# Split Array With Same Average in C++

Suppose we have one array A, we must move every element of A to either list B or list C. (These lists B and C are initially empty.) We have to check whether after such a move, it is possible that the average value of B is equal to the average value of C, and B and C are both non-empty.

So if the input is like − [1,2,3,4,5,6,7,8,9,10], then the result will be true,

To solve this, we will follow these steps −

• n := size of A, total := 0
• for initialize i := 0, when i < n, update (increase i by 1), do −
• total := total + A[i]
• isPossible := false, m := n / 2
• for initialize i := 1, when i <= m and not isPossible is non-zero, update (increase i by 1), do −
• if total * i mod n is same as 0, then −
• isPossible := true
• if not isPossible is non-zero, then −
• return false
• Define one 2D array dp of size (total + 1) x (n / 2) + 1)
• dp[0, 0] := true
• for initialize i := 0, when i < n, update (increase i by 1), do −
• x := A[i]
• for initialize j := total, when j >= x, update (decrease j by 1), do −
• for initialize l := 1, when l <= (n / 2), update (increase l by 1), do −
• dp[j, l] := dp[j, l] OR dp[j - x, l - 1]
• for initialize i := 1, when i <= (n / 2), update (increase i by 1), do −
• if (total * i) mod n is same as 0 and dp[total * i / n, i] is non-zero, then −
• return true
• return false

Let us see the following implementation to get better understanding −

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
bool splitArraySameAverage(vector<int>& A) {
int n = A.size();
int total = 0 ;
for(int i = 0; i < n; i++) total += A[i];
bool isPossible = false;
int m = n / 2;
for (int i = 1; i <= m && !isPossible; ++i)
if (total*i%n == 0) isPossible = true;
if (!isPossible) return false;
vector < vector <bool> > dp(total + 1, vector <bool>((n / 2) + 1));
dp = true;
for(int i = 0; i < n; i++){
int x = A[i];
for(int j = total; j >= x; j--){
for(int l = 1; l <= (n / 2); l++){
dp[j][l] = dp[j][l] || dp[j - x][l - 1];
}
}
}
for(int i = 1 ; i <= (n / 2); i++){
if((total * i) % n == 0 && dp[total * i / n][i]) return true;
}
return false;
}
};
main(){
Solution ob;
vector<int> v = {1,2,3,4,5,6,7,8,9,10};
cout << (ob.splitArraySameAverage(v));
}

## Input

{1,2,3,4,5,6,7,8,9,10}

## Output

1