<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:
    int BucSize;
    int NumSubset;
    int StateCnt;
    unordered_map<int, unordered_map<int, unordered_map<int, int>>> DP;
    bool backtrack(vector<int> &Nums, int CurSize, int Cnt, int State) {
        if (Cnt == NumSubset && State == StateCnt - 1) {
            return true;
        }
        if (DP.find(CurSize) != DP.end() && DP[CurSize].find(Cnt) != DP[CurSize].end() && DP[CurSize][Cnt].find(State) != DP[CurSize][Cnt].end())
            return false;
        for(int i = 0 ; i < Nums.size() ; i++) {
            if (State & (1 << i))
                continue;
            int Val = Nums[i];
            if (CurSize + Val < BucSize) {
                if (backtrack(Nums, CurSize + Val, Cnt, State | (1 << i)))
                    return true;
            } else if (CurSize + Val == BucSize) {
                if (backtrack(Nums, 0, Cnt + 1, State | (1 << i)))
                    return true;
            } else {
                break;
            }
        }
        DP[CurSize][Cnt][State] = 1;
        return false;
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int Sum = 0;
        for(int num : nums)
            Sum += num;
        BucSize = Sum / k;
        NumSubset = k;
        if (Sum % k != 0)
            return false;
        StateCnt = pow(2,nums.size());
        std::sort(nums.begin(), nums.end());
        return backtrack(nums, 0, 0, 0);
    }
};
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