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

Intermediate
May 2026

Summary

Amazon SWE coding round with a combinatorics/optimization problem. Not a lot of context in what was shared but the problem itself was pretty gnarly.

Questions Asked (1)

Q1

Given a set of servers each with a reliability value and an availability value, find the maximum possible 'stability' of any subset of those servers. Return the answer modulo 10^9+7. For example, with reliability = [1, 2, 2] and availability = [1, 1, 3], what is the maximum stability?

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The modulo part threw me off more than the actual subset logic.

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AI HintsAI Generated

Suggested Approach

First, clarify the definition of 'stability' for a subset—likely the product of the sum of reliabilities and the minimum availability (or similar). Then, sort servers by availability in descending order and use a max-heap to maintain the largest reliabilities, computing the product at each step. Finally, return the maximum product modulo 10^9+7.

Pro tip: Always discuss trade-offs: sorting gives O(n log n) time, and using a heap ensures we efficiently track the top reliabilities. Mention that modulo is applied only at the end to avoid precision issues, but be prepared to handle large numbers with modular arithmetic.

1. Clarify the problem

Ask the interviewer to confirm the definition of 'stability' (e.g., sum of reliabilities times minimum availability) and any constraints on subset size.

2. Sort by availability

Sort the servers in descending order of availability so that as we iterate, the current availability is the minimum for any subset including the current server.

3. Use a min-heap for reliabilities

Iterate through the sorted servers, maintaining a min-heap of the largest reliabilities seen so far. If the heap size exceeds the number of servers considered, remove the smallest reliability.

4. Compute stability and track maximum

At each step, compute the product of the current availability and the sum of reliabilities in the heap, updating the maximum stability found.

5. Return modulo

After the loop, return the maximum stability modulo 10^9+7, ensuring to handle large numbers appropriately.

Key Points to Mention

  • Definition of stability: product of sum of reliabilities and minimum availability.
  • Sorting by availability to efficiently consider subsets where the current server has the minimum availability.
  • Using a heap to maintain the top k reliabilities for any subset size.
  • Time complexity: O(n log n) due to sorting and heap operations.
  • Space complexity: O(n) for the heap.
  • Modulo operation: apply only at the end to avoid unnecessary mod operations, but be aware of potential overflow in other languages.

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