Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jul 2026

Summary

Amazon SWE interview with a geometry/sorting problem. Pretty standard coding round, nothing too wild.

Questions Asked (1)

Given a list of points on a 2D plane, find the K points closest to the origin.

Algorithms & Data Structures

Author's notes

My first instinct was to sort by distance and call it a day, which works but they pushed on the time complexity pretty fast.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints (e.g., input size, duplicates, tie-breaking) and then propose an efficient solution using a max-heap of size K to track the K closest points, achieving O(n log K) time. Discuss alternative approaches like sorting or quickselect, and analyze trade-offs.

Pro tip: Mention that you avoid computing square roots by comparing squared distances, and discuss how to handle ties or duplicate points to show attention to edge cases.

1. Clarify requirements and constraints

Ask about input size, whether points can be duplicated, how to handle ties, and if the output order matters. This ensures you understand the problem fully before coding.

2. Choose an efficient algorithm

Propose using a max-heap of size K to maintain the K closest points seen so far, iterating through all points. This gives O(n log K) time and O(K) space, which is optimal for large n and small K.

3. Implement the solution

Write code that computes squared distances (avoiding sqrt), uses a heap (e.g., priority queue) to keep the K smallest distances, and returns the points. Handle edge cases like K >= n or empty input.

4. Analyze complexity and trade-offs

Explain time and space complexity of your approach and compare with alternatives like sorting (O(n log n)) or quickselect (O(n) average). Discuss when each might be preferable.

5. Test with examples and edge cases

Walk through a small example, test with duplicate points, points at the same distance, and K equal to the number of points. Verify correctness and performance.

Key Points to Mention

Use squared Euclidean distance to avoid unnecessary square root calculations.
Max-heap of size K for O(n log K) time complexity, which is efficient for large n and small K.
Alternative approaches: sorting all points by distance (O(n log n)) or quickselect (O(n) average).
Handling ties: if multiple points have the same distance, any K of them is acceptable unless specified otherwise.
Space complexity: O(K) for the heap, which is optimal.
Edge cases: empty input, K=0, K >= n, duplicate points.

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