Took me a while to get past the cloud server flavor text and see what the actual problem was.
First, clarify the problem constraints and edge cases. Then, sort the server capacities and use a greedy two-pointer approach to pair each primary with a backup of at least equal capacity, ensuring the primary is the smaller in each pair. Finally, analyze the time complexity and discuss potential optimizations.
Pro tip: Demonstrate awareness of Amazon's leadership principles by explicitly discussing trade-offs between time and space complexity, and by validating your solution with edge cases like duplicate capacities or odd number of servers.
Ask questions to confirm: Can servers be partitioned arbitrarily? Is it required that each primary has a unique backup? What if n is odd? Are capacities integers? This ensures you understand the exact requirements.
Sort the capacities in ascending order. Use two pointers: one starting at the beginning (for primaries) and one at the middle (for backups). Pair the smallest available primary with the smallest backup that is >= it, ensuring the primary is always the smaller in the pair.
By always choosing the smallest possible backup for each primary, you leave larger capacities for other primaries, thereby maximizing the total sum of primaries. This greedy choice is optimal.
Sorting takes O(n log n). The two-pointer pass takes O(n). Space complexity is O(1) if sorting in-place, or O(n) if using extra space. Discuss if a more efficient approach exists.
Test with small examples, including edge cases like all equal capacities, strictly increasing, or odd n (if allowed). Confirm the sum is maximized and all conditions are met.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.