Start by clarifying the problem: confirm the set of bracket types (e.g., (), [], {}) and that the string contains only brackets. Then propose a stack-based solution: iterate through the string, push opening brackets, and for closing brackets, check if the top of the stack matches; at the end, the stack must be empty. Walk through an example to demonstrate correctness and discuss time and space complexity.
Pro tip: Mention edge cases like empty string, odd length, and strings with only opening or only closing brackets, and explain how your solution handles them. Also, note that a stack is ideal because brackets must close in LIFO order, and you can optimize space by early termination if a mismatch is found.
Ask if the string contains only bracket characters and which types are included (e.g., (), [], {}). Confirm that an empty string is considered valid and that mismatched types (e.g., '(]') are invalid.
Explain that a stack is the natural choice because brackets must be closed in last-in-first-out order. Alternatively, mention that a counter could work for a single bracket type, but a stack generalizes to multiple types.
Iterate through each character: if it's an opening bracket, push it onto the stack; if it's a closing bracket, check if the stack is empty or if the top doesn't match, and return false if so; otherwise pop. After the loop, return true only if the stack is empty.
State that time complexity is O(n) and space complexity is O(n) in the worst case. Discuss edge cases: empty string, odd length, strings with only opening or only closing brackets, and nested vs. sequential brackets.
Walk through a few examples, such as '()[]{}' (valid), '([)]' (invalid), and '{[]}' (valid), to demonstrate the algorithm's correctness and your ability to verify solutions.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.