Minimum Incompatibility
<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&#39;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>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,1,4], k = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> 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.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [6,3,8,1,3,1,2,2], k = 4
<strong>Output:</strong> 6
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,3,3,6,3,3], k = 3
<strong>Output:</strong> -1
<strong>Explanation:</strong> It is impossible to distribute nums into 3 subsets where no two elements are equal in the same subset.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= nums.length &lt;= 16</code></li>
	<li><code>nums.length</code> is divisible by <code>k</code></li>
	<li><code>1 &lt;= nums[i] &lt;= nums.length</code></li>
</ul>
Bit Manipulation; Array; Dynamic Programming; Bitmask
func minimumIncompatibility(nums []int, k int) int {
	n := len(nums)
	m := n / k
	const inf = 1 << 30
	f := make([]int, 1<<n)
	g := make([]int, 1<<n)
	for i := range g {
		f[i] = inf
		g[i] = -1
	}
	for i := 1; i < 1<<n; i++ {
		if bits.OnesCount(uint(i)) != m {
			continue
		}
		s := map[int]struct{}{}
		mi, mx := 20, 0
		for j, x := range nums {
			if i>>j&1 == 1 {
				if _, ok := s[x]; ok {
					break
				}
				s[x] = struct{}{}
				mi = min(mi, x)
				mx = max(mx, x)
			}
		}
		if len(s) == m {
			g[i] = mx - mi
		}
	}
	f[0] = 0
	for i := 0; i < 1<<n; i++ {
		if f[i] == inf {
			continue
		}
		s := map[int]struct{}{}
		mask := 0
		for j, x := range nums {
			if _, ok := s[x]; !ok && i>>j&1 == 0 {
				s[x] = struct{}{}
				mask |= 1 << j
			}
		}
		if len(s) < m {
			continue
		}
		for j := mask; j > 0; j = (j - 1) & mask {
			if g[j] != -1 {
				f[i|j] = min(f[i|j], f[i]+g[j])
			}
		}
	}
	if f[1<<n-1] == inf {
		return -1
	}
	return f[1<<n-1]
}