minimize_maximum_pair_sum_in_an_array.py

"""
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

"""

class Solution:
    def minPairSum(self, nums: List[int]) -> int:
        nums.sort()
        max_sum = 0
        left = 0
        right = len(nums) - 1

        while left < right:
            max_sum = max(max_sum, nums[left] + nums[right])
            left = left + 1
            right = right - 1
        return max_sum