Introduction

In this blog post, we will explore how to solve the LeetCode problem "1877" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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

Explanation

Here's the breakdown of the solution:

• Sorting: Sort the input array nums in ascending order. This is the crucial step to enable optimal pairing.
• Pairing: Pair the smallest element with the largest, the second smallest with the second largest, and so on. This strategy minimizes the maximum pair sum because it avoids pairing large numbers with each other.

• Finding Maximum: Iterate through the pairs and find the maximum pair sum.

• Runtime Complexity: O(n log n) due to sorting. Storage Complexity: O(1) (in-place sorting if possible, otherwise O(n) depending on the sorting algorithm implementation).

Code

    def minPairSum(nums):
    """
    Finds the minimized maximum pair sum after optimally pairing up the elements.

    Args:
        nums: A list of integers of even length.

    Returns:
        The minimized maximum pair sum.
    """

    nums.sort()
    max_pair_sum = 0
    n = len(nums)
    for i in range(n // 2):
        max_pair_sum = max(max_pair_sum, nums[i] + nums[n - 1 - i])
    return max_pair_sum