<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 dfs(vector<int> &num, int mask, int cursum, int sum, int k, unordered_map<int,bool>&dp) {
        if (k == 0 && cursum == 0) {
            return true;
        } else if (k < 0 || cursum > sum) {
            return false;
        } else if (dp.count(mask)) return dp[mask];

        bool ret = false;
        // !!! IMPORTANT
        for (int i = 0; i < num.size(); i++) {
            if (((mask >> i) & 1)) continue;
            if (cursum + num[i] == sum) {
                ret |= dfs(num, mask | (1<<i), 0, sum, k - 1, dp);
            } else {
                ret |= dfs(num, mask | (1<<i), cursum + num[i], sum, k, dp);
            }
        }
        return dp[mask] = ret;
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = 0;
        for (auto n: nums) {
            sum += n;
        }
        if (sum % k) return false;
        unordered_map<int, bool> dp;

        return dfs(nums, 0, 0, sum / k, k, dp);
    }
};
71069