My first instinct was to just sort it and index in, which works fine, but I spent a weird amount of time second-guessing whether they wanted something fancier like a quickselect.
Start by clarifying the problem: confirm whether k is 0-indexed or 1-indexed, and discuss trade-offs between sorting the entire array (O(n log n)) and using a selection algorithm like Quickselect (average O(n)). Then present a solution, ideally Quickselect, explaining its partitioning logic and handling edge cases.
Pro tip: Mention that Quickselect can be optimized with random pivot selection or median-of-medians for worst-case O(n), and note that for small arrays or when simplicity is preferred, sorting might be acceptable. This shows awareness of practical engineering trade-offs.
Ask about indexing (0-based or 1-based), input constraints (array size, value range), and whether the array can be modified. Confirm expected time/space complexity.
Mention sorting the array and returning the element at index k. This takes O(n log n) time and O(1) extra space (if in-place) or O(n) if copying.
Introduce Quickselect: partition the array around a pivot, then recursively search only the side containing the k-th element. Average time O(n), worst-case O(n^2) without optimizations.
Describe partitioning (e.g., Lomuto or Hoare), pivot selection (random or median-of-medians), and how to handle duplicates. Walk through a small example.
State time and space complexity, and discuss edge cases: k out of bounds, empty array, all equal elements. Mention that median-of-medians guarantees O(n) worst-case.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.