Edit distance with swaps

Question

Edit distance finds the number of insertion, deletion or substitutions required to one string to another. I want to to also include swaps in this algorithm. For example "apple" and "appel" should give a edit distance of 1.

Answer 1

See the algorithm here.

http://www.csse.monash.edu.au/~lloyd/tildeAlgDS/Dynamic/Edit/

You can give different costs for swap, add, deletions.

m[i,j] = min(m[i-1,j-1]
         + if s1[i]=s2[j] then 0 else cost_swap fi,
         m[i-1, j] + cost_insert,
         m[i, j-1] + cost_delete ),  i=1..|s1|, j=1..|s2|

Answer 2

The edit distance that you are defining is called the Damerau–Levenshtein distance. You can find possible implementations on the Wikipedia page.