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