<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:
//     sum1 + sum2 = totalsum
//     n1 + n2 = n
//     sum1/n1 = sum2/n2
//     sum1 = sum2(n - n2)/n2
//     sum1 = sum2*n/n2 - sum2
//     totalsum = sum1*n/n1
//     sum1 = totalsum*n1/n
    
    unordered_map<string, int> dp;
    bool find(int ind, int remsum, int k, vector<int>& nums){
        int n = nums.size();
        if(ind == n){
            if(k == 0 and remsum == 0)
                return true;
            return false;
        }
        string s = to_string(ind) + " " + to_string(remsum) + " " + to_string(k);
        if(dp.find(s) != dp.end()) return dp[s];
        bool ans = false;
        if(nums[ind] <= remsum and k > 0)
            ans = ans || find(ind + 1, remsum - nums[ind], k - 1, nums);
        ans = ans || find(ind + 1, remsum, k, nums);
        return dp[s] = ans;
    }
    bool splitArraySameAverage(vector<int>& nums) {
        int n = nums.size();
        int totalsum = accumulate(nums.begin(), nums.end(), 0);
        for(int n1 = 1; n1 < n; n1++){
            int sum1 = (totalsum * n1);
            if(sum1 % n)
                continue;
            sum1 = sum1 / n;
            if(find(0, sum1, n1, nums))
                return true;
        }
        return false;
    }
};
157895