Write an algorithm to find the size of a binary tree without using recursion.

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

We discussed how to find the size of a binary tree using the recursive method in this post:-

• Write an algorithm to find the size of a binary tree

This technique involved recursion and the understanding can be a bit complicated. If you prefer to go through the iterative way, we can simple do a level order traversal on the tree. At the time of printing the node, if we increment a counter variable, that will give us the number of total nodes in the end. So with a simple modification, we can write the code as:-

#include<stdio.h>

struct binaryTreeNode{
	int data;
	struct binaryTreeNode * left;
	struct binaryTreeNode * right;
};

// Iterative method to find the size of a binary tree
// FInding the number of nodes
int sizeOfBinaryTree(struct binaryTreeNode * root)
{
	// Counter variable to store the number of nodes
	int count = 0;
	
	// Level order traversal
	struct binaryTreeNode * temp = NULL;
	struct queue * Q = NULL;
	if(root == NULL)
		return 0;

	Q = enQueue(Q, root);
	while(!isQueueEmpty(Q))
	{
		temp = Q -> front -> data;
		Q = deQueue(Q);

		// We increment the counter here
		count++;

		if(temp -> left)
			Q = enQueue(Q, temp -> left);
		if(temp -> right)
			Q = enQueue(Q, temp -> right);
	}
	free(Q);
	
	return count;
}

Time Complexity:- O(n)
Space Complexity:- O(n)

Ideone link for running code:- http://ideone.com/UgS9nO