2616 - Minimize the Maximum Difference of Pairs\.

Medium

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(|nums1 - nums4|, |nums2 - nums5|) = 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:

• <code>1 <= nums.length <= 10⁵</code>

• <code>0 <= numsi<= 10⁹</code>

• 0 <= p <= (nums.length)/2