<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<string,int>dp;
    bool solver(vector<int>& nums, string&vis, int start_index, int k, int current_sum, int target) 
    {
        if (k == 0) return dp[vis] = true;
        if(dp.find(vis)!=dp.end()) return dp[vis];
        if (current_sum == target) 
        {
            return solver(nums, vis, 0, k - 1, 0, target);
        }
        for (int i = start_index; i < nums.size(); i++) 
        {
            if (vis[i] == '0' && current_sum + nums[i] <= target) 
            {
                vis[i] = '1';
                if (solver(nums, vis, i + 1, k, current_sum + nums[i], target)) 
                {
                    return dp[vis] = true;
                }
                vis[i] = '0';
            }
        }
        return dp[vis] = false;
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) 
    {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        if (sum % k != 0) 
        return false;  

        int target = sum / k;
        vector<int> visited(nums.size(), 0);
        string vis = "";
        int n = nums.size();
        for(int i = 0;i<n;i++)
        {
            vis += '0';
        }
        sort(nums.rbegin(), nums.rend()); 
        return solver(nums, vis, 0, k, 0, target);
    }
};
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