2116 - Check if a Parentheses String Can Be Valid.

Medium

A parentheses string is a non-empty string consisting only of '(' and ')'. It is valid if any of the following conditions is true:

• It is ().

• It can be written as AB (A concatenated with B), where A and B are valid parentheses strings.

• It can be written as (A), where A is a valid parentheses string.

You are given a parentheses string s and a string locked, both of length n. locked is a binary string consisting only of '0's and '1's. For each index i of locked,

• If locked[i] is '1', you cannot change s[i].

• But if locked[i] is '0', you can change s[i] to either '(' or ')'.

Return true if you can make s a valid parentheses string. Otherwise, return false.

Example 1:

Input: s = "))()))", locked = "010100"

Output: true

Explanation: locked1 == '1' and locked3 == '1', so we cannot change s1 or s3. We change s0 and s4 to '(' while leaving s2 and s5 unchanged to make s valid.

Example 2:

Input: s = "()()", locked = "0000"

Output: true

Explanation: We do not need to make any changes because s is already valid.

Example 3:

Input: s = ")", locked = "0"

Output: false

Explanation: locked permits us to change s0. Changing s0 to either '(' or ')' will not make s valid.

Constraints:

• n == s.length == locked.length

• <code>1 <= n <= 10⁵</code>

• s[i] is either '(' or ')'.

• locked[i] is either '0' or '1'.