Three distinct steps to the solution, and the interviewer wanted me to optimize it in a specific direction he had in mind.
Clarify the problem constraints (e.g., list size, word length, character set) and discuss the trade-offs between brute force, dynamic programming, and greedy approaches. Then propose an efficient solution, such as bitmask DP, and analyze its time and space complexity.
Pro tip: Mention that the problem is NP-hard in general (related to maximum coverage), so for large inputs you might need approximation or heuristic approaches. This shows you understand the theoretical limits and can discuss practical trade-offs.
Ask about the input size, character set (e.g., lowercase English letters), and whether words can be used multiple times. Confirm the goal is to maximize unique characters, not total characters.
Discuss generating all subsets (2^n) and computing unique characters for each, which is exponential and impractical for large n. This sets the stage for optimization.
Represent each word as a bitmask of its characters. Use DP over subsets of words or characters to find the maximum union size, reducing complexity to O(2^m * n) where m is the alphabet size (e.g., 26).
Compare the DP approach with greedy or approximation algorithms. Explain that while DP is exact, it may be exponential in alphabet size; for large alphabets, consider heuristics.
Walk through examples like empty list, duplicate words, and words with overlapping characters. Ensure the solution handles all cases and returns the correct subset.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.