<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>

class Solution {
public:
    int n, K, INF = 1<<29;
    vector<int>nums;
    vector<pair<int, int>>validMask;
    int memo[17][(1<<16) + 10];
    bool isValid(int mask) {
        unordered_map<int, bool> seen;
        for (int i =0 ; i < n; i++) {
            if (mask&(1<<i) ) {
                if (seen.count(nums[i])) return false;
                seen[nums[i]] = true;
            }
        }
        return true;
    }
    int solve(int idx, int mask) {
        if (idx == K) return 0;
        if (memo[idx][mask] != -1) return memo[idx][mask];
        int ret = INF;
        for (auto m : validMask) if ((m.first&mask) == 0){
            ret = min(ret, solve(idx + 1, mask|m.first) + m.second);
        }
        return memo[idx][mask] = ret;
    }
    int getMin(int mask) {
        int mini = n + 1;
        for (int i =0 ; i < n; i++) if (mask&(1<<i) ) mini = min(mini, nums[i]);
        return mini;
    }
    int getMax(int mask) {
        int maxi = 0;
        for (int i =0 ; i < n; i++) if (mask&(1<<i) ) maxi = max(maxi, nums[i]);
        return maxi;
    }
    int minimumIncompatibility(vector<int>& N, int k) {
        nums = N, K = k;
        n = nums.size();
        int G = n /k;
        for (int i = 0; i < (1<<n); i++) {
            int c =0;
            for (int j =0 ; j < n; j++) if (i&(1<<j)) c++;
            if (c == G && isValid(i)) validMask.push_back({i, getMax(i)- getMin(i)});
        }
        int m = validMask.size();
        memset(memo, -1, sizeof(memo));
        int ans = solve(0, 0);
        return ans >= INF ? -1 : ans;
    }
};
25400