Amazon·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026Remote

Summary

Amazon SWE coding round, one algorithmic problem that looked manageable until I started thinking about the neighbor-update logic. Took a while to land on the right data structure combo.

Questions Asked (1)

You have an array treated as a circular sequence. Each round, pick the smallest remaining element, add it to a running total, then remove it and both of its current neighbors. Repeat until nothing is left. Return the total. What's your approach and what's the time complexity?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I got the greedy logic pretty fast, smallest element each round, sure.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints and edge cases first, then propose an efficient algorithm using a priority queue (min-heap) and a doubly linked list to simulate the circular array. Explain the time complexity as O(n log n) due to heap operations and justify why this is optimal for the given problem.

Pro tip: Demonstrate awareness of the trade-offs: a naive simulation would be O(n^2), but using a heap and linked list achieves O(n log n). Also, mention that the problem is similar to the 'optimal strategy for a game' but with a greedy twist, and discuss potential pitfalls like handling the circular structure and updating neighbors correctly.

1. Clarify the problem

Ask clarifying questions to ensure you understand the rules: Is the array circular? What if there are ties? Can elements be negative? What is the expected input size? This shows attention to detail and avoids misinterpretation.

2. Outline a naive approach

Briefly describe a straightforward simulation: repeatedly scan the array to find the minimum, remove it and its neighbors, and update the total. Mention its O(n^2) time complexity to set a baseline.

3. Propose an optimized approach

Suggest using a min-heap to efficiently retrieve the smallest element and a doubly linked list (or circular array with pointers) to maintain the circular structure and allow O(1) removal of neighbors. Explain how to handle the removal and update the heap.

4. Analyze time and space complexity

State that each element is inserted into the heap once and removed once, leading to O(n log n) time. The linked list and heap use O(n) space. Compare with the naive approach to highlight efficiency.

5. Discuss edge cases and trade-offs

Mention edge cases: n=1, n=2, all elements equal, negative numbers. Discuss potential optimizations or alternative data structures (e.g., balanced BST) and why the heap+linked list is suitable.

Key Points to Mention

Use a min-heap to efficiently get the smallest element in O(log n) time.
Maintain a doubly linked list to represent the circular array and enable O(1) removal of neighbors.
Handle the circular nature by connecting the last node to the first.
Time complexity: O(n log n) due to heap operations; space complexity: O(n).
Compare with naive O(n^2) approach to justify the optimization.
Consider edge cases like single element, two elements, and ties in values.

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