Problem Statement:

Given an array of integers and a threshold value k, the task is to divide the array into triplets such that the absolute difference between adjacent elements in each triplet does not exceed k. If such division is possible, return the triplets; otherwise, return an empty array.

Approach:

To efficiently divide the array into triplets while satisfying the maximum difference constraint, we can follow these steps:

1. Sort the array in non-decreasing order to facilitate easier traversal.
2. Initialize variables to track the total number of possible triplets and an array to store the triplets.
3. Iterate over the sorted array, forming triplets at each step.
4. For each triplet, ensure that the absolute difference between adjacent elements does not exceed the given threshold k.
5. If a valid triplet is formed, store it in the result array; otherwise, return an empty array indicating that such division is not possible.

https://leetcode.com/problems/divide-array-into-arrays-with-max-difference

class Solution {
    public int[][] divideArray(int[] nums, int k) {
       // Sort Array
       Arrays.sort(nums);
       int totalPossibleArrays = nums.length/3;
       int answer[][] = new int[totalPossibleArrays][3];
       int counter = 0;
       for(int i=0;i<totalPossibleArrays;i++) {
           answer[i][0] = nums[counter++];
           if ((nums[counter]-answer[i][0]) <= k) {
               answer[i][1] = nums[counter++];
           } else {
               return new int[0][0];
           }

           if ((nums[counter]-answer[i][0]) <= k) {
               answer[i][2] = nums[counter++];
           } else {
               return new int[0][0];
           }
       }
       return answer;
    }
}

Conclusion:

Dividing an array into triplets while ensuring a maximum difference constraint can be efficiently achieved using the algorithm described above. By sorting the array and carefully forming triplets, we can divide the array in O(nlogn) time complexity, where n is the size of the input array. This approach provides an effective solution to this common problem in algorithmic programming.