1877. Minimize Maximum Pair Sum in Array

Problem

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.

• For example, if we have pairs (1,5), (2,3), and (4,4), the maximum pair sum would be max(1+5, 2+3, 4+4) = max(6, 5, 8) = 8.

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

• Each element of nums is in exactly one pair, and

• The **maximum pair sum **is minimized.

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

  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

Solution (Java)

class Solution {
    public int minPairSum(int[] nums) {
        Arrays.sort(nums);
        int start = 0;
        int end = nums.length - 1;
        int min = Integer.MIN_VALUE;
        while (start < end) {
            min = Math.max(min, nums[start] + nums[end]);
            --end;
            ++start;
        }
        return min;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).