Levenshtein distance

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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.

For example, the Levenshtein distance between "kitten" and "sitting" is 3, since the following three edits change one into the other, and there is no way to do it with fewer than three edits:

kitten → sitten (substitution of 'k' with 's')
sitten → sittin (substitution of 'e' with 'i')
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 is reversed.

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

Other edit distance at Rosetacode.org :

Longest common subsequence

D

The standard library std.algorithm module includes a Levenshtein distance function. <lang d>import std.algorithm ;

   writeln(levenshteinDistance("kitten", "sitting")) ; // print 3</lang>

J

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

<lang j>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

)</lang>

However, this is a rather slow and bulky approach. Another alternative would be:

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 "reduce" operator.

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.

Example use:

<lang j> 'kitten' levenshtein 'sitting' 3

  'kitten' lev 'sitting'

3</lang>

Time and space use:

<lang j> ts=: 6!:2,7!:2

  ts kitten levenshtein sitting

0.00153132 12800

  ts kitten lev sitting

0.000132101 5376</lang>

(The J flavored variant winds up being about 10 times faster, in J, for this test case, than the explicit version.)

See the Levenshtein distance essay on the Jwiki for additional solutions.

PureBasic

Based on Wikipedia's pseudocode. <lang PureBasic>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))</lang>

Tcl

<lang tcl>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]

}</lang> Usage: <lang tcl>puts [levenshteinDistance "kitten" "sitting"]; # Prints 3</lang>