Maximum Number of Eaten Apples (Priority Queue)
Given the number of apples growing each day and how long they stay fresh, find the maximum number of apples you can eat. Use a Min-Heap based on expiration date.
Why Interviewers Ask This
Airbnb asks this problem to evaluate a candidate's ability to optimize resource allocation under strict temporal constraints. It specifically tests mastery of Priority Queues for greedy scheduling, as managing perishable inventory requires selecting the most urgent items first. The interviewer looks for candidates who can translate a real-world logistics challenge into an efficient algorithmic solution without over-engineering.
How to Answer This Question
1. Clarify Constraints: Immediately confirm if apples can be eaten on their expiration day and how daily growth interacts with existing stock.
2. Define the Greedy Strategy: Explain that to maximize consumption, you must always eat the apple expiring soonest to prevent waste.
3. Select Data Structure: Propose a Min-Heap storing pairs of (expiration_date, count) to efficiently retrieve the earliest expiring batch.
4. Simulate Day-by-Day: Outline a loop iterating through days, adding new apples to the heap and removing expired ones before consuming one unit.
5. Handle Edge Cases: Discuss scenarios where the heap is empty or when the simulation continues beyond the input array length due to remaining fresh apples.
6. Analyze Complexity: Conclude by stating Time Complexity is O(N log N) due to heap operations and Space Complexity is O(N) for the heap storage.
Key Points to Cover
- Explicitly state the greedy choice property: always pick the item with the earliest deadline.
- Demonstrate correct handling of the expiration condition (current day >= expiration day).
- Justify the Min-Heap selection based on the need for O(log N) retrieval of minimum values.
- Address the scenario where the simulation extends beyond the input array duration.
- Clearly articulate the Time and Space complexity analysis.
Sample Answer
To solve the Maximum Number of Eaten Apples problem, I would approach it using a greedy strategy supported by a Min-Heap. The core logic is that we should always consume the apples that are closest to spoiling to minimiz…
Common Mistakes to Avoid
- Failing to remove expired apples from the heap before processing, leading to counting invalid items.
- Using a simple list or sorting every day instead of a heap, resulting in inefficient O(N^2) performance.
- Incorrectly handling the case where multiple apples expire on the same day without tracking counts.
- Stopping the simulation immediately after the input array ends, ignoring remaining fresh apples in the heap.
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