What is the time complexity of Binary Tree Preorder Traversal?

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

What data structures are used to solve Binary Tree Preorder Traversal?

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

What are the key insights for solving Binary Tree Preorder Traversal?

Insight 1: Understanding Preorder Traversal: The core concept is the specific order of visiting nodes (Root, Left, Right). Insight 2: Iterative Approach using a Stack: Using a stack allows us to simulate recursion without the overhead and risk of stack overflow in the case of very deep trees.

Which companies ask LeetCode 144. Binary Tree Preorder Traversal in interviews?

This problem is frequently asked at Yahoo.

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Binary Tree Preorder Traversal - LeetCode 144 Solution

Q: How to solve Binary Tree Preorder Traversal?

The provided solutions use an iterative approach with a stack to perform the preorder traversal. The algorithm pushes the root node onto the stack. Then, it repeatedly pops a node from the stack, adds its value to the result list, and pushes its right and then left children onto the stack (right child first to maintain preorder). This ensures that the left subtree is processed after the right subtree, following the preorder traversal order. The process continues until the stack is empty.

Binary Tree Preorder Traversal - Complete Solution Guide

Binary Tree Preorder Traversal is LeetCode problem 144, 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 the root of a binary tree, return the preorder traversal of its nodes' values . Example 1: Input: root = [1,null,2,3] Output: [1,2,3] Explanation: Example 2: Input: root = [1,2,3,4,5,null,8,null,null,6,7,9] Output: [1,2,4,5,6,7,3,8,9] Explanation: Example 3: Input: root = [] Output: [] Example 4: Input: root = [1] Output: [1] Constraints: The number of nodes in the tree is in the range [0, 100] . -100 <= Node.val <= 100 Follow up: Recursive solution is trivial, could you do it iteratively?

Detailed Explanation

The problem asks you to perform a preorder traversal of a given binary tree and return the values of the nodes in the order they are visited. Preorder traversal follows the order: Root, Left Subtree, Right Subtree. The input is the root node of the binary tree, which can be empty (null). The output is a list (or array) of integers representing the node values in preorder sequence. Constraints limit the number of nodes and the range of node values.

Solution Approach

The provided solutions use an iterative approach with a stack to perform the preorder traversal. The algorithm pushes the root node onto the stack. Then, it repeatedly pops a node from the stack, adds its value to the result list, and pushes its right and then left children onto the stack (right child first to maintain preorder). This ensures that the left subtree is processed after the right subtree, following the preorder traversal order. The process continues until the stack is empty.

Step-by-Step Algorithm

Step 1: Initialize an empty list `result` to store the preorder traversal sequence and an empty stack `stack`.
Step 2: If the `root` is null, return the empty `result` list.
Step 3: Push the `root` node onto the `stack`.
Step 4: While the `stack` is not empty:
Step 5: Pop a node from the `stack`.
Step 6: Append the node's value to the `result` list.
Step 7: If the node has a right child, push the right child onto the `stack`.
Step 8: If the node has a left child, push the left child onto the `stack`.
Step 9: Return the `result` list.

Key Insights

Insight 1: Understanding Preorder Traversal: The core concept is the specific order of visiting nodes (Root, Left, Right).
Insight 2: Iterative Approach using a Stack: Using a stack allows us to simulate recursion without the overhead and risk of stack overflow in the case of very deep trees.
Insight 3: Handling Empty Tree: The code needs to gracefully handle the case where the input `root` is null (empty tree), returning an empty list.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Stack, Tree, Depth-First Search, Binary Tree.

Companies

Asked at: Yahoo.

Binary Tree Preorder Traversal | LeetCode 144

Easy

Stack Tree Depth-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;
 *     }
 * }
 */
class Solution {
    public List<Integer> preorderTraversal(TreeNode root) {
        List<Integer> result = new ArrayList<>();
        if (root == null) {
            return result;
        }

        Stack<TreeNode> stack = new Stack<>();
        stack.push(root);

        while (!stack.isEmpty()) {
            TreeNode node = stack.pop();
            result.add(node.val);

            if (node.right != null) {
                stack.push(node.right);
            }
            if (node.left != null) {
                stack.push(node.left);
            }
        }

        return result;
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 144: Binary Tree Preorder Traversal - Detailed explanation and solution approaches.

Topics

Stack Tree Depth-First Search Binary Tree

Companies

Yahoo

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:144

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

9 steps

1
Step 1: Initialize an empty list `result` to store the preorder traversal sequence and an empty stack `stack`.
2
Step 2: If the `root` is null, return the empty `result` list.
3
Step 3: Push the `root` node onto the `stack`.
4
Step 4: While the `stack` is not empty:
5
Step 5: Pop a node from the `stack`.
6
Step 6: Append the node's value to the `result` list.
7
Step 7: If the node has a right child, push the right child onto the `stack`.
8
Step 8: If the node has a left child, push the left child onto the `stack`.
9
Step 9: 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 each node in the tree is visited and processed exactly once. The space complexity is O(n) in the worst case because the stack can hold up to the maximum height of the tree (which is n in the case of a skewed tree). In a balanced tree the height would be log(n), reducing the space complexity.

📖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

Recursive Approach

A recursive function can directly implement the preorder traversal definition: visit the root, recursively traverse the left subtree, then recursively traverse the right subtree.

Time: O(n)Space: O(h) (where h is the height of the tree)

Trade-offs: The recursive approach is more concise but can lead to stack overflow errors for very deep trees. The iterative approach, using a stack, avoids this risk.

✨

Key Insights

1Insight 1: Understanding Preorder Traversal: The core concept is the specific order of visiting nodes (Root, Left, Right).
2Insight 2: Iterative Approach using a Stack: Using a stack allows us to simulate recursion without the overhead and risk of stack overflow in the case of very deep trees.
3Insight 3: Handling Empty Tree: The code needs to gracefully handle the case where the input `root` is null (empty tree), returning an empty list.

📚

Key Terms Explained

For Students

Stack

LIFO structure - Last In, First Out. Like a stack of plates!

Tree

Hierarchical structure with nodes. Like a family tree!

Edge Cases

Edge case 1: Empty Tree: The code correctly handles an empty tree (root == null) by returning an empty list.
Edge case 2: Single Node Tree: The code correctly handles a tree with only one node by adding the node's value to the result.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrect Stack Ordering: Pushing the left child before the right child onto the stack would result in an incorrect traversal order (not preorder).

✗Common mistake 2: Not Handling Empty Tree: Forgetting to check for an empty tree (null root) can cause runtime errors.

✅

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: XML/HTML Parsing: Preorder traversal can be used to process XML or HTML documents, systematically visiting each element in a defined order.

🏦Real-world scenario 2: Serialization/Deserialization of Trees: Preorder traversal is commonly used in algorithms for saving and restoring tree structures.

💡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

Stacks are perfect for problems involving matching (parentheses) or "next greater element" patterns. If you need to look back at recent elements, think stack.

🎯 Interview Tip

Even for easy problems, discuss time and space complexity. Interviewers want to see you think analytically.

⚠️ Watch Out

Popping from an empty stack. Always check if the stack is non-empty before popping.

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: October 23, 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 14

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

@DevExpert92Jul 7

❓

Frequently Asked Questions

What problems are best solved with a stack?

Stacks excel at: matching problems (parentheses validation), next greater/smaller element, expression evaluation, backtracking, and undo operations. The key pattern is LIFO (Last In, First Out) - when you need to access the most recently added element.

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.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

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 Preorder Traversal"?

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

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