minimize-maximum-pair-sum-in-array_1877.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.

# ---------------------------------------Runtime 1009 ms Beats 30.47% Memory 30.9 MB Beats 13.42%---------------------------------------

from typing import List


class Solution:
    def minPairSum(self, nums: List[int]) -> int:
        nums.sort()

        max_sum = 0
        l_nums = len(nums)
        for i in range(len(nums) // 2):
            max_sum = max(max_sum, nums[i] + nums[l_nums - 1 - i])

        return max_sum