<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>& arr, int index, int count, int currSum, int k, 
                   int targetSum, string& taken, unordered_map<string, bool>& memo) {
        if(count == k-1) {
            return true;
        }

        if(currSum > targetSum) {
            return false;
        }

        if(memo.find(taken) != memo.end()) {
            return memo[taken];
        }

        if(currSum == targetSum) {
            return memo[taken] = backtrack(arr, 0, count+1, 0, k, targetSum, taken, memo);
        }

        for(int j=index; j<arr.size(); j++) {
            if(taken[j] == '0') {
                taken[j] = '1';
                if(backtrack(arr, j+1, count, currSum+arr[j], k, targetSum, taken, memo)) {
                    return true;
                }
                taken[j] = '0';
            }
        }
        return memo[taken] = false;
    }

    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int n = nums.size();
        int totalSum = 0;

        for(int i=0; i<nums.size(); i++) {
            totalSum += nums[i];
        }

        if(totalSum % k != 0)
            return false;

        int targetSum = totalSum/k;
        string taken(n, '0');

        unordered_map<string, bool> memo;
        return backtrack(nums, 0, 0, 0, k, targetSum, taken, memo);

        
    }
};
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