My first instinct was a hash map for counts, then sort with a custom comparator.
Clarify the problem constraints and edge cases, then propose a solution using a hash map to count frequencies, followed by sorting the distinct elements with a custom comparator. Discuss the time and space complexity and consider potential optimizations or alternative approaches.
Pro tip: Mention that you can achieve O(n log n) time by sorting the distinct elements, but if the frequency range is small, you could use bucket sort to get O(n) time. This shows awareness of trade-offs and optimization.
Ask about input size, range of integers, and whether the array can be empty or contain duplicates. Confirm that output should be distinct elements sorted by decreasing frequency and increasing value for ties.
Use a hash map to count the frequency of each distinct element in O(n) time.
Extract the distinct elements and sort them using a custom comparator: primarily by decreasing frequency, and for equal frequencies, by increasing value.
State that the sorting step takes O(d log d) where d is the number of distinct elements, leading to O(n + d log d) overall. Mention that bucket sort can achieve O(n) if frequencies are bounded.
Walk through a small example to verify correctness, such as [4,4,4,2,2,1,1,1,3] resulting in [4,1,2,3].
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.