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Minimum Insertions to Balance a Parentheses String

Given a parentheses string s containing only the characters '(' and ')'.

Given a parentheses string s containing only the characters '(' and ')'. A parentheses string is balanced if:

In other words, we treat '(' as an opening parenthesis and '))' as a closing parenthesis.

You can insert the characters '(' and ')' at any position of the string to balance it if needed.

Return the minimum number of insertions needed to make s balanced.

Minimum Insertions to Balance a Parentheses String diagram

Example 1

Input: s = "(()))"

Output: 1

Explanation: The second '(' has two matching '))', but the first '(' has only ')' matching. We need to add one more ')' at the end of the string to be "(())))" which is balanced.

Example 2

Input: s = "())"

Output: 0

Explanation: The string is already balanced.

Example 3

Input: s = "))())("

Output: 3

Explanation: Add '(' to match the first '))', Add '))' to match the last '('.

Constraints

  • 1 <= s.length <= 10^5
  • s consists of '(' and ')' only.

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