#1614

Easy

auto_awesomeStack-based state management

LeetCode Problem Workspace

Maximum Nesting Depth of the Parentheses

Find the maximum nesting depth of parentheses in a valid string using stack-based state management.

Problem Statement

Given a string s that consists of digits, operators, and valid parentheses, return the maximum nesting depth of the parentheses. The nesting depth is defined as the number of open parentheses that are inside other parentheses. For each character in the string, you must compute the depth level based on how many open parentheses precede it.

For example, in the string (1+(2*3)+((8)/4))+1, the digit 8 is inside three nested parentheses, so the maximum depth is 3. Similarly, in (1)+((2))+(((3))), the digit 3 is inside three nested parentheses, leading to a depth of 3. Your task is to implement a solution that efficiently calculates the maximum nesting depth using stack-based state management.

Examples

Example 1

Input: s = "(1+(2*3)+((8)/4))+1"

Output: 3

Digit 8 is inside of 3 nested parentheses in the string.

Example 2

Input: s = "(1)+((2))+(((3)))"

Output: 3

Digit 3 is inside of 3 nested parentheses in the string.

Example 3

Input: s = "()(())((()()))"

Output: 3

Example details omitted.

Constraints

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

Solution Approach

Initialize variables

Start by initializing a variable maxDepth to store the maximum depth encountered during the traversal of the string. Also, create a counter currentDepth to track the current level of nesting as you process the string.

Process the string with a stack

As you iterate through each character in the string, increase currentDepth when encountering an open parenthesis (. If a closing parenthesis ) is found, decrease currentDepth. Update maxDepth whenever currentDepth exceeds its current value.

Return the result

Once the entire string is processed, return maxDepth as the result, which represents the maximum depth of nested parentheses in the string.

Complexity Analysis

Metric	Value
Time	O(N)
Space	O(1)

The time complexity is O(N) because we process each character in the string exactly once. The space complexity is O(1) as we only need a constant amount of extra space for variables like maxDepth and currentDepth.

What Interviewers Usually Probe

Check for the candidate's ability to implement a simple stack-based approach.
Assess whether the candidate correctly manages nested depths during the traversal.
Evaluate the candidate's understanding of time and space complexity optimizations.

Common Pitfalls or Variants

Common pitfalls

Failing to properly track the maximum depth during traversal.
Incorrectly managing the depth counters, such as failing to update maxDepth when necessary.
Overcomplicating the solution with unnecessary data structures when a simple stack-based approach suffices.

Follow-up variants

Consider adding invalid parentheses in the string to check for error handling.
Introduce additional operators and operands to test how the candidate manages complex expressions with nested parentheses.
Test with edge cases such as strings with a single pair of parentheses or no parentheses at all.

FAQ

How do I solve the Maximum Nesting Depth of the Parentheses problem?

To solve this problem, use a stack-based approach where you track the number of open parentheses. Update the maximum depth each time the depth increases.

What is the time complexity of this problem?

The time complexity is O(N), where N is the length of the string, because you process each character exactly once.

Can I use a recursive approach to solve this problem?

While a recursive approach can work, a stack-based solution is more efficient and straightforward for this problem.

What is meant by the 'nesting depth' in this problem?

Nesting depth refers to how many layers of parentheses an expression is enclosed in. The maximum depth is the highest number of nested parentheses.

How can GhostInterview help me with this problem?

GhostInterview helps by providing a detailed, step-by-step approach for solving stack-based problems like this one, ensuring you avoid common mistakes and optimize your solution.

terminal

Solution

Solution 1: Traversal

We use a variable $d$ to record the current depth, initially $d = 0$.

1

2

3

4

5

6

7

8

9

10

class Solution:
    def maxDepth(self, s: str) -> int:
        ans = d = 0
        for c in s:
            if c == '(':
                d += 1
                ans = max(ans, d)
            elif c == ')':
                d -= 1
        return ans

Continue Practicing

#1598 crawler log folder #1653 minimum deletions to make string balanced #1544 make the string great