<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 solve(unordered_map<string, bool> &dp, int ind, int sum, int sz, vector<int> &nums)
    {
        // if(sum==0) return (sz==0);
        // if(sz==0) return (sum==0);
        // if(ind>=nums.size()) return 0;
        if(ind>=nums.size()) return (sum==0)&&(sz==0);
        if(sz==0) return (sum==0);
        string k=to_string(ind)+" "+to_string(sum)+" "+to_string(sz);
        // if(dp[ind][sum][sz]!=-1) return dp[ind][sum][sz];
        if(dp.find(k)!=dp.end()) return dp[k];
        int ans=0;
        ans|=solve(dp, ind+1, sum, sz, nums);
        if(ans) return dp[k]=ans;
        if(sum>=nums[ind]) ans|=solve(dp, ind+1, sum-nums[ind], sz-1, nums);
        return dp[k]=ans;
    }

    bool splitArraySameAverage(vector<int>& nums) {
        int sum=0;
        int n=nums.size();
        for(int i=0 ; i<n ; i++) sum+=nums[i];
        // vector<vector<vector<int>>> dp(n+1, vector<vector<int>> (sum+1, vector<int> (n+1, -1)));
        unordered_map<string, bool> dp;
        for(int i=1 ; i<n ; i++)
        {
            if((sum*i)%n==0)
            {
                int s1=(sum*i)/n;
                if(solve(dp, 0, s1, i, nums)) return true;
            }
        }
        return false;
    }
};
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