Airbnb·Software Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say

Jul 2026

Summary

Airbnb software engineer interview with a meaty tree design problem that went deeper than I expected. The mutation support is what tripped me up.

Questions Asked (1)

Design a data structure for a mutable rooted tree where leaves store integers and internal nodes store the sum of their children. Support efficient value queries by node ID, plus two mutations: converting any node into a leaf with a given value (dropping its subtree), and converting a leaf into an internal node by attaching a provided subtree. Queries must stay correct after any sequence of mutations. Walk through your algorithms, complexity, how you maintain parent/child links and subtree sums, and edge cases like overflow, very deep trees, and empty children.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

I started with the preprocessing angle and felt pretty good about that part.

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AI HintsAI Generated

Suggested Approach

Start by clarifying requirements and constraints, then propose a node-based tree with parent pointers and cached subtree sums. Explain how to update sums efficiently by walking up from the modified node to the root, and discuss trade-offs like lazy propagation for deep trees or overflow handling.

Pro tip: Mention that you would use an iterative approach for upward sum updates to avoid stack overflow on deep trees, and consider using a sentinel or null checks for empty children to simplify edge cases.

1. Clarify requirements and constraints

Ask about expected tree size, depth, mutation frequency, and whether node IDs are stable. Confirm that queries are by node ID and that mutations can happen anywhere.

2. Design the data structure

Propose a node class with fields: id, value (for leaves), children list, parent pointer, and subtree sum. For internal nodes, value is null and sum is maintained. Use a hash map for O(1) node lookup by ID.

3. Implement queries and mutations

For query, return node.sum. For leaf-to-internal, attach provided subtree, set node's children, and update sums upward. For internal-to-leaf, detach children, set value, and update sums upward.

4. Analyze complexity and edge cases

Query is O(1). Mutations are O(depth) for sum updates. Discuss overflow (use big integers or modular arithmetic), deep trees (iterative updates), and empty children (handle as sum 0).

5. Discuss trade-offs and optimizations

Consider lazy propagation for frequent mutations, or a balanced tree structure if depth is a concern. Mention that parent pointers enable efficient upward updates but add memory overhead.

Key Points to Mention

Use of parent pointers to efficiently update subtree sums upward after mutations.
Maintaining a hash map from node ID to node object for O(1) access.
Handling of empty children: internal nodes with no children should have sum 0.
Overflow considerations: use arbitrary-precision integers or discuss modular arithmetic if sums can exceed typical integer limits.
Deep tree handling: iterative upward traversal to avoid stack overflow, or consider balancing.
Complexity analysis: O(1) query, O(depth) mutation, and potential optimizations like lazy propagation.

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