<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:
    def canPartitionKSubsets2(self, nums: List[int], k: int) -> bool:
        total = sum(nums)
        if total % k:
            return False
        target = total // k
        nums.sort(reverse=True)
        if any(n > target for n in nums):
            return False

        visited = set()
        def dfs(i, k, val):
            if k == 0:
                return True
            if val == target:
                return dfs(0, k - 1, 0)
            
            for j in range(i, len(nums)):
                if j not in visited and val + nums[j] <= target:
                    visited.add(j)
                    if dfs(j + 1, k, val + nums[j]):
                        return True
                    visited.remove(j)

            return False

        return dfs(0, k, 0)


    def canPartitionKSubsets(self, nums: List[int], k: int) -> bool:
        total = sum(nums)
        if total % k:
            return False
        
        target = total // k
        nums.sort(reverse=True)
        if any(n > target for n in nums):
            return False

        def dfs(i, vals):
            if i == len(nums):
                return all(val == target for val in vals)
            
            for j in range(k):
                if vals[j] + nums[i] <= target:
                    vals[j] += nums[i]
                    if dfs(i + 1, vals):
                        return True
                    vals[j] -= nums[i]
                if vals[j] == 0:
                    return False
            return False

        return dfs(0, [0]*k)
16501