<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return <code>true</code> if it is possible to divide this array into <code>k</code> non-empty subsets whose sums are all equal.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [4,3,2,3,5,2,1], k = 4
<strong>Output:</strong> true
<strong>Explanation:</strong> It is possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4], k = 3
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= nums.length &lt;= 16</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
	<li>The frequency of each element is in the range <code>[1, 4]</code>.</li>
</ul>

class Solution {
public:
    // the length of the nums array is 16 max so 2^16 subsets are possible
   
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        vector<int> dp((1 << 16) + 2 , -1);
        int n = nums.size();
        int sum = 0;
    
        for(int i = 0; i < n ; i++){
            sum += nums[i];
        }

        if(sum % k != 0) return false;

        int target = sum/k;

        int subset_cnt = (1 << n);

        dp[0] = 0;

        for(int mask = 0; mask < subset_cnt ; mask++){
            if (dp[mask] == -1) continue;  
            for(int i = 0 ; i < n ; i++){
                // dp[mask] represent the sum of the subset modulo target represented by mask
                
                // !(mask & (1<<i)) checks if the i-th bit of the bitmask mask is 0 hence that nums[i] is
                // not yet included in the subset

                if(!(mask & (1<<i)) && dp[mask] + nums[i] <= target){
                    // set the ith bit to one coz nums[i] is selected
                    dp[mask | (1 << i)] = (dp[mask] + nums[i]) % target;
                }
            }
        }

        return dp[(1 << n)-1] == 0;
    }
};
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