Is Minimize the Maximum Difference of Pairs easy or hard?

The problem is rated Medium on LeetCode. The main challenge is recognizing that the answer can be searched using binary search and validated with a greedy pairing strategy after sorting.

Minimize the Maximum Difference of Pairs Python or Java solution

Typical implementations sort the array and apply binary search on the difference range. The greedy feasibility check counts how many pairs can be formed without overlapping indices. This pattern translates directly to Python, Java, C++, C#, and JavaScript.

How to solve Minimize the Maximum Difference of Pairs in O(n log n)?

First sort the array so nearby numbers have small differences. Then binary search the maximum allowed difference. For each candidate value, iterate through the array and greedily pair adjacent elements if their difference is within the limit, counting how many pairs can be formed.

What is the best approach for Minimize the Maximum Difference of Pairs?

The most efficient approach sorts the array and then uses binary search on the maximum allowed pair difference. For each candidate difference, a greedy scan forms pairs whenever adjacent numbers differ by at most that value. This method runs in O(n log n) time due to sorting and binary search iterations.

What data structure is used in Minimize the Maximum Difference of Pairs?

The optimal solution primarily uses arrays with sorting and a greedy scan. Binary search is applied over the range of possible differences. An alternative implementation may use a priority queue (min-heap) to process pair differences in increasing order.

What is the time complexity of Minimize the Maximum Difference of Pairs?

The optimal solution runs in O(n log n) time. Sorting the array takes O(n log n), and each binary search step performs a linear greedy scan to count valid pairs. Space complexity is O(1) auxiliary aside from sorting.

Is Minimize the Maximum Difference of Pairs asked at Google or Amazon interviews?

Problems combining binary search with greedy validation appear frequently in interviews at companies like Google, Amazon, and Meta. Variants of this question test your ability to recognize monotonic search spaces and design feasibility checks efficiently.

Description Hints 3 Solution Video 16:56

2616. Minimize the Maximum Difference of Pairs

Medium50.9% acceptance6 companies

You are given a 0-indexed integer array nums and an integer p. Find p pairs of indices of nums such that the maximum difference amongst all the pairs is minimized. Also, ensure no index appears more than once amongst the p pairs.

Note that for a pair of elements at the index i and j, the difference of this pair is |nums[i] - nums[j]|, where |x| represents the absolute value of x.

Return the minimum maximum difference among all p pairs. We define the maximum of an empty set to be zero.

Example 1:

Input: nums = [10,1,2,7,1,3], p = 2
Output: 1
Explanation: The first pair is formed from the indices 1 and 4, and the second pair is formed from the indices 2 and 5. 
The maximum difference is max(|nums[1] - nums[4]|, |nums[2] - nums[5]|) = max(0, 1) = 1. Therefore, we return 1.

Example 2:

Input: nums = [4,2,1,2], p = 1
Output: 0
Explanation: Let the indices 1 and 3 form a pair. The difference of that pair is |2 - 2| = 0, which is the minimum we can attain.

Constraints: