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The hint about quicksort was actually what saved me.
Clarify the definition of median for even-sized lists and discuss the trade-offs between different selection algorithms. Propose using Quickselect (average O(n)) or Median of Medians (worst-case O(n)) to find the k-th smallest element(s) without fully sorting. If the list is small or nearly sorted, consider simpler approaches like sorting or heaps, but justify your choice based on constraints.
Pro tip: Mention that Quickselect can be optimized with random pivot selection to avoid worst-case O(n^2) on adversarial inputs, and that for streaming data, a heap-based approach might be more suitable. This shows awareness of practical considerations beyond textbook algorithms.
Ask about the definition of median for even-length lists, input size, memory constraints, and whether the input can be modified. This ensures you address the correct problem.
Select Quickselect for average O(n) performance or Median of Medians for guaranteed O(n). Explain why sorting (O(n log n)) is suboptimal.
Describe how partitioning works in Quickselect, how to handle even-length lists (find two middle elements), and how Median of Medians guarantees linear time.
State the average and worst-case time complexities, and note that Quickselect is in-place (O(1) extra space) while Median of Medians uses O(n) extra space.
Cover empty list, single element, duplicates, and potential optimizations like random pivot selection or using a heap for streaming data.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.