Dynamic Programming on binary tree
Last updated: August 29, 2025
Quick Overview
Given a binary tree, implement a function that utilizes dynamic programming to find the maximum sum of non-adjacent nodes. The function should take the root of the binary tree as input and return the maximum sum as an integer. Ensure that you do not select both a node and its direct children in the sum calculation.
Waymo
August 29, 202515
13
4,416 solved
Given a binary tree, implement a function that utilizes dynamic programming to find the maximum sum of non-adjacent nodes. The function should take the root of the binary tree as input and return the maximum sum as an integer. Ensure that you do not select both a node and its direct children in the sum calculation.
Waymo uses this problem in the Phone Screen to evaluate your algorithmic thinking. They expect you to discuss multiple approaches, analyze trade-offs between them, and implement the optimal solution with clean, readable code.
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
- How would you modify your solution to handle streaming input?
- How would you test this solution thoroughly?
- Can you optimize the space complexity of your solution?
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Practice DSA ProblemsSample Answer
Problem Analysis
The problem requires us to find the maximum sum of non-adjacent nodes in a binary tree. Here, 'non-adjacent' means that if we include a node in our sum, we cannot include its direct children (left and...
Approach
- DFS Traversal: Start from the root node and recursively visit each node in the binary tree. For each node, we will calculate two values:
include_node: the maximum sum we can achieve by i...
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