<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:
    unordered_map<string,bool>dp;
    
    bool split(int idx, int sum, int c, vector<int>& nums){

        if(sum == 0 && c == 0) return true;

        if(idx >= nums.size() || sum < 0 || c < 0) return false;

        string key = to_string(idx)+" "+to_string(sum)+" "+to_string(c);

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

        return dp[key] =  split(idx+1, sum - nums[idx], c-1, nums) || split(idx+1, sum, c, nums);
    }
    bool splitArraySameAverage(vector<int>& nums) {
        
        int n = nums.size();
        int sum = accumulate(nums.begin(), nums.end(), 0);
        
        bool ans = false;
        for(int c=1; c<n-1; c++){
            if((sum*c)%n) continue;
            
            int sum_req = (sum*c)/n;
            ans = split(0,sum_req,c,nums);

            if(ans)
               return true;
        }
        return false;
    }
};
152091