Check leaf nodes of binary tree are at same level – BFS / example

• Given a binary tree, We would like to find out, whether leaf nodes of a binary are at same level.
• We will use level order traversal or breadth first search (BFS) algorithm to traverse the binary tree.
• What is level in a binary tree?
  • Level is distance or hops of node with respect to root node.
  • The root node is considered to be at level 0 and immediate children of root node will be at level 1 (level of root node + 1).
  • We can calculate the level of all the nodes in binary tree (Refer Fig 1).

Example 1:  Given a binary tree (Fig 2), Check whether leaf nodes are at same level.

• Traverse the binary tree using breadth first search algorithm.
• Find out the level of each leaf node. (refer below table).

We have discussed similar the problem Find Max width of a binary tree . Let us discuss the breadth first search algorithm to check whether leaf nodes are at same level.

• Create variable level=0, signify the level of binary tree
  • Root is at level 0, push the root to queue.
• Add null to the queue (delimiter to know that we have finished the current level)
• Iterate through the Queue
  • Pop node from queue
  • Check node is null [The delimiter added earlier]
    • We are at next level and increment the level
  • Verify that popped up node is leaf node (or not)
    • First time, we are visiting the leaf node
      • Note down the level of leaf node and mark it visited.
    • We got the leaf node again
      • Compare the already stored level with current level
        • If difference return false
    • Else perform rest operations
  • Add next level children (left & right child)
• Once we exit the loop, we will know, whether leaves are same level (or not)

Example 2: Check level of leaf nodes in a given binary tree (Fig 3)

We will follow the similar algorithm for current example and we will find out level of each leaf node.
Time complexity:  O(n).
Let us look into the complete code as follows:
1.) IsLeafAtSameLevel Class: IsLeafAtSameLevel class is used to check whether leaf nodes of binary tree are at same level using breadth first search recursive algorithm.

package org.learn.Question;

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

public class IsLeavesAtSameLevel {
	public static boolean isLeavesAtSameLevel(Node root) {
		if (root == null) {
			System.out.println("Tree is empty");
			return false;
		}
		Queue<Node> queue = new LinkedList<Node>();
		queue.offer(root);
		// level delimiter
		queue.offer(null);
		int level = 0;
		boolean bLeafFound = false;
		int leafLevel = -1;

		while (!queue.isEmpty()) {
			Node node = queue.poll();
			// Level change
			if (null == node) {
				if (!queue.isEmpty()) {
					// level delimiter
					queue.offer(null);
				}
				level++;
			} else {
				if (node.left == null && node.right == null) {
					// first leaf found
					if (bLeafFound == false) {
						bLeafFound = true;
						leafLevel = level;
					} else { // Leaves are at different level
						if (leafLevel != level) {
							return false;
						}
					}
				}
				if (node.left != null) {
					queue.offer(node.left);
				}
				if (node.right != null) {
					queue.offer(node.right);
				}
			}
		}
		return true;
	}
}

2.) Node Class: Node class representing the nodes of a binary tree.  Node class has following attributes

• Data Node
• left child
• right child

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 the binary tree in main function & we are calling IsLeafAtSameLevel class, to find out whether leaf nodes are at same level using level order traversal.

package org.learn.Client;

import org.learn.Question.IsLeavesAtSameLevel;
import org.learn.Question.Node;

public class App 
{
    public static void main( String[] args )
    {  
       //root level 0
       Node A = Node.createNode(50);
       //Level 1
       Node B = Node.createNode(25);
       Node C = Node.createNode(75);
       //Level 2
       Node D = Node.createNode(10);
       Node E = Node.createNode(30);
       Node F = Node.createNode(60);
       Node G = Node.createNode(80);
       //Level 3
       Node H = Node.createNode(55);
       Node I = Node.createNode(65);
             
       //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;
       
       boolean isLeafAtSameLevel = IsLeavesAtSameLevel.isLeavesAtSameLevel(A);      
       if(isLeafAtSameLevel) {
    	   System.out.println("1. Leaf nodes of binary tree are at same level");
       } else {
    	   System.out.println("1. Leaf nodes of binary tree are not at same level");
       }
       
       //Connect level 2 and level 3
       F.left = H;
       F.right = I; 
       isLeafAtSameLevel = IsLeavesAtSameLevel.isLeavesAtSameLevel(A);      
       if(isLeafAtSameLevel) {
    	   System.out.println("2. Leaf nodes of binary tree are at same level");
       } else {
    	   System.out.println("2. Leaf nodes of binary tree are not at same level");
       }
    }
}

The output of main function [Fig 2 and Fig 3] is as follows:

1. Leaf nodes of binary tree are at same level
2. Leaf nodes of binary tree are not at same level

Download Code – Level of leaf node in binary tree (BFS)