Find top-k frequent elements with tiebreaks

Q: Find top-k frequent elements with tiebreaks

This question evaluates a candidate's skills in frequency counting, tie-breaking rules, data-structure selection, algorithmic time/space complexity analysis, combinatorial reasoning about frequency distributions, and robustness/input validation.

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Question

Given an array of elements and an integer k, return the k elements with highest frequency. If multiple elements share the same frequency, break ties by smaller numeric value (or lexicographically for strings). If k exceeds the number of unique elements, return all uniques. Discuss approaches using heaps versus bucket/ordering structures, and analyze time and space complexity. Follow-up 1: For an array of length n, derive the maximum possible number of distinct frequency values achievable across its unique elements and justify your formula. Follow-up 2: How would you validate and guard against invalid inputs (e.g., non-integers, negative k, extremely large n) while keeping the service robust?

Find top-k frequent elements with tiebreaks

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