<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 splitArray(vector<int>& nums, int i, int sum, int count, map<string, bool> &dp){
        int n = nums.size();

        string key = to_string(i) + ' ' + to_string(sum) + ' ' + to_string(count);
        
        if(sum == 0 && count == 0){
            return true;
        }

        if(i >= n || count < 0 || sum < 0)
            return false;

        if(dp.find(key) != dp.end()){
            return dp[key];
        }

        return dp[key] = 
            splitArray(nums, i + 1, sum - nums[i], count - 1, dp) || 
            splitArray(nums, i + 1, sum , count, dp);
    }

    bool splitArraySameAverage(vector<int>& nums) {
        int n = nums.size();
        int sum = accumulate(nums.begin(), nums.end(), 0);
    
        map<string, bool> dp;

        bool ans = false;
        
        for(int c = 1; c <= n / 2 && !ans; c++){
            if((sum * c) % n)
                continue;
                
            int s = sum * c / n;

            ans = splitArray(nums, 0, s, c, dp);

        }

        return ans;
    }
};
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