My first instinct was to just use a plain array and I almost went with it before catching myself.
Start by clarifying the requirements and constraints of the sparse vector, such as the expected sparsity level and operations. Then propose a data structure like a hash map or sorted list of (index, value) pairs, explaining trade-offs. Finally, implement the dot product by iterating over the smaller vector and looking up indices in the larger one, or by merging two sorted lists.
Pro tip: Discuss the trade-offs between different representations (e.g., hash map vs. sorted array) in terms of time and space complexity, and mention that the choice depends on the frequency of updates versus queries. Also, consider edge cases like vectors of different dimensions and zero values.
Ask about the expected sparsity, typical operations (e.g., updates, queries), and constraints like memory or time. This shows you consider the practical context.
Suggest using a hash map (dictionary) mapping indices to values for O(1) access, or a sorted array of (index, value) pairs for memory efficiency and cache locality. Explain the trade-offs.
For hash map: iterate over the smaller vector and check if the index exists in the other, summing products. For sorted arrays: use two pointers to merge and compute dot product in O(nnz1 + nnz2) time.
State time and space complexity for both data structure and dot product. For hash map, dot product is O(min(nnz1, nnz2)) average; for sorted arrays, O(nnz1 + nnz2).
Mention handling of different dimensions, zero values, and potential optimizations like early termination if one vector is empty or using binary search for sorted arrays.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.