Classic problem, you'd think it's easy but there's a real choice to make between a min-heap of size k versus sorting the whole thing.
Clarify the problem constraints (e.g., array size, k value, duplicates) and then propose using a min-heap of size k to efficiently find the k largest elements. Explain the algorithm step-by-step, analyze its time and space complexity, and discuss potential optimizations or alternative approaches.
Pro tip: Mention that a min-heap of size k is optimal for streaming data or when k is much smaller than n, and be prepared to discuss trade-offs with quickselect (average O(n) but worst-case O(n^2)).
Ask about input size, range of values, whether k is guaranteed valid, and if the output needs to be sorted. This shows attention to detail and helps tailor the solution.
Select a min-heap of size k because it allows efficient tracking of the k largest elements by keeping the smallest among them at the root for easy replacement.
Iterate through the array: push each element onto the heap; if heap size exceeds k, pop the smallest. At the end, the heap contains the k largest elements.
State that time complexity is O(n log k) and space complexity is O(k). Compare with sorting (O(n log n)) and quickselect (average O(n)).
Cover cases like k=0, k>=n, duplicates, and negative numbers. Mention that if the output must be sorted, an extra O(k log k) step is needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.