Maximum Nesting Depth of the Parentheses SOLUTIONS

Maximum Nesting Depth of the Parentheses SOLUTIONS

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(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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