I went straight for the heap solution because it felt safer under pressure, and the interviewer immediately asked me to do it with quickselect instead.
Start by clarifying constraints (e.g., array size, value range, duplicates, memory limits) and then present multiple solutions: sorting, min-heap of size k, and Quickselect. Compare their time/space trade-offs and recommend Quickselect for average O(n) time, but mention heap for guaranteed O(n log k) and streaming scenarios.
Pro tip: Meta interviewers value practical trade-offs: mention that Quickselect has O(n) average but O(n^2) worst-case, and that you can use a randomized pivot or Median of Medians to avoid worst-case. Also, note that for small k, a heap is often faster in practice due to lower constant factors.
Ask about input size, value range, duplicates, whether the array can be modified, and memory constraints. This determines which approach is optimal.
Outline at least three methods: sorting (O(n log n)), min-heap of size k (O(n log k)), and Quickselect (average O(n)). Briefly explain each.
Compare time and space complexity, stability, and practicality. Discuss when each approach is preferable (e.g., heap for streaming data, Quickselect for in-memory large arrays).
Write clean code for the most suitable approach, handling edge cases like k=1, k=n, and duplicates. Use randomization for Quickselect to avoid worst-case.
Walk through examples, test edge cases, and discuss potential optimizations (e.g., early termination in Quickselect, using a max-heap for small n-k).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is the streaming follow-up and I actually saw it coming, which was a relief.
Clarify that this is a streaming data problem where we need to maintain the k-th largest element dynamically. Propose using a min-heap of size k to efficiently track the k largest elements seen so far, with O(log k) insertion and O(1) retrieval. Discuss trade-offs with other approaches like sorted containers or balanced BSTs, and consider edge cases like k > number of elements.
Pro tip: Mention that you can optimize for the common case where k is small by using a min-heap, but if k is large or queries are frequent, consider a balanced BST or order-statistic tree. Also, discuss how to handle duplicates and whether the k-th largest is distinct or not.
Ask whether k is fixed or can change, whether elements can be negative, and if duplicates count as separate. Confirm that we need to return the k-th largest after each insertion.
Select a min-heap of size k to store the k largest elements. The root will be the k-th largest. Alternatively, consider a balanced BST if k is large or we need order statistics.
For each new element, if heap size < k, push it. Else if element > heap root, pop root and push element. Otherwise, ignore. This maintains the k largest elements.
After each insertion, if heap size == k, return heap root as the k-th largest. If heap size < k, return null or indicate insufficient elements.
Insertion is O(log k), retrieval O(1). Discuss edge cases: k=1 (max heap), k > stream length, duplicates, and memory usage.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.