Divide Array Into Arrays With Max Difference

Medium

You receive 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.

Find and provide a 2D array containing the arrays. If it is imvalid to satisfy the conditions, provide an empty array. And if there are multiple answers, provide 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 <= 10^5
n is a multiple of 3
1 <= nums[i] <= 10^5
1 <= k <= 10^5

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