Count median in binary tree
Last updated: May 29, 2026
Quick Overview
Given a binary tree, write a function to calculate the median of all the values stored in the nodes. The function should return a single floating-point number representing the median, which is defined as the middle value when the values are sorted; if there is an even number of values, return the average of the two middle values.
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Given a binary tree, write a function to calculate the median of all the values stored in the nodes. The function should return a single floating-point number representing the median, which is defined as the middle value when the values are sorted; if there is an even number of values, return the average of the two middle values.
This coding problem is frequently asked during Phone Screen at Google. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Google expects candidates to write production-quality code, not just solve the puzzle.
What the Interviewer Expects
- Recognize the underlying problem pattern (sliding window, two pointers, BFS/DFS, etc.)
- Discuss multiple approaches and trade-offs before coding
- Implement an optimal solution with clean, production-quality code
- Handle all edge cases including boundary conditions and invalid input
- Optimize both time and space complexity with clear justification
- Test your solution systematically with well-chosen examples
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?
- What happens if the input contains duplicates?
- How would you test this solution thoroughly?
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Problem Analysis
To find the median in a binary tree, we need to consider the properties of the tree and how to traverse it to gather all values. The median is defined as the middle value in a sorted list of numbers. ...
Approach
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Traverse the Tree: Use a DFS approach (in-order traversal) to visit each node in the binary tree and collect the values into a list.
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Sort the Values: After collecting the values, sort t...
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