Meta Coding Interview: Max-Unique-Characters Subset (Bitmask)

This is a two-stage, AI-enabled coding task that tests bit-level thinking and DFS/backtracking. You will first fix a small helper, word_to_mask(word: str) -> int, that converts a word (digits 0-9 and lowercase letters a-z) into a 36-bit integer mask. The helper must return -1 if the word contains invalid characters or any character appears more than once. The common bug to watch for is treating the bit index as a mask; you must use (1 << bit) when checking duplicates and when setting bits.

After repairing the helper, you implement max_unique_chars_subset(words: list[str]) -> list[str]. You should:

• Use word_to_mask to precompute and filter out invalid or self-duplicating words.
• Use bitmasks to represent used characters and backtracking (DFS) to search subsets.
• Apply pruning: sort candidates (or precompute remaining potential character counts) and cut branches when the best possible remaining characters cannot beat the current best. Use int.bit_count() (or bin(x).count('1')) to measure mask size. You may return early if you reach 36 distinct characters.

Flow in an interview often follows: quick fix of word_to_mask, explain time/space complexity, then implement and optimize the backtracking solver with pruning and small-n DP/bitmask techniques. Skills assessed: bit manipulation, bitmask representation, backtracking, pruning/branch-and-bound, and clear complexity reasoning. Expect follow-ups that generalize weights, larger alphabets, or ask for dynamic-programming alternatives.