<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)
    {
        // adds all numbers of nums
        int sum = reduce(nums.begin(), nums.end());
        int n = nums.size();
        // dp[index][subarray_size][subarray_sum]
        vector<vector<vector<bool>>> dp(n, vector<vector<bool>>(n + 1, vector<bool>(sum + 1, true)));

        for (int size = 1; size < n; size++)
        {
            if (sum * size % n == 0 && dfs(nums, dp, n - 1, size, sum * size / n))
                return true;
        }
        return false;
    }

private:
    bool dfs(vector<int> &nums, vector<vector<vector<bool>>> &dp, int i, int size, int sum)
    {
        if (i < 0 || size < 0 || sum < 0)
            return false;
        if (dp[i][size][sum] == false)
            return false;

        if (size == 0)
            return dp[i][size][sum] = (sum == 0);

        // we have 2 choice at element i, take it or leave it
        bool include = dfs(nums, dp, i - 1, size - 1, sum - nums[i]);
        if (include)
            return dp[i][size][sum] = include;

        bool dontInclude = dfs(nums, dp, i - 1, size, sum);
        return dp[i][size][sum] = dontInclude;
    }
};
192718