Maximum Nesting Depth of Parentheses

Given a valid parentheses string, return the maximum nesting depth. "(1+(2*3)+((8)/4))+1" → 3. "()(())((()()))" → 3. (LeetCode problem)

Why a stack? The LIFO nature of a stack matches how parentheses nest (the most recently opened must close first). Each push is a deeper level of nesting; each pop returns to a shallower level.

Approach: initialize an empty stack and maxDepth = 0. On '(', push and update maxDepth with the current stack size. On ')', pop. Return maxDepth.

import java.util.Stack;

public class MaximumNestingDepth {
    public static int maxDepthUsingStack(String s) {
        Stack<Character> stack = new Stack<>();
        int maxDepth = 0;

        for (char c : s.toCharArray()) {
            if (c == '(') {
                stack.push(c);  // Push on '('
                maxDepth = Math.max(maxDepth, stack.size());  // Update max depth
            } else if (c == ')') {
                stack.pop();  // Pop on ')'
            }
        }

        return maxDepth;
    }
}

Time: O(n). Space: O(n) in the worst case (a string of all ().