1614. Maximum Nesting Depth of the Parentheses

https://leetcode.com/problems/maximum-nesting-depth-of-the-parentheses

Description

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 1:

**Input:** s = "(1+(2*3)+((8)/4))+1"
**Output:** 3
**Explanation:** Digit 8 is inside of 3 nested parentheses in the string.

Example 2:

**Input:** s = "(1)+((2))+(((3)))"
**Output:** 3

Example 3:

**Input:** s = "1+(2*3)/(2-1)"
**Output:** 1

Example 4:

**Input:** s = "1"
**Output:** 0

Constraints:

• 1 <= s.length <= 100

• s consists of digits 0-9 and characters '+', '-', '*', '/', '(', and ')'.

• It is guaranteed that parentheses expression s is a VPS.

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