What is the time complexity of Maximum Depth of N-ary Tree?

The optimal solution has a time complexity of O(N).

What data structures are used to solve Maximum Depth of N-ary Tree?

This problem uses Tree, Depth-First Search, Breadth-First Search. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Maximum Depth of N-ary Tree?

Insight 1: The problem can be solved using a recursive Depth-First Search (DFS) approach. Insight 2: The maximum depth of a node is 1 plus the maximum depth of its children.

Which companies ask LeetCode 559. Maximum Depth of N-ary Tree in interviews?

This problem is frequently asked at Datadog.

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Maximum Depth of N-ary Tree - LeetCode 559 Solution

Maximum Depth of N-ary Tree - Complete Solution Guide

Maximum Depth of N-ary Tree is LeetCode problem 559, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given a n-ary tree, find its maximum depth. The maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node. Nary-Tree input serialization is represented in their level order traversal, each group of children is separated by the null value (See examples). Example 1: Input: root = [1,null,3,2,4,null,5,6] Output: 3 Example 2: Input: root = [1,null,2,3,4,5,null,null,6,7,null,8,null,9,10,null,null,11,null,12,null,13,null,null,14] Output: 5 Constraint

Detailed Explanation

The problem asks us to find the maximum depth of an N-ary tree. The depth of a tree is the number of nodes along the longest path from the root node down to the farthest leaf node. An N-ary tree is a tree where each node can have up to N children. The input is the root node of the N-ary tree, and the output is an integer representing the maximum depth of the tree. The constraints state that the total number of nodes is between 0 and 10^4, and the depth of the tree is less than or equal to 1000.

Solution Approach

The provided code uses a recursive Depth-First Search (DFS) approach to find the maximum depth of the N-ary tree. The algorithm traverses the tree by recursively calling the `maxDepth` function on each of the children of the current node. The maximum depth of the current node is then calculated as 1 (for the current node itself) plus the maximum depth of its children. This process continues until a null node is reached, which represents the end of a branch. The base case returns 0, allowing the recursion to unwind and calculate the depths of the parent nodes.

Step-by-Step Algorithm

Step 1: Check if the root is null. If it is, return 0 (base case).
Step 2: Initialize a variable `depth` to 0.
Step 3: Iterate through the children of the root.
Step 4: For each child, recursively call the `maxDepth` function to get the depth of that subtree.
Step 5: Update `depth` to be the maximum of its current value and the depth of the child's subtree.
Step 6: After iterating through all the children, return `depth + 1`. This represents the depth of the current node plus the maximum depth of its children.

Key Insights

Insight 1: The problem can be solved using a recursive Depth-First Search (DFS) approach.
Insight 2: The maximum depth of a node is 1 plus the maximum depth of its children.
Insight 3: The base case for the recursion is when the node is null, in which case the depth is 0.

Complexity Analysis

Time Complexity: O(N)

Space Complexity: O(H)

Topics

This problem involves: Tree, Depth-First Search, Breadth-First Search.

Companies

Asked at: Datadog.

Maximum Depth of N-ary Tree | LeetCode 559

Easy

Tree Depth-First Search Breadth-First Search

Time: O(N)Space: O(H)

Solution Code

Available in:

/*
// Definition for a Node.
class Node {
    public int val;
    public List<Node> children;

    public Node() {}

    public Node(int _val) {
        val = _val;
    }

    public Node(int _val, List<Node> _children) {
        val = _val;
        children = _children;
    }
};
*/

class Solution {
    public int maxDepth(Node root) {
        if (root == null) return 0;
        int maxDepth = 0;
        for (Node child : root.children) {
            maxDepth = Math.max(maxDepth, maxDepth(child));
        }
        return maxDepth + 1;
    }
}

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Problem Info

Description

Problem 559: Maximum Depth of N-ary Tree - Detailed explanation and solution approaches.

Topics

Tree Depth-First Search Breadth-First Search

Companies

Datadog

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:559

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

6 steps

1
Step 1: Check if the root is null. If it is, return 0 (base case).
2
Step 2: Initialize a variable `depth` to 0.
3
Step 3: Iterate through the children of the root.
4
Step 4: For each child, recursively call the `maxDepth` function to get the depth of that subtree.
5
Step 5: Update `depth` to be the maximum of its current value and the depth of the child's subtree.
6
Step 6: After iterating through all the children, return `depth + 1`. This represents the depth of the current node plus the maximum depth of its children.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(N)

💾

Space Complexity

O(H)

📝

Why?

The time complexity is O(N) because the algorithm visits each node once. The space complexity is O(H) due to the recursive call stack. The depth of the recursion is bounded by the height of the tree.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Breadth-First Search (BFS)

Use a queue to perform a level-order traversal of the tree. Keep track of the current level. The depth is the number of levels traversed.

Time: O(N)Space: O(W), where W is the maximum width of the tree. In the worst case (a complete N-ary tree), W can be O(N).

Trade-offs: BFS uses more memory than DFS, especially for wide trees. However, BFS can be more suitable for finding the shortest path in a graph or tree where edge weights are uniform (not applicable here, but relevant for related problems).

✨

Key Insights

1Insight 1: The problem can be solved using a recursive Depth-First Search (DFS) approach.
2Insight 2: The maximum depth of a node is 1 plus the maximum depth of its children.
3Insight 3: The base case for the recursion is when the node is null, in which case the depth is 0.

📚

Key Terms Explained

For Students

Tree

Hierarchical structure with nodes. Like a family tree!

Edge Cases

Edge case 1: Empty tree (root is null). The solution correctly handles this case by returning 0.
Edge case 2: A tree with only one node (the root). The solution will return 1 in this case, which is correct.
Edge case 3: Skewed tree (all nodes are in one branch). The solution will still correctly compute the depth, although the space complexity will be O(N) in this case.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting the base case (root is null). This will lead to a stack overflow error.

✗Common mistake 2: Not adding 1 to the maximum depth of the children. This will result in an incorrect depth calculation.

✗Common mistake 3: Not handling the case where a node has no children correctly. The `for` loop will simply not execute, and the depth will remain 0, which is then incremented to 1.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Representing organizational structures. The depth of the tree can represent the level of hierarchy in the organization.

🏦Real-world scenario 2: Representing file systems. The depth of the tree can represent the depth of a directory in the file system.

🎮Real-world scenario 3: Representing XML or JSON data structures. The depth of the tree can represent the level of nesting in the data structure.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

Most tree problems can be solved recursively. The base case is usually a null node. Think about what information needs to flow up vs down the tree.

🎯 Interview Tip

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ Watch Out

Not handling null nodes properly. Always check if the current node exists before accessing its children.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: June 20, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 13

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 6

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJun 29

❓

Frequently Asked Questions

What is the difference between DFS and BFS for trees?

DFS (using recursion or stack) explores depth-first, useful for path-finding and backtracking problems. BFS (using queue) explores level-by-level, ideal for finding shortest paths or processing nodes by depth. Choose based on whether level information matters.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Maximum Depth of N-ary Tree"?

For this easy-level Tree problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether depth-first search techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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