Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jul 2026

Summary

Amazon SWE interview with a tricky optimization problem about maximizing total bandwidth across ordered node pairs. The problem looked approachable at first but the constraints pushed you toward something smarter than brute force.

Questions Asked (1)

You have n processing nodes each with a bandwidth value. You need to select exactly streamCount distinct ordered pairs (i, j) of nodes, where each pair contributes bandwidth[i] + bandwidth[j] to a total sum. Pairs (i, j) and (j, i) count as different, and i == j is allowed. Maximize the total sum across all selected pairs. Your solution must handle n and streamCount up to around 10^5 efficiently, not by enumerating all n^2 pairs.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The setup sounds like a greedy problem and it basically is, but I kept second-guessing myself on the i==j case and whether that changes the counting.

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AI HintsAI Generated

Suggested Approach

Recognize that the maximum sum is achieved by repeatedly selecting the top two bandwidth values, since each pair contributes the sum of two nodes and the largest sums come from the largest values. Use a max-heap or sort the bandwidth array to efficiently extract the top two values, then compute the total by multiplying the sum of the top two by streamCount, handling the case where the top two are the same node by allowing i == j. This yields an O(n log n) or O(n) solution, well within the constraints.

Pro tip: Clarify that pairs are ordered and i == j is allowed, so the optimal strategy is to always pick the two highest bandwidth nodes (even if they are the same) for every pair; this simplifies the problem to a constant-time computation after finding the top two values.

1. Understand the problem and constraints

Restate the problem: select exactly streamCount ordered pairs (i, j) to maximize the sum of bandwidth[i] + bandwidth[j], with i == j allowed. Note that n and streamCount can be up to 10^5, so O(n^2) enumeration is infeasible.

2. Identify the optimal selection strategy

Observe that each pair's contribution is the sum of two bandwidth values. To maximize the total, every pair should use the two largest bandwidth values available, since any other choice would yield a smaller or equal sum. Because pairs are independent and ordered, we can reuse the same two nodes for all pairs.

3. Find the top two bandwidth values efficiently

Scan the bandwidth array once to find the largest and second largest values (or sort the array). This takes O(n) time and O(1) extra space. Handle duplicates and the case where the largest value appears multiple times.

4. Compute the total sum

The maximum sum per pair is the sum of the top two values (which may be the same node if it is the unique maximum). Multiply this sum by streamCount to get the total. Ensure the result fits in a 64-bit integer.

5. Analyze complexity and edge cases

State that the solution runs in O(n) time and O(1) space, which is optimal. Discuss edge cases: n=1 (only one node, so all pairs are (0,0)), streamCount=0 (sum=0), and large values causing overflow.

Key Points to Mention

Greedy choice: always pick the two highest bandwidth nodes for every pair.
Ordered pairs and i == j allowed means we can reuse the same node multiple times.
Efficient top-two selection using a single pass or sorting, avoiding O(n^2) enumeration.
Time complexity O(n) and space complexity O(1) after reading input.
Use 64-bit integers to prevent overflow when summing up to 10^5 pairs of values up to 10^5.
Edge cases: n=1, streamCount=0, duplicate maximum values.

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