# Check if max sum level of Binary tree divides tree into two equal sum halves

Given a Binary Tree, the task is to check if the maximum sum level divides the binary tree into the two parts of two equal sum halves.

Examples:

```Input:
1
/   \
2      3
/  \      \
4    5      8
/   \
2     4
Output: YES
Explanation:
The maximum sum level is 2 and
its sum is (4 + 5 + 8 = 17)
Sum of the upper half (1 + 2 + 3) = 6
Sum of the Lower half (2 + 4) = 6

Input:
10
/    \
20     30
/  \      \
4    5      1
Output: YES
Explanation:
The maximum sum level is 1 and
its sum is (20 + 30 = 50)
Sum of the upper half (10) = 10
Sum of the lower half (5 + 4 + 1) = 10
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to use level order traversal to compute the sum of every level of the binary tree. Then, find the maximum sum of the in all the levels. Finally check that the total sum of all the levels less than the maximum level sum is equal to the total sum of the levels of the greater than the maximum level sum.

Below is the implementation of the above approach:

 `// C++ implementation to check if ` `// maximum level sum divides the ` `// Binary tree into two equal sum halves ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Structure of the node ` `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node *left, *right; ` `}; ` ` `  `// Utility function to ` `// create a new node ` `struct` `Node* newNode(``int` `x) ` `{ ` `    ``struct` `Node* temp = ``new` `Node; ` `    ``temp->data = x; ` `    ``temp->left = temp->right = NULL; ` `    ``return` `temp; ` `}; ` ` `  `// Function to  check if ` `// maximum level sum divides the ` `// Binary tree into two equal sum halves ` `bool` `check_horizontal(``struct` `Node* root) ` `{ ` `    ``// Vector used to store the sum  ` `    ``// of all levels of the Binary Tree ` `    ``vector<``int``> sumLevel; ` `     `  `    ``// In index variable we store the  ` `    ``// level of the maximum level sum ` `    ``int` `index = -1, maxSum = 0, level = 0; ` ` `  `    ``queue q; ` `    ``q.push(root); ` ` `  `    ``while` `(!q.empty()) { ` `         `  `        ``// Varible to store the  ` `        ``// current level sum. ` `        ``int` `sum = 0; ` `         `  `        ``// Size of the Queue ` `        ``int` `n = q.size(); ` `         `  `        ``// Loop to iterate over the  ` `        ``// elements nodes of current level ` `        ``for` `(``int` `i = 0; i < n; i++) { ` `             `  `            ``// Inserting the next level  ` `            ``// elements to the Queue ` `            ``Node* temp = q.front(); ` `            ``sum += temp->data; ` `            ``if` `(temp->left != NULL) ` `                ``q.push(temp->left); ` `            ``if` `(temp->right != NULL) ` `                ``q.push(temp->right); ` `                 `  `            ``// Popping out the current  ` `            ``// level element from the Queue ` `            ``q.pop(); ` `        ``} ` `         `  `        ``// Storing the current level ` `        ``// sum into the vector ` `        ``sumLevel.push_back(sum); ` `         `  `        ``// Level of maximum  ` `        ``// horizontal sum line ` `        ``if` `(sum > maxSum) { ` `            ``maxSum = sum; ` `            ``index = level; ` `        ``} ` `        ``level++; ` `    ``} ` `    ``// Find the left half and right  ` `    ``// half sum and check if they are equal ` `    ``int` `leftSum = 0, rightSum = 0; ` `    ``for` `(``int` `i = 0; i < index; i++) { ` `        ``leftSum += sumLevel[i]; ` `    ``} ` ` `  `    ``for` `(``int` `i = index + 1;  ` `         ``i < sumLevel.size(); i++) { ` `        ``rightSum += sumLevel[i]; ` `    ``} ` `    ``return` `(leftSum == rightSum); ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` ` `  `    ``struct` `Node* root = newNode(1); ` `    ``root->left = newNode(2); ` `    ``root->right = newNode(3); ` `    ``root->left->left = newNode(4); ` `    ``root->left->right = newNode(5); ` `    ``root->right->right = newNode(8); ` `    ``root->right->right->left = newNode(2); ` `    ``root->right->right->right = newNode(4); ` ` `  `    ``// Condition to check if the  ` `    ``// maxumum sum level divides  ` `    ``// it into two equal half ` `    ``if` `(check_horizontal(root)) ` `        ``cout << ``"YES"` `<< endl; ` `    ``else` `        ``cout << ``"NO"` `<< endl; ` `} `

Output:
```YES
```

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