Find number of nodes/size of binary tree in java (BFS / example)

• Given a binary tree, count number of nodes using non recursive algorithm.
• We will calculate size of binary tree using breadth first search (bfs) or level order traversal algorithm.
• During binary tree traversal, we will keep on adding the number of elements at each level.
  • At end of traversal, we will get number of nodes in a binary tree.

Algorithm: count number of nodes in a binary tree using java(Fig 1)

• Create local variable nNodes (signify the node count)
  • nNodes initialized to 0
• Visit the Level 0
  • visit all nodes in Level 0 and found only node A
  • nNodes increment by 1 [nNodes = 1]
• Go to Level 1 and visit all nodes in Level 1
  • Found node B,  nNodes increment by 1  [nNodes = 2]
  • Found node C, nNodes increment by 1  [nNodes = 3]
• Go to Level 2 and visit all nodes in Level 2
  • Found node D, nNodes increment by 1 [nNodes = 4]
  • Found node E, nNodes increment by 1  [nNodes = 5]
  • Found node F, nNodes increment by 1   [nNodes = 6]
  • Found node G, nNodes increment by 1 [nNodes = 7]
• Visited all nodes in binary tree [Refer Fig 2]

The time complexity of algorithm is O(n).

Program – number of nodes or size of a binary tree using java (BFS)

1.) CountNodes Class:

• Find number of nodes or size of a binary tree.
• Traverse binary tree using level order traversal.

package org.learn.Question;

import java.util.LinkedList;
import java.util.Queue;

public class CountNodes {
	public static int countNodes(Node root) {
		if (root == null) {
			System.out.println("Tree is empty");
			return -1;
		}
		int nNodes = 0;
		Queue<Node> queue = new LinkedList<Node>();
		queue.offer(root);

		while (!queue.isEmpty()) {
			Node node = queue.poll();									
			if (node.left != null) {
				queue.offer(node.left);
			}
			if (node.right != null) {
				queue.offer(node.right);
			}
			nNodes++;
		}
		System.out.println("Number of nodes in a binary tree : " + nNodes);
		return nNodes;
	}
}

2.) Node Class:

• Node class is representing the nodes of a binary tree.

package org.learn.Question;

public class Node {
	public int data;
	public Node left;
	public Node right;

	public Node(int num) {
		this.data = num;
		this.left = null;
		this.right = null;
	}

	public Node() {
		this.left = null;
		this.right = null;
	}
	
	public static Node createNode(int number) {
		return new Node(number);
	}
}

3.) App Class:

• We are creating a binary tree in main method
• We are calling method of CountNodes class, to find number of nodes in a binary tree.

package org.learn.Client;

import org.learn.Question.CountNodes;
import org.learn.Question.Node;

public class App {
	public static void main(String[] args) {
		// root level 0
		Node A = Node.createNode(55);
		// Level 1
		Node B = Node.createNode(50);
		Node C = Node.createNode(40);
		// Level 2
		Node D = Node.createNode(25);
		Node E = Node.createNode(80);
		Node F = Node.createNode(45);
		Node G = Node.createNode(90);

		// connect Level 0 and 1
		A.left = B;
		A.right = C;
		// connect level 1 and level 2
		B.left = D;
		B.right = E;
		C.left = F;
		C.right = G;

		CountNodes.countNodes(A);
	}
}

Output – Size of binary tree using level order traversal using java

Number of nodes in a binary tree : 7

Download code – size of binary tree non recursive algorithm in java