Check if a Parentheses String Can Be Valid

A valid parentheses string has even length. Then perform two greedy checks. Left to right, maintain available opens: a locked '(' or any unlocked position can serve as an open, while a locked ')' consumes one. If the balance becomes negative, that prefix contains more forced closes than positions that could open, so validity is impossible. Right to left, perform the symmetric check: a locked ')' or unlocked position can serve as a close, while a locked '(' consumes one. A negative balance now means some suffix has too many forced opens. If both scans succeed, unlocked positions can be assigned to satisfy both prefix and suffix constraints. Time is O(n) and extra space is O(1). Counting total opens and closes alone is insufficient because their order matters.