Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Amazon SWE interview with a greedy algorithm problem that looked clean on the surface but had a tricky correctness proof hiding underneath. The kind of question where you can get to a working solution and still feel like you didn't fully nail it.

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 backup whose memory is at least as large. Maximize the total memory across all chosen primary servers. Walk through a sort-based greedy approach and justify why it's correct.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was right but I couldn't articulate why.

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AI HintsAI Generated

Suggested Approach

Sort the memory values, then use a greedy two-pointer strategy to pair the largest possible backups with the smallest possible primaries, ensuring each primary gets a backup at least as large. To maximize the sum of primaries, we want the largest n/2 values to be primaries, but we must verify that each can be paired with a backup from the smaller half. The optimal solution is to take the largest n/2 values as primaries and pair them with the smallest n/2 values as backups in sorted order.

Pro tip: Emphasize that the greedy choice is safe because any feasible solution can be transformed into the greedy one without decreasing the primary sum, and mention that this is a classic exchange argument. Also, note that the problem is equivalent to maximizing the sum of the larger half of a partition where each larger element is paired with a smaller or equal element.

1. Understand the problem and constraints

Restate the problem: given an even number of servers with memory values, split into two equal-sized groups (primary and backup) such that each primary is paired with a backup of >= memory. Maximize the sum of primary memories.

2. Sort the memory values

Sort the array of memory values in non-decreasing order. This allows us to reason about which elements can serve as backups for which primaries.

3. Identify the greedy choice

The optimal primary set is the largest n/2 elements. Pair the smallest primary with the smallest backup, the next smallest primary with the next smallest backup, and so on. This ensures each primary has a backup at least as large.

4. Prove correctness via exchange argument

Show that any feasible solution can be transformed into the greedy solution without decreasing the primary sum. If a smaller element is a primary while a larger element is a backup, swapping them maintains feasibility and does not decrease the sum.

5. Analyze complexity and edge cases

Sorting takes O(n log n) time and O(1) extra space (if in-place). The pairing is O(n). Discuss edge cases like all equal values or when the largest n/2 cannot be paired (but they always can because the smallest n/2 are <= the largest n/2).

Key Points to Mention

Sorting the array to enable greedy pairing.
The greedy strategy: take the largest n/2 elements as primaries and pair them with the smallest n/2 elements as backups in sorted order.
Correctness proof using an exchange argument: any optimal solution can be converted to the greedy one without loss.
Time complexity: O(n log n) due to sorting, and O(n) for pairing.
Space complexity: O(1) if sorting in-place, otherwise O(n) for the sorted copy.
Edge cases: all elements equal, or when the largest n/2 are exactly equal to the smallest n/2 (e.g., all same value).

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