921. Minimum Add to Make Parentheses Valid

-
https://leetcode.com/problems/minimum-add-to-make-parentheses-valid/

Given a string S of '(' and ')' parentheses, we add the minimum number of parentheses ( '(' or ')', and in any positions ) so that the resulting parentheses string is valid.
Formally, a parentheses string is valid if and only if:
  • It is the empty string, or
  • It can be written as AB (A concatenated with B), where A and B are valid strings, or
  • It can be written as (A), where A is a valid string.
Given a parentheses string, return the minimum number of parentheses we must add to make the resulting string valid.

Example 1:
Input: "())"
Output: 1
Example 2:
Input: "((("
Output: 3
Example 3:
Input: "()"
Output: 0
Example 4:
Input: "()))(("
Output: 4

Note:
  1. S.length <= 1000
  2. S only consists of '(' and ')' characters.
----
Time - O(N)
Space - O(1)
---