I went straight to a stack-based approach and it worked fine, but I fumbled explaining why I was tracking unmatched opens separately from unmatched closes.
Use a single-pass counter approach: track the number of unmatched opening parentheses and the number of unmatched closing parentheses. Iterate through the string, incrementing the opening counter for '(' and decrementing it for ')' if possible; otherwise, increment the closing counter. The answer is the sum of both counters.
Pro tip: Clarify that only parentheses matter; other characters are ignored. Also, mention that this greedy approach works because any unmatched closing parenthesis must be fixed by adding an opening before it, and any unmatched opening must be fixed by adding a closing after it.
Restate the problem: Given a string with parentheses and other characters, find the minimum number of parentheses to add to make it valid. Confirm that only parentheses are considered and that other characters are ignored.
Initialize two counters: one for unmatched opening parentheses (open) and one for unmatched closing parentheses (close). These will track the minimum additions needed.
Traverse the string. For each '(', increment open. For each ')', if open > 0, decrement open (match it); otherwise, increment close (unmatched closing). Ignore other characters.
After traversal, the minimum number of parentheses to add is open + close. Return this sum.
State that the algorithm runs in O(n) time and O(1) space, which is optimal. Discuss edge cases like empty string, all parentheses, or no parentheses.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.