I came across this variation of edit-distance problem:
Find the shortest path from one word to another, for example storm->power, validating each intermediate word by using a isValidWord() function. There is no other access to the dictionary of words and therefore a graph cannot be constructed.
I am trying to figure this out but it doesn't seem to be a distance related problem, per se. Use simple recursion maybe? But then how do you know that you're going the right direction?
Anyone else find this interesting? Looking forward to some help, thanks!
This is a puzzle from Lewis Carroll known as Word Ladders. Donald Knuth covers this in The Stanford Graphbase. This also
You can view it as a breadth first search. You will need access to a dictionary of words, otherwise the space you will have to search will be huge. If you just have access to a valid word you can generate all the permutations of words and then just use isValidWord() to filter it down (Norvig's "How to Write a Spelling Corrector" is a great explanation of generating the edits).
You can guide the search by trying to minimize the edit distance between where you currently are and where you can to be. For example, generate the space of all nodes to search, and sort by minimum edit distance. Follow the links first that are closest (e.g. minimize the edit distance) to the target. In the example, follow the nodes that are closest to "power".
I found this interesting as well, so there's a Haskell implementation here which works reasonably well. There's a link in the comments to a Clojure version which has some really nice visualizations.