<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>

#include <vector>
#include <utility>
#include <limits.h>

class Solution {
public:
    int minimumIncompatibility(std::vector<int>& nums, int k) {
        int n = nums.size(), grp_size = n/k;
        const std::vector<std::pair<int,int>> &b_map = genMaps(nums, grp_size);
        std::vector<int> dp(1 << n, INT_MAX);
        dp[0] = 0;
        for(int b = 0; b < (1 << n); b++){
            if(__builtin_popcount(b) % grp_size != 0) continue;
            for(auto &[sub_b, inc_sub_b]: b_map){
                if(sub_b > b) break;
                if((sub_b & b) != sub_b) continue;
                if(dp[b - sub_b] == INT_MAX) continue;
                dp[b] = std::min(dp[b], dp[b - sub_b] + inc_sub_b);
            }
        }
        return dp.back()==INT_MAX ? -1 : dp.back();
    }
private:
    std::vector<std::pair<int,int>> genMaps(std::vector<int>& nums, int grp_size){
        int n = nums.size();
        std::vector<std::pair<int,int>> b_map;
        for(int b = 0; b < (1 << n); b++){
            if(__builtin_popcount(b) != grp_size)continue;
            int vis = 0;
            int mx = 0, mn = 16;
            bool duplicates = false;
            for(int i = 0; i < n; i++){
                if((b & 1 << i) == 0) continue;
                if(vis & 1 << nums[i]){
                    duplicates = true;
                    break;
                }
                vis |= 1 << nums[i];
                mx = std::max(mx, nums[i]);
                mn = std::min(mn, nums[i]);
            }
            if(duplicates == false){
                b_map.emplace_back(b, mx-mn);
            }
        }
        return b_map;
    }
};


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