<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 {
private:
    int n;
    vector<bool> visited;
    unordered_map<int, bool> m;

    bool calc(vector<int>& nums, int k, int count, int targetSum, int sum, int index, int state) {
        if(sum > targetSum)
            return false;

        if(count == k)
            return true;

        if(m.find(state) != m.end())
            return m[state];

        if(sum == targetSum)
            return calc(nums, k, count + 1, targetSum, 0, 0, state);

        bool found = false;
        for(int i = index; i < n; i++) {
            if((state & (1 << i)) == 0) {
                if(calc(nums, k, count, targetSum, sum + nums[i], i + 1, (state | (1 << i)))) {
                    found = true;
                    break;
                }
            }
        }

        return m[state] = found;
    }
public:
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        n = nums.size();
        int totalSum = 0, state = 0;

        for(int element : nums)
            totalSum += element;

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

        sort(nums.begin(), nums.end());

        int target = totalSum / k;

        visited = vector<bool>(n, false);

        return calc(nums, k, 1, target, 0, 0, state);
    }
};
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