Given a Binary Tree having positive and negative nodes, the task is to find the maximum sum of non-leaf nodes among all level of given binary tree.

**Examples:**

Input:4 / \ 2 -5 / \ -1 3Output:4 Sum of all non-leaf nodes at 0^{th}level is 4. Sum of all non-leaf nodes at 1^{st}level is 2. Sum of all non-leaf nodes at 2^{nd}level is 0. Hence maximum sum is 4Input:1 / \ 2 3 / \ \ 4 5 8 / \ 6 7Output:8

**Approach:** The idea to solve the above problem is to do level order traversal of tree. While doing traversal, process nodes of different level separately. For every level being processed, compute the sum of non-leaf nodes in the level and keep track of the maximum sum.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// A binary tree node has data, pointer to left child ` `// and a pointer to right child ` `struct` `Node { ` ` ` `int` `data; ` ` ` `struct` `Node *left, *right; ` `}; ` ` ` `// Function to return the maximum sum of non-leaf nodes ` `// at any level in tree using level order traversal ` `int` `maxNonLeafNodesSum(` `struct` `Node* root) ` `{ ` ` ` `// Base case ` ` ` `if` `(root == NULL) ` ` ` `return` `0; ` ` ` ` ` `// Initialize result ` ` ` `int` `result = 0; ` ` ` ` ` `// Do Level order traversal keeping track ` ` ` `// of the number of nodes at every level ` ` ` `queue<Node*> q; ` ` ` `q.push(root); ` ` ` `while` `(!q.empty()) { ` ` ` ` ` `// Get the size of queue when the level order ` ` ` `// traversal for one level finishes ` ` ` `int` `count = q.size(); ` ` ` ` ` `// Iterate for all the nodes in the queue currently ` ` ` `int` `sum = 0; ` ` ` `while` `(count--) { ` ` ` ` ` `// Dequeue a node from queue ` ` ` `Node* temp = q.front(); ` ` ` `q.pop(); ` ` ` ` ` `// Add non-leaf node's value to current sum ` ` ` `if` `(temp->left != NULL || temp->right != NULL) ` ` ` `sum = sum + temp->data; ` ` ` ` ` `// Enqueue left and right children of ` ` ` `// dequeued node ` ` ` `if` `(temp->left != NULL) ` ` ` `q.push(temp->left); ` ` ` `if` `(temp->right != NULL) ` ` ` `q.push(temp->right); ` ` ` `} ` ` ` ` ` `// Update the maximum sum of leaf nodes value ` ` ` `result = max(sum, result); ` ` ` `} ` ` ` ` ` `return` `result; ` `} ` ` ` `// Helper function that allocates a new node with the ` `// given data and NULL left and right pointers ` `struct` `Node* newNode(` `int` `data) ` `{ ` ` ` `struct` `Node* node = ` `new` `Node; ` ` ` `node->data = data; ` ` ` `node->left = node->right = NULL; ` ` ` `return` `(node); ` `} ` ` ` `// 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(6); ` ` ` `root->right->right->right = newNode(7); ` ` ` `cout << maxNonLeafNodesSum(root) << endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Python3

`# Python3 implementation of the approach ` `import` `queue ` ` ` `# A binary tree node has data, pointer to ` `# left child and a pointer to right child ` `class` `Node: ` ` ` ` ` `def` `__init__(` `self` `, data): ` ` ` `self` `.data ` `=` `data ` ` ` `self` `.left ` `=` `None` ` ` `self` `.right ` `=` `None` ` ` `# Function to return the maximum Sum of ` `# non-leaf nodes at any level in tree ` `# using level order traversal ` `def` `maxNonLeafNodesSum(root): ` ` ` ` ` `# Base case ` ` ` `if` `root ` `=` `=` `None` `: ` ` ` `return` `0` ` ` ` ` `# Initialize result ` ` ` `result ` `=` `0` ` ` ` ` `# Do Level order traversal keeping track ` ` ` `# of the number of nodes at every level ` ` ` `q ` `=` `queue.Queue() ` ` ` `q.put(root) ` ` ` `while` `not` `q.empty(): ` ` ` ` ` `# Get the size of queue when the level ` ` ` `# order traversal for one level finishes ` ` ` `count ` `=` `q.qsize() ` ` ` ` ` `# Iterate for all the nodes ` ` ` `# in the queue currently ` ` ` `Sum` `=` `0` ` ` `while` `count: ` ` ` ` ` `# Dequeue a node from queue ` ` ` `temp ` `=` `q.get() ` ` ` ` ` `# Add non-leaf node's value to current Sum ` ` ` `if` `temp.left !` `=` `None` `or` `temp.right !` `=` `None` `: ` ` ` `Sum` `+` `=` `temp.data ` ` ` ` ` `# Enqueue left and right ` ` ` `# children of dequeued node ` ` ` `if` `temp.left !` `=` `None` `: ` ` ` `q.put(temp.left) ` ` ` `if` `temp.right !` `=` `None` `: ` ` ` `q.put(temp.right) ` ` ` ` ` `count ` `-` `=` `1` ` ` ` ` `# Update the maximum Sum of leaf nodes value ` ` ` `result ` `=` `max` `(` `Sum` `, result) ` ` ` ` ` `return` `result ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `root ` `=` `Node(` `1` `) ` ` ` `root.left ` `=` `Node(` `2` `) ` ` ` `root.right ` `=` `Node(` `3` `) ` ` ` `root.left.left ` `=` `Node(` `4` `) ` ` ` `root.left.right ` `=` `Node(` `5` `) ` ` ` `root.right.right ` `=` `Node(` `8` `) ` ` ` `root.right.right.left ` `=` `Node(` `6` `) ` ` ` `root.right.right.right ` `=` `Node(` `7` `) ` ` ` `print` `(maxNonLeafNodesSum(root)) ` ` ` `# This code is contributed by Rituraj Jain ` |

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**Output:**

8

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