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Question:Given the root pointer to a binary tree, find its size.

Input:Sample Tree (Pointer to node 1 is given). Find the size

Output:Size = 7

** The size of the binary tree is basically the number of nodes in a binary tree**. Since, the tree follows a recursive approach we can easily solve this problem by recursion. We calculate the size of left and right sub-tree recursively, add 1 (current node) and return to its parent.

The recursive implementation can be done as:-

#include<stdio.h> struct binaryTreeNode{ int data; struct binaryTreeNode * left; struct binaryTreeNode * right; }; // Recursive method to find the size of binary tree // Finding the number of nodes int sizeOfBinaryTreeRecursive(struct binaryTreeNode * root) { if(root == NULL) return 0; else { // We recursively travel the left sub-tree // Add 1 for the root nodes // We then recursively travel the right sub-tree return (sizeOfBinaryTreeRecursive(root -> left) + 1 + sizeOfBinaryTreeRecursive(root -> right)); } }

### EXPLANATION

#### CASE 1 :

When the root is null, it simply returns 0, because no nodes are present in tree.

if(root == NULL) return 0;

#### CASE 2 :

Now let us take a case when only 1 node is present.

The else block executes

return (sizeOfBinaryTreeRecursive(root -> left) + 1 + sizeOfBinaryTreeRecursive(root -> right));

This happens in the statement:-

**root -> left is NULL**in this case and from above CASE 1 it will**return = 0****add 1****root -> right is NULL**again and from above CASE 1 it will**return = 0**

**So the statement will return = 0 + 1 + 0**

** Hence, the size of the tree = 1**

#### CASE 3 :

Taking a case of 1 node and left sub-tree.

Now when the command is executed

sizeOfBinaryTreeRecursive(root -> left)

The left sub-tree comes into consideration and we have the **root pointer as -> 2**

And from the above case we know that **this tree will return a value of = 1**

So, now we again have:-

**root -> left is sub-tree**in this case and from above CASE 2 it will**return = 1****add 1****root -> right is NULL**again and from above CASE 1 it will**return = 0**

**So, the statement will return = 1 + 1 + 0**

** Hence, the size of tree = 2**

#### CASE 4 :

Taking the generalized case of 3 nodes, root left sub-tree and right sub-tree.

Now we simply have a right sub-tree as well.

**root -> left is sub-tree**in this case and from above CASE 2**it will return = 1****add 1****root -> right is a sub-tree**which will be similar to above CASE 2 and**return = 1**

**So, the statement will return = 1 + 1 + 1**

** Hence, the size of the tree = 3**

Thus, from the visualization of the above algorithm we can see that because of the repeating property of tree structure, size of tree can be calculated.

*Time Complexity:-* O(n)

* Space Complexity:-* O(n)

**Method 2:-** Find the size of the binary tree without using recursion.