1681 - Minimum Incompatibility\.

Hard

You are given an integer array nums and an integer k. You are asked to distribute this array into k subsets of equal size such that there are no two equal elements in the same subset.

A subset's incompatibility is the difference between the maximum and minimum elements in that array.

Return the minimum possible sum of incompatibilities of the k subsets after distributing the array optimally, or return -1 if it is not possible.

A subset is a group integers that appear in the array with no particular order.

Example 1:

Input: nums = 1,2,1,4, k = 2

Output: 4

Explanation: The optimal distribution of subsets is 1,2 and 1,4.

The incompatibility is (2-1) + (4-1) = 4.

Note that 1,1 and 2,4 would result in a smaller sum, but the first subset contains 2 equal elements.

Example 2:

Input: nums = 6,3,8,1,3,1,2,2, k = 4

Output: 6

Explanation: The optimal distribution of subsets is 1,2, 2,3, 6,8, and 1,3.

The incompatibility is (2-1) + (3-2) + (8-6) + (3-1) = 6.

Example 3:

Input: nums = 5,3,3,6,3,3, k = 3

Output: -1

Explanation: It is impossible to distribute nums into 3 subsets where no two elements are equal in the same subset.

Constraints:

• 1 <= k <= nums.length <= 16

• nums.length is divisible by k

• 1 <= nums[i] <= nums.length