Started with a stack because it felt intuitive for parentheses problems, but I quickly realized it wasn't getting me to all valid combinations.
Use BFS level-by-level removal of parentheses to find the minimum number of deletions, stopping at the first level where valid strings appear. At each level, generate all strings by removing one parenthesis, and collect valid ones while deduplicating to avoid redundant work.
Pro tip: Mention that BFS guarantees minimal removals and that using a set for deduplication and a visited set prevents exponential blowup. Also note that if asked for optimization, you can precompute the number of misplaced parentheses to prune the search space.
Write a helper function to check if a string is valid: balance never negative and ends at zero. Clarify that only parentheses matter.
Start with the original string in a queue. For each level, process all strings, check validity, and if any valid, return them. Otherwise, generate next level by removing one parenthesis at each position.
Use a set to avoid processing the same string multiple times. Only add newly generated strings to the next level if not visited.
When valid strings are found at a level, collect all valid ones from that level and return them immediately, as BFS ensures minimal removals.
Discuss time complexity O(2^n) worst-case but pruned by BFS; space O(2^n). Handle empty string, already valid, and no valid possible (return empty list).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.