Maximum Nesting Depth of the Parentheses

Easy

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

• It is an empty string "", or a single character not equals 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 excluding "(" and ")" ,
• 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 " ( ) ( ( ) ( ) ) " and 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 = " ((5+2)(3+4)((6))) "
Output: 3
Explanation: Character '6' is inside three nested parentheses.

 

Example 2:

Input: " (43+4++3)((3)(9))+1 "
Output: 2
Explanation: Character '3' and '9' both are inside two nested parentheses.

 

Your Task:
You don't need to read input or print anything. Your task is to complete the function maxDepth() which takes the string s as input parameters and returns nesting depth of the given string s .

Expected Time Complexity: O(|s|)
Expected Auxiliary Space: O(1)

Constraints:
1<=|s|<=100
s consists of digits 0-9 and characters ' + ' , ' - ' , ' * ' , ' / ' , ' ( ' , and ' ) '.
It is guaranteed that parentheses expression s is a VPS.