<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 canPartitionKSubsets(vector<int>& nums, int k) {
        int total = 0;
        for (int val: nums) {
            total += val;
        }
        if (total % k != 0) {
            return false;
        }
        int target = total / k;
        sort(nums.begin(), nums.end());
        string taken(nums.size(), '0');
        unordered_map<string, bool> cache;
        return backtracking(nums, k, 0, target, 0, 0, taken, cache);
    }
    bool backtracking(vector<int>& nums, int k, int start, int target, int cnt, int sum, string& taken, unordered_map<string, bool>& cache) {
        if (cnt == k - 1) {
            return true;
        }
        if (cache.count(taken)) {
            return cache[taken];
        }
        if (sum > target) {
            return false;
        }
        if (sum == target) {
            return backtracking(nums, k, 0, target, cnt + 1, 0, taken, cache);
        }
        
        for (int i = start; i < nums.size(); ++i) {
            if (taken[i] == '0') {
                taken[i] = '1';
                bool res = backtracking(nums, k, i + 1, target, cnt, sum + nums[i], taken, cache);
                taken[i] = '0';
                if (res) {
                    return true;
                }
            }
        }
        cache[taken] = false;
        return cache[taken];
    }
};
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