Optimize traversal for O(n) time
Last updated: November 30, 2025
Quick Overview
Given a binary tree, implement a function to traverse the tree in-order while optimizing the traversal to achieve O(n) time complexity. The function should return a list of the node values in the order they were visited.
Apple
November 30, 202563
13
898 solved
Given a binary tree, implement a function to traverse the tree in-order while optimizing the traversal to achieve O(n) time complexity. The function should return a list of the node values in the order they were visited.
This coding problem is frequently asked during Take-home Project at Apple. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Apple expects candidates to write production-quality code, not just solve the puzzle.
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
How to Approach This
- Clarify input constraints and edge cases before writing code.
- Walk through your approach verbally and confirm with the interviewer before coding.
- Start with a brute force solution, then optimize. Mention time and space complexity.
- Test your solution with examples, including edge cases like empty input or duplicates.
- Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
- Can you optimize the space complexity of your solution?
- How would your solution change if the input was sorted?
- What if the input doesn't fit in memory?
- How would you test this solution thoroughly?
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Problem Analysis
The task is to perform an in-order traversal of a binary tree in O(n) time complexity, where n is the number of nodes in the tree. In-order traversal visits nodes in the following order: left child, c...
Approach
- Initialize an empty stack and an empty result list.
- Start from the root node and go as left as possible, pushing nodes onto the stack until you reach a null node.
- Once you hit a null node...
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