I went with a stack of indices, single pass, mark the unmatched ones and skip them when building the output.
Clarify the problem first: confirm whether to return the valid string or just the minimum number of removals, and whether multiple valid answers are acceptable. Then propose a two-pass stack-based solution that identifies unmatched parentheses and removes them, achieving O(n) time and O(n) space. Walk through a concrete example to demonstrate correctness and discuss edge cases.
Pro tip: After presenting the stack solution, mention that you can optimize space to O(1) by using a counter for unmatched closing parentheses and a second pass to remove excess opening ones. This shows you think about trade-offs and can adapt to constraints.
Ask whether to return the valid string or the count of removals, and if multiple valid outputs are acceptable. Confirm input size and character set (only parentheses or other chars).
Explain that you'll use a stack to track indices of unmatched opening parentheses and a set to mark unmatched closing parentheses. After one pass, remove all marked characters.
Choose a string like 'a)b(c)d' and demonstrate step-by-step how the stack and set identify unmatched parentheses, then show the resulting valid string.
State time and space complexity (O(n) each). Discuss edge cases: empty string, all parentheses, nested, multiple valid answers, and strings with other characters.
Mention the O(1) space two-pass counter approach and compare trade-offs. Optionally, note that a greedy approach doesn't work for minimum removals.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Generalize the stack-based solution by using a mapping of closing brackets to opening brackets. Iterate through the string, pushing opening brackets onto the stack and, for closing brackets, checking that the stack is non-empty and the top matches the expected opening bracket. At the end, ensure the stack is empty.
Pro tip: Mention that this approach runs in O(n) time and O(n) space, and that using a hash map for bracket pairs makes the solution easily extensible to new bracket types. Also, clarify that you validate the input (e.g., non-null) and handle edge cases like empty strings.
Confirm that the input is a string containing only bracket characters, and discuss edge cases such as empty string, single bracket, and mismatched types.
Use a stack to track opening brackets, and a hash map to associate each closing bracket with its corresponding opening bracket.
Traverse the string: if the character is an opening bracket, push it; if it's a closing bracket, check that the stack is not empty and the top matches the expected opening bracket, then pop.
After iteration, ensure the stack is empty to confirm all brackets are closed. State the time and space complexity: O(n) time and O(n) space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.