What is the time complexity of Binary Tree Level Order Traversal?

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

What data structures are used to solve Binary Tree Level Order Traversal?

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

What are the key insights for solving Binary Tree Level Order Traversal?

Insight 1: Breadth-First Search (BFS) is the most suitable algorithm for level order traversal. Insight 2: A queue data structure is essential for implementing BFS efficiently.

Which companies ask LeetCode 102. Binary Tree Level Order Traversal in interviews?

This problem is frequently asked at Adobe, Apple, Bloomberg, Gojek, Intuit and 8 more companies.

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Binary Tree Level Order Traversal - LeetCode 102 Solution

Q: How to solve Binary Tree Level Order Traversal?

The provided solutions use Breadth-First Search (BFS) to traverse the binary tree level by level. A queue is used to store the nodes to be visited. The algorithm iterates while the queue is not empty. In each iteration, it processes all nodes at the current level and adds their children to the queue. This ensures that nodes are visited in the correct level order.

Binary Tree Level Order Traversal - Complete Solution Guide

Binary Tree Level Order Traversal is LeetCode problem 102, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given the root of a binary tree, return the level order traversal of its nodes' values . (i.e., from left to right, level by level). Example 1: Input: root = [3,9,20,null,null,15,7] Output: [[3],[9,20],[15,7]] Example 2: Input: root = [1] Output: [[1]] Example 3: Input: root = [] Output: [] Constraints: The number of nodes in the tree is in the range [0, 2000] . -1000 <= Node.val <= 1000

Detailed Explanation

The problem asks us to perform a level order traversal of a binary tree. Level order traversal means visiting the nodes of the tree level by level, starting from the root node. For each level, we must visit the nodes from left to right. The output should be a list of lists, where each inner list represents a level of the tree and contains the values of the nodes at that level.

Solution Approach

The provided solutions use Breadth-First Search (BFS) to traverse the binary tree level by level. A queue is used to store the nodes to be visited. The algorithm iterates while the queue is not empty. In each iteration, it processes all nodes at the current level and adds their children to the queue. This ensures that nodes are visited in the correct level order.

Step-by-Step Algorithm

Step 1: Initialize an empty list `result` to store the level order traversal.
Step 2: If the root is null, return the empty `result` list.
Step 3: Initialize a queue and add the root node to the queue.
Step 4: While the queue is not empty:
Step 5: Get the size of the queue, which represents the number of nodes at the current level.
Step 6: Initialize an empty list `current_level` to store the values of nodes at the current level.
Step 7: Iterate `level_size` times:
Step 8: Dequeue a node from the queue.
Step 9: Add the node's value to the `current_level` list.
Step 10: Enqueue the node's left child (if it exists).
Step 11: Enqueue the node's right child (if it exists).
Step 12: After processing all nodes at the current level, add the `current_level` list to the `result` list.
Step 13: Return the `result` list.

Key Insights

Insight 1: Breadth-First Search (BFS) is the most suitable algorithm for level order traversal.
Insight 2: A queue data structure is essential for implementing BFS efficiently.
Insight 3: We need to keep track of the number of nodes at each level to process each level separately.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

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

Companies

Asked at: Adobe, Apple, Bloomberg, Gojek, Intuit, LinkedIn, Meta, Microsoft, Palo Alto Networks, PhonePe, TikTok, Uber, Yahoo.

Binary Tree Level Order Traversal | LeetCode 102

Medium

Tree Breadth-First Search Binary Tree

Time: O(n)Space: O(n)

Solution Code

Available in:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.List;
import java.util.Queue;

class Solution {
    public List<List<Integer>> levelOrder(TreeNode root) {
        if (root == null) {
            return new ArrayList<>();
        }

        List<List<Integer>> result = new ArrayList<>();
        Queue<TreeNode> queue = new LinkedList<>();
        queue.offer(root);

        while (!queue.isEmpty()) {
            int levelSize = queue.size();
            List<Integer> currentLevel = new ArrayList<>();

            for (int i = 0; i < levelSize; i++) {
                TreeNode node = queue.poll();
                currentLevel.add(node.val);

                if (node.left != null) {
                    queue.offer(node.left);
                }
                if (node.right != null) {
                    queue.offer(node.right);
                }
            }

            result.add(currentLevel);
        }

        return result;
    }
}

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Problem Info

Description

Problem 102: Binary Tree Level Order Traversal - Detailed explanation and solution approaches.

Topics

Tree Breadth-First Search Binary Tree

Companies

AdobeAppleBloombergGojekIntuitLinkedInMetaMicrosoft

Stats

Difficulty:Medium

Languages:4

Companies:13

Problem #:102

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

13 steps

1
Step 1: Initialize an empty list `result` to store the level order traversal.
2
Step 2: If the root is null, return the empty `result` list.
3
Step 3: Initialize a queue and add the root node to the queue.
4
Step 4: While the queue is not empty:
5
Step 5: Get the size of the queue, which represents the number of nodes at the current level.
6
Step 6: Initialize an empty list `current_level` to store the values of nodes at the current level.
7
Step 7: Iterate `level_size` times:
8
Step 8: Dequeue a node from the queue.
9
Step 9: Add the node's value to the `current_level` list.
10
Step 10: Enqueue the node's left child (if it exists).
11
Step 11: Enqueue the node's right child (if it exists).
12
Step 12: After processing all nodes at the current level, add the `current_level` list to the `result` list.
13
Step 13: Return the `result` list.

💡

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)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is O(n) because we visit each node once. The space complexity is determined by the maximum number of nodes stored in the queue at any given time, which corresponds to the maximum width 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

Depth-First Search (DFS) with level information

An alternative approach is to use Depth-First Search (DFS) and maintain a level number for each node. We can traverse the tree using DFS and store the node's value in the corresponding level's list in the result.

Time: O(n)Space: O(n)

Trade-offs: While DFS also has a time complexity of O(n), it might be slightly less efficient than BFS for this specific problem. BFS is a more natural fit for level-order traversal. The advantage of DFS might be its reduced memory usage for skewed trees compared to BFS's worst-case space usage of O(w) where w is the maximum width.

✨

Key Insights

1Insight 1: Breadth-First Search (BFS) is the most suitable algorithm for level order traversal.
2Insight 2: A queue data structure is essential for implementing BFS efficiently.
3Insight 3: We need to keep track of the number of nodes at each level to process each level separately.

📚

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 an empty list.
Edge case 2: Tree with only one node (root has no children). The solution correctly processes the root node and returns a list containing a single list with the root's value.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to handle the case where the root is null.

✗Common mistake 2: Not correctly calculating the level size before iterating through the nodes at that level. This can lead to incorrect level order traversal.

✗Common mistake 3: Not adding the left and right children to the queue in the correct order (left child first, then right child).

✅

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 where you need to process employees level by level (e.g., CEO, VPs, Managers, Employees).

🏦Real-world scenario 2: Finding the shortest path in a graph where the graph is represented as a tree-like structure. BFS can be used to find the shortest path from a starting node to all other nodes.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ 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: September 11, 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

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 14

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 7

❓

Frequently Asked Questions

How do I choose between recursive and iterative tree traversal?

Use recursive traversal for cleaner code when stack depth isn't a concern (tree height < ~1000). Use iterative with explicit stack for very deep trees to avoid stack overflow. Iterative is also preferred when you need fine-grained control over the traversal process.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Binary Tree Level Order Traversal"?

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

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