My first instinct was to sort it and index from the end, which works but they pushed back on complexity pretty fast.
Start by clarifying the problem constraints (e.g., array size, memory limits, whether the array can be modified) and then present multiple solutions with trade-offs. Focus on the optimal heap-based approach (O(n log k)) and the Quickselect algorithm (average O(n)), explaining when each is appropriate. Conclude by discussing data structure choices and their impact on time/space complexity.
Pro tip: At Meta, interviewers value practical trade-offs: mention that Quickselect has poor worst-case performance (O(n^2)) and that a heap guarantees O(n log k) but uses O(k) space. Also, note that for small K, a min-heap of size K is more memory-efficient than sorting the entire array.
Ask about input size, memory limits, whether the array can be modified, and if K is guaranteed valid. This shows you consider edge cases and scalability.
Mention that sorting the array takes O(n log n) time and then indexing gives the answer, but it's inefficient for large n. This sets a baseline for comparison.
Explain using a min-heap of size K: iterate through the array, push elements, and if size exceeds K, pop the smallest. The root will be the Kth largest. Time: O(n log k), Space: O(k).
Describe Quickselect (based on QuickSort partition): pick a pivot, partition, and recurse on the side containing the Kth largest. Average O(n) time, worst-case O(n^2), and O(1) extra space if done in-place.
Discuss trade-offs: heap is better for streaming data or when K is small; Quickselect is faster on average for static arrays but has worst-case risk. Mention that a heap is more predictable and easier to implement.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.