First, clarify the problem requirements and constraints, then identify if the data can be bucketed by a key (e.g., value range, frequency, or digit). Explain why bucket sort is optimal (e.g., O(n) time when buckets are balanced) and outline the steps: create buckets, distribute elements, sort within buckets if needed, and concatenate. Finally, discuss trade-offs and edge cases.
Pro tip: Mention that bucket sort is stable and can be adapted for distributed systems, which is relevant for large-scale data processing at Waymo. Also, proactively discuss how to handle skewed data by choosing bucket boundaries wisely or using a hybrid approach.
Restate the problem in your own words, ask clarifying questions about input size, value range, and expected output. Identify if the data has a natural bucketing key (e.g., numeric range, frequency, or digit).
Explain why bucket sort is suitable: it can achieve O(n) average time when data is uniformly distributed. Compare with other sorting algorithms (e.g., quick sort, counting sort) and highlight trade-offs.
Define how to map elements to buckets (e.g., value ranges, hash function). Decide the number of buckets and how to handle collisions or uneven distribution. Consider if buckets need to be sorted individually.
Write pseudocode or actual code, explaining each step. Trace through a small example to demonstrate correctness, including edge cases like empty input or all elements in one bucket.
State time and space complexity: O(n + k) average, O(n^2) worst-case if buckets are unbalanced. Discuss optimizations like using insertion sort for small buckets or dynamic bucket sizing.
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