Binary Tree Maximum Path Sum
Last updated: March 3, 2025
Quick Overview
Find the maximum path sum in a binary tree where the path can start and end at any node. Tests recursive tree traversal with global state.
ByteDance
March 3, 20255
8
4,064 solved
Find the maximum path sum in a binary tree where the path can start and end at any node. Tests recursive tree traversal with global state.
Tree problems are a top-5 pattern at ByteDance. This hard variant requires careful handling of negative values and path constraints.
What the Interviewer Expects
- Implement recursive DFS with post-order traversal
- Track global maximum across all recursive calls
- Handle negative node values correctly
- Understand the difference between path through a node and path ending at a node
- Discuss time and space complexity
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 return the actual path, not just the sum?
- What if the tree has billions of nodes?
- How would you handle this on a tree stored on disk?
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Problem Analysis
The problem requires us to find the maximum path sum in a binary tree, where the path can start and end at any node. This prompts the use of a depth-first search (DFS) approach, specifically post-orde...
Approach
- Define a Recursive Function: Create a helper function that takes the current node as input and computes the maximum path sum from that node.
- Base Case: If the current node is
None, re...
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