BFS on graph
Last updated: April 17, 2026
Quick Overview
Apply the DFS algorithm on a binary tree to solve this optimization problem.
Amazon
April 17, 202624
6
1,507 solved
Apply the DFS algorithm on a binary tree to solve this optimization problem.
Coding interviews at Amazon 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
- Quickly identify the optimal approach and its theoretical basis
- Handle complex algorithm design with multiple interacting components
- Write concise, elegant code under time pressure
- Prove correctness of your approach and discuss alternative solutions
- Optimize beyond the obvious: discuss constant factor improvements
- Address follow-up variations and explain how the solution generalizes
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?
- What happens if the input contains duplicates?
- Can you solve this in a single pass?
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Practice DSA ProblemsSample Answer
Problem Analysis
This problem is best modeled as **DFS on a binary tree with dynamic programming / memoization by subtree**. Even though the title says "BFS on graph,...
Approach
Use DFS where each recursive call returns one value: `best_downward_gain(node)` = the maximum path sum starting at `node` and extending downward thro...
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