Meta·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Meta SWE coding round, one problem the whole time about storing vectors with duplicates and computing dot products efficiently. Pretty focused session, felt like they cared more about the design reasoning than just getting to a working answer.

Questions Asked (1)

Design a space-efficient data structure for storing integer vectors that may contain many duplicate or zero values, then implement a dot product function that computes the dot product with another such vector efficiently.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

My first instinct was to just store the raw array and call it a day, but the 'space-efficient' part is doing a lot of work in this prompt.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by clarifying the constraints and requirements, then propose a sparse representation that stores only non-zero elements (e.g., index-value pairs) to save space. Discuss trade-offs between different sparse formats and implement the dot product by iterating through the smaller non-zero set and looking up indices in the other vector, using a hash map or binary search for efficient lookup.

Pro tip: Emphasize the importance of considering the distribution of non-zero elements and the frequency of dot product operations to choose the optimal data structure; for example, if one vector is much sparser, iterating over its non-zeros and probing the other can be more efficient.

1. Clarify Requirements and Constraints

Ask about the expected size of vectors, sparsity level, frequency of dot product operations, and whether vectors are immutable or can be preprocessed. This guides the choice of data structure.

2. Propose Sparse Representation

Suggest storing only non-zero elements as a list of (index, value) pairs, or as two parallel arrays (indices and values). Mention alternatives like hash maps for O(1) lookups or sorted arrays for binary search.

3. Analyze Trade-offs

Compare space and time complexity of different representations: e.g., hash map offers O(1) average lookup but higher memory overhead; sorted arrays allow binary search O(log n) with less memory. Consider preprocessing costs.

4. Implement Dot Product Efficiently

Iterate over the non-zero elements of the sparser vector, and for each index, look up the corresponding value in the other vector (using the chosen lookup method). Accumulate the product if the index exists.

5. Discuss Optimizations and Edge Cases

Mention handling of zero vectors, vectors of different lengths, and potential parallelization. Also discuss if one vector is dense, maybe use a dense array for it.

Key Points to Mention

Sparse vector representation: coordinate list (COO), compressed sparse row (CSR), or dictionary of keys (DOK).
Time complexity: O(min(nnz1, nnz2)) with hash map lookups, or O(nnz1 log nnz2) with binary search if sorted.
Space complexity: O(nnz) where nnz is number of non-zeros, significantly less than O(n) for sparse vectors.
Trade-offs: hash map vs sorted array for lookup speed vs memory overhead.
Handling duplicates: if duplicates exist, aggregate values during construction to maintain sparsity.
Edge cases: empty vectors, vectors with all zeros, different lengths (treat missing as zero).

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