<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) {
        long long sum = accumulate(nums.begin(), nums.end(), (long long)0);
        if (sum % k != 0) return false;
        //vector<int> bucket(k);
        //sort(nums.begin(), nums.end());
        //return dfs(nums, nums.size()-1, sum/k, bucket);

        int size = nums.size();
        int target = sum/k;

        // dp[i | 1 << j] = (dp[i] + nums[j]) % target, result is in dp[1 << size].
        unordered_map<int, int> dp;
        dp[0] = 0;
        for (int i = 0; i < (1 << size); i++) {
            if (!dp.count(i)) continue;
            for (int j = 0; j < size; j++) {
                if (!(i & (1 << j)) && dp[i] + nums[j] <= target)
                dp[i | (1 << j)] = (dp[i] + nums[j]) % target;
            }
        }

        int index = (1 << size) - 1;

        return dp.count(index) && dp[index] == 0;
    }

    bool dfs(vector<int>& nums, int index, long long t, vector<int>& bucket) {
        if (index == -1) {
            for (int n : bucket) {
                if (n != t) return false;
            }
            return true;
        }
        int n = nums[index];
        for (int i = 0; i < bucket.size(); i++) {
            if (bucket[i] + n > t) continue;
            bucket[i] += n;
            if (dfs(nums, index-1, t, bucket)) return true;
            bucket[i] -= n;
        }
        return false;
    }
};
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