Divide Array Into Arrays With Max Difference

Problem Description

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.

Key Insights

• The problem requires grouping elements into triplets while ensuring that the maximum difference within each triplet does not exceed k.
• Sorting the array helps in easily finding valid triplets since it ensures that the elements are in order.
• A greedy approach can be used to create the triplets sequentially from the sorted array.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the array.
Space Complexity: O(n) - for storing the output.

Solution

To solve the problem, we can use the following approach:

1. Sort the input array nums.
2. Iterate through the sorted array in steps of 3 to form groups of three.
3. Check if the difference between the maximum and minimum elements in each group is less than or equal to k.
4. If all groups are valid, return them; otherwise, return an empty array.

This approach utilizes sorting to facilitate the grouping of elements based on their values, ensuring that the condition of maximum difference is met.

Code Solutions