Find the Root of N-ary Tree (Graph Traversal)
Given a list of nodes in an $N$-ary tree, where each node has a list of its children, find the root node. The root is the only node that is not a child of any other node.
Why Interviewers Ask This
Google interviewers ask this to evaluate your ability to recognize patterns beyond standard binary trees and apply graph traversal logic efficiently. They specifically test if you can optimize from a naive O(N^2) brute force approach to an optimal O(N) solution using mathematical properties or hash sets, demonstrating strong algorithmic thinking under constraints.
How to Answer This Question
1. Clarify the Input: Immediately define the data structure. Ask if nodes are objects with IDs and children lists, or just integers, and confirm if the tree is guaranteed to be valid without cycles.
2. Analyze Constraints: Discuss time and space complexity requirements. Google values optimal solutions, so aim for linear time O(N).
3. Evaluate Naive Approaches: Briefly mention checking every node against all others (O(N^2)) to show you understand the baseline before optimizing.
4. Propose Optimized Strategy: Introduce the 'Sum of Children' or 'Set Difference' method. Explain that the root is the only node never appearing in a children list. Suggest using a HashSet to track all children, then iterating to find the missing node.
5. Walk Through Code: Pseudocode the solution step-by-step. Iterate through the input, add each child to a set, then check which node ID is not in that set. Mention handling edge cases like null inputs or single-node trees.
Key Points to Cover
- Identifying the root as the node that is never a child of another node
- Optimizing from O(N^2) brute force to O(N) using a Hash Set
- Explicitly handling N-ary tree structures rather than assuming binary
- Demonstrating clear communication of the algorithm before coding
- Considering edge cases like empty inputs or single-node trees
Sample Answer
To solve finding the root of an N-ary tree, I would first clarify the input format. Assuming we have a list of nodes where each contains an ID and a list of child IDs, my goal is to identify the node that never appears a…
Common Mistakes to Avoid
- Attempting to build the full tree structure first, which wastes time and memory
- Using recursive traversal to find the root, causing stack overflow risks on deep trees
- Ignoring the possibility of duplicate IDs or malformed input data
- Failing to explain why the chosen approach is better than a simple nested loop comparison
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