Amazon·Software Engineer·Onsite - Coding / Algorithms·Intermediate

Intermediate

Jun 2026

Summary

Amazon SWE coding round with a simulation/heap problem that looks deceptively straightforward but has a subtle edge case hiding in it. Decent problem overall, made me think harder than I expected about minimum tracking.

Questions Asked (1)

You have n VM types each with an initial stock count. m customers arrive sequentially, and each picks the VM type with the highest current stock. The profit for that rental is (current max stock) + (current minimum non-zero stock), and then that VM type's stock drops by 1. What's the total profit after all m rentals?

Algorithms & Data Structures

Author's notes

I got the max-heap part pretty quickly, that felt natural.

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AI HintsAI Generated

Suggested Approach

Model the process as a greedy simulation where we repeatedly select the VM type with the maximum stock, compute the profit as max + min non-zero, and decrement that stock. To handle large n and m efficiently, use a max-heap for the maximum and a min-heap (or balanced BST) for the minimum non-zero, updating both after each rental.

Pro tip: Clarify edge cases upfront: if all stocks become zero before m rentals, the process stops; also discuss how to handle ties when multiple VM types have the same max stock. This shows attention to detail and robustness.

1. Understand the problem and constraints

Restate the problem: n VM types with initial stock, m customers, each picks the VM type with the highest current stock. Profit per rental = current max stock + current min non-zero stock. After rental, that VM type's stock decreases by 1. Ask about constraints (n, m, stock values) to determine if simulation is feasible.

2. Design a data structure for efficient max and min queries

Use a max-heap to track the VM type with the highest stock, and a min-heap (or balanced BST) to track the minimum non-zero stock. Both heaps store (stock, type) pairs and support updates when a stock changes.

3. Simulate the rentals

For each of the m customers: extract the max from the max-heap, find the current min non-zero (from the min-heap, skipping zeros), compute profit, decrement the max type's stock, and update both heaps. If all stocks become zero, stop early.

4. Handle edge cases and optimizations

Consider cases where multiple types have the same max stock (tie-breaking doesn't affect profit), and when the min non-zero is the same as the max (if only one type has non-zero stock). Discuss lazy deletion for heaps to avoid O(n) updates.

5. Analyze time and space complexity

Each rental involves O(log n) heap operations, so total time O(m log n). Space O(n) for the heaps. If m is large, this is efficient. Mention potential optimizations if needed.

Key Points to Mention

Greedy simulation is correct because the choice is deterministic (always pick max stock).
Use of max-heap and min-heap to efficiently get max and min non-zero.
Handling of zero stocks: min-heap must skip zeros; if all zero, stop.
Tie-breaking when multiple VM types have the same max stock: any choice yields same profit.
Time complexity: O(m log n) with heap operations; space O(n).
Edge cases: m larger than total stock, initial stocks all zero, n=1.

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