Meta·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

May 2026Remote

Summary

Meta SWE technical phone screen, one coding problem the whole time. Pretty focused session, just the sparse vector design question with some follow-ups on complexity and data representation.

Questions Asked (1)

Design a SparseVector class that stores integer vectors efficiently when most values are zero, and implement a dot product method that works efficiently between two such vectors. The vector length can be up to 10^5 but only a few positions are non-zero. Also explain your data representation, how it handles different sparsity patterns between two vectors, and analyze the time and space complexity of both construction and the dot product.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

My first instinct was a hashmap from index to value, which is fine, but then they asked what happens when one vector is dense and the other is sparse.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints and then propose a hash map (dictionary) representation that stores only non-zero indices and their values. Implement the dot product by iterating over the smaller map and checking for matching indices in the larger map, ensuring efficiency regardless of sparsity patterns. Finally, analyze the time and space complexity for both construction and dot product, highlighting the benefits of this sparse representation.

Pro tip: Mention that you would iterate over the smaller of the two vectors' non-zero entries to minimize lookups, and discuss potential trade-offs between hash maps and sorted arrays for different access patterns.

1. Clarify requirements and constraints

Confirm the vector length, sparsity, and expected operations. Ask about the need for updates, thread safety, or other operations beyond dot product.

2. Choose data representation

Propose using a hash map (dictionary) mapping index to value for non-zero elements. Explain why this is efficient for sparse vectors and how it handles construction from a dense array.

3. Implement dot product efficiently

Iterate over the smaller map's entries, and for each index, check if it exists in the other map. Accumulate the product of values. This minimizes lookups and handles different sparsity patterns.

4. Analyze complexity

State that construction takes O(n) time to scan the dense array and O(k) space for k non-zeros. Dot product takes O(min(k1, k2)) time and O(1) extra space, where k1 and k2 are the number of non-zeros in each vector.

5. Discuss trade-offs and alternatives

Mention that sorted arrays could allow two-pointer intersection in O(k1 + k2) time but with O(k) space and slower updates. Hash maps offer O(1) average lookups and are simpler for dynamic updates.

Key Points to Mention

Sparse representation using a hash map (index -> value) for non-zero elements only.
Construction from a dense array: iterate through array, store non-zero entries.
Dot product algorithm: iterate over the smaller map, lookup indices in the larger map.
Time complexity: O(n) for construction, O(min(k1, k2)) for dot product.
Space complexity: O(k) for each vector, where k is the number of non-zeros.
Handling different sparsity patterns: iterating over the smaller map ensures efficiency even if one vector is much sparser.

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