Balance Parentheses

Problem Given a string of parentheses, return the minimum number of operations (insertions and/or removals) needed to make it valid — or, in the simpler variant, just determine whether it is balanced.

Input / Output

• Input: string s of '(' and ')'.
• Output: minimum operations to make s valid (0 means already balanced).

Constraints

• |s| up to 10^5; O(n) time, O(1) space expected.

Example

• s = "()))((" → 4 (two unmatched ')' and two unmatched '(').
• s = "(()" → 1.

Expected approach

• Single pass with two counters: open tracks currently unmatched '('; on ')' either consume an open or increment unmatchedClose. Answer = open + unmatchedClose. A stack works too but the counters avoid O(n) space. For the multi-type-bracket variant ({[ ]}), a stack becomes necessary — be ready to explain why.