Implement and Optimize Vector Multiplication

Q: Implement and Optimize Vector Multiplication

This question evaluates a candidate's ability to implement vector–vector multiplication and to reason about performance optimizations and sparse data structures, assessing competencies in algorithm design, parallel computing, memory hierarchy, and numerical operations.

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Question

Implement vector–vector multiplication for dense vectors (e.g., dot product). Then, describe how you would optimize the implementation for a parallel architecture (e.g., SIMD, multithreading, memory alignment, cache behavior). Finally, explain how you would perform the same operation when the vectors are sparse, including data structures you would use and how sparsity affects complexity and parallelization.

Implement and Optimize Vector Multiplication

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