# Leetcode 1614 - Maximum Nesting Depth of the Parentheses

Note:

• Don’t use stack and make it too complicate.

Question:

A string is a valid parentheses string (denoted VPS) if it meets one of the following:

• It is an empty string "", or a single character not equal to "(" or “)”,
• It can be written as AB (A concatenated with B), where A and B are VPS’s, or
• It can be written as (A), where A is a VPS.

We can similarly define the nesting depth depth(S) of any VPS S as follows:

• depth(“”) = 0
• depth(C) = 0, where C is a string with a single character not equal to “(“ or “)”.
• depth(A + B) = max(depth(A), depth(B)), where A and B are VPS’s.
• depth(“(“ + A + “)”) = 1 + depth(A), where A is a VPS.

For example, “”, “()()”, and “()(()())” are VPS’s (with nesting depths 0, 1, and 2), and “)(“ and “(()” are not VPS’s.

Given a VPS represented as string s, return the nesting depth of s.

Example:

Code: