Package g1601_1700.s1681_minimum_incompatibility

Class Solution

  • public class Solution
extends Object
    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

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • minimumIncompatibility

        public int minimumIncompatibility​(int[] nums,
                                  int k)