Levenshtein distance: how to better handle words swapping positions?

Question

I\'ve had some success comparing strings using the PHP levenshtein function.

However, for two strings which contain substrings that have swapped positions, the algorithm

Answer 1

I've been implementing levenshtein in a spell checker.

What you're asking for is counting transpositions as 1 edit.

This is easy if you only wish to count transpositions of one word away. However for transposition of words 2 or more away, the addition to the algorithm is worst case scenario !(max(wordorder1.length(), wordorder2.length())). Adding a non-linear subalgorithm to an already quadratic algorithm is not a good idea.

This is how it would work.

if (wordorder1[n] == wordorder2[n-1])
{
  min(workarray[x-1, y] + 1, workarray[x, y-1] + 1, workarray[x-2, y-2]);
}
  else
{
  min(workarray[x-1, y] + 1, workarray[x, y-1] + 1);
}

JUST for touching transpositions. If you want all transpositions, you'd have to for every position work backwards from that point comparing

1[n] == 2[n-2].... 1[n] == 2[0]....

So you see why they don't include this in the standard method.