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Went with quickselect after briefly mentioning the heap approach.
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 the choice based on expected input and system constraints.
Pro tip: Mention that Quickselect has O(n) average but O(n^2) worst-case, and you can avoid the worst-case by using a randomized pivot or the Median of Medians algorithm. Also, note that for streaming data or when k is small, a heap is more practical.
Ask about input size, value range, whether duplicates count as separate elements, and if the array can be modified. This shows you consider edge cases and practical limits.
Suggest sorting the array and returning the element at index n-k. This is simple and O(n log n) time, O(1) extra space if in-place, but may be inefficient for large n.
Explain using a min-heap of size k: iterate through the array, push elements, and if heap size exceeds k, pop the smallest. At the end, the heap root is the kth largest. This is O(n log k) time and O(k) space, good for large n and small k.
Describe the Quickselect algorithm: partition the array around a pivot, then recursively search the side that contains the kth largest. Average O(n) time, worst-case O(n^2), but can be mitigated with random pivots.
Discuss when to use each approach: sorting for simplicity, heap for streaming or small k, Quickselect for optimal average time when the array can be modified. Mention that Quickselect modifies the array, which may not be allowed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use Union-Find (Disjoint Set Union) to dynamically track connected components as cells are added. For each operation, mark the cell as land, increment the island count, then union with any adjacent land cells, decrementing the count for each successful union. This yields O(1) amortized time per operation.
Pro tip: Mention that Union-Find with path compression and union by rank is optimal here, and briefly discuss how you'd handle edge cases like duplicate operations or out-of-bounds cells. Also, note that a DFS/BFS approach would be too slow due to repeated traversals.
Confirm the grid dimensions, operation sequence format, and whether operations can be duplicate or invalid. Ask about expected time/space complexity.
Select Union-Find (Disjoint Set Union) to efficiently manage connected components. Explain why it's better than BFS/DFS for dynamic updates.
Initialize a DSU for all cells. For each operation, if the cell is already land, skip; otherwise, set to land, increment island count, and union with adjacent land cells, decrementing count on each successful union.
State that each operation is nearly O(1) amortized, total O(k α(mn)). Discuss handling duplicates, out-of-bounds, and initial empty grid.
Walk through a small example (e.g., 3x3 grid with a few operations) to demonstrate correctness and update of island count.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.