<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:
   map<vector<bool>, bool>memo;
    bool backtrack(int pos, vector<int>& nums, vector<bool>& taken, int target, int curr,
                   int subsetCount, int k) {

        if (subsetCount == k-1)
            return true;
        if (curr > target)
            return false;

        if(memo.count(taken)) return memo[taken];
        if (curr == target) {
            // start here forming new subset
            return memo[taken] = backtrack(0, nums, taken, target, 0, subsetCount + 1, k);
        }
        int n = nums.size();
        for (int index = pos; index < n; index++) {
            if (!taken.at(index)) {
                taken[index] = true;
                if (backtrack(index+1, nums, taken, target, curr + nums.at(index),
                              subsetCount, k)) {
                    return true;
                }
                taken[index] = false;
            }
        }
        return memo[taken] = false;
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = accumulate(nums.begin(), nums.end(), 0);

        if(sum%k != 0) return false;
        sort(nums.begin(), nums.end(), greater<int>());
        vector<bool> taken(nums.size(), false);
        return backtrack(0, nums, taken, sum/k, 0, 0, k);
    }
};

// sum/2 sum/k exist ?
// all have different partiiton
// {} {} {} {}
// no of subset but two subsets cannt share a element
// 1,1,1,1
// 1,4 ,1 and 4,2
55900