<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 {
    // bool partitionSubsetsUtil(vector<int>& nums, int itr, vector<int>& subsets, int part_size){

    //     if(itr == nums.size()){
    //         for(int i = 0; i < subsets.size(); i++){
    //             if(subsets[i] != part_size)
    //                 return false;
    //         }
    //         return true;
    //     }

    //     for(int i = 0; i < subsets.size(); i++){

    //         if(subsets[i] + nums[itr] <= part_size){
    //             subsets[i] += nums[itr];
    //             bool possible = partitionSubsetsUtil(nums, itr + 1, subsets, part_size);
    //             if(possible)
    //                 return true;
    //             subsets[i] -= nums[itr];
    //         }
    //     }
    //     return false;
    // }
    bool partitionSubsetsUtil(vector<int>& nums, int k, string taken, unordered_map<string, bool>& memo, int count, int part_size, int curr_sum, int index){

        if(count == k - 1)
            return true;

        if(curr_sum > part_size)
            return false;
        
        if(memo.count(taken))
            return memo[taken];

        if(curr_sum == part_size){
            return partitionSubsetsUtil(nums, k, taken, memo, count + 1, part_size, 0, 0);
        }

        for(int i = index; i < nums.size(); i++){

            if(taken[i] == '0'){

                taken[i] = '1';
                bool possible = partitionSubsetsUtil(nums, k, taken, memo, count, part_size, curr_sum + nums[i], i + 1);
                if(possible){
                    memo[taken] = true;
                    return true;
                }
                taken[i] = '0';
            }
        }
        memo[taken] = false;
        return false;
    }
public:
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        
        int sum = 0;
        for(int i = 0; i < nums.size(); i++){
            sum += nums[i];
        }
        if(sum % k != 0)
            return false;
        int part_size = sum / k;
        for(int i = 0; i < nums.size(); i++){
            if(nums[i] > part_size)
                return false;
        }
        string taken = "";
        for(int i = 0; i < nums.size(); i++){
            taken += "0";
        }
        unordered_map<string, bool> memo;
        return partitionSubsetsUtil(nums, k, taken, memo, 0, part_size, 0, 0);
        // vector<int> subsets(k, 0);
        // return partitionSubsetsUtil(nums, 0, subsets, part_size);
    }
};
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