The example in the problem says 3+3=6 which is clearly a typo (should be 3+4=7...
Sort the array, then pair the smallest half with the largest half to maximize the sum of the larger elements. The primary group consists of the larger elements from each pair, ensuring each has a backup with equal or greater memory.
Pro tip: After sorting, the optimal primary group is simply the second half of the sorted array. This greedy pairing is optimal because any other pairing would force a larger element to be a backup for a smaller one, reducing the total primary memory.
Clarify that we need to partition the array into two equal-sized groups (primary and backup) such that each primary has a backup with memory >= primary's memory, and the sum of primary memories is maximized.
Sort the memory capacities in non-decreasing order. This allows us to easily pair smaller elements with larger ones.
Pair the first half (smallest n/2 elements) with the second half (largest n/2 elements) in order: smallest with smallest of the larger half, etc. This ensures each primary (from the larger half) has a backup (from the smaller half) with <= memory.
The primary group is the second half of the sorted array. Sum these elements to get the maximum total primary memory.
Test with small examples to confirm the greedy approach works and consider edge cases like duplicate values.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.