Put Edit('Levenshtein distance  =',
          LevenshteinDistance(s,length(s),t,length(t)))
         (Skip,a,f(3));
 Put Edit('')(Skip,a);
 End;

 LevenshteinDistance: Proc(s,sl,t,tl) Recursive Returns(Bin Fixed(31));
 Dcl (s,t) Char(*);
 Dcl (sl,tl) Bin Fixed(31);
 Dcl cost    Bin Fixed(31);
 If ld(sl,tl)^=-1 Then
   Return(ld(sl,tl));
 Select;
   When(sl=0) ld(sl,tl)=tl;
   When(tl=0) ld(sl,tl)=sl;
   Otherwise Do;
     /* test if last characters of the strings match */
     cost=(substr(s,sl,1)^=substr(t,tl,1));
     /* return minimum of delete char from s, delete char from t,
        and delete char from both */
     ld(sl,tl)=min(LevenshteinDistance(s,sl-1,t,tl  )+1,
                   LevenshteinDistance(s,sl  ,t,tl-1)+1,
                   LevenshteinDistance(s,sl-1,t,tl-1)+cost));
     End;
   End;
 Return(ld(sl,tl));
 End;
 End;

Output is the same as for version 1.

PL/M[edit]

Works with: 8080 PL/M Compiler
... under CP/M (or an emulator)
Translation of: Action!
100H: /* CALCULATE THE LEVENSHTEIN DISTANCE BETWEEN STRINGS                  */
      /* TRANS:ATED FROM THE ACTION! SAMPLE                                  */

   /* CP/M BDOS SYSTEM CALL, IGNORE THE RETURN VALUE                         */
   BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5;     END;
   PR$CHAR:   PROCEDURE( C );  DECLARE C BYTE;    CALL BDOS( 2, C );     END;
   PR$STRING: PROCEDURE( S );  DECLARE S ADDRESS; CALL BDOS( 9, S );     END;
   PR$NL:     PROCEDURE; CALL PR$CHAR( 0DH ); CALL PR$CHAR( 0AH );       END;
   PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH  */
      DECLARE N ADDRESS;
      DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
      V = N;
      W = LAST( N$STR );
      N$STR( W ) = '$';
      N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
      DO WHILE( ( V := V / 10 ) > 0 );
         N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
      END;
      CALL PR$STRING( .N$STR( W ) );
   END PR$NUMBER;

   DECLARE WIDTH       LITERALLY '17';  /* ALLOW STRINGS UP TO 16 CHARACTERS */
   DECLARE MATRIX$SIZE LITERALLY '289'; /* 17*17 ELEMENTS                    */
   DECLARE STRING      LITERALLY '( WIDTH )BYTE';
 
   SCOPY: PROCEDURE( WORD, STR );    /* CONVEET PL/M STYLE STRING TO ACTION! */
      DECLARE ( WORD, STR ) ADDRESS;
      DECLARE ( W BASED WORD, S BASED STR ) STRING;
      DECLARE ( I, C ) BYTE;

      I = 0;
      DO WHILE( ( C := S( I ) ) <> '$' );
         W( I := I + 1 ) = C;
      END;
      W( 0 ) = I;
   END SCOPY;

   SET2DM: PROCEDURE( MATRIX, X, Y, VAL );
      DECLARE ( MATRIX, X, Y, VAL ) ADDRESS;
      DECLARE M BASED MATRIX ( MATRIX$SIZE )ADDRESS;
      M( X + ( Y * WIDTH ) ) = VAL;
   END SET2DM;
 
   GET2DM: PROCEDURE( MATRIX, X, Y )ADDRESS;
      DECLARE ( MATRIX, X, Y, VAL ) ADDRESS;
      DECLARE M BASED MATRIX ( MATRIX$SIZE )ADDRESS;
      RETURN M( X + ( Y * WIDTH ) );
   END GET2DM;
 
   LEVENSHTEIN$DISTANCE: PROCEDURE( S1, S2 )ADDRESS;
      DECLARE ( S1, S2 ) ADDRESS;
      DECLARE STR1 BASED S1 STRING, STR2 BASED S2 STRING; 
      DECLARE MATRIX ( MATRIX$SIZE ) ADDRESS;
      DECLARE ( MIN, K, L, I, J, M, N ) BYTE;
 
      M = STR1( 0 );
      N = STR2( 0 );
 
      DO I = 0 TO MATRIX$SIZE - 1; MATRIX( I ) = 0; END;
      DO I = 0 TO M; CALL SET2DM( .MATRIX, I, 1, I ); END;
      DO J = 0 TO N; CALL SET2DM( .MATRIX, 1, J, J ); END;
 
      DO J = 1 TO N;
         DO I = 1 TO M;
            IF STR1( I ) = STR2( J ) THEN DO;
               CALL SET2DM( .MATRIX, I, J, GET2DM( .MATRIX, I - 1, J - 1 ) );
               END;
            ELSE DO;
               MIN = GET2DM( .MATRIX, I - 1, J     ) + 1; /* DELETION        */
               K   = GET2DM( .MATRIX, I,     J - 1 ) + 1; /* INSERTION       */
               L   = GET2DM( .MATRIX, I - 1, J - 1 ) + 1; /* SUBSTITUTION    */
               IF K < MIN THEN MIN = K;
               IF L < MIN THEN MIN = L;
               CALL SET2DM( .MATRIX, I, J, MIN );
            END; 
         END;
      END;
      RETURN GET2DM( .MATRIX, M, N );
   END LEVENSHTEIN$DISTANCE;

   TEST: PROCEDURE( W1, W2 );
      DECLARE ( W1, W2 ) ADDRESS;
      DECLARE ( WORD$1, WORD$2 ) STRING;

      CALL SCOPY( .WORD$1, W1 );
      CALL SCOPY( .WORD$2, W2 );

      CALL PR$STRING( W1 ); CALL PR$STRING( .' -> $' ); CALL PR$STRING( W2 );
      CALL PR$STRING( .', LEVENSHTEIN DISTANCE: $' );
      CALL PR$NUMBER( LEVENSHTEIN$DISTANCE( .WORD$1, .WORD$2 ) );
      CALL PR$NL;
   END TEST;

   /* TEST CASES                                                         */
   CALL TEST( .'KITTEN$',      .'SITTING$'       );
   CALL TEST( .'ROSETTACODE$', .'RAISETHYSWORD$' );
   CALL TEST( .'QWERTY$',      .'QWERYT$'        );
   CALL TEST( .( 'ACTION', 33, '$' ), .'PL/M$'   );

EOF
Output:
KITTEN -> SITTING, LEVENSHTEIN DISTANCE: 3
ROSETTACODE -> RAISETHYSWORD, LEVENSHTEIN DISTANCE: 8
QWERTY -> QWERYT, LEVENSHTEIN DISTANCE: 2
ACTION! -> PL/M, LEVENSHTEIN DISTANCE: 4

PowerShell[edit]

This version does not allow empty strings.

function Get-LevenshteinDistance
{
    [CmdletBinding()]
    [OutputType([PSCustomObject])]
    Param
    (
        [Parameter(Mandatory=$true, Position=0)]
        [ValidateNotNullOrEmpty()]
        [Alias("s")] 
        [string]
        $ReferenceObject,

        [Parameter(Mandatory=$true, Position=1)]
        [ValidateNotNullOrEmpty()]
        [Alias("t")] 
        [string]
        $DifferenceObject
    )

    [int]$n = $ReferenceObject.Length
    [int]$m = $DifferenceObject.Length

    $d = New-Object -TypeName 'System.Object[,]' -ArgumentList ($n + 1),($m + 1)

    $outputObject = [PSCustomObject]@{
        ReferenceObject  = $ReferenceObject
        DifferenceObject = $DifferenceObject
        Distance         = $null
    }

    for ($i = 0; $i -le $n; $i++)
    { 
        $d[$i, 0] = $i
    }

    for ($i = 0; $i -le $m; $i++)
    { 
        $d[0, $i] = $i
    }

    for ($i = 1; $i -le $m; $i++)
    { 
        for ($j = 1; $j -le $n; $j++)
        { 
            if ($ReferenceObject[$j - 1] -eq $DifferenceObject[$i - 1])
            {
                $d[$j, $i] = $d[($j - 1), ($i - 1)]
            }
            else
            {
                $d[$j, $i] = [Math]::Min([Math]::Min(($d[($j - 1), $i] + 1), ($d[$j, ($i - 1)] + 1)), ($d[($j - 1), ($i - 1)] + 1))
            }
        }
    }

    $outputObject.Distance = $d[$n, $m]

    $outputObject
}
Get-LevenshteinDistance "kitten" "sitting"
Get-LevenshteinDistance rosettacode raisethysword
Output:
ReferenceObject DifferenceObject Distance
--------------- ---------------- --------
kitten          sitting                 3
rosettacode     raisethysword           8

Processing[edit]

void setup() {
  println(distance("kitten", "sitting"));
}
int distance(String a, String b) {
  int [] costs = new int [b.length() + 1];
  for (int j = 0; j < costs.length; j++)
    costs[j] = j;
  for (int i = 1; i <= a.length(); i++) {
    costs[0] = i;
    int nw = i - 1;
    for (int j = 1; j <= b.length(); j++) {
      int cj = min(1 + min(costs[j], costs[j - 1]), a.charAt(i - 1) == b.charAt(j - 1) ? nw : nw + 1);
      nw = costs[j];
      costs[j] = cj;
    }
  }
  return costs[b.length()];
}

Processing Python mode[edit]

def setup():
    println(distance("kitten", "sitting"))

def distance(a, b):
    costs = []
    for j in range(len(b) + 1):
        costs.append(j)
    for i in range(1, len(a) + 1):
        costs[0] = i
        nw = i - 1
        for j in range(1, len(b) + 1):
            cj = min(1 + min(costs[j], costs[j - 1]),
                     nw if a[i - 1] == b[j - 1] else nw + 1)
            nw = costs[j]
            costs[j] = cj

    return costs[len(b)]

Prolog[edit]

Without Tabling[edit]

Works with SWI-Prolog.
Based on Wikipedia's pseudocode.

levenshtein(S, T, R) :-
	length(S, M),
	M1 is M+1,
	length(T, N),
	N1 is N+1,
	length(Lev, N1),
	maplist(init(M1), Lev),
	numlist(0, N, LN),
	maplist(init_n, LN, Lev),
	nth0(0, Lev, Lev0),
	numlist(0, M, Lev0),

	% compute_levenshtein distance
	numlist(1, N, LN1),
	maplist(work_on_T(Lev, S), LN1, T),
	last(Lev, LevLast),
	last(LevLast, R).


work_on_T(Lev, S, J, TJ) :-
	length(S, M),
	numlist(1, M, LM),
	maplist(work_on_S(Lev, J, TJ), LM, S).

work_on_S(Lev, J, C, I, C) :-
	% same char
	!,
	I1 is I-1, J1 is J-1,
	nth0(J1, Lev, LevJ1),
	nth0(I1, LevJ1, V),
	nth0(J, Lev, LevJ),
	nth0(I, LevJ, V).


work_on_S(Lev, J, _C1, I, _C2) :-
	I1 is I-1, J1 is J - 1,
	% compute the value for deletion
	nth0(J, Lev, LevJ),
	nth0(I1, LevJ, VD0),
	VD is VD0 + 1,

	% compute the value for insertion
	nth0(J1, Lev, LevJ1),
	nth0(I, LevJ1, VI0),
	VI is VI0 + 1,

	% compute the value for substitution
	nth0(I1, LevJ1, VS0),
	VS is VS0 + 1,

	% set the minimum value to cell(I,J)
	sort([VD, VI, VS], [V|_]),

	nth0(I, LevJ, V).


init(Len, C) :-
	length(C, Len).

init_n(N, L) :-
	nth0(0, L, N).
Output examples:
 ?- levenshtein("kitten", "sitting", R).
R = 3.

 ?- levenshtein("saturday", "sunday", R).
R = 3.

 ?- levenshtein("rosettacode", "raisethysword", R).
R = 8.

With Tabling[edit]

Using so called mode directed tabling:

:- table lev(_,_,min).
lev([], [], 0).
lev([X|L], [X|R], D) :- !, lev(L, R, D).
lev([_|L], [_|R], D) :- lev(L, R, H), D is H+1.
lev([_|L], R, D) :- lev(L, R, H), D is H+1.
lev(L, [_|R], D) :- lev(L, R, H), D is H+1.

?- set_prolog_flag(double_quotes, codes).
true.

?- lev("kitten", "sitting", R).
R = 3.

PureBasic[edit]

Based on Wikipedia's pseudocode.

Procedure LevenshteinDistance(A_string$, B_String$)
  Protected m, n, i, j, min, k, l
  m = Len(A_string$)
  n = Len(B_String$)
  Dim D(m, n)
  
  For i=0 To m: D(i,0)=i: Next
  For j=0 To n: D(0,j)=j: Next
  
  For j=1 To n
    For i=1 To m
      If Mid(A_string$,i,1) = Mid(B_String$,j,1)
        D(i,j) = D(i-1, j-1); no operation required
      Else
        min = D(i-1, j)+1   ; a deletion
        k   = D(i, j-1)+1   ; an insertion
        l   = D(i-1, j-1)+1 ; a substitution
        If k < min: min=k: EndIf
        If l < min: min=l: EndIf
        D(i,j) = min
      EndIf
    Next
  Next
  ProcedureReturn D(m,n)
EndProcedure

;- Testing
n = LevenshteinDistance("kitten", "sitting")
MessageRequester("Info","Levenshtein Distance= "+Str(n))

Python[edit]

Iterative 1[edit]

Faithful implementation of "Iterative with full matrix" from Wikipedia

def levenshteinDistance(str1, str2):
    m = len(str1)
    n = len(str2)
    d = [[i] for i in range(1, m + 1)]   # d matrix rows
    d.insert(0, list(range(0, n + 1)))   # d matrix columns
    for j in range(1, n + 1):
        for i in range(1, m + 1):
            if str1[i - 1] == str2[j - 1]:   # Python (string) is 0-based
                substitutionCost = 0
            else:
                substitutionCost = 1
            d[i].insert(j, min(d[i - 1][j] + 1,
                               d[i][j - 1] + 1,
                               d[i - 1][j - 1] + substitutionCost))
    return d[-1][-1]

print(levenshteinDistance("kitten","sitting"))
print(levenshteinDistance("rosettacode","raisethysword"))
Output:
3
8

Iterative 2[edit]

Implementation of the Wikipedia algorithm, optimized for memory

def minimumEditDistance(s1,s2):
    if len(s1) > len(s2):
        s1,s2 = s2,s1
    distances = range(len(s1) + 1)
    for index2,char2 in enumerate(s2):
        newDistances = [index2+1]
        for index1,char1 in enumerate(s1):
            if char1 == char2:
                newDistances.append(distances[index1])
            else:
                newDistances.append(1 + min((distances[index1],
                                             distances[index1+1],
                                             newDistances[-1])))
        distances = newDistances
    return distances[-1]
 
print(minimumEditDistance("kitten","sitting"))
print(minimumEditDistance("rosettacode","raisethysword"))
Output:
3
8

Iterative 3[edit]

Iterative space optimized (even bounded)

def ld(a, b, mx=-1):	
    def result(d): return d if mx < 0 else False if d > mx else True
    
    if a == b: return result(0)
    la, lb = len(a), len(b)
    if mx >= 0 and abs(la - lb) > mx: return result(mx+1)
    if la == 0: return result(lb)
    if lb == 0: return result(la)
    if lb > la: a, b, la, lb = b, a, lb, la
    
    cost = array('i', range(lb + 1))
    for i in range(1, la + 1):
        cost[0] = i; ls = i-1; mn = ls
        for j in range(1, lb + 1):
            ls, act = cost[j], ls + int(a[i-1] != b[j-1])
            cost[j] = min(ls+1, cost[j-1]+1, act)
            if (ls < mn): mn = ls
        if mx >= 0 and mn > mx: return result(mx+1)
    if mx >= 0 and cost[lb] > mx: return result(mx+1)
    return result(cost[lb])

print(
    ld('kitten','kitten'), # 0
    ld('kitten','sitten'), # 1
    ld('kitten','sittes'), # 2
    ld('kitten','sityteng'), # 3
    ld('kitten','sittYing'), # 4
    ld('rosettacode','raisethysword'), # 8 
    ld('kitten','kittenaaaaaaaaaaaaaaaaa'), # 17
    ld('kittenaaaaaaaaaaaaaaaaa','kitten') # 17
)

print(
    ld('kitten','kitten',3), # True
    ld('kitten','sitten',3), # True
    ld('kitten','sittes',3), # True
    ld('kitten','sityteng',3), # True
    ld('kitten','sittYing',3), # False
    ld('rosettacode','raisethysword',3), # False
    ld('kitten','kittenaaaaaaaaaaaaaaaaa',3), # False
    ld('kittenaaaaaaaaaaaaaaaaa','kitten',3) # False
)
Output:
0 1 2 3 4 8 17 17
True True True True False False False False

Functional[edit]

Memoized recursion[edit]

(Uses this cache from the standard library).

>>> from functools import lru_cache
>>> @lru_cache(maxsize=4095)
def ld(s, t):
	if not s: return len(t)
	if not t: return len(s)
	if s[0] == t[0]: return ld(s[1:], t[1:])
	l1 = ld(s, t[1:])
	l2 = ld(s[1:], t)
	l3 = ld(s[1:], t[1:])
	return 1 + min(l1, l2, l3)

>>> print( ld("kitten","sitting"),ld("rosettacode","raisethysword") )
3 8

Non-recursive: reduce and scanl[edit]

Works with: Python version 3.7
'''Levenshtein distance'''

from itertools import (accumulate, chain, islice)
from functools import reduce


# levenshtein :: String -> String -> Int
def levenshtein(sa):
    '''Levenshtein distance between
       two strings.'''
    s1 = list(sa)

    # go :: [Int] -> Char -> [Int]
    def go(ns, c):
        n, ns1 = ns[0], ns[1:]

        # gap :: Int -> (Char, Int, Int) -> Int
        def gap(z, c1xy):
            c1, x, y = c1xy
            return min(
                succ(y),
                succ(z),
                succ(x) if c != c1 else x
            )
        return scanl(gap)(succ(n))(
            zip(s1, ns, ns1)
        )
    return lambda sb: reduce(
        go, list(sb), enumFromTo(0)(len(s1))
    )[-1]


# TEST ----------------------------------------------------
# main :: IO ()
def main():
    '''Tests'''

    pairs = [
        ('rosettacode', 'raisethysword'),
        ('kitten', 'sitting'),
        ('saturday', 'sunday')
    ]

    print(
        tabulated(
            'Levenshtein minimum edit distances:\n'
        )(str)(str)(
            uncurry(levenshtein)
        )(concat(map(
            list,
            zip(pairs, map(swap, pairs))
        )))
    )


# GENERIC -------------------------------------------------

# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
    '''Right to left function composition.'''
    return lambda f: lambda x: g(f(x))


# concat :: [[a]] -> [a]
# concat :: [String] -> String
def concat(xxs):
    '''The concatenation of all the elements in a list.'''
    xs = list(chain.from_iterable(xxs))
    unit = '' if isinstance(xs, str) else []
    return unit if not xs else (
        ''.join(xs) if isinstance(xs[0], str) else xs
    )


# enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
    '''Integer enumeration from m to n.'''
    return lambda n: list(range(m, 1 + n))


# scanl :: (b -> a -> b) -> b -> [a] -> [b]
def scanl(f):
    '''scanl is like reduce, but returns a succession of
       intermediate values, building from the left.'''
    return lambda a: lambda xs: (
        list(accumulate(chain([a], xs), f))
    )


# swap :: (a, b) -> (b, a)
def swap(tpl):
    '''The swapped components of a pair.'''
    return (tpl[1], tpl[0])


# succ :: Int => Int -> Int
def succ(x):
    '''The successor of a value.
       For numeric types, (1 +).'''
    return 1 + x


# tabulated :: String -> (a -> String) ->
#                        (b -> String) ->
#                        (a -> b) -> [a] -> String
def tabulated(s):
    '''Heading -> x display function ->
                 fx display function ->
                 f -> value list -> tabular string.'''
    def go(xShow, fxShow, f, xs):
        w = max(map(compose(len)(xShow), xs))
        return s + '\n' + '\n'.join([
            xShow(x).rjust(w, ' ') + ' -> ' + fxShow(f(x))
            for x in xs

        ])
    return lambda xShow: lambda fxShow: (
        lambda f: lambda xs: go(
            xShow, fxShow, f, xs
        )
    )


# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
    '''The prefix of xs of length n,
       or xs itself if n > length xs.'''
    return lambda xs: (
        xs[0:n]
        if isinstance(xs, list)
        else list(islice(xs, n))
    )


# uncurry :: (a -> b -> c) -> ((a, b) -> c)
def uncurry(f):
    '''A function over a tuple
       derived from a curried function.'''
    return lambda xy: f(xy[0])(
        xy[1]
    )


# MAIN ---
if __name__ == '__main__':
    main()
Output:
Levenshtein minimum edit distances:

('rosettacode', 'raisethysword') -> 8
('raisethysword', 'rosettacode') -> 8
           ('kitten', 'sitting') -> 3
           ('sitting', 'kitten') -> 3
          ('saturday', 'sunday') -> 3
          ('sunday', 'saturday') -> 3

Racket[edit]

A memoized recursive implementation.

#lang racket

(define (levenshtein a b)
  (define (ls0 a-index b-index)
    (cond [(or (= a-index -1) (= b-index -1)) (abs (- a-index b-index))]
          [else 
           (define a-char (string-ref a a-index))
           (define b-char (string-ref b b-index))
           (if (equal? a-char b-char)
               (ls (sub1 a-index) (sub1 b-index))
               (min (add1 (ls (sub1 a-index) b-index))
                    (add1 (ls a-index (sub1 b-index)))
                    (add1 (ls (sub1 a-index) (sub1 b-index)))))]))
  (define memo (make-hash))
  (define (ls a-i b-i)
    (hash-ref! memo (cons a-i b-i) (λ() (ls0 a-i b-i))))
  (ls (sub1 (string-length a)) (sub1 (string-length b))))

(levenshtein "kitten" "sitting")
(levenshtein "rosettacode" "raisethysword")
Output:
3
8

Raku[edit]

(formerly Perl 6)

Implementation of the Wikipedia algorithm. Since column 0 and row 0 are used for base distances, the original algorithm would require us to compare "@s[$i-1] eq @t[$j-1]", and reference $m and $n separately. Prepending an unused value (undef) onto @s and @t makes their indices align with the $i,$j numbering of @d, and lets us use .end instead of $m,$n.

sub levenshtein-distance ( Str $s, Str $t --> Int ) {
    my @s = *, |$s.comb;
    my @t = *, |$t.comb;

    my @d;
    @d[$_;  0] = $_ for ^@s.end;
    @d[ 0; $_] = $_ for ^@t.end;

    for 1..@s.end X 1..@t.end -> ($i, $j) {
        @d[$i; $j] = @s[$i] eq @t[$j]
            ??   @d[$i-1; $j-1]    # No operation required when eq
            !! ( @d[$i-1; $j  ],   # Deletion
                 @d[$i  ; $j-1],   # Insertion
                 @d[$i-1; $j-1],   # Substitution
               ).min + 1;
    }

    @d[*-1][*-1];
}

for <kitten sitting>, <saturday sunday>, <rosettacode raisethysword> -> ($s, $t) {
    say "Levenshtein distance('$s', '$t') == ", levenshtein-distance($s, $t)
}
Output:
Levenshtein distance('kitten', 'sitting') == 3
Levenshtein distance('saturday', 'sunday') == 3
Levenshtein distance('rosettacode', 'raisethysword') == 8

REXX[edit]

version 1[edit]

As per the task's requirements, this version includes a driver to display the results.

/*REXX program  calculates and displays the  Levenshtein distance  between two strings. */
call Levenshtein   'kitten'                        ,     "sitting"
call Levenshtein   'rosettacode'                   ,     "raisethysword"
call Levenshtein   'Sunday'                        ,     "Saturday"
call Levenshtein   'Vladimir Levenshtein[1965]'    ,     "Vladimir Levenshtein[1965]"
call Levenshtein   'this algorithm is similar to'  ,     "Damerau─Levenshtein distance"
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Levenshtein: procedure; parse arg o,t;  oL= length(o);   tL= length(t);     @.= 0
    say '        original string  = '    o                          /*show   old  string*/
    say '          target string  = '    t                          /*  "   target   "  */
                     do #=1  for tL;   @.0.#= #;   end  /*#*/       /*the   drop  array.*/
                     do #=1  for oL;   @.#.0= #;   end  /*#*/       /* "   insert   "   */
         do    j=1  for tL;   jm= j-1;    q= substr(t, j, 1)        /*obtain character. */
            do k=1  for oL;   km= k-1
            if q==substr(o, k, 1)  then @.k.j= @.km.jm              /*use previous char.*/
                                   else @.k.j= 1   +   min(@.km.j,  @.k.jm,  @.km.jm)
            end   /*k*/
         end      /*j*/                                             /* [↑]  best choice.*/
    say '   Levenshtein distance  = '  @.oL.tL;    say;      return
output   when using the internal default inputs:
        original string  =  kitten
          target string  =  sitting
   Levenshtein distance  =  3

        original string  =  rosettacode
          target string  =  raisethysword
   Levenshtein distance  =  8

        original string  =  Sunday
          target string  =  Saturday
   Levenshtein distance  =  3

        original string  =  Vladimir Levenshtein[1965]
          target string  =  Vladimir Levenshtein[1965]
   Levenshtein distance  =  0

        original string  =  this algorithm is similar to
          target string  =  Damerau─Levenshtein distance
   Levenshtein distance  =  24

version 2[edit]

same as Similar to version 1 (but does not include a driver for testing), reformatted and commented

/*rexx*/

call test 'kitten'      ,'sitting'
call test 'rosettacode' ,'raisethysword'
call test 'Sunday'      ,'Saturday'
call test 'Vladimir_Levenshtein[1965]',,
          'Vladimir_Levenshtein[1965]'
call test 'this_algorithm_is_similar_to',,
          'Damerau-Levenshtein_distance'
call test '','abc'
exit 0


test: Procedure
  Parse Arg s,t
  ld.=''
  Say '          1st string  = >'s'<'
  Say '          2nd string  = >'t'<'
  Say 'Levenshtein distance  =' Levenshtein(s,length(s),t,length(t))
  Say ''
  Return


Levenshtein: Procedure
Parse Arg s,t
/* for all i and j, d[i,j] will hold the Levenshtein distance between     */
/* the first i characters of s and the first j characters of t;           */
/* note that d has (m+1)*(n+1) values                                     */
  m=length(s)
  n=length(t)
  d.=0
  Do i=1 To m  /* source prefixes can be transformed into empty string by */
    d.i.0=i    /* dropping all characters                                 */
    End
  Do j=1 To n  /* target prefixes can be reached from empty source prefix */
    d.0.j=j    /* by inserting every character                            */
    End
  Do j=1 To n
    jj=j-1
    Do i=1 To m
      ii=i-1
      If substr(s,i,1)=substr(t,j,1) Then
        d.i.j=d.ii.jj          /* no operation required                   */
      else
        d.i.j=min(d.ii.j+1,,   /* a deletion                              */
                  d.i.jj+1,,   /* an insertion                            */
                  d.ii.jj+1)   /* a substitution                          */
      End
    End
  Say '          1st string  = '    s
  Say '          2nd string  = '    t
  say 'Levenshtein distance  = ' d.m.n;   say ''
  Return d.m.n
Output:
          1st string  = >kitten<
          2nd string  = >sitting<
          1st string  =  kitten
          2nd string  =  6
Levenshtein distance  =  6

Levenshtein distance  = 6

          1st string  = >rosettacode<
          2nd string  = >raisethysword<
          1st string  =  rosettacode
          2nd string  =  11
Levenshtein distance  =  11

Levenshtein distance  = 11

          1st string  = >Sunday<
          2nd string  = >Saturday<
          1st string  =  Sunday
          2nd string  =  6
Levenshtein distance  =  6

Levenshtein distance  = 6

          1st string  = >Vladimir_Levenshtein[1965]<
          2nd string  = >Vladimir_Levenshtein[1965]<
          1st string  =  Vladimir_Levenshtein[1965]
          2nd string  =  26
Levenshtein distance  =  25

Levenshtein distance  = 25

          1st string  = >this_algorithm_is_similar_to<
          2nd string  = >Damerau-Levenshtein_distance<
          1st string  =  this_algorithm_is_similar_to
          2nd string  =  28
Levenshtein distance  =  28

Levenshtein distance  = 28

          1st string  = ><
          2nd string  = >abc<
          1st string  =
          2nd string  =  0
Levenshtein distance  =  1

Levenshtein distance  = 1

version 3[edit]

Alternate algorithm from Wikipedia (but does not include a driver for testing).

/*rexx*/

call test 'kitten'      ,'sitting'
call test 'rosettacode' ,'raisethysword'
call test 'Sunday'      ,'Saturday'
call test 'Vladimir_Levenshtein[1965]',,
          'Vladimir_Levenshtein[1965]'
call test 'this_algorithm_is_similar_to',,
          'Damerau-Levenshtein_distance'
call test '','abc'
exit 0


test: Procedure
  Parse Arg s,t
  ld.=''
  Say '          1st string  = >'s'<'
  Say '          2nd string  = >'t'<'
  Say 'Levenshtein distance  =' LevenshteinDistance(s,length(s),t,length(t))
  Say ''
  Return


LevenshteinDistance: Procedure
Parse Arg s,t
If s==t Then Return 0;
sl=length(s)
tl=length(t)
If sl=0 Then Return tl
If tl=0 Then Return sl
Do i=0 To tl
  v0.i=i
  End
Do i=0 To sl-1
  v1.0=i+1
  Do j=0 To tl-1
    jj=j+1
    cost=substr(s,i+1,1)<>substr(t,j+1,1)
    v1.jj=min(v1.j+1,v0.jj+1,v0.j+cost)
    End
  Do j=0 to tl-1
    v0.j=v1.j
    End
  End
return v1.tl
Output:
          1st string  = >kitten<
          2nd string  = >sitting<
Levenshtein distance  = 2

          1st string  = >rosettacode<
          2nd string  = >raisethysword<
Levenshtein distance  = 3

          1st string  = >Sunday<
          2nd string  = >Saturday<
Levenshtein distance  = 2

          1st string  = >Vladimir_Levenshtein[1965]<
          2nd string  = >Vladimir_Levenshtein[1965]<
Levenshtein distance  = 3

          1st string  = >this_algorithm_is_similar_to<
          2nd string  = >Damerau-Levenshtein_distance<
Levenshtein distance  = 3

          1st string  = ><
          2nd string  = >abc<
Levenshtein distance  = 1

version 4 (recursive)[edit]

Recursive algorithm from Wikipedia with memoization

/*rexx*/

call test 'kitten'      ,'sitting'
call test 'rosettacode' ,'raisethysword'
call test 'Sunday'      ,'Saturday'
call test 'Vladimir_Levenshtein[1965]',,
          'Vladimir_Levenshtein[1965]'
call test 'this_algorithm_is_similar_to',,
          'Damerau-Levenshtein_distance'
call test '','abc'
Exit


test: Procedure
  Parse Arg s,t
  ld.=''
  Say '          1st string  = >'s'<'
  Say '          2nd string  = >'t'<'
  Say 'Levenshtein distance  =' LevenshteinDistance(s,length(s),t,length(t))
  Say ''
  Return


LevenshteinDistance: Procedure Expose ld.
/* sl and tl are the number of characters in string s and t respectively */
  Parse Arg s,sl,t,tl
  If ld.sl.tl<>'' Then
    Return ld.sl.tl
  Select
    When sl=0 Then ld.sl.tl=tl
    When tl=0 Then ld.sl.tl=sl
    Otherwise Do
      /* test if last characters of the strings match */
      cost=substr(s,sl,1)<>substr(t,tl,1)
      /* return minimum of delete char from s, delete char from t,
         and delete char from both */
      ld.sl.tl=min(LevenshteinDistance(s,sl-1,t,tl  )+1,,
                   LevenshteinDistance(s,sl  ,t,tl-1)+1,,
                   LevenshteinDistance(s,sl-1,t,tl-1)+cost)
      End
    End
  Return ld.sl.tl
Output:
          1st string  = >kitten<
          2nd string  = >sitting<
Levenshtein distance  = 3

          1st string  = >rosettacode<
          2nd string  = >raisethysword<
Levenshtein distance  = 8

          1st string  = >Sunday<
          2nd string  = >Saturday<
Levenshtein distance  = 3

          1st string  = >Vladimir_Levenshtein[1965]<
          2nd string  = >Vladimir_Levenshtein[1965]<
Levenshtein distance  = 0

          1st string  = >this_algorithm_is_similar_to<
          2nd string  = >Damerau-Levenshtein_distance<
Levenshtein distance  = 24

          1st string  = ><
          2nd string  = >abc<
Levenshtein distance  = 3

Ring[edit]

# Project : Levenshtein distance

load "stdlib.ring"
see "" + "distance(kitten, sitting) = " + levenshteindistance("kitten", "sitting") + nl
see "" + "distance(saturday, sunday) = " + levenshteindistance("saturday", "sunday") + nl
see "" + "distance(rosettacode, raisethysword) = " + levenshteindistance("rosettacode", "raisethysword") + nl

func levenshteindistance(s1, s2)
        n = len(s1)
        m = len(s2)
        if n = 0 
            levenshteindistance = m
            return
        ok
        if m = 0 
            levenshteindistance = n
            return
        ok
        d = newlist(n, m)
        for i = 1 to n
             d[i][1] = i
        next i
        for i = 1 to m
             d[1][i] = i
        next
        for i = 2 to n
             si = substr(s1, i, 1)
             for j = 2 to m
                  tj = substr(s2, j, 1)
                  if si = tj
                     cost = 0 
                  else
                     cost = 1
                  ok
                  d[i][ j] = min((d[i - 1][ j]), min((d[i][j - 1] + 1), (d[i - 1][j - 1] + cost)))
             next 
        next
        levenshteindistance = d[n][m]
        return levenshteindistance

Output:

distance(kitten, sitting) = 3
distance(saturday, sunday) = 3
distance(rosettacode, raisethysword) = 8

Ruby[edit]

Implementation of the wikipedia algorithm. Invariant is that for current loop indices i and j, costs[k] for k < j contains lev(i, k) and for k >= j contains lev(i-1, k). The inner loop body restores the invariant for the new value of j.

module Levenshtein
  
  def self.distance(a, b)
    a, b = a.downcase, b.downcase
    costs = Array(0..b.length) # i == 0
    (1..a.length).each do |i|
      costs[0], nw = i, i - 1  # j == 0; nw is lev(i-1, j)
      (1..b.length).each do |j|
        costs[j], nw = [costs[j] + 1, costs[j-1] + 1, a[i-1] == b[j-1] ? nw : nw + 1].min, costs[j]
      end
    end
    costs[b.length]
  end
  
  def self.test
    %w{kitten sitting saturday sunday rosettacode raisethysword}.each_slice(2) do |a, b|
      puts "distance(#{a}, #{b}) = #{distance(a, b)}"
    end
  end
  
end

Levenshtein.test
Output:
distance(kitten, sitting) = 3
distance(saturday, sunday) = 3
distance(rosettacode, raisethysword) = 8

A variant can be found used in Rubygems [2]

def levenshtein_distance(str1, str2)
  n = str1.length
  m = str2.length
  max = n/2
  
  return m if 0 == n
  return n if 0 == m
  return n if (n - m).abs > max
  
  d = (0..m).to_a
  x = nil
  
  str1.each_char.with_index do |char1,i|
    e = i+1
    
    str2.each_char.with_index do |char2,j|
      cost = (char1 == char2) ? 0 : 1
      x = [ d[j+1] + 1, # insertion
            e + 1,      # deletion
            d[j] + cost # substitution
          ].min
      d[j] = e
      e = x
    end
    
    d[m] = x
  end
  
  x
end

%w{kitten sitting saturday sunday rosettacode raisethysword}.each_slice(2) do |a, b|
  puts "distance(#{a}, #{b}) = #{levenshtein_distance(a, b)}"
end

same output

Run BASIC[edit]

print levenshteinDistance("kitten", "sitting")
print levenshteinDistance("rosettacode", "raisethysword")
end
function levenshteinDistance(s1$, s2$)
    n = len(s1$)
    m = len(s2$)
    if n = 0 then
        levenshteinDistance = m
        goto [ex]
    end if
    if m = 0 then
        levenshteinDistance = n
        goto [ex]
    end if
    dim d(n, m)
    for i = 0 to n
        d(i, 0) = i
    next i
    for i = 0 to m
        d(0, i) = i
    next i
    for i = 1 to n
        si$ = mid$(s1$, i, 1)
        for j = 1 to m
            tj$ = mid$(s2$, j, 1)
            if si$ = tj$ then cost = 0 else cost = 1
            d(i, j) = min((d(i - 1, j) + 1),min((d(i, j - 1) + 1),(d(i - 1, j - 1) + cost)))
        next j
    next i
    levenshteinDistance = d(n, m)
[ex]
end function
Output:
3
8

Rust[edit]

Implementation of the wikipedia algorithm.

Works with: Rust version 1.45
fn main() {
    println!("{}", levenshtein_distance("kitten", "sitting"));
    println!("{}", levenshtein_distance("saturday", "sunday"));
    println!("{}", levenshtein_distance("rosettacode", "raisethysword"));
}
 
fn levenshtein_distance(word1: &str, word2: &str) -> usize {
    let w1 = word1.chars().collect::<Vec<_>>();
    let w2 = word2.chars().collect::<Vec<_>>();
 
    let word1_length = w1.len() + 1;
    let word2_length = w2.len() + 1;
 
    let mut matrix = vec![vec![0; word1_length]; word2_length];
 
    for i in 1..word1_length { matrix[0][i] = i; }
    for j in 1..word2_length { matrix[j][0] = j; }
 
    for j in 1..word2_length {
        for i in 1..word1_length {
            let x: usize = if w1[i-1] == w2[j-1] {
                matrix[j-1][i-1]
            } else {
                1 + std::cmp::min(
                        std::cmp::min(matrix[j][i-1], matrix[j-1][i])
                        , matrix[j-1][i-1])
            };
            matrix[j][i] = x;
        }
    }
    matrix[word2_length-1][word1_length-1]
}
Output:
3
3
8

Scala[edit]

Translated Wikipedia algorithm.[edit]

object Levenshtein0 extends App {

  def distance(s1: String, s2: String): Int = {
    val dist = Array.tabulate(s2.length + 1, s1.length + 1) { (j, i) => if (j == 0) i else if (i == 0) j else 0 }

    @inline
    def minimum(i: Int*): Int = i.min

    for {j <- dist.indices.tail
         i <- dist(0).indices.tail} dist(j)(i) =
        if (s2(j - 1) == s1(i - 1)) dist(j - 1)(i - 1)
        else minimum(dist(j - 1)(i) + 1, dist(j)(i - 1) + 1, dist(j - 1)(i - 1) + 1)

    dist(s2.length)(s1.length)
  }

  def printDistance(s1: String, s2: String) {
    println("%s -> %s : %d".format(s1, s2, distance(s1, s2)))
  }

  printDistance("kitten", "sitting")
  printDistance("rosettacode", "raisethysword")

}
Output:
kitten -> sitting : 3
rosettacode -> raisethysword : 8

Functional programmed, memoized[edit]

Output:
Best seen running in your browser either by (ES aka JavaScript, non JVM) or Scastie (remote JVM).
import scala.collection.mutable
import scala.collection.parallel.ParSeq

object Levenshtein extends App {

  def printDistance(s1: String, s2: String) =
    println(f"$s1%s -> $s2%s : ${levenshtein(s1, s2)(s1.length, s2.length)}%d")

  def levenshtein(s1: String, s2: String): mutable.Map[(Int, Int), Int] = {
    val memoizedCosts = mutable.Map[(Int, Int), Int]()

    def lev: ((Int, Int)) => Int = {
      case (k1, k2) =>
        memoizedCosts.getOrElseUpdate((k1, k2), (k1, k2) match {
          case (i, 0) => i
          case (0, j) => j
          case (i, j) =>
            ParSeq(1 + lev((i - 1, j)),
              1 + lev((i, j - 1)),
              lev((i - 1, j - 1))
                + (if (s1(i - 1) != s2(j - 1)) 1 else 0)).min
        })
    }

    lev((s1.length, s2.length))
    memoizedCosts
  }

  printDistance("kitten", "sitting")
  printDistance("rosettacode", "raisethysword")
  printDistance("Here's a bunch of words", "to wring out this code")
  printDistance("sleep", "fleeting")

}

Scheme[edit]

Recursive version from wikipedia article.

(define (levenshtein s t)
  (define (%levenshtein s sl t tl)
    (cond ((zero? sl) tl)
          ((zero? tl) sl)
          (else
	    (min (+ (%levenshtein (cdr s) (- sl 1) t tl) 1)
                 (+ (%levenshtein s sl (cdr t) (- tl 1)) 1)
                 (+ (%levenshtein (cdr s) (- sl 1) (cdr t) (- tl 1))
		    (if (char=? (car s) (car t)) 0 1))))))
  (%levenshtein (string->list s)
		(string-length s)		
		(string->list t)
		(string-length t)))
Output:
> (levenshtein "kitten" "sitting")
3
> (levenshtein "rosettacode" "raisethysword")
8

Seed7[edit]

$ include "seed7_05.s7i";

const func integer: levenshteinDistance (in string: s, in string: t) is func
  result
    var integer: distance is 0;
  local
    var array array integer: d is 0 times 0 times 0;
    var integer: i is 0;
    var integer: j is 0;
  begin
    d := [0 .. length(s)] times [0 .. length(t)] times 0;
    for key i range s do
      d[i][0] := i;
    end for;
    for key j range t do
      d[0][j] := j;
      for key i range s do
        if s[i] = t[j] then
          d[i][j] := d[pred(i)][pred(j)];
        else
          d[i][j] := min(min(succ(d[pred(i)][j]), succ(d[i][pred(j)])), succ(d[pred(i)][pred(j)]));
        end if;
      end for;
    end for;
    distance := d[length(s)][length(t)];
  end func;

const proc: main is func
  begin
    writeln("kitten -> sitting: " <& levenshteinDistance("kitten", "sitting"));
    writeln("rosettacode -> raisethysword: " <& levenshteinDistance("rosettacode", "raisethysword"));
  end func;
Output:
kitten -> sitting: 3
rosettacode -> raisethysword: 8

SenseTalk[edit]

SenseTalk has a built-in TextDifference function for this.

put textDifference("kitten", "sitting") // --> 3
put textDifference("rosettacode", "raisethysword") // --> 8

SequenceL[edit]

This implementation is based on the "Iterative with two matrix rows" version on Wikipedia.

import <Utilities/Sequence.sl>;
import <Utilities/Math.sl>;

main(args(2)) := LenenshteinDistance(args[1], args[2]);

LenenshteinDistance(s(1), t(1)) :=
	0 when equalList(s,t) else
	size(t) when size(s) = 0 else
	size(s) when size(t) = 0 else
	LenenshteinDistanceIterative(s, t, 0 ... size(t), duplicate(0, size(t) + 1), 1);

LenenshteinDistanceIterative(s(1), t(1), v0(1), v1(1), n) :=
	v0[size(t) + 1] when n > size(s) else
	LenenshteinDistanceIterative(s, t, iterate(s[n], t, v0, setElementAt(v1, 1, n + 0), 1), v0, n + 1);

iterate(s, t(1), v0(1), v1(1), n) :=
	v1 when n > size(t) else
	iterate(s, t, v0,
		setElementAt(v1, n + 1,
			min(min(v1[n] + 1, v0[n + 1] + 1), v0[n] + (0 when s = t[n] else 1))),
		n + 1);

Sidef[edit]

Recursive[edit]

func lev(s, t) is cached {
 
    s || return t.len
    t || return s.len
 
    var s1 = s.ft(1)
    var t1 = t.ft(1)
 
    s[0] == t[0] ? __FUNC__(s1, t1)
                 : 1+Math.min(
                        __FUNC__(s1, t1),
                        __FUNC__(s,  t1),
                        __FUNC__(s1, t )
                     )
}

Iterative[edit]

func lev(s, t) {
    var d = [@(0 .. t.len), s.len.of {[_]}...]
    for i,j in (^s ~X ^t) {
        d[i+1][j+1] = (
            s[i] == t[j]
                ? d[i][j]
                : 1+Math.min(d[i][j+1], d[i+1][j], d[i][j])
        )
    }
    d[-1][-1]
}

Calling the function:

say lev(%c'kitten', %c'sitting');               # prints: 3
say lev(%c'rosettacode', %c'raisethysword');    # prints: 8

Simula[edit]

BEGIN

    INTEGER PROCEDURE LEVENSHTEINDISTANCE(S1, S2); TEXT S1, S2;
    BEGIN
        INTEGER N, M;
        N := S1.LENGTH;
        M := S2.LENGTH;
        IF N = 0 THEN LEVENSHTEINDISTANCE := M ELSE
        IF M = 0 THEN LEVENSHTEINDISTANCE := N ELSE
        BEGIN
            INTEGER ARRAY D(0:N, 0:M);
            INTEGER I, J;
            FOR I := 0 STEP 1 UNTIL N DO D(I, 0) := I;
            FOR I := 0 STEP 1 UNTIL M DO D(0, I) := I;
            S1.SETPOS(1);
            FOR I := 1 STEP 1 UNTIL N DO
            BEGIN
                CHARACTER SI, TJ;
                SI := S1.GETCHAR;
                S2.SETPOS(1);
                FOR J := 1 STEP 1 UNTIL M DO
                BEGIN
                    INTEGER COST;
                    TJ := S2.GETCHAR;
                    COST := IF SI = TJ THEN 0 ELSE 1;
                    D(I, J) := MIN(D(I - 1, J) + 1, MIN(D(I, J - 1) + 1, D(I - 1, J - 1) + COST));
                END;
            END;
            LEVENSHTEINDISTANCE := D(N, M);
        END;
    END LEVENSHTEINDISTANCE;

    OUTINT(LEVENSHTEINDISTANCE("kitten", "sitting"), 0); OUTIMAGE;
    OUTINT(LEVENSHTEINDISTANCE("rosettacode", "raisethysword"), 0); OUTIMAGE;

END
Output:
3
8

Smalltalk[edit]

Works with: Smalltalk/X

ST/X provides a customizable levenshtein method in the String class (weights for individual operations can be passed in):

'kitten' levenshteinTo: 'sitting' s:1 k:1 c:1 i:1 d:1 -> 3
'rosettacode' levenshteinTo: 'raisethysword' s:1 k:1 c:1 i:1 d:1 -> 8

Swift[edit]

Version using entire matrix:

func levDis(w1: String, w2: String) -> Int {
  
  let (t, s) = (w1.characters, w2.characters)
  
  let empty = Repeat(count: s.count, repeatedValue: 0)
  var mat = [[Int](0...s.count)] + (1...t.count).map{[$0] + empty}
  
  for (i, tLett) in t.enumerate() {
    for (j, sLett) in s.enumerate() {
      mat[i + 1][j + 1] = tLett == sLett ?
        mat[i][j] : min(mat[i][j], mat[i][j + 1], mat[i + 1][j]).successor()
    }
  }
  return mat.last!.last!
}

Version using only two rows at a time:

func levDis(w1: String, w2: String) -> Int {
  
  let (t, s) = (w1.characters, w2.characters)
  
  let empty = Repeat(count: s.count, repeatedValue: 0)
  var last = [Int](0...s.count)
  
  for (i, tLett) in t.enumerate() {
    var cur = [i + 1] + empty
    for (j, sLett) in s.enumerate() {
      cur[j + 1] = tLett == sLett ? last[j] : min(last[j], last[j + 1], cur[j]).successor()
    }
    last = cur
  }
  return last.last!
}

Single array version[edit]

Translation of: C++
func levenshteinDistance(string1: String, string2: String) -> Int {
    let m = string1.count
    let n = string2.count
    if m == 0 {
        return n
    }
    if n == 0 {
        return m
    }
    var costs = Array(0...n)
    for (i, c1) in string1.enumerated() {
        costs[0] = i + 1
        var corner = i
        for (j, c2) in string2.enumerated() {
            let upper = costs[j + 1]
            if c1 == c2 {
                costs[j + 1] = corner
            } else {
                costs[j + 1] = 1 + min(costs[j], upper, corner)
            }
            corner = upper
        }
    }
    return costs[n]
}

print(levenshteinDistance(string1: "rosettacode", string2: "raisethysword"))
Output:
8

Tcl[edit]

proc levenshteinDistance {s t} {
    # Edge cases
    if {![set n [string length $t]]} {
	return [string length $s]
    } elseif {![set m [string length $s]]} {
	return $n
    }
    # Fastest way to initialize
    for {set i 0} {$i <= $m} {incr i} {
	lappend d 0
	lappend p $i
    }
    # Loop, computing the distance table (well, a moving section)
    for {set j 0} {$j < $n} {} {
	set tj [string index $t $j]
	lset d 0 [incr j]
	for {set i 0} {$i < $m} {} {
	    set a [expr {[lindex $d $i]+1}]
	    set b [expr {[lindex $p $i]+([string index $s $i] ne $tj)}]
	    set c [expr {[lindex $p [incr i]]+1}]
	    # Faster than min($a,$b,$c)
	    lset d $i [expr {$a<$b ? $c<$a ? $c : $a : $c<$b ? $c : $b}]
	}
	# Swap
	set nd $p; set p $d; set d $nd
    }
    # The score is at the end of the last-computed row
    return [lindex $p end]
}
Usage:
puts [levenshteinDistance "kitten" "sitting"];   # Prints 3

TSE SAL[edit]

// library: math: get: damerau: levenshtein <description></description> <version>1.0.0.0.23</version> <version control></version control> (filenamemacro=getmadle.s) [kn, ri, th, 08-09-2011 23:04:55]
INTEGER PROC FNMathGetDamerauLevenshteinDistanceI( STRING s1, STRING s2 )
 INTEGER L1 = Length( s1 )
 INTEGER L2 = Length( s2 )
 INTEGER substitutionCostI = 0
 STRING h1[255] = ""
 STRING h2[255] = ""
 IF ( ( L1 == 0 ) OR ( L2 == 0 ) )
  // Trivial case: one string is 0-length
  RETURN( Max( L1, L2 ) )
 ELSE
  // The cost of substituting the last character
  IF   ( ( s1[ L1 ] ) == ( s2[ L2 ] ) )
   substitutionCostI = 0
  ELSE
   substitutionCostI = 1
  ENDIF
  // h1 and h2 are s1 and s2 with the last character chopped off
  h1 = SubStr( s1, 1,  L1 - 1 )
  h2 = SubStr( s2, 1,  L2 - 1 )
  IF ( ( L1 > 1 ) AND  ( L2 > 1 ) AND  ( s1[ L1 - 0 ] == s2[ L2 - 1 ] ) AND ( s1[ L1 - 1 ] == s2[ L2 - 0 ] ) )
   RETURN( Min( Min( FNMathGetDamerauLevenshteinDistanceI( h1, s2 ) + 1, FNMathGetDamerauLevenshteinDistanceI( s1, h2 ) + 1 ), Min( FNMathGetDamerauLevenshteinDistanceI( h1 , h2 ) + substitutionCostI, FNMathGetDamerauLevenshteinDistanceI( SubStr( s1, 1,  L1 - 2 ), SubStr( s2, 1, L2 - 2 ) ) + 1 ) ) )
  ENDIF
  RETURN( Min( Min( FNMathGetDamerauLevenshteinDistanceI( h1, s2 ) + 1, FNMathGetDamerauLevenshteinDistanceI( s1, h2 ) + 1 ), FNMathGetDamerauLevenshteinDistanceI( h1 ,  h2 ) + substitutionCostI ) )
 ENDIF
END

PROC Main()
STRING s1[255] = "arcain"
STRING s2[255] = "arcane"
Warn( "Minimum amount of steps to convert ", s1, " to ", s2, " = ", FNMathGetDamerauLevenshteinDistanceI( s1, s2 ) ) // gives e.g. 2
s1 = "algorithm"
s2 = "altruistic"
Warn( "Minimum amount of steps to convert ", s1, " to ", s2, " = ", FNMathGetDamerauLevenshteinDistanceI( s1, s2 ) ) // gives e.g. 6
END

Turbo-Basic XL[edit]

10 DIM Word_1$(20), Word_2$(20), DLDm(21, 21)
11 CLS
20 Word_1$="kitten" : Word_2$="sitting" : ? Word_1$;" - ";Word_2$ : EXEC _DLD_ : ?
30 Word_1$="rosettacode" : Word_2$="raisethysword" : ? Word_1$;" - ";Word_2$ : EXEC _DLD_ : ?

11000 END
11600 REM DamerauLevenshteinDistance INPUT(Word_1$, Word_2$, DLDm[]) USE(I, J, K, L, M, N, Min) RETURN(INT Result)
11600 PROC _DLD_
11610   Result=0 : M=LEN(Word_1$) : N=LEN(Word_2$)
11620   FOR I=0 TO M : DLDm(I,0)=I : NEXT I
11630   FOR J=0 TO N : DLDm(0,J)=J : NEXT J
11640   FOR J=1 TO N
11650     FOR I=1 TO M
11660       IF Word_1$(I,I) = Word_2$(J,J)
11670         DLDm(I,J) = DLDm(I-1, J-1) : REM no operation required
11680       ELSE
11690         Min = DLDm(I-1, J)+1 : REM delete
11700         K = DLDm(I, J-1)+1   : REM insert
11710         L = DLDm(I-1, J-1)+1 : REM substitution
11720         IF K < Min THEN Min=K
11730         IF L < Min THEN Min=L
11740         DLDm(I,J) = Min
11750 REM     IF I>1 AND J>1 
11760 REM          IF Word_1$(I,I) = Word_2$(J-1,J-1) AND Word_1$(I-1,I-1) = Word_2$(J,J)
11770 REM              Min=DLDm(I,J) : IF Min>(DLDm(I-2,J-2)+1) THEN Min=(DLDm(I-2,J-2)+1)
11780 REM              DLDm(I,J) = Min : REM transposition
11790 REM          ENDIF
11800 REM     ENDIF
11810       ENDIF
11820     NEXT I
11830   NEXT J
11840   Result=DLDm(M,N)
11845   REM ? "Damerau Levenshtein Distance=";Result
11846   ? "Damerau Distance=";Result
11850 ENDPROC
Output:
kitten, sitting: 3
rosettacode, raisethysword: 8

TUSCRIPT[edit]

$$ MODE TUSCRIPT
distance=DISTANCE ("kitten", "sitting")
PRINT distance

Output:

3

TypeScript[edit]

Translation of: JavaScript
  function levenshtein(a: string, b: string): number {
    const m: number = a.length,
      n: number = b.length;
    let t: number[] = [...Array(n + 1).keys()],
      u: number[] = [];
    for (let i: number = 0; i < m; i++) {
      u = [i + 1];
      for (let j: number = 0; j < n; j++) {
        u[j + 1] = a[i] === b[j] ? t[j] : Math.min(t[j], t[j + 1], u[j]) + 1;
      }
      t = u;
    }
    return u[n];
  }

Vala[edit]

class LevenshteinDistance : Object {
    public static int compute (owned string s, owned string t, bool case_sensitive = false) {
        var n = s.length;
        var m = t.length;
        var d = new int[n + 1, m + 1];
        if (case_sensitive == false) {
            s = s.down ();
            t = t.down ();
        }
        if (n == 0) {
            return m;
        }
        if (m == 0) {
            return n;
        }
        for (var i = 0; i <= n; d[i, 0] = i++) {}
        for (var j = 0; j <= m; d[0, j] = j++) {}
        for (var i = 1; i <= n; i++) {
            for (var j = 1; j <= m; j++) {
                var cost = (t[j - 1] == s[i - 1]) ? 0 : 1;
                d[i, j] = int.min (int.min (d[i - 1, j] + 1, d[i, j - 1] + 1), d[i - 1, j - 1] + cost);
            }
        }
        return d[n, m];
    }
}

VBA[edit]

Translation of: Phix
Option Base 1
Function levenshtein(s1 As String, s2 As String) As Integer
    Dim n As Integer: n = Len(s1) + 1
    Dim m As Integer: m = Len(s2) + 1
    Dim d() As Integer, i As Integer, j As Integer
    ReDim d(n, m)
 
    If n = 1 Then
        levenshtein = m - 1
        Exit Function
    Else
        If m = 1 Then
            levenshtein = n - 1
            Exit Function
        End If
    End If
 
    For i = 1 To n
        d(i, 1) = i - 1
    Next i
 
    For j = 1 To m
        d(1, j) = j - 1
    Next j
 
    For i = 2 To n
        For j = 2 To m
            d(i, j) = WorksheetFunction.Min( _
                           d(i - 1, j) + 1, _
                           d(i, j - 1) + 1, _
                           (d(i - 1, j - 1) - (Mid(s1, i - 1, 1) <> Mid(s2, j - 1, 1))) _
                           )
        Next j
    Next i
 
    levenshtein = d(n, m)
End Function
Public Sub main()
    Debug.Print levenshtein("kitten", "sitting")
    Debug.Print levenshtein("rosettacode", "raisethysword")
End Sub
Output:
 3 
 8 

VBScript[edit]

' Levenshtein distance - 23/04/2020

Function Min(a,b)  
    If a < b then Min = a : Else  Min = b
End Function 'Min

Function Levenshtein(s1, s2)
    Dim d(), i, j, n1, n2, d1, d2, d3
    n1 = Len(s1) + 1
    n2 = Len(s2) + 1
    ReDim d(n1, n2)
    If n1 = 1 Then
        Levenshtein = n2 - 1
        Exit Function
    End If
    If n2 = 1 Then
        Levenshtein = n1 - 1
        Exit Function
    End If
    For i = 1 To n1
        d(i, 1) = i - 1
    Next
    For j = 1 To n2
        d(1, j) = j - 1
    Next
    For i = 2 To n1
        For j = 2 To n2
            d1 = d(i - 1, j    ) + 1
            d2 = d(i,     j - 1) + 1
            d3 = d(i - 1, j - 1) + Abs(Mid(s1, i - 1, 1) <> Mid(s2, j - 1, 1))
            d(i, j) = Min(d1, Min(d2, d3))
        Next
    Next
    Levenshtein = d(n1, n2)
End Function 'Levenshtein

Sub PrintLevenshtein(c1, c2)
	WScript.StdOut.WriteLine c1&" "& c2&" "& Levenshtein(c1, c2)
End Sub 'PrintLevenshtein

PrintLevenshtein "kitten", "sitting"
PrintLevenshtein "rosettacode", "raisethysword"
PrintLevenshtein "saturday", "sunday"
PrintLevenshtein "sleep", "fleeting"
Output:
kitten sitting 3
rosettacode raisethysword 8
saturday sunday 3
sleep fleeting 5


Visual Basic[edit]

Translation of: FreeBASIC
Works with: Visual Basic version 5
Works with: Visual Basic version 6
Works with: VBA version Access 97
Works with: VBA version 6.5
Works with: VBA version 7.1
Function min(x As Integer, y As Integer) As Integer
    If x < y Then
        min = x
    Else
        min = y
    End If
End Function
 
Function levenshtein(s As String, t As String) As Integer
Dim ls As Integer, lt As Integer
Dim i As Integer, j As Integer, cost As Integer
    ' degenerate cases
    ls = Len(s)
    lt = Len(t)
    If ls = lt Then
        If s = t Then
            Exit Function ' return 0
        End If
    ElseIf ls = 0 Then
        levenshtein = lt
        Exit Function
    ElseIf lt = 0 Then
        levenshtein = ls
        Exit Function
    End If
 
    ' create two integer arrays of distances
    ReDim v0(0 To lt) As Integer  '' previous
    ReDim v1(0 To lt) As Integer  '' current
 
    ' initialize v0
    For i = 0 To lt
        v0(i) = i
    Next i
 
    For i = 0 To ls - 1
       ' calculate v1 from v0
       v1(0) = i + 1
  
       For j = 0 To lt - 1
           cost = Abs(CInt(Mid$(s, i + 1, 1) <> Mid$(t, j + 1, 1)))
           v1(j + 1) = min(v1(j) + 1, min(v0(j + 1) + 1, v0(j) + cost))
       Next j
  
       ' copy v1 to v0 for next iteration
       For j = 0 To lt
           v0(j) = v1(j)
       Next j
    Next i
 
    levenshtein = v1(lt)
End Function

Sub Main()
' tests
    Debug.Print "'kitten' to 'sitting'            => "; levenshtein("kitten", "sitting")
    Debug.Print "'sitting' to 'kitten'            => "; levenshtein("sitting", "kitten")
    Debug.Print "'rosettacode' to 'raisethysword' => "; levenshtein("rosettacode", "raisethysword")
    Debug.Print "'sleep' to 'fleeting'            => "; levenshtein("sleep", "fleeting")
End Sub
Output:
'kitten' to 'sitting'            =>  3
'sitting' to 'kitten'            =>  3
'rosettacode' to 'raisethysword' =>  8
'sleep' to 'fleeting'            =>  5

Visual Basic .NET[edit]

 Function LevenshteinDistance(ByVal String1 As String, ByVal String2 As String) As Integer
        Dim Matrix(String1.Length, String2.Length) As Integer
        Dim Key As Integer
        For Key = 0 To String1.Length
            Matrix(Key, 0) = Key
        Next
        For Key = 0 To String2.Length
            Matrix(0, Key) = Key
        Next
        For Key1 As Integer = 1 To String2.Length
            For Key2 As Integer = 1 To String1.Length
                If String1(Key2 - 1) = String2(Key1 - 1) Then
                    Matrix(Key2, Key1) = Matrix(Key2 - 1, Key1 - 1)
                Else
                    Matrix(Key2, Key1) = Math.Min(Matrix(Key2 - 1, Key1) + 1, Math.Min(Matrix(Key2, Key1 - 1) + 1, Matrix(Key2 - 1, Key1 - 1) + 1))
                End If
            Next
        Next
        Return Matrix(String1.Length - 1, String2.Length - 1)
    End Function

Wren[edit]

Translation of: Go
var levenshtein = Fn.new { |s, t|
    var ls = s.count
    var lt = t.count
    var d = List.filled(ls + 1, null)
    for (i in 0..ls) {
        d[i] = List.filled(lt + 1, 0)
        d[i][0] = i
    }
    for (j in 0..lt) d[0][j] = j
    for (j in 1..lt) {
        for (i in 1..ls) {
            if (s[i-1] == t[j-1]) {
                d[i][j] = d[i-1][j-1]
            } else {
                var min = d[i-1][j]
                if (d[i][j-1] < min) min = d[i][j-1]
                if (d[i-1][j-1] < min) min = d[i-1][j-1]
                d[i][j] = min + 1
            }
        }
    }
    return d[-1][-1]
}

System.print(levenshtein.call("kitten", "sitting"))
Output:
3

zkl[edit]

Translation of: D
fcn levenshtein(s1,s2){
   sz2,costs:=s2.len() + 1, List.createLong(sz2,0);  // -->zero filled List
   foreach i in (s1.len() + 1){
      lastValue:=i;
      foreach j in (sz2){
         if (i==0) costs[j]=j;
	 else if (j>0){
	    newValue:=costs[j-1];
	    if (s1[i-1]!=s2[j-1])
	       newValue=newValue.min(lastValue, costs[j]) + 1;
	    costs[j-1]=lastValue;
	    lastValue =newValue;
	 }
      }
      if (i>0) costs[-1]=lastValue;
   }
   costs[-1]
}
foreach a,b in (T(T("kitten","sitting"), T("rosettacode","raisethysword"),
	T("yo",""), T("","yo"), T("abc","abc")) ){
   println(a," --> ",b,": ",levenshtein(a,b));
}
Output:
kitten --> sitting: 3
rosettacode --> raisethysword: 8
yo --> : 2
 --> yo: 2
abc --> abc: 0

ZX Spectrum Basic[edit]

10  REM ZX Spectrum Basic - Levenshtein distance
20  INPUT "first word:",n$
30  INPUT "second word:",m$
40  LET n=LEN n$:LET m=LEN m$:DIM d(m+1,n+1)
50  FOR i=1 TO m:LET d(i+1,1)=i:NEXT i
60  FOR j=1 TO n:LET d(1,j+1)=j:NEXT j
70  FOR j=1 TO n
80    FOR i=1 TO m
90       LET r=d(i,j)-(n$(j)=m$(i)):REM substitution
100      IF r>d(i,j+1) THEN LET r=r-1:REM insertion
110      LET d(i+1,j+1)=r+(r<=d(i+1,j)):REM deletion
120   NEXT i
130 NEXT j
140 PRINT "The Levenshtein distance between """;n$;""", """;m$;""" is ";d(m+1,n+1);"."
Output:
The Levenshtein distance between "rosettacode", "raisethysword" is 8.