Classic problem but there are a few ways to go at it and picking the right one under pressure is where people slip up.
Start by clarifying constraints (e.g., array size, value range, duplicates, memory limits) and then present multiple solutions: sorting (O(n log n)), min-heap of size k (O(n log k)), and Quickselect (average O(n)). Emphasize Quickselect as the optimal average-case solution, explaining its partitioning logic and handling of duplicates, then discuss trade-offs and edge cases.
Pro tip: Mention that Quickselect's worst-case O(n^2) can be avoided with a randomized pivot or Median of Medians, and note that for small k a max-heap of size k is often more practical due to guaranteed O(n log k) and lower constant factors.
Ask about input size, value range, duplicates, memory limits, and whether the array can be modified. This shows you consider practical constraints before diving into algorithms.
Outline at least three methods: sorting, heap-based, and Quickselect. Briefly state their time and space complexities to demonstrate breadth of knowledge.
Explain Quickselect in detail: choose a pivot, partition the array, and recurse on the appropriate side. Discuss average O(n) time and how to handle duplicates (e.g., three-way partitioning).
Cover edge cases like k=1, k=n, empty array, and duplicates. Mention randomized pivot or Median of Medians to avoid worst-case O(n^2).
Summarize when to use each approach: Quickselect for average-case efficiency, heap for streaming or when k is small, sorting for simplicity. Highlight that Quickselect modifies the array.
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