The key click for me was sorting the array descending and then pairing adjacent elements, treating the larger as primary and the smaller as backup.
Sort the array in ascending order. Then, pair the largest elements as Primary with the next largest as Backup, ensuring each Primary is ≤ its Backup. To maximize total Primary memory, consider pairing the smallest possible Backup for each Primary, which can be achieved by iterating from the end and greedily selecting pairs.
Pro tip: Clarify that the goal is to maximize the sum of Primary memories, not the total memory of all servers. Also, mention that if the array length is odd, one server must be left out, and it should be the smallest to maximize the sum.
Restate the problem: Given an array of memory sizes, select pairs (Primary, Backup) such that Primary ≤ Backup, and maximize the sum of Primary memories. The total number of servers used must be even, so if the array length is odd, one server is unused.
Sort the memory sizes in ascending order. This helps in efficiently pairing servers where each Primary is paired with a Backup of equal or greater memory.
To maximize the sum of Primary memories, we want the largest possible elements to be Primary. However, each Primary needs a Backup ≥ itself. A greedy approach: pair the largest element as Backup with the second largest as Primary, then the third largest as Backup with the fourth largest as Primary, and so on. This ensures each Primary is ≤ its Backup and maximizes the sum of Primaries.
If the array length is odd, the smallest element will be left out. This is optimal because leaving out a larger element would reduce the potential sum of Primaries.
Sum the elements at even indices (0-based) from the sorted array, starting from the second element if length is odd? Actually, after sorting, if we pair from the end, the Primaries are at indices n-2, n-4, ... So sum those.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.