I went straight to run-length encoding (value, count pairs) which felt right for the example they gave.
Start by clarifying the requirements: what operations are needed (random access, iteration, append), memory constraints, and expected distribution of repeated values. Then propose a run-length encoding (RLE) scheme as a baseline, analyze its tradeoffs, and compare with alternatives like dictionary encoding, delta encoding, or hybrid approaches. Conclude by recommending a format based on the specific use case.
Pro tip: Quantify the tradeoffs with concrete numbers (e.g., memory savings vs. access time) and mention real-world systems like Parquet or ORC that use similar techniques. This shows practical experience and depth.
Ask about the expected operations (random access, iteration, append), memory constraints, and characteristics of the data (e.g., average run length, value range). This ensures the design meets actual needs.
Describe RLE: store pairs of (value, count) for consecutive repeated values. Explain how it compresses long runs and its simplicity.
Discuss pros: excellent compression for long runs, simple encoding/decoding. Cons: poor for random access (need to scan runs), overhead for short runs, and worst-case expansion (e.g., alternating values).
Consider dictionary encoding (map values to IDs, store IDs), delta encoding (store differences), or hybrid approaches (e.g., RLE for long runs, raw for short). Discuss tradeoffs in compression ratio, access speed, and complexity.
Based on the clarified requirements, recommend a format (e.g., RLE with block-based indexing for random access) and justify why it best balances memory and performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the compressed format and its decoding cost, then propose an algorithm that decodes and multiplies on the fly to avoid materializing full vectors. Discuss trade-offs between time, space, and potential for parallelization or vectorization.
Pro tip: Mention that you would handle edge cases like different compression schemes or zero-length vectors, and that you would benchmark against a naive decode-then-dot approach to validate efficiency.
Ask questions to understand how the vectors are compressed (e.g., run-length encoding, sparse representation, dictionary encoding) and whether random access is supported.
Propose an algorithm that iterates over the compressed representations simultaneously, decoding only the necessary elements and accumulating the dot product without fully decompressing the vectors.
Discuss time and space complexity, comparing your approach to naive decoding. Mention potential optimizations like early termination for zeros or using SIMD instructions.
Consider cases where the vectors have different compression schemes, are empty, or contain special values (e.g., NaN, infinity). Explain how your algorithm handles them.
Summarize why your approach is efficient for Google-scale data, and mention testing, profiling, and potential parallelization.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.