How do you solve Minimize Maximum Pair Sum in Array on LeetCode?

Minimize Maximum Pair Sum in Array (LeetCode #1877) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Pairing the smallest and largest elements minimizes the maximum sum.

What is the time complexity of Minimize Maximum Pair Sum in Array?

The optimal solution for Minimize Maximum Pair Sum in Array runs in O(n log n) time and uses O(1) space. The sorting step dominates the time complexity, while we only use a constant amount of extra space.

What is the brute force solution for Minimize Maximum Pair Sum in Array?

The brute force approach for Minimize Maximum Pair Sum in Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible pairs of elements and calculating their sums. This method is straightforward but inefficient, as it checks every possible combination. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Minimize Maximum Pair Sum in Array?

Minimize Maximum Pair Sum in Array uses the following concepts: Array, Two Pointers, Greedy, Sorting. The recommended patterns to study are: Two Pointers, Greedy, Sorting.

What are the interview tips for Minimize Maximum Pair Sum in Array?

Always think about how sorting can help in optimization problems. Explain your thought process clearly; interviewers value understanding over just getting the right answer. Practice dry runs of your algorithm with different inputs to solidify your understanding.

What are common mistakes when solving Minimize Maximum Pair Sum in Array?

Not considering the effect of pairing extremes. Overlooking the need to sort the array before pairing.

#1877

Minimize Maximum Pair Sum in Array

Medium

ArrayTwo PointersGreedySortingTwo PointersGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

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Intuition

Time O(n log n)Space O(1)

By sorting the array and pairing the smallest and largest elements, we can minimize the maximum pair sum effectively. This is because pairing extremes balances the sums.

⚙️

Algorithm

4 steps

1Step 1: Sort the array in non-decreasing order.
2Step 2: Initialize a variable to track the maximum pair sum.
3Step 3: Pair the first element with the last, the second with the second last, and so on, calculating the sums.
4Step 4: Keep track of the maximum sum encountered during the pairing.

solution.py7 lines

1def minimize_max_pair_sum(nums):
2    nums.sort()
3    n = len(nums)
4    max_pair_sum = 0
5    for i in range(n // 2):
6        max_pair_sum = max(max_pair_sum, nums[i] + nums[n - 1 - i])
7    return max_pair_sum

ℹ

Complexity note: The sorting step dominates the time complexity, while we only use a constant amount of extra space.

1Pairing the smallest and largest elements minimizes the maximum sum.
2Sorting the array is a crucial step to achieve optimal pairing.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.