Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Amazon SWE interview with a warehouse inventory management problem that looked straightforward until the checkpoint constraints made it genuinely tricky. One question, but it had enough moving parts to keep me busy.

Questions Asked (1)

You're managing warehouse inventory over n days. Each day has a delta value that changes the inventory level. The inventory can never exceed a maximum capacity, and on any day where the delta is zero (a checkpoint day), the inventory must be non-negative. You can trigger an emergency restock on any day to bring inventory back to a valid state. What's the minimum number of restock days needed?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The part that tripped me up was figuring out when exactly to trigger a restock.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem constraints and define what constitutes a valid state, especially the role of checkpoint days. Then, model the inventory changes as a cumulative sum and identify the minimum number of restocks needed to keep the inventory within bounds and non-negative at checkpoints, likely using a greedy approach or dynamic programming.

Pro tip: Demonstrate awareness of edge cases such as multiple consecutive zero deltas or capacity violations, and discuss how your solution scales with large n. Mention that you would validate with small examples and consider trade-offs between time and space complexity.

1. Clarify the problem

Ask questions to confirm the exact rules: what is the initial inventory? Can it be negative initially? What does 'emergency restock' do exactly (set to zero, to capacity, or add a fixed amount)? Are there any constraints on when restocks can occur?

2. Define state and constraints

Represent the inventory level as a running sum of deltas. Identify the constraints: inventory must never exceed capacity, and on checkpoint days (delta=0) inventory must be >=0. A restock resets inventory to a valid state (e.g., 0 or capacity).

3. Identify necessary restocks

Scan through days and track the inventory. Whenever a constraint is about to be violated (e.g., inventory would exceed capacity or become negative on a checkpoint), a restock is needed. Use a greedy strategy: restock as late as possible to minimize count.

4. Prove optimality

Argue that the greedy choice is optimal: delaying a restock cannot increase the number of restocks needed because it only postpones the reset and may avoid unnecessary resets. Use exchange argument or induction.

5. Analyze complexity and edge cases

The algorithm runs in O(n) time and O(1) space. Discuss edge cases: all deltas zero, capacity=0, large positive/negative deltas, and multiple restocks on the same day (not allowed).

Key Points to Mention

Clarify the exact effect of a restock (e.g., set to 0, set to capacity, or add a fixed amount).
Model inventory as a cumulative sum and track violations of capacity and non-negativity at checkpoints.
Use a greedy approach: restock only when necessary, and as late as possible.
Prove that the greedy strategy yields the minimum number of restocks.
Discuss time and space complexity: O(n) time, O(1) space.
Consider edge cases: consecutive zero deltas, capacity=0, initial inventory, and large deltas.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.