2616. Minimize the Maximum Difference of Pairs

Problem Link

Description

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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:

• 1 <= nums.length <= 105
• 0 <= nums[i] <= 109
• 0 <= p <= (nums.length)/2

Solution

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Python3

class Solution:
    def minimizeMax(self, nums: List[int], p: int) -> int:
        N = len(nums)
        nums.sort()
        
        def good(k):
            i = 1
            count = 0
            
            while i < N:
                if nums[i] - nums[i - 1] <= k:
                    i += 1
                    count += 1
                i += 1
            
            return count >= p
        
        left, right = 0, 10 ** 9
        
        while left < right:
            mid = left + (right - left) // 2
            
            if good(mid):
                right = mid
            else:
                left = mid + 1
        
        return left