Bloomberg·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Bloomberg SWE interview with a tree problem that looks easy until you realize you don't even know which node is the root. The follow-up asking for O(1) space is where things get spicy.

Questions Asked (1)

You're given a shuffled list of nodes from an N-ary tree, where each node has a value and a list of children. You don't know which node is the root. Find and return the root. Follow-up: can you do it in O(n) time and O(1) extra space?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The base version isn't bad once you realize the root is just the node that never appears as anyone's child.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints and edge cases, then present a straightforward solution using a hash set to track all child nodes and identify the root as the node not appearing as a child. For the follow-up, explain how to achieve O(n) time and O(1) extra space by leveraging the fact that each node has a unique value and using XOR or sum of values to cancel out children, or by temporarily modifying the tree structure.

Pro tip: Demonstrate awareness of trade-offs: the hash set solution is simple but uses O(n) space, while the O(1) solution may require mutating the input or assuming unique values. Discuss with the interviewer which constraints are acceptable.

1. Clarify the problem

Ask about constraints: Are node values unique? Can we modify the input? Is the tree guaranteed to be valid? This ensures you understand the problem fully before diving in.

2. Propose a simple solution

Use a hash set to store all child nodes, then iterate through the list to find the node not in the set. This is O(n) time and O(n) space.

3. Address the follow-up

For O(1) space, if values are unique, compute the XOR of all node values and all child values; the result is the root's value. Alternatively, use the sum of values. If values are not unique, consider temporarily modifying the tree (e.g., marking visited nodes) or using a two-pass approach with pointer manipulation.

4. Analyze trade-offs

Compare the hash set and XOR/sum approaches: the former is simpler and works with duplicate values, while the latter achieves O(1) space but requires unique values or input mutation. Discuss which is preferable based on constraints.

5. Test with examples

Walk through a small example to verify the logic, including edge cases like a single node or a tree where the root has no children.

Key Points to Mention

Root is the only node that never appears as a child.
Hash set approach: O(n) time, O(n) space.
XOR or sum trick: O(n) time, O(1) space if values are unique.
Handling duplicate values: may require input mutation or additional assumptions.
Edge cases: empty list, single node, multiple roots (invalid tree).
Trade-offs between simplicity and space efficiency.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.