My first instinct was to just loop through both arrays, which works but completely misses the point of the word 'sparse'.
Clarify the sparse vector representation (e.g., dictionary of index-value pairs or sorted index-value lists) and then propose an efficient algorithm that iterates over the non-zero elements, using a merge-like approach for sorted lists or a hash lookup for dictionaries. Analyze time and space complexity, emphasizing O(nnz1 + nnz2) time and O(1) extra space for sorted lists, and discuss trade-offs for different representations.
Pro tip: Mention that in ML systems like Meta's, sparse vectors often come from embedding tables or feature hashes, so you should also consider memory layout and cache efficiency when choosing the representation. Demonstrating awareness of real-world constraints beyond just algorithmic complexity will set you apart.
Ask the interviewer how the sparse vectors are represented (e.g., dictionary, sorted list of (index, value) pairs, or CSR format) and whether they are sorted by index. This determines the optimal algorithm.
For sorted lists, use a two-pointer merge to find common indices and accumulate products. For dictionaries, iterate over the smaller dictionary and look up indices in the larger one.
State the time complexity: O(nnz1 + nnz2) for sorted lists, O(min(nnz1, nnz2)) for hash-based. Space complexity is O(1) extra for sorted lists, O(nnz) for hash-based if building a lookup.
Compare representations: sorted lists are memory-efficient and allow streaming, while hash maps offer faster lookups but higher memory overhead. Handle empty vectors, no common indices, and negative values.
Connect to ML applications: sparse features, embeddings, and large-scale dot products in recommendation systems. Mention potential optimizations like parallelization or GPU acceleration if relevant.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.