I started with brute force distance calculation which they seemed fine with, but then they pushed on complexity and I fumbled a bit explaining why KD-trees help.
Start by clarifying the problem scope (e.g., dataset size, dimensionality, distance metric) and then outline the algorithm steps: training (just storing data), prediction (computing distances, finding k nearest, and aggregating). Discuss trade-offs like brute-force vs. tree-based approaches and how to handle ties or weighted voting.
Pro tip: Mention that for large-scale production systems, you'd likely use approximate nearest neighbor libraries (e.g., FAISS, Annoy) and discuss the trade-off between exactness and speed, showing awareness of real-world constraints.
Ask about dataset size, dimensionality, distance metric, and whether it's for classification or regression. This determines the appropriate implementation strategy.
Explain that training is trivial (store data) and prediction involves computing distances from the query point to all training points, selecting the k smallest, and aggregating labels (majority vote or average).
Cover distance computation (e.g., Euclidean), efficient k-smallest selection (e.g., heap), tie-breaking, and weighted voting. Mention handling of edge cases like k > n.
State time complexity for prediction (O(n*d)) and space complexity (O(n*d)). Discuss alternatives like KD-trees or ball trees for lower-dimensional data, and approximate methods for large-scale.
Suggest optimizations: vectorization, parallelization, or using approximate nearest neighbor libraries. Mention Amazon-specific considerations like scalability and latency.
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