I started with the brute force just to show I understood the problem, which I think was fine, but I could tell they were waiting for me to push further.
Start by clarifying constraints (n, L, alphabet size) and discussing the naive O(n^2 * L) approach. Then propose a bitmask-based solution: represent each string as a bitmask of characters, and for each string, count compatible strings using a frequency map of masks. Optimize by iterating over submasks of the complement or using SOS DP to achieve O(n + 2^A) where A is alphabet size.
Pro tip: Always discuss trade-offs: bitmask approach is fast for small alphabets (e.g., lowercase letters) but may be memory-heavy for large alphabets; consider hybrid approaches or pruning based on constraints. Also, mention that the interviewer likely wants to see how you handle ambiguity and optimize for the given constraints.
Ask about input size (n, L), alphabet size, and whether strings can be empty or contain duplicates. Confirm that pairs are unordered and i < j.
Explain the O(n^2 * L) solution: for each pair, check common characters by iterating through strings or using sets. This sets a baseline for optimization.
Convert each string to a bitmask where each bit represents a character's presence. This reduces character comparison to bitwise AND operations.
Count frequencies of each mask. For each mask, find compatible masks by enumerating submasks of the complement (characters not present) and summing their frequencies. Alternatively, use SOS DP to precompute sums over subsets.
Compare O(n^2 * L) vs O(n + 2^A) where A is alphabet size. Discuss when each is preferable and potential memory usage.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.