My first instinct was brute force all pairs and pick greedily, which works but I spent too long second-guessing whether a node could appear in multiple pairs.
First clarify the problem constraints and edge cases, then propose a greedy algorithm that sorts the bandwidth array and pairs the largest values together to maximize the sum of each pair. Analyze the time and space complexity, and discuss potential optimizations or alternative approaches.
Pro tip: Demonstrate awareness of Amazon's leadership principles by explicitly discussing trade-offs between different approaches and how you would validate the solution with test cases, showing customer obsession and ownership.
Ask questions to confirm that each channel uses a unique pair of nodes, that all nodes can be used at most once, and that the goal is to maximize the total sum of bandwidths across all channels. Also check if the number of channels is fixed and if there are any constraints on array size or bandwidth values.
Recognize that to maximize the sum of pair sums, you should pair the largest bandwidth values together. This is because the sum of all selected elements is fixed if you select the top 2k elements, and pairing them arbitrarily yields the same total sum. However, if the problem requires each channel to have a unique pair and you can choose any nodes, the maximum total is simply the sum of the 2k largest bandwidths.
Sort the array in descending order and take the sum of the first 2k elements, where k is the number of channels. Alternatively, use a min-heap of size 2k to find the sum of the largest 2k elements in O(n log k) time. If the problem implies that each node can be used only once and you must form exactly k pairs, this approach works.
State the time complexity (O(n log n) for sorting or O(n log k) for heap) and space complexity (O(1) or O(k)). Discuss edge cases: k=0, insufficient nodes (n < 2k), negative bandwidths (if allowed), and duplicate values.
Walk through a small example to verify the approach. If needed, discuss whether a more efficient selection algorithm (like quickselect) could achieve O(n) average time. Also consider if the problem has hidden constraints that require a different interpretation.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.