The key thing they're probing is whether you reach for a min-heap of size k instead of sorting the whole array.
Clarify that since N is much larger than k, we should avoid sorting the entire array. Instead, use a min-heap of size k to efficiently track the k largest elements in O(N log k) time and O(k) space, or consider Quickselect for O(N) average time if modifying the array is acceptable.
Pro tip: Mention that for very large N, a streaming approach with a min-heap is often preferred because it handles data that doesn't fit in memory and provides predictable performance. Also, discuss the trade-offs between heap and Quickselect, including worst-case time and space.
Confirm that the array is unsorted, elements can be compared, and we only need the k largest without sorting. Ask about memory constraints, whether the array can be modified, and if the data is streaming.
Explain that we can maintain a min-heap of size k, iterating through the array: if the heap has fewer than k elements, add the current element; otherwise, if the current element is larger than the heap's minimum, replace it. At the end, the heap contains the k largest elements.
State that the heap approach takes O(N log k) time and O(k) space, which is efficient when N >> k. Compare with sorting (O(N log N)) and Quickselect (O(N) average, O(N^2) worst-case).
Mention Quickselect (or introselect) as an alternative that can achieve O(N) average time and O(1) extra space if in-place partitioning is allowed, but note its worst-case O(N^2) time and that it modifies the array.
Based on constraints, recommend the min-heap for its balance of efficiency, simplicity, and suitability for streaming or large data. If the array can be modified and average-case performance is acceptable, Quickselect is also viable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.