Optimize traversal for O(1) space

Last updated: October 3, 2025

Quick Overview

Given a binary tree, implement a traversal algorithm that visits each node while using O(1) space. You should return the values of the nodes in the order they are visited. The input will be the root of the binary tree, and the output should be a list of integers representing the node values in traversal order.

Palo Alto Networks
Coding & Algorithms
Software Engineer
Palo Alto Networks
October 3, 2025
Software Engineer
Onsite
Coding & Algorithms
Easy

177

3

4,483 solved


Given a binary tree, implement a traversal algorithm that visits each node while using O(1) space. You should return the values of the nodes in the order they are visited. The input will be the root of the binary tree, and the output should be a list of integers representing the node values in traversal order.

Coding interviews at Palo Alto Networks focus on problem-solving approach as much as the final solution. The interviewer wants to see you break down the problem, consider edge cases, and optimize iteratively. Communication throughout the process is key.

What the Interviewer Expects
  • Identify the correct data structure and algorithm for the problem
  • Write clean, bug-free code with proper variable naming
  • Analyze time and space complexity correctly
  • Handle basic edge cases (empty input, single element)
  • Communicate your thought process while coding
Key Topics to Cover
Binary search and divide and conquer
Sorting and searching
Data structure selection and trade-offs
Hash maps and frequency counting
How to Approach This
  1. Clarify input constraints and edge cases before writing code.
  2. Walk through your approach verbally and confirm with the interviewer before coding.
  3. Start with a brute force solution, then optimize. Mention time and space complexity.
  4. Test your solution with examples, including edge cases like empty input or duplicates.
  5. Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
  • What if the input doesn't fit in memory?
  • What is the worst-case input for your solution?
  • What happens if the input contains duplicates?
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Sample Answer
Problem Analysis

The problem requires us to traverse a binary tree using O(1) space. This indicates that we cannot use any additional data structures like stacks or queues that would require extra space. A suitable ap...

Approach
  1. Start at the root of the binary tree.
  2. For each node, check if it has a left child:
    • If it does, find the rightmost node in the left subtree (this will be the predecessor).
    • Connect the p...

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