LinkedIn·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

May 2026

Summary

LinkedIn SWE interview that came down to a single meaty data structure design problem. The question had layers to it and the conversation went pretty deep into trade-offs, which I wasn't fully prepared for.

Questions Asked (1)

Design a SumTable class for a 2D matrix that supports two operations: querying the sum of any rectangular submatrix, and updating the value at a specific cell. Walk through the trade-offs between different implementation approaches.

Algorithms & Data StructuresTechnical Trade-offsSystem Design

Author's notes

I started with the prefix sum approach because it felt clean.

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AI HintsAI Generated

Suggested Approach

Start by clarifying requirements and constraints, then present multiple implementation approaches (naive, prefix sum, Fenwick tree, segment tree) with their time/space trade-offs. Finally, recommend an approach based on the expected query/update frequency and justify your choice.

Pro tip: Mention that a 2D Fenwick tree is often the sweet spot for balanced workloads, but if updates are rare, a 2D prefix sum array is simpler and faster for queries. Also, discuss how to handle edge cases like empty matrices or out-of-bounds indices.

1. Clarify requirements and constraints

Ask about the expected frequency of queries vs. updates, matrix size, and whether the matrix is static or dynamic. This determines the optimal data structure.

2. Present naive approach

Describe a straightforward implementation: for query, sum all elements in the rectangle (O(m*n)); for update, change the cell (O(1)). Highlight its inefficiency for large matrices.

3. Introduce optimized approaches

Explain 2D prefix sum (O(1) query, O(m*n) update), 2D Fenwick tree (O(log m * log n) for both), and 2D segment tree (O(log m * log n) for both, but more complex).

4. Compare trade-offs

Discuss time/space complexity, implementation complexity, and suitability for different scenarios (e.g., read-heavy vs. write-heavy).

5. Recommend and justify

Choose an approach based on the clarified requirements and explain why it's the best fit, mentioning potential optimizations like sparse Fenwick trees for large sparse matrices.

Key Points to Mention

Time complexity of query and update for each approach
Space complexity and memory overhead
Implementation complexity and code maintainability
Handling of edge cases (empty matrix, out-of-bounds, negative values)
Real-world applicability and scalability
Potential optimizations like coordinate compression or lazy propagation

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