<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:
    
    bool backtrack(vector<int> &nums, int k , int index, int currSum, int targetSum, int partitions, string taken,
                  map<string, bool> &memo)
    {
        if (index >= nums.size())
            return false;
        
        if (memo.find(taken) != memo.end())
            return memo[taken];
        
        if (currSum > targetSum)
            return false;
        
        if (partitions == (k-1))
        {
            return true;
        }
        
        if (currSum == targetSum)
        {
            return memo[taken] = backtrack(nums, k, 0, 0, targetSum, partitions+1, taken, memo);
        }
        
        for(int i=index;i<nums.size();i++)
        {
            if (taken[i] == '0')
            {
                taken[i] = '1';
                int ans = backtrack(nums, k, i+1, currSum + nums[i], targetSum, partitions, taken, memo);
                if (ans)
                    return true;
                taken[i] = '0';
            }
        }
        return false;
    }
    
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int n = nums.size();
        string taken(n, '0');
        int currSum = 0;
        
        int sum = 0;
        for(int num: nums)
        {
            sum+=num;
        }
        
        if ((sum%k) != 0)
            return false;
        int targetSum = sum/k;
        int partitions = 0;
        int index = 0;
        map<string, bool> memo;
        return backtrack(nums, k, 0, currSum, targetSum, partitions, taken, memo);
    }
};
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