1877. Minimize Maximum Pair Sum in Array

Description

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 <= 10⁵
n is even.
1 <= nums[i] <= 10⁵

Solutions

Solution: Greedy

Time complexity: O(nlogn)
Space complexity: O(1)

JavaScript

js

/**
 * @param {number[]} nums
 * @return {number}
 */
const minPairSum = function (nums) {
  nums.sort((a, b) => a - b);

  const size = nums.length;
  let result = 0;

  for (let index = 0; index < size / 2; index++) {
    const sum = nums[index] + nums[size - index - 1];

    result = Math.max(sum, result);
  }
  return result;
};