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# Count Non-Leaf nodes in a Binary Tree in C++

We are given with a binary tree and the task is to calculate the count of non-leaf nodes available in a binary tree.

Binary Tree is a special data structure used for data storage purposes. A binary tree has a special condition that each node can have a maximum of two children. A binary tree has the benefits of both an ordered array and a linked list as search is as quick as in a sorted array and insertion or deletion operation are as fast as in linked list. Non-leaf nodes are also known as parent nodes as they have more than 0 child and less than two children.

Structure of a binary tree is given below −

## For example

**Input** −

**Output **− count of non-leaf nodes is: 3

**Explanation** − In the given tree, we have 27, 14 and 35 as non-leaf nodes since they have more than 0 children and less than 2 children.

## Approach used in the below program is as follows

Create the structure of a binary tree containing, pointer to a left node, pointer to a right node and a data part stored in a node

Create a function that will insert a node whenever this function is called. For that, insert data in a new node and also set the right and left pointer of a new node to a NULL and return the node.

Create a recursive function that will count the number of non-leaf nodes in a binary tree.

- Check If root is NULL or left of root is NULL and right of root is NULL then return 0
- Return 1 + recursive call to this function with left pointer + recursive call to this function with right pointer

Print the count

## Example

#include <iostream> using namespace std; // Node's structure struct Node { int data; struct Node* left; struct Node* right; }; // To define the new node struct Node* newNode(int data){ struct Node* node = new Node; node->data = data; node->left = node->right = NULL; return (node); } // Count the non leaf nodes. int nonleaf(struct Node* root){ if (root == NULL || (root->left == NULL && root->right == NULL)){ return 0; } return 1 + nonleaf(root->left) + nonleaf(root->right); } // Main function int main(){ struct Node* root = newNode(10); root->left = newNode(21); root->right = newNode(33); root->left->left = newNode(48); root->left->right = newNode(51); cout << nonleaf(root); return 0; }

## Output

If we run the above code it will generate the following output −

count of non-leaf nodes is: 2

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