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.

class Solution {
    public int minAddToMakeValid(String S) {
        int not_opened = 0, not_closed = 0;
        for (int i = 0; i < S.length(); ++i) {
            if (S.charAt(i) == '(') {
                not_closed++;
            } else if (not_closed > 0) {
                not_closed--;
            } else {
                not_opened++;
            }
        }
        return not_opened + not_closed;
    }
}