<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 {
    
//     int n;
//     vector<int>nums;
//     unordered_map<string, int>mymap;
    // bool helper(vector<int>&nums,  int i, int count, int sum )
    // {
    //     if(count==0)
    //     {
    //         return sum==0;
    //     }
    //     else if(i==n)
    //     {
    //         return 0;
    //     }
    //     string s1=to_string(i)+"?"+to_string(count)+"?"+to_string(sum);
    //     if(mymap.count(s1))
    //     {
    //         return mymap[s1];
    //     }
    //     if(nums[i]>sum)
    //     {
    //         return mymap[s1]=helper(nums,i+1, count, sum);
    //     }
    //     bool b1=helper(nums,i+1, count, sum);
    //     bool b2=helper(nums,i+1, count-1, sum-nums[i]);
    //     return mymap[s1]=b1||b2;
    // } 
// public:
//     bool splitArraySameAverage(vector<int>& nums) {
//         this->n=nums.size();
//         this->nums=nums;
//         if(n==1)
//         {
//             return 0;
//         }
//         int sum=0;
//         for(auto &it: nums)
//         {
//             sum+=it;
//         }
//         if(sum==0)
//         {
//             return 1;
//         }
//         for(int i=1; i<=(n+1)/2; i++)
//         {
//             if((sum*i)%n==0)
//             {
                
//                 bool b1=helper(nums,0, i, (sum*i)/n);
//                 if(b1==true)
//                 {
//                     return true;
//                 }
//             }
//         }
//         return false;
//     }
// };


class Solution {
public:
    int n;
            unordered_map<string, int>mymap;

    bool helper(vector<int>&nums,  int i, int count, int sum )
    {
        if(count==0)
        {
            return sum==0;
        }
        else if(i==n)
        {
            return 0;
        }
        string s1=to_string(i)+""+to_string(count)+"?"+to_string(sum);
        if(mymap.count(s1))
        {
            return mymap[s1];
        }
        if(nums[i]>sum)
        {
            return mymap[s1]=helper(nums,i+1, count, sum);
        }
        bool b1=helper(nums,i+1, count, sum)||helper(nums,i+1, count-1, sum-nums[i]);
        return mymap[s1]=b1;
    }

    // declare a map
    
    // unordered_map<string, int> mp;
    
    // bool helper(vector<int>& nums, int i, int n, int sum, int n1)
    // {
    //     // base case
        
    //     if(n1 == 0)
    //         return sum == 0;
        
    //     if(i == n)
    //         return false;
        
    //     // create a key
        
    //     string key = to_string(i) + "#" + to_string(n1) + "#" + to_string(sum);
        
    //     // if already calculated
        
    //     if(mp.count(key))
    //         return mp[key];
        
    //     // if nums[i] <= sum, then we will either include or exclude
        
    //     // calculate the result and store in map
       
    //     if(nums[i] <= sum)
    //     {
    //         return mp[key] = helper(nums, i + 1, n, sum - nums[i], n1 - 1) || helper(nums, i + 1, n, sum, n1);
    //     }
    //     else
    //         return mp[key] = helper(nums, i + 1, n, sum, n1);
    // }
    
    bool splitArraySameAverage(vector<int>& nums) {
        
         n = nums.size();
        
        // find the total sum

        int sum = 0;
        
        for(int i = 0; i < n; i++)
        {
            sum += nums[i];
        }
        
        // check for every possible size of subset from 1 to n - 1
        
        for(int n1 = 1; n1 < n; n1++)
        {
            if((sum * n1) % n == 0)
            {
                int req_sum = (sum * n1) / n;
                
                // check if there is any subset of n1 that has sum of req_sum
            
                // if(helper(nums, 0, n, req_sum, n1))
                //     return true;
                if(helper(nums, 0, n1, req_sum ))
                    return true;
            }
        }
        
        return false;
    }
};
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