Maximum Nesting Depth of the Parentheses

Problem Statement

Given a valid parentheses string s, return the nesting depth of s — the maximum number of nested parentheses.

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Input / Output

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

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Constraints

1 ≤ s.length ≤ 100 s consists of digits 0-9 and characters '+', '-', '*', '/', '(', and ')' It is guaranteed that s is a valid parentheses string

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Understanding the Problem

• ( → go one level deeper
• ) → come back up one level
• Answer = deepest level ever reached
• Other characters don't matter

Edge Cases

• No parentheses → 0
• Input is guaranteed valid → no need to check for unmatched )