My first instinct was to just sort and index from the end, which works but they pushed back on efficiency pretty fast.
Start by clarifying the problem constraints (e.g., array size, value range, duplicates) and then present multiple solutions with trade-offs. Begin with a simple sorting approach, then optimize using a min-heap of size k or Quickselect for average O(n) time. Discuss time/space complexity and edge cases.
Pro tip: Mention that Quickselect has O(n) average time but O(n^2) worst-case, and that you can use randomized pivot selection or the median-of-medians algorithm to guarantee O(n) worst-case. This shows depth and awareness of practical considerations.
Ask about array size, value range, whether duplicates count as separate elements, and if the array can be modified. This ensures you understand the problem fully.
Suggest sorting the array and returning the element at index n-k. This is simple but O(n log n) time and O(1) extra space if in-place.
Use a min-heap of size k to keep track of the k largest elements. Iterate through the array, push elements, and if heap size exceeds k, pop the smallest. The root will be the k-th largest. Time O(n log k), space O(k).
Use the partition step from QuickSort to find the k-th largest in average O(n) time. Discuss pivot selection and worst-case O(n^2) with potential mitigation.
Compare time/space complexity of each approach and discuss when to use which (e.g., large n, small k, memory constraints). Mention edge cases like k=1, k=n, empty array, duplicates.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.