Classic stack problem but I second-guessed myself on the edge cases, like empty strings and nested mixed brackets.
Clarify the problem constraints (e.g., only parentheses or other bracket types, empty string, invalid characters) and then propose a stack-based solution that scans the string once, pushing opening brackets and popping for closing brackets. Walk through the algorithm with a simple example, analyze time and space complexity, and discuss edge cases and potential optimizations.
Pro tip: Mention that a counter-based approach works only for a single bracket type, but a stack generalizes to multiple types; also note that early termination on invalid characters or mismatched closing brackets can improve efficiency.
Ask whether the string contains only parentheses or multiple bracket types, whether empty strings are valid, and if there are any other characters to consider. This ensures you solve the correct problem.
Explain that you will iterate through the string, pushing opening brackets onto a stack and for each closing bracket, check if the stack is non-empty and the top matches. At the end, the stack must be empty.
Trace the algorithm on a sample string like '([{}])' to demonstrate correctness, and also on an invalid string like '([)]' to show how mismatches are detected.
State that time complexity is O(n) and space complexity is O(n) in the worst case. Discuss edge cases: empty string, single bracket, unbalanced closing bracket at start, and strings with non-bracket characters.
Mention that for a single bracket type, a counter suffices, but a stack is needed for multiple types. Also note that early termination can be done if an invalid character is encountered or if a closing bracket appears when the stack is empty.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.