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

IntermediatePrefer not to say

Apr 2026

Summary

Amazon SWE coding round, one algorithmic problem about server memory partitioning. The constraint was tight enough that a naive approach would've timed out, so they wanted you to think carefully about efficiency.

Questions Asked (1)

You have an even number of servers, each with a memory value. Split them into equal-sized primary and backup groups such that every primary is paired with a distinct backup whose memory is at least as large. Maximize the total memory of all primary servers. Your solution needs to run well under O(n^2).

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

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AI HintsAI Generated

Suggested Approach

Sort the memory values and use a greedy two-pointer approach to pair the smallest possible backup with each primary, ensuring feasibility. To maximize the sum of primaries, consider binary searching on the minimum primary value or using a priority queue to select the largest possible primaries while maintaining a valid matching.

Pro tip: Always discuss the trade-offs between different approaches (e.g., sorting vs. heap) and mention that the greedy choice is optimal because it preserves larger backups for larger primaries.

1. Understand the problem and constraints

Clarify that we need to partition 2n servers into n primaries and n backups, with each primary paired to a distinct backup of >= memory, maximizing sum of primaries. Note the requirement for sub-O(n^2) time.

2. Sort and analyze pairing feasibility

Sort the memory array. For a given set of primaries, a valid pairing exists if and only if after sorting, each primary can be matched to a backup with >= memory. This can be checked greedily.

3. Determine optimal primary selection

To maximize sum, we want the largest possible values as primaries, but they must be pairable. Use binary search on the minimum primary value or a max-heap to iteratively select the largest feasible primary.

4. Implement efficient algorithm

Use sorting (O(n log n)) and two pointers or a priority queue to achieve O(n log n) time. For example, sort, then use a min-heap to track backups and select primaries from largest to smallest.

5. Validate with examples and edge cases

Test with small cases, duplicates, and extreme values. Ensure the algorithm handles all even n and returns the maximum sum.

Key Points to Mention

Sorting the array to enable efficient pairing and selection.
Greedy matching: pair the smallest possible backup with each primary to preserve larger backups.
Binary search on the answer (minimum primary value) to find the optimal threshold.
Using a priority queue (min-heap) to efficiently select backups for primaries.
Time complexity: O(n log n) due to sorting and heap operations, which is well under O(n^2).
Proof of optimality: exchange argument showing that any optimal solution can be transformed to the greedy one without decreasing the sum.

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