My first instinct was some kind of greedy but I spent too long second-guessing whether I needed dynamic programming.
Sort the array, then use a greedy two-pointer strategy: pair the smallest available server as primary with the smallest server that can serve as its backup, ensuring the backup is at least as large. This maximizes the sum of primaries by always assigning the smallest possible backup to each primary, leaving larger servers available as primaries.
Pro tip: Clarify edge cases upfront, such as odd-length arrays (one server left unpaired) and duplicate memory values, and discuss how your solution handles them. Also, mention that the greedy approach is optimal because any other pairing would either reduce the primary sum or violate the backup constraint.
Restate the problem: pair servers such that in each pair, backup memory ≥ primary memory, and maximize the sum of primary memories. Ask clarifying questions about input size, duplicates, and odd-length arrays.
Sort the server memory values in non-decreasing order. This allows efficient pairing using a two-pointer technique.
Use two pointers: one starting at the beginning (candidate primary) and one at the middle (candidate backup). For each primary, find the smallest backup that is ≥ primary. If found, pair them and add primary to sum; otherwise, move the primary pointer forward.
Sum the primaries from all valid pairs. If the array length is odd, one server remains unpaired; it cannot contribute to the sum. Return the total.
State time complexity O(n log n) due to sorting, and space O(1) or O(n) depending on sorting implementation. Discuss edge cases: all equal, strictly increasing, odd length, and no valid pairs.
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