Count Non-Leaf nodes in a Binary Tree

Given a Binary tree, count total number of non-leaf nodes in the tree

Examples:

Input :


Output :2
Explanation
In the above tree only two nodes 1 and 2 are non-leaf nodes

We recursively traverse the given tree. While traversing, we count non-leaf nodes in left and right subtrees and add 1 to the result.

// CPP program to count total number of
// non-leaf nodes in a binary tree
#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;
    struct Node* right;
};

/* 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);
}

/* Computes the number of non-leaf nodes in a tree. */
int countNonleaf(struct Node* root)
{
    // Base cases.
    if (root == NULL || (root->left == NULL && 
                         root->right == NULL))
        return 0;

    // If root is Not NULL and its one of its
    // child is also not NULL
    return 1 + countNonleaf(root->left) + 
               countNonleaf(root->right);
}

/* Driver program to test size function*/
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);
    cout << countNonleaf(root);
    return 0;
}

Output:

2

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