Started with the brute force scan approach, O(n) per step, which works fine for small inputs.
First, restate the problem to ensure understanding, then discuss a naive simulation approach and its inefficiency. Next, propose an optimized solution using a max-heap for the highest stock and a data structure to track the minimum non-zero stock, analyzing time and space complexity.
Pro tip: Mention that in real-world scenarios like Amazon's inventory systems, such problems often require efficient data structures to handle large-scale data, and discussing trade-offs between different approaches demonstrates engineering maturity.
Restate the problem in your own words and ask clarifying questions about edge cases, such as what happens when multiple types have the same max stock, or when the minimum stock is zero.
Describe a straightforward simulation: for each rental, scan all types to find max and min non-zero, compute revenue, and decrement. Analyze its O(m*n) time complexity and why it's inefficient for large inputs.
Suggest using a max-heap to efficiently get the type with highest stock, and a min-heap (or balanced BST) to track the minimum non-zero stock. Explain how to update these structures after each decrement.
Derive the time complexity of the optimized approach, typically O((n + m) log n), and space complexity O(n). Compare with the naive approach to highlight improvement.
Discuss how to handle cases like all stocks becoming zero, ties for max stock, and ensuring the minimum non-zero is correctly identified when stocks change.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.