Find maximum width of binary tree using BFS (with example)

• Given a binary tree, find out maximum width of a binary tree using non recursive algorithm.
• Traverse the binary tree using breadth first search  (BFS) or level order traversal algorithm.
• What is width of a binary tree?
  • The number of nodes at any level gives the width of binary tree (at that level)
  • Calculate the width at each level of binary tee.
  • The maximum among the widths, calculate at each level, is maximum width of binary tree.
• We have discussed the similar problem Find Level in binary tree having maximum sum.

Example: find width of binary tree bfs algorithm

• Traverse the binary tree using level order traversal.
• Calculate the width at each level.
• Maximum width = max (level 1, ,level 2 …level n)

Let us calculate the width at each level. The table is showing the width at each level.

The maximum width of binary tree is 4 at level 2.

Algorithm – calculate width of binary tree (level order traversal)

We will use breadth first search or level order traversal to iterate through the binary tree.

• Create variable maxWidth=0 for maximum width of binary tree
• Create variable to localWidth=0 for width at each level
• Insert root to queue
• Add null to the queue (level delimiter)
• Iterate through the Queue
  • Pop node from queue & check for null
    • We are at next level & compare localWidth of current level with maxWidth
    • If localWidth is more than maxWidth then update maxWidth
    • Reset localWidth to zero
  • Add next level children (left and right child)
  • Increment width of current level by 1 (localWidth++)
• Once we exit the loop, we will get the maximum width.

Program – calculate width of binary tree (level order traversal)

1.) MaxWidthOfBTree Class: MaxWidthOfBTree class is used to find the maximum width of a binary tree.

package org.learn.Question;

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

import org.learn.PrepareTree.Node;

public class MaxWidthOfBTree {
	public static void  maxWidthOfBTree(Node root) {
		if (root == null) {
			System.out.println("Tree is empty");
			return ;
		}
		Queue<Node> queue = new LinkedList<Node>();
		queue.offer(root);
		//level delimiter
		queue.offer(null);

		int maxWidth = 0;
		int level = 0;
		//default root level
		int localLevel = 0;
		int localWidth = 0;
		while (!queue.isEmpty()) {
			Node node = queue.poll();
			//Level change
			if (null == node) {
				if (!queue.isEmpty()) {
					//level delimiter
					queue.offer(null);
				}
				
				if(localWidth > maxWidth) {
					maxWidth = localWidth;
					level = localLevel;
				}
				//Reset the level sum for next level calculation
				localWidth = 0;		
				localLevel ++;
			} else {
				if (node.left != null) {
					queue.offer(node.left);
				}
				if (node.right != null) {
					queue.offer(node.right);
				}
				localWidth ++;
			}
		}
		System.out.printf("Max Width %d is at level %d \n",maxWidth,level);
		return;
	}
}

2.) Node Class: The class representing the nodes of a binary tree.

package org.learn.PrepareTree;

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 the binary tree in a main method & calling the method of MaxWidthOfBTree class, to find the maximum width in a binary tree.

package org.learn.Client;

import org.learn.PrepareTree.Node;
import org.learn.Question.MaxWidthOfBTree;

public class App 
{
    public static void main( String[] args )
    {  
       //root level 0
       Node A = Node.createNode(100);
       
       //Level 1
       Node B = Node.createNode(50);
       Node C = Node.createNode(150);
       
       //Level 2
       Node D = Node.createNode(25);
       Node E = Node.createNode(75);
       Node F = Node.createNode(125);
       Node G = Node.createNode(175);
       
       //Level 3
       Node H = Node.createNode(120);
       Node I = Node.createNode(140);
             
       //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;
       //Connect level 2 and level 3
       F.left = H;
       F.right = I;
       MaxWidthOfBTree.maxWidthOfBTree(A);   
    }
}

Output – width of binary tree using non recursive algorithm

Max Width 4 is at level 2

Download Code – calculate max width of binary tree(BFS)