# Count Number of Nodes in a Binary Tree

“** Count Number of Nodes in a Binary Tree**” is again a very basic problem of tree data structure. Here, we are given a tree and our task is to count the number of nodes in a tree.

There can be multiple methods to count the number of nodes in a binary tree. Some of them are:

- Using Recursive Approach
- Using Queue Data Structure

**METHOD 1: Using Recursive Approach**

This is a brute-force approach to count number of nodes in a binary tree. The steps required to count number of nodes in a binary tree are as follows:

- Initialize “count” variable as 1.
- If root is NULL, return 0.
- Else,

count = count + countNodes(root -> left) and

count = count + countNodes(root -> right

- Then, return count.

#### C++ Program to count number of nodes in a binary tree is as follows:

/* C++ Program to count number of nodes in a Binary Tree */ #include<bits/stdc++.h> using namespace std; typedef struct Node { int data; struct Node *left; struct Node *right; Node(int ele) { data = ele; left = NULL; right = NULL; } } Node; /* Function to count number of nodes in a Binary Tree */ int countNodes(Node *root) { int count = 1; /* Node itself should be counted */ if(root == NULL) { return 0; } else { count = count + countNodes(root -> left); count = count + countNodes(root -> right); return count; } } int main() { /* Creating a Binary tree and inserting some nodes in it */ Node *root = NULL; root = new Node(1); root -> left = new Node(2); root -> right = new Node(3); root -> left -> left = new Node(4); root -> left -> right = new Node(5); root -> right -> left = new Node(6); root -> right -> right = new Node (7); root -> left -> right -> left = new Node(8); root -> right -> left -> right = new Node(9); /* Calling function to Count Total Number of Nodes in a Binary Tree */ cout<<"The Total Number of Nodes in a Binary Tree are "<<countNodes(root); }

**OUTPUT:**

The Total Number of Nodes in a Binary Tree are 9

**METHOD 2: Using Queue Data Structure**

Here, the idea is to use level-order traversal to count number of nodes in a binary tree.

The steps required to count number of nodes in a binary tree are as follows:

- Create an empty queue and push root node in it.
- Initialize count as 0.
- Do following while queue not empty:
- Increment count with 1.
- If left child of current node exists, push it into queue.
- If right child of current node exists, push it into queue.
- Pop out the current node from queue.

#### C++ Program to count number of nodes in a binary tree are as follows:

/* C++ Program to count number of nodes in a Binary Tree */ #include<bits/stdc++.h> using namespace std; typedef struct Node { int data; struct Node *left; struct Node *right; Node(int ele) { data = ele; left = NULL; right = NULL; } } Node; /* Function to count number of nodes in a Binary Tree */ int countNodes(Node *root) { /* Basic Test Case Scenerio */ if(root == NULL) return 0; /* Create Queue and push root node in it */ queue <Node *> qu; qu.push(root); int count = 0; /* Apply Level-Order Traversal */ while(!qu.empty()) { count ++; if(qu.front() -> left) qu.push(qu.front() -> left); if(qu.front() -> right) qu.push(qu.front() -> right); qu.pop(); } return count; } int main() { /* Creating a Binary tree and inserting some nodes in it */ Node *root = NULL; root = new Node(1); root -> left = new Node(2); root -> right = new Node(3); root -> left -> left = new Node(4); root -> left -> right = new Node(5); root -> right -> left = new Node(6); root -> right -> right = new Node (7); root -> left -> right -> left = new Node(8); root -> right -> left -> right = new Node(9); /* Calling function to Count Total Number of Nodes in a Binary Tree */ cout<<"The Total Number of Nodes in a Binary Tree are "<<countNodes(root); }

**OUTPUT:**

The Total Number of Nodes in a Binary Tree are 9

**Related Posts:**

**Introduction to Tree Data Structure****Binary Tree Traversals****Print All Leaf Nodes of a Binary Tree****Print Alternate Levels of Binary Tree****Maximum Width of Binary Tree****Level Order Tree Traversal****Left View of Binary Tree****Right View of Binary Tree****Compute Height of Binary Tree****Inorder Tree Traversal Using Stack****Preorder Tree Trasversal Using Stack****Postorder Tree Traversal Using Stack****Vertical Order Tree Traversal****Top View of Binary Tree****Bottom View of Binary Tree****Delete Complete Binary Tree****Check if two trees are mirror Trees of Each Other****Convert Binary Tree to its Mirror Tree****Check if Binary Tree is Symmetric or Not****Print All Root to Leaf Paths in a Binary Tree**