Divide Array Into Arrays With Max Difference

arraygreedysorting

Problem Statement

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.

Examples

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]]
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: []
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]]
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

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicGreedy