Given a dictionary and a list of letters find all valid words that can be built with the letters

Question

The brute force way can solve the problem in O(n!), basically calculating all the permutations and checking the results in a dictionary. I am looking for ways to improve the com

Answer 1

1. "Sign" the letters available by sorting them in order; that's O(m log m), where m is the number of letters.

2. "Sign" each word in the dictionary by sorting the letters of the word in order; that's O(k log k), where k is the length of the word.

3. Compare the letter signature to each word signature; that's O(min(m, k) * n), where n is the number of words in the dictionary. Output any word that matches.

Assuming an English word list of approximately a quarter-million words, and no more than about half a dozen, that should be nearly instantaneous.