Package g1601_1700.s1681_minimum_incompatibility

Class Solution

java.lang.Object

g1601_1700.s1681_minimum_incompatibility.Solution

public class Solution
extends Object

1681 - Minimum Incompatibility.<p>Hard</p> <p>You are given an integer array <code>nums</code> and an integer <code>k</code>. You are asked to distribute this array into <code>k</code> subsets of <strong>equal size</strong> such that there are no two equal elements in the same subset.</p> <p>A subset&rsquo;s <strong>incompatibility</strong> is the difference between the maximum and minimum elements in that array.</p> <p>Return <em>the <strong>minimum possible sum of incompatibilities</strong> of the</em> <code>k</code> <em>subsets after distributing the array optimally, or return</em> <code>-1</code> <em>if it is not possible.</em></p> <p>A subset is a group integers that appear in the array with no particular order.</p> <p><strong>Example 1:</strong></p> <p><strong>Input:</strong> nums = [1,2,1,4], k = 2</p> <p><strong>Output:</strong> 4</p> <p><strong>Explanation:</strong> The optimal distribution of subsets is [1,2] and [1,4].</p> <p>The incompatibility is (2-1) + (4-1) = 4.</p> <p>Note that [1,1] and [2,4] would result in a smaller sum, but the first subset contains 2 equal elements.</p> <p><strong>Example 2:</strong></p> <p><strong>Input:</strong> nums = [6,3,8,1,3,1,2,2], k = 4</p> <p><strong>Output:</strong> 6</p> <p><strong>Explanation:</strong> The optimal distribution of subsets is [1,2], [2,3], [6,8], and [1,3].</p> <p>The incompatibility is (2-1) + (3-2) + (8-6) + (3-1) = 6.</p> <p><strong>Example 3:</strong></p> <p><strong>Input:</strong> nums = [5,3,3,6,3,3], k = 3</p> <p><strong>Output:</strong> -1</p> <p><strong>Explanation:</strong> It is impossible to distribute nums into 3 subsets where no two elements are equal in the same subset.</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 <= k <= nums.length <= 16</code></li> <li><code>nums.length</code> is divisible by <code>k</code></li> <li><code>1 <= nums[i] <= nums.length</code></li> </ul>

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)