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

Intermediate
May 2026

Summary

Amazon SWE interview that leaned heavily on algorithms and system design. Two meaty problems back to back, both with follow-ups on concurrency and trade-offs that I wasn't fully ready for.

Questions Asked (2)

Q1

Using a sliding window approach, design an algorithm to find the maximum sum of any contiguous subarray of length k. Walk through the time and space complexity, and explain how you'd adapt it for concurrent execution.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The sliding window part itself was fine, add the new element drop the old one, O(n) time O(1) space, standard stuff.

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AI HintsAI Generated

Suggested Approach

Start by clearly explaining the sliding window technique for finding the maximum sum of a contiguous subarray of length k, then analyze time and space complexity, and finally discuss how to adapt the algorithm for concurrent execution by partitioning the array and combining results.

Pro tip: Emphasize that the sliding window approach reduces time complexity from O(n*k) to O(n), and when discussing concurrency, highlight the importance of handling overlapping windows and minimizing synchronization overhead.

1. Explain the Sliding Window Algorithm

Describe how to compute the sum of the first k elements, then slide the window by subtracting the element leaving the window and adding the new element, updating the maximum sum.

2. Analyze Time and Space Complexity

State that the time complexity is O(n) because each element is processed once, and space complexity is O(1) as only a few variables are used.

3. Discuss Concurrency Adaptation

Propose partitioning the array into chunks, computing local maximum sums in parallel, and then combining results while handling boundary overlaps between chunks.

4. Address Trade-offs and Edge Cases

Mention potential issues like load balancing, synchronization overhead, and edge cases such as k > n or negative numbers, and how to handle them.

Key Points to Mention

  • Sliding window technique reduces redundant computations by reusing the previous sum.
  • Time complexity O(n) and space complexity O(1) for the sequential version.
  • Concurrent execution can be achieved by dividing the array into segments and processing them in parallel.
  • Boundary handling: ensure windows that cross segment boundaries are considered when combining results.
  • Synchronization overhead and load balancing are key considerations in concurrent adaptation.
  • Edge cases: k larger than array length, empty array, or all negative numbers.

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

Q2

Design a system to maintain the running median of the last k integers in a real-time data stream. Which data structures would you use, and what are the trade-offs between them?

Algorithms & Data StructuresSystem DesignTechnical Trade-offs
Author's notes

Two heaps is the obvious answer and I went there immediately, a max-heap for the lower half and a min-heap for the upper half.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (e.g., k size, data types, update frequency) and then propose a solution using two heaps (max-heap for lower half, min-heap for upper half) to maintain the median in O(log k) per insertion. Discuss the trade-offs with alternative approaches like a balanced BST, sorted list, or order-statistic tree, and explain how to handle the sliding window of last k integers.

Pro tip: Mention that for a sliding window, you need to handle deletions, which complicates the two-heap approach; consider using a balanced BST with node counts or a Fenwick tree over a compressed value range for O(log k) updates and median queries.

1. Clarify requirements and constraints

Ask about the size of k, the range of integers, the rate of incoming data, and whether deletions are needed (sliding window). This determines the appropriate data structure.

2. Propose a baseline solution

Describe the two-heap approach for a static stream (no deletions) and explain how it maintains the median in O(log k) per insertion and O(1) median retrieval.

3. Address the sliding window challenge

Explain that deletions from the heaps are non-trivial; propose alternatives like a balanced BST with subtree sizes, an order-statistic tree, or a Fenwick tree with coordinate compression to support O(log k) insert, delete, and median queries.

4. Compare trade-offs

Discuss time and space complexity, implementation complexity, and suitability for real-time constraints for each data structure (heaps, BST, Fenwick tree, sorted list).

5. Summarize and recommend

Based on the constraints, recommend the most appropriate data structure and justify your choice, mentioning any optimizations like lazy deletion or bucketing.

Key Points to Mention

  • Two-heap approach: max-heap for lower half, min-heap for upper half, balancing to keep sizes within 1.
  • Sliding window requires deletions; heaps alone are inefficient for arbitrary deletions.
  • Balanced BST (e.g., Red-Black Tree) with node counts supports O(log k) insert, delete, and median query.
  • Fenwick tree (Binary Indexed Tree) with coordinate compression for O(log k) updates and median via binary search.
  • Trade-offs: heaps are simple but don't support deletion; BST and Fenwick are more complex but handle sliding window efficiently.
  • Space complexity: O(k) for all approaches; time complexity: O(log k) per operation for BST/Fenwick, O(k) for sorted list.

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