<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 = accumulate(nums.begin(), nums.end(), 0);
        if (total % k != 0 || nums.size() < k) {
            return false;
        }
        sort(nums.begin(), nums.end(), greater());
        vector<bool> visited(nums.size(), false);
        int target = total / k;
        return dfs(nums, k, 0, 0, visited, target);
    }
    bool dfs(vector<int>& nums, int k, int i, int subsetSum, vector<bool>& visited, int& target) {
        if (k == 1) {
            return true;
        }
        if (subsetSum == target) {
            return dfs(nums, k - 1, 0, 0, visited, target);
        }
        if (subsetSum > target) {
            return false;
        }
        for (int j = i; j < nums.size(); j++) {
            if (visited[j] || nums[j] + subsetSum > target) {
                continue;
            }
            visited[j] = true;
            if (dfs(nums, k, j + 1, subsetSum + nums[j], visited, target)) {
                return true;
            }
            visited[j] = false;
            if (subsetSum == 0) {
                break;
            }
        }
        return false;
    }
};
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