<p>You are given an integer array <code>nums</code>.</p>

<p>You should move each element of <code>nums</code> into one of the two arrays <code>A</code> and <code>B</code> such that <code>A</code> and <code>B</code> are non-empty, and <code>average(A) == average(B)</code>.</p>

<p>Return <code>true</code> if it is possible to achieve that and <code>false</code> otherwise.</p>

<p><strong>Note</strong> that for an array <code>arr</code>, <code>average(arr)</code> is the sum of all the elements of <code>arr</code> over the length of <code>arr</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5,6,7,8]
<strong>Output:</strong> true
<strong>Explanation:</strong> We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have an average of 4.5.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,1]
<strong>Output:</strong> false
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 30</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    bool splitArraySameAverage(vector<int>& A) {
        int n = A.size(), m = n/2, totalSum = accumulate(A.begin(), A.end(), 0);
        // early pruning
        bool isPossible = false;
        for (int i = 1; i <= m && !isPossible; ++i) 
            if (totalSum*i%n == 0) isPossible = true;
        if (!isPossible) return false;
        // DP like knapsack
        vector<unordered_set<int>> sums(m+1);
        sums[0].insert(0);
        for (int num: A) {
            for (int i = m; i >= 1; --i) 
                for (const int t: sums[i-1]) 
                    sums[i].insert(t + num);
        }
        for (int i = 1; i <= m; ++i) 
            if (totalSum*i%n == 0 && sums[i].find(totalSum*i/n) != sums[i].end()) return true;
        return false;
    }
};
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