Minimize the Maximum Difference of Pairs

arraybinary searchdynamic programming

Problem Statement

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.

Examples

Example 1

Input: nums = [10,1,2,7,1,3], p = 2
Output: 1
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
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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Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBinary Search