<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:
    vector<vector<vector<bool>>> dp;
    bool func(int idx, int cnt, int sum, vector<int>& nums){
        if(idx == -1 or sum < 0) return false;
        if(cnt == 0) return !sum; 
        if(dp[idx][cnt][sum] == false) return false;
        return dp[idx][cnt][sum] = func(idx - 1, cnt, sum, nums) || (nums[idx] <= sum and func(idx - 1, cnt - 1, sum - nums[idx], nums)); 
    }
    bool splitArraySameAverage(vector<int>& nums) { 
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        int sum = accumulate(nums.begin(), nums.end(), 0), n = nums.size();
        dp.resize(n, vector<vector<bool>>(n, vector<bool>(sum + 1, true)));
        for(int i = 1; i <= n-1; i++)
            if((sum * i) % n == 0 and func(n-1, i, (i * sum) / n, nums)) 
                return 1;
        return 0;
    }
};
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