Start by clarifying the problem constraints (e.g., array size, value range, whether k is valid) and then systematically present three approaches: naive (count and sort), heap-based (count and use a min-heap of size k), and linear-time (bucket sort by frequency). For each, analyze time and space complexity, discuss trade-offs, and justify which approach is optimal for given constraints.
Pro tip: Meta values production-ready code and clear communication. After presenting the optimal approach, mention edge cases (e.g., k > unique elements, ties) and how you would test your solution, showing you think beyond the algorithm.
Ask about input size, value range, whether k is guaranteed valid, and if the output order matters. This shows you consider practical scenarios before diving into solutions.
Describe counting frequencies with a hash map, then sorting the unique elements by frequency and taking the top k. Analyze time O(n + m log m) and space O(m), where m is unique elements.
Explain using a hash map for frequencies, then maintaining a min-heap of size k to keep the top k frequent elements. Time O(n + m log k), space O(m + k). Discuss when this is better than sorting (e.g., k << m).
Introduce bucket sort: create buckets indexed by frequency (up to n), place elements into buckets, then iterate from highest frequency to collect k elements. Time O(n), space O(n). Note it requires frequency as index and works when frequencies are bounded by n.
Summarize when each approach is preferable: naive for simplicity, heap for large m and small k, bucket for optimal time when memory allows. Mention that bucket sort is not comparison-based and leverages the frequency range.
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