The month abbreviations example actually helped me see the constraint clearly.
Model each word as a bitmask of its distinct characters, then use dynamic programming over character subsets to find the maximum number of distinct characters covered by a set of words with disjoint masks. Alternatively, use backtracking with pruning to explore combinations, but DP is more efficient for larger alphabets.
Pro tip: Clarify the constraints first (e.g., alphabet size, number of words) to choose between DP and backtracking; mentioning this shows you think about scalability and trade-offs.
Ask about the alphabet size, maximum number of words, and whether words can be empty or contain duplicates. This determines the optimal approach.
For each word, compute a bitmask representing the set of distinct characters it contains. Remove duplicate masks and words that are subsets of others to reduce the search space.
If alphabet size is small (e.g., ≤20), use DP over subsets of characters. Otherwise, use backtracking with pruning, sorting words by mask size descending.
For DP, iterate over masks and update the maximum covered characters. For backtracking, recursively try including/excluding each word, pruning when the remaining potential cannot exceed the current best.
Discuss time and space complexity, and test with edge cases like no words, all words sharing characters, and maximum alphabet size.
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