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g1601_1700.s1681_minimum_incompatibility.readme.md Maven / Gradle / Ivy

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`