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Minimize Maximum Pair Sum in Array

Difficulty: Medium

Problem Description

Given an array nums of even length n, pair up the elements of nums into n / 2 pairs such that the maximum pair sum is minimized. Each element of nums must be in exactly one pair. Return the minimized maximum pair sum after optimally pairing up the elements.

Key Insights

  • The goal is to minimize the maximum pair sum formed by pairing elements from the array.
  • To achieve optimal pairing, we should pair the smallest available numbers with the largest ones.
  • Sorting the array allows for a straightforward pairing strategy using two pointers: one starting from the beginning and the other from the end of the array.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the array.
Space Complexity: O(1) - no additional space is required beyond a few variables.

Solution

The solution involves the following steps:

  1. Sort the input array.
  2. Use a two-pointer approach to pair elements from the start and the end of the sorted array.
  3. Calculate the maximum pair sum for each pairing and keep track of the maximum value found.
  4. Return the minimized maximum pair sum.

This approach ensures that we are effectively pairing the largest remaining number with the smallest one, hence minimizing the overall maximum pair sum.

Code Solutions

def minimizeMax(nums):
    nums.sort()  # Sort the array
    n = len(nums)
    max_pair_sum = 0

    # Pair elements from both ends
    for i in range(n // 2):
        pair_sum = nums[i] + nums[n - 1 - i]
        max_pair_sum = max(max_pair_sum, pair_sum)  # Keep track of the maximum pair sum

    return max_pair_sum
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