My first instinct was to reach for a stack and just track unmatched opens and closes separately.
Clarify that the goal is to remove the minimum number of parentheses to make the string balanced, and that multiple valid outputs may exist. Use a stack to identify unmatched parentheses in one pass, then construct the result by excluding those indices. Discuss time and space complexity, and consider edge cases like empty strings or already balanced inputs.
Pro tip: Mention that the stack can store indices instead of characters to easily mark invalid parentheses, and that a two-pass approach with counters can achieve O(1) space if only the length of the longest valid substring is needed—but for reconstruction, the stack method is straightforward.
Confirm that we need to remove the fewest characters to make the string balanced, and that any valid balanced string is acceptable. Ask about input size, character set, and whether the output should be a string or just the length.
Decide between using a stack to track unmatched parentheses or a two-pass counting method. For reconstruction, the stack approach is intuitive: push indices of '(' and mark ')' as invalid if no matching '(' exists.
Iterate through the string, using a stack to record indices of unmatched '('. For each ')', if stack is non-empty, pop; otherwise, mark this ')' as invalid. After the pass, any indices left in the stack are unmatched '(' and should be marked invalid. Then build the result by skipping invalid indices.
State that time complexity is O(n) and space complexity is O(n) for the stack and boolean array. Discuss edge cases: empty string, all parentheses, already balanced, and strings with other characters (if allowed).
Walk through examples like '(()', ')()', and 'a)b(c' to verify correctness. Explain how the algorithm handles them and produces a balanced result with minimum removals.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.