Started with backtracking, which felt fine, but they kept asking 'can you do better?' three more times.
Start by clarifying constraints and defining a bitmask representation for each string's character set, then walk through brute force, backtracking with pruning, and finally a DP over masks. Emphasize the trade-offs between time and space and how bitmasks enable efficient state representation.
Pro tip: Mention that you can pre-filter strings with duplicate characters and deduplicate identical masks, which drastically reduces the search space in practice. Also, note that the DP over masks is essentially a knapsack-like problem where each string is an item with a 'weight' (character mask) and you maximize count.
Ask about input size, character set (e.g., lowercase English), and whether order matters. Define the problem as selecting a subset of strings whose concatenated characters are all unique.
Discuss generating all subsets (2^n) and checking each for character uniqueness, noting O(2^n * L) time. This establishes a starting point but is impractical for large n.
Represent each string as a 26-bit integer mask. Pre-filter strings with internal duplicates and deduplicate masks. Then use backtracking with pruning or DP over masks to find the maximum subset size.
Define dp[mask] = max strings achievable with combined character mask 'mask'. Iterate over strings and update dp[new_mask] = max(dp[new_mask], dp[mask] + 1) if masks don't overlap. This is O(n * 2^26) but can be optimized with sparse states.
Analyze time and space: DP is O(n * 2^26) worst-case but often much less due to pruning. Compare with backtracking which may be faster for small n. Mention that 2^26 is large but feasible with sparse maps or if character set is smaller.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.