Given a dictionary, what's the optimal way to find all possible words that contains a particular set of characters and a string

Question

I'm writing a word game. I have access to the dictionary object to validate the words. I need to find all possible words that contains a word and a set of additional characters. for example: lets the say the word is "MEN" and the set of additional characters are "WALOHTD". I need a way to find words like.... 1.MEND 2.WOMEN 3.MENTAL 4. etc.... basically we are looking at all possible words that contain "MEN" and any of the specific additional characters.

I can certainly write code that can loop through the entire dictionary to first words that contains the subword and then check for the specific characters existance but that is not optimal. It's taking more than a second. Any help towards optimal solution is greatly appreciated. _rey

Answer 1

The problem is a mixture of that of regular language and that of searching a data structure.

Considering the first aspect alone, we'd be inclined to use a regular expression. You don't say if we can repeat the "additional characters". If we can, it's easy enough [WALOTHD]*MEN[WALOTHD]* for your case, and that's easily adapted.

If we can't repeat, then we can start with [WALOTHD]{0,7}MEN[WALOTHD]{0,7} and filter out any that break the rule ("ALLOTMENT" matches that expression, but repeats L and T).

Or we can try to build a much more complicated regular expression, though I'm not sure if the gains in the better expression would out-weigh the cost of working out what it was though.

Coming from the other side of searching a dictionary, a DAWG is very space-efficient and makes finding matches that contain substrings relatively efficient. It's not a complete match to this puzzle, as we have quite a few permutations of prefixes and suffixes to worry about. Without testing, I'd guess it'd being reasonably good if we can't repeat from the "additional", and horrible if we can. But that is just a guess. A GADDAG might well be worth looking at, it'd be bigger than a DAWG, but likely faster for this sort of search (GADDAGs are used in scrabble-solving, which is pretty much the same problem that you have here).