2616. Minimize the Maximum Difference of Pairs

Medium

413

18

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`

**Example 1:**

Input:nums = [10,1,2,7,1,3], p = 2Output:1Explanation: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 = 1Output:0Explanation: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:**

`1 <= nums.length <= 10`

^{5}`0 <= nums[i] <= 10`

^{9}`0 <= p <= (nums.length)/2`

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