2966. Divide Array Into Arrays With Max Difference

Problem Link

Description

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You are given an integer array nums of size n where n is a multiple of 3 and a positive integer k.

Divide the array nums into n / 3 arrays of size 3 satisfying the following condition:

• The difference between any two elements in one array is less than or equal to k.

Return a 2D array containing the arrays. If it is impossible to satisfy the conditions, return an empty array. And if there are multiple answers, return any of them.

 

Example 1:

Input: nums = [1,3,4,8,7,9,3,5,1], k = 2

Output: [[1,1,3],[3,4,5],[7,8,9]]

Explanation:

The difference between any two elements in each array is less than or equal to 2.

Example 2:

Input: nums = [2,4,2,2,5,2], k = 2

Output: []

Explanation:

Different ways to divide nums into 2 arrays of size 3 are:

• [[2,2,2],[2,4,5]] (and its permutations)
• [[2,2,4],[2,2,5]] (and its permutations)

Because there are four 2s there will be an array with the elements 2 and 5 no matter how we divide it. since 5 - 2 = 3 > k, the condition is not satisfied and so there is no valid division.

Example 3:

Input: nums = [4,2,9,8,2,12,7,12,10,5,8,5,5,7,9,2,5,11], k = 14

Output: [[2,2,2],[4,5,5],[5,5,7],[7,8,8],[9,9,10],[11,12,12]]

Explanation:

The difference between any two elements in each array is less than or equal to 14.

 

Constraints:

• n == nums.length
• 1 <= n <= 105
• n is a multiple of 3
• 1 <= nums[i] <= 105
• 1 <= k <= 105

Solution

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Python3

class Solution:
    def divideArray(self, nums: List[int], k: int) -> List[List[int]]:
        N = len(nums) 
        nums.sort()
        res = []
 
        for i in range(0, N, 3):
            if nums[i + 2] - nums[i] > k:
                return []
            
            res.append(nums[i : i + 3])
        
        return res