題目來源：https://leetcode.com/contest/weekly-contest-106/problems/minimum-add-to-make-parentheses-valid/

問題描述

921. 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.

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題意

給定一個由”(“和”)”組成的序列，可以在序列的任意位置新增”(“或”)”，問最少新增多少個”(“/”)”可以使得原序列變成合法的序列

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思路

用棧模擬左右括號的匹配過程，剩下多少個不能匹配就是需要增加的括號數量的最小值。

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程式碼

class Solution {
public:
    int minAddToMakeValid(string S) {
        vector<char> v;
        int i, n = S.size();
        char ch;
        for (i=0; i<n; i++)
        {
            ch = S.at(i);
            if (ch == '(')
            {
                v.push_back(ch);
            }
            else
            {
                if (!v.empty() && v.back() == '(')
                {
                    v.pop_back();
                }
                else
                {
                    v.push_back(ch);
                }
            }
        }
        return v.size();
    }
};