<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>

// itoa?
// ---------
// def of subset?
class Solution {
public:
    bool backtrack(int start, int cur_sum, int subset_sum, int k, vector<int>& nums, string& used, unordered_map<string, bool>& memo) {
        if (k == 1) {
            return true;
        }

        if (cur_sum > subset_sum) {
            return false;
        }
        
        if (memo.find(used) != memo.end()) {
            return memo[used];
        }
        
        if (cur_sum == subset_sum) {
            return memo[used] = backtrack(0, 0, subset_sum, k - 1, nums, used, memo);
        }

        for (int i = start; i < nums.size(); ++i) {
            if (used[i] == '0') {

                if (cur_sum + nums[i] > subset_sum) {
                    break;
                }
                used[i] = '1';

                if (backtrack(i + 1, cur_sum + nums[i] , subset_sum, k, nums, used, memo)) {
                    return true;
                }
                used[i] = '0';
            }
        }

        return memo[used] = false;
    }

    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int total_sum = std::accumulate(nums.begin(), nums.end(), 0);
        if (total_sum % k != 0) {
            return false;
        }
        int subset_sum = total_sum / k;
        sort(nums.begin(), nums.end());
        // String to represent taken array.
        string used(nums.size(), '0');
        
        // Memoize the ans using taken element's string as key.
        unordered_map<string, bool> memo;

        return backtrack(0, 0, subset_sum, k, nums, used, memo);
        
    }
};
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