2966. Divide Array Into Arrays With Max Difference

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.

 

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

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

 

Solutions

Solution: Greedy

• Time complexity: O(nlogn)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number[]} nums
 * @param {number} k
 * @return {number[][]}
 */
const divideArray = function (nums, k) {
  const n = nums.length;
  const result = [];

  nums.sort((a, b) => a - b);

  for (let index = 2; index < n; index += 3) {
    if (nums[index] - nums[index - 2] > k) return [];

    result.push([nums[index - 2], nums[index - 1], nums[index]]);
  }

  return result;
};