The leftmost-on-tie rule tripped me up more than I expected.
Clarify the problem constraints and edge cases, then propose an efficient algorithm using a priority queue to always select the smallest undeleted element, while tracking deletions with a doubly linked list or a boolean array. Analyze time and space complexity, and discuss potential optimizations or alternative approaches.
Pro tip: Demonstrate Amazon Leadership Principles by proactively discussing trade-offs between different data structures and considering scalability for large inputs. Also, walk through a small example to validate your approach before coding.
Restate the problem in your own words, ask clarifying questions about constraints (e.g., array size, element range, duplicates), and confirm the deletion rule: when an element is selected, its immediate original neighbors are deleted if not already deleted.
Recognize that you need to efficiently find the minimum among undeleted elements and support deletion of an element and its neighbors. This suggests using a min-heap for selection and a doubly linked list or union-find for tracking neighbors.
Propose using a min-heap of (value, index) pairs, and a doubly linked list to represent the current sequence of undeleted elements. When popping the heap, skip if already deleted; otherwise, add to total, mark as deleted, and delete its current left and right neighbors from the linked list.
Explain that each element is pushed and popped once, and each deletion is O(1) with the linked list, leading to O(n log n) time and O(n) space. Discuss if any further optimization is possible.
Walk through a small example (e.g., [3,1,2]) to verify the algorithm, and consider edge cases like all elements equal, single element, or already sorted array.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the problem constraints and edge cases, especially the temporary negative inventory rule. Then, model the problem as a greedy or dynamic programming task, focusing on when to refill to minimize refill days. Finally, discuss the algorithm's time and space complexity and potential optimizations.
Pro tip: Emphasize the importance of handling the temporary negative inventory correctly—many candidates overlook that only zero-change days require non-negative end-of-day inventory. Also, consider using a priority queue or greedy approach to decide refill days efficiently.
Restate the problem in your own words and ask clarifying questions about constraints, such as the range of daily changes, capacity limits, and whether refills can be done on any day including zero-change days.
Discuss edge cases like empty warehouse, capacity zero, large negative changes, and sequences that might make it impossible. Determine what makes the problem infeasible (e.g., a single day's change exceeds capacity).
Propose a greedy approach: simulate day by day, and when inventory would go below zero on a zero-change day, refill as late as possible (or as early as needed) to maximize future flexibility. Alternatively, consider dynamic programming if greedy fails.
Explain the time and space complexity of your approach. Compare greedy vs. DP in terms of efficiency and correctness, and justify your choice.
Walk through a few examples, including edge cases, to validate your algorithm. Mention how you would handle large inputs and ensure correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.