<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>& nums) {
    int sum{0};

    for (int num : nums)
      sum += num;

    int n{static_cast<int>(nums.size())};
    vector<vector<vector<bool>>> record(n, vector<vector<bool>>(n, vector<bool>(sum / 2 + 1, true)));

    for (int i = 1; i <= n / 2; i++) {
      if (sum * i % n == 0 && recursiveSolve(record, nums, 0, i, sum * i / n))
        return true;
    }

    return false;
  }

 private:
  bool recursiveSolve(vector<vector<vector<bool>>>& record, vector<int>& nums, int startIndex, int nums2Select, int sum) {
    if (sum < 0)
      return false;

    if (!nums2Select)
      return sum == 0;

    if (startIndex == record.size())
      return false;
    
    if (!record[startIndex][nums2Select][sum])
      return false;

    if (recursiveSolve(record, nums, startIndex + 1, nums2Select - 1, sum - nums[startIndex]) || recursiveSolve(record, nums, startIndex + 1, nums2Select, sum))
      return true;

    record[startIndex][nums2Select][sum] = false;
    return false;
  }
};
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