Start by clarifying the sparse matrix representation (e.g., dictionary of keys, CSR) and the expected output format. Then propose an efficient multiplication algorithm that avoids iterating over zero elements, such as iterating over non-zero entries and accumulating results in a hash map. Finally, discuss time and space complexity and potential optimizations for the given representation.
Pro tip: Mention that in production systems (like AI pipelines), sparse matrices often come from embeddings or graph data, so leveraging libraries like SciPy or custom CUDA kernels is common. Showing awareness of real-world constraints (memory, parallelization) sets you apart.
Ask about the sparse matrix format (e.g., dictionary, CSR, COO) and the expected output format. Confirm whether the matrices are large and if memory or speed is more critical.
Propose an algorithm that iterates only over non-zero elements, such as for each non-zero in A, multiply with corresponding row/column in B and accumulate in a result dictionary. Avoid dense multiplication.
Use hash maps (dictionaries) for accumulation to handle sparse output. If using CSR, iterate over rows of A and columns of B efficiently. Code the solution clearly.
Discuss time complexity in terms of number of non-zeros (nnz) and dimensions, and space complexity. Mention edge cases: empty matrices, dimension mismatch, all-zero rows/columns.
Suggest optimizations like blocking, parallelization, or using specialized libraries. Compare with dense multiplication and explain when sparse is beneficial.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.