<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:
    unordered_map<int,bool> cache;
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        if(nums.empty() || k < 1){
            return false;
        }
        sort(nums.begin(),nums.end());
        int n = nums.size();
        int a = 0;
        for(int i = 0; i < n; ++i){
            a+=nums[i];
        }
        if(a % k){
            return false;
        }
        return helper(nums,0,k,0, a/k);
    }
    bool helper(vector<int>& nums, int mask, int k, int cur, int sum){
        if(cache.count(mask)){
            return cache[mask];
        }
        if(k == 1){
            // if(mask == 0){
            //     cache[mask] = false;
            //     return false;
            // }
            int total = 0;
            for(int i = 0; i < nums.size(); ++i){
                if(mask & (1 << i)){
                    continue;
                }
                total += nums[i];
            }
            cache[mask] = (total == sum);
            return total == sum;
        }
        // if(k == 0){
        //     return mask == ((1 << nums.size()) - 1);
        // }
        else{
            for(int i = 0; i < nums.size(); ++i){
                if(mask & (1 << i)){
                    continue;
                }

                if(cur + nums[i] > sum){
                    cache[mask]=false;
                    return false;
                }
                int newmask = (mask | (1 << i));
                if(cur + nums[i] < sum){
                    if(helper(nums,newmask,k,cur + nums[i], sum)){
                        cache[mask] = true;
                        return true;
                    }
                }else{
                    if(helper(nums, newmask, k-1, 0, sum)){
                        cache[mask] = true;
                        return true;
                    }
                }
            } 
        }
        cache[mask] = false;
        return false;
    }
};
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