Find maximum path in binary tree
Last updated: July 11, 2025
Quick Overview
Given a binary tree, write a function to find the maximum path sum. A path is defined as any sequence of nodes from any starting node to any ending node, where the path must be downward (i.e., moving from parent to child nodes). The function should return the maximum path sum as an integer.
ServiceNow
July 11, 20250
11
4,009 solved
Given a binary tree, write a function to find the maximum path sum. A path is defined as any sequence of nodes from any starting node to any ending node, where the path must be downward (i.e., moving from parent to child nodes). The function should return the maximum path sum as an integer.
This coding problem is frequently asked during Take-home Project at ServiceNow. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. ServiceNow expects candidates to write production-quality code, not just solve the puzzle.
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?
- How would you parallelize this solution?
- Can you optimize the space complexity of your solution?
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Practice DSA ProblemsSample Answer
Problem Analysis
To solve the problem of finding the maximum path sum in a binary tree, we can identify that this is a tree traversal problem that requires a depth-first search (DFS) approach. The key pattern here is ...
Approach
- Define a recursive function that returns the maximum path sum that can be obtained starting from the current node.
- For each node, calculate the maximum contribution from its left and right child...
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