I started with sorting because it's the easiest to reason about, but they pushed back pretty fast asking if I could do better.
Start by clarifying the problem constraints (e.g., array size, duplicates, k validity) and then present multiple approaches: sorting, min-heap, and quickselect. Compare their time/space complexities and trade-offs, then implement the partition-based quickselect algorithm from scratch, explaining each step and handling edge cases.
Pro tip: Mention that quickselect has O(n) average time but O(n^2) worst-case, and that randomizing the pivot or using median-of-medians can guarantee O(n) worst-case. Also, note that for small k, a min-heap of size k is often more practical in real systems due to predictable performance and streaming capability.
Ask about input size, range of values, duplicates, and whether k is guaranteed valid. Confirm if the array can be modified and if additional space is allowed.
Outline sorting (O(n log n)), min-heap of size k (O(n log k)), and quickselect (O(n) average). Compare their time/space complexities and suitability for different scenarios.
Describe the partition-based selection: choose a pivot, partition the array, and recursively search only the side containing the k-th largest. Emphasize average O(n) time and in-place nature.
Write code for the partition function (e.g., Lomuto or Hoare) and the recursive/iterative quickselect. Handle edge cases like k=1, k=n, and duplicates.
Summarize time/space complexity, worst-case scenarios, and optimizations (random pivot, median-of-medians). Discuss when to prefer heap or sorting.
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