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Minimize Maximum Pair Sum in Array

The pair sum of a pair (a,b) is equal to a + b.

The pair sum of a pair (a,b) is equal to a + b. The maximum pair sum is the largest pair sum in a list of pairs.

Given an array nums of even length n, pair up the elements of nums into n / 2 pairs such that:

Return the minimized maximum pair sum after optimally pairing up the elements.

Minimize Maximum Pair Sum in Array diagram

Example 1

Input: nums = [3,5,2,3]

Output: 7

Explanation: The elements can be paired up into pairs (3,3) and (5,2). The maximum pair sum is max(3+3, 5+2) = max(6, 7) = 7.

Example 2

Input: nums = [3,5,4,2,4,6]

Output: 8

Explanation: The elements can be paired up into pairs (3,5), (4,4), and (6,2). The maximum pair sum is max(3+5, 4+4, 6+2) = max(8, 8, 8) = 8.

Constraints

  • n == nums.length
  • 2 <= n <= 10^5
  • n is even.
  • 1 <= nums[i] <= 10^5

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