Algorithm to Count the 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:
S.length <= 1000
S only consists of ‘(‘ and ‘)’ characters.

Parentheses Balance Algorithm

The algorithm is to count the number of the left Parentheses and, if we meet right Parentheses, we increment the answer if there is no enough left Parentheses, or we decrement the counter as to close the corresponding left Parentheses.

The final answer (the minimal add) plus the counter of the left Parentheses as we need to add to close them.

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class Solution {
public:
    int minAddToMakeValid(string S) {
        int left = 0;
        int ans = 0;
        for (const auto &n: S) {
            if (n == '(') {
                left ++;
            } else {
                if (left > 0) {
                    left --;
                } else {
                    ans ++;
                }
            }
        }
        return ans + left;
    }
};

class Solution {
public:
    int minAddToMakeValid(string S) {
        int left = 0;
        int ans = 0;
        for (const auto &n: S) {
            if (n == '(') {
                left ++;
            } else {
                if (left > 0) {
                    left --;
                } else {
                    ans ++;
                }
            }
        }
        return ans + left;
    }
};

O(N) time as we need to scan the entire string and O(1) space, obviously.

–EOF (The Ultimate Computing & Technology Blog) —