Find shortest distance in binary tree
Last updated: November 3, 2025
Quick Overview
Given a binary tree, write a function to find the shortest distance between two nodes in the tree. The function should take the root of the binary tree and the two target nodes as input and return the shortest distance as an integer. If either of the nodes does not exist in the tree, return -1.
Palantir
November 3, 202523
11
2,378 solved
Given a binary tree, write a function to find the shortest distance between two nodes in the tree. The function should take the root of the binary tree and the two target nodes as input and return the shortest distance as an integer. If either of the nodes does not exist in the tree, return -1.
Palantir uses this problem in the Take-home Project 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 your solution change if the input was sorted?
- How would you modify your solution to handle streaming input?
- Can you solve this iteratively instead of recursively (or vice versa)?
Sharpen Your Skills on Codemia
Practice similar problems with our interactive workspace, get AI feedback, and track your progress.
Practice DSA ProblemsSample Answer
Problem Analysis
To find the shortest distance between two nodes in a binary tree, we need to first identify the lowest common ancestor (LCA) of the two nodes. The distance between two nodes can be expressed as the di...
Approach
- Find the LCA: Implement a DFS function that returns the LCA of the two nodes. During the traversal, if we find either of the target nodes, we will return that node. If we find both, we can dete...
Submit Your Answer
