1614. Maximum Nesting Depth of the Parentheses-括号的最大嵌套深度

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.

Solution in python:

class Solution:
    def maxDepth(self, s: str) -> int:
        depth = 0
        stack = []
        for c in s:
            if c == '(':
                stack.append(c)
                if len(stack) > depth:
                    depth = len(stack)
            elif c == ')':
                stack.pop()
        return depth