Package g1601_1700.s1681_minimum_incompatibility

Class Solution

java.lang.Object
g1601_1700.s1681_minimum_incompatibility.Solution
public class Solution extends java.lang.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 Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    minimumIncompatibility(int[] nums, int k)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • minimumIncompatibility

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