Introduction
Imagine exploring a multi-story building one floor at a time, from the ground level up. That's precisely how Level Order Traversal explores a tree, layer by layer. It's a fundamental technique, also known as Breadth-First Traversal, for solving a wide range of programming problems.
This comprehensive tutorial is your perfect starting point. We'll delve into the definition and mechanics of the Level Order Traversal of Tree, breaking down its concepts with simple, practical examples. You'll quickly grasp why this algorithm is an essential tool in any programmer's arsenal.
Don't just write code—architect solutions. With upGrad's Software Engineering courses, you'll learn to build powerful applications and secure the high-impact tech career you deserve.
Overview
Level Order Traversal is a tree traversal algorithm that begins to process the root node, and then moves on to the parent nodes at each level, before starting with the child nodes at the next level. This algorithm uses a queue data structure to ensure nodes are processed in the order of insertion.
Level Order Traversal is a fundamental algorithm with various applications, such as finding the shortest path, searching, and processing hierarchical data. Its simplicity and efficiency make it a valuable tool for solving programming challenges involving tree-like structures.
Also Read: What are Data Structures & Algorithm
How does Level Order Traversal work?
To understand how Level Order Traversal works we have to first mark the starting point of the algorithm, which is the root node. It then begins the process of enqueueing it into the queue structure. After this, the algorithm enters a loop where it constantly dequeues nodes from the front of the queue.
It performs the required functions and processes the dequeued node, before moving to the back of the queue gradually to enqueue its child nodes (if any). This loop continues until the queue becomes empty, indicating that all nodes in the tree have been visited.
By traversing nodes level by level, Level Order Traversal ensures that nodes at the same level are processed before moving to the next level. This approach ensures that each node in the tree is visited systematically. It is particularly helpful in scenarios where data needs to be manipulated, searched, printed, or processed in a breadth-first sequence. Moreover, the algorithm is efficient in finding the shortest path in unweighted graphs and is often employed in graph algorithms like Dijkstra's algorithm.
Ready to fast-track your tech career? Our Software Engineering Courses are your launchpad. Learn to innovate, lead projects, and build the future of tech.
Level Order Traversal (Naive Approach)
The naive approach to performing level order traversal involves iterating through the binary tree level by level and printing the nodes at each level. This is typically done using a loop for each level and another loop to traverse nodes at that level.
Here is the pseudocode for level order traversal of a binary tree using the naive approach:
levelOrderNaive(root):
if root is null:
return
height = getHeight(root)
for level = 1 to height:
printNodesAtLevel(root, level)
printNodesAtLevel(node, level):
if node is null:
return
if level == 1:
print(node.value)
else:
printNodesAtLevel(node.left, level - 1)
printNodesAtLevel(node.right, level - 1)
The naive approach involves calculating the height of the tree and then iterating through each level. In this approach, getHeight calculates the height of the tree, and printNodesAtLevel prints the nodes at a specific level using recursive calls. At each level, nodes are printed using recursive calls. This approach is less efficient because it involves a lot of redundant traversals as it repeatedly traverses the same nodes.
Here is the Java implementation of the naive approach:
Code:
class TreeNode {
int value;
TreeNode left;
TreeNode right;
TreeNode(int val) {
value = val;
left = null;
right = null;
}
}
public class BinaryTree {
TreeNode root;
public int getHeight(TreeNode node) {
if (node == null) {
return 0;
}
int leftHeight = getHeight(node.left);
int rightHeight = getHeight(node.right);
return Math.max(leftHeight, rightHeight) + 1;
}
public void printNodesAtLevel(TreeNode node, int level) {
if (node == null) {
return;
}
if (level == 1) {
System.out.print(node.value + " ");
} else {
printNodesAtLevel(node.left, level - 1);
printNodesAtLevel(node.right, level - 1);
}
}
public void levelOrderNaive(TreeNode root) {
if (root == null) {
return;
}
int height = getHeight(root);
for (int level = 1; level <= height; level++) {
printNodesAtLevel(root, level);
}
}
public static void main(String[] args) {
BinaryTree tree = new BinaryTree();
tree.root = new TreeNode(1);
tree.root.left = new TreeNode(2);
tree.root.right = new TreeNode(3);
tree.root.left.left = new TreeNode(4);
tree.root.left.right = new TreeNode(5);
tree.levelOrderNaive(tree.root);
}
}This program defines a TreeNode class representing a node in the tree, with integer value, left, and right children. The BinaryTree class contains methods to calculate the height of the tree and print nodes at a specific level. In the levelOrderNaive method, it calculates the height of the tree and then iterates through levels, calling printNodesAtLevel to print nodes at each level using recursive calls. The main function constructs a sample binary tree, and levelOrderNaive is called on the root node to perform level order traversal.
Also Read: Naive Bayes Explained: Function, Advantages & Disadvantages, Applications in 2025
Level Order Traversal Using Queue
The more efficient approach to level order traversal uses a queue data structure to keep track of nodes to be visited. This eliminates the need for recursive calls and nested loops.
Here is the pseudocode for level order traversal of a binary tree using a queue:
levelOrderQueue(root):
if root is null:
return
queue = new Queue()
queue.enqueue(root)
while queue is not empty:
current = queue.dequeue()
print(current.value)
if current.left is not null:
queue.enqueue(current.left)
if current.right is not null:
queue.enqueue(current.right)
The queue-based approach is much more efficient as it leverages a queue to process nodes in a level order manner. It starts by enqueueing the root node and then iterates through the queue. For each node dequeued, its value is printed, and its children are enqueued if they exist. This way, the traversal progresses in a breadth-first fashion, ensuring efficient utilization of the nodes and reducing redundant traversals.
Here is the Java implementation of the queue-based approach:
import java.util.LinkedList;
import java.util.Queue;
class TreeNode {
int value;
TreeNode left;
TreeNode right;
TreeNode(int val) {
value = val;
left = null;
right = null;
}
}
public class BinaryTree {
TreeNode root;
public void levelOrderQueue(TreeNode root) {
if (root == null) {
return;
}
Queue<TreeNode> queue = new LinkedList<>();
queue.add(root);
while (!queue.isEmpty()) {
TreeNode current = queue.poll();
System.out.print(current.value + " ");
if (current.left != null) {
queue.add(current.left);
}
if (current.right != null) {
queue.add(current.right);
}
}
}
public static void main(String[] args) {
BinaryTree tree = new BinaryTree();
tree.root = new TreeNode(1);
tree.root.left = new TreeNode(2);
tree.root.right = new TreeNode(3);
tree.root.left.left = new TreeNode(4);
tree.root.left.right = new TreeNode(5);
tree.levelOrderQueue(tree.root);
}
}
This program also defines a TreeNode class. The BinaryTree class has a levelOrderQueue method which leverages a queue to process nodes in a breadth-first manner. It starts with the root node and iterates through the queue, dequeuing nodes, printing their values, and enqueueing their children if available. The main function constructs a sample binary tree, and levelOrderQueue is called on the root node to perform efficient level order traversal using a queue.
Also Read: 50+ Data Structures and Algorithms Interview Questions for 2025
Level Order Traversal of a Binary Tree in Java
Using Recursion
This approach uses recursion to traverse the binary tree level by level.
Here is the pseudocode for level order traversal of a binary tree using recursion:
levelOrderRecursive(root):
if root is null:
return
height = getHeight(root)
for level = 1 to height:
printLevel(root, level)
getHeight(node):
if node is null:
return 0
leftHeight = getHeight(node.left)
rightHeight = getHeight(node.right)
return max(leftHeight, rightHeight) + 1
printLevel(node, level):
if node is null:
return
if level == 1:
print(node.value)
else:
printLevel(node.left, level - 1)
printLevel(node.right, level - 1)
Implementation
Here is the Java implementation of the above:
Code:
class TreeNode {
int value;
TreeNode left;
TreeNode right;
TreeNode(int val) {
value = val;
left = null;
right = null;
}
}
public class BinaryTree {
TreeNode root;
public void levelOrderRecursive(TreeNode root) {
int height = getHeight(root);
for (int level = 1; level <= height; level++) {
printLevel(root, level);
}
}
private int getHeight(TreeNode node) {
if (node == null) {
return 0;
}
int leftHeight = getHeight(node.left);
int rightHeight = getHeight(node.right);
return Math.max(leftHeight, rightHeight) + 1;
}
private void printLevel(TreeNode node, int level) {
if (node == null) {
return;
}
if (level == 1) {
System.out.print(node.value + " ");
} else {
printLevel(node.left, level - 1);
printLevel(node.right, level - 1);
}
}
public static void main(String[] args) {
BinaryTree tree = new BinaryTree();
tree.levelOrderRecursive(tree.root);
}
}The code defines a TreeNode class that represents a node in a binary tree. Each node has an integer value and references to its left and right child nodes. The constructor of the TreeNode class initializes these properties. The main functionality is implemented in the BinaryTree class. This class contains a method called levelOrderRecursive that performs level order traversal using a recursive approach.
Also Read: A Comprehensive Guide to Types of Graphs in Data Structures
Using Queue
This approach uses a queue data structure to perform level order traversal iteratively.
Here are the steps for the queue-based approach:
- Create a queue to store nodes to be visited.
- Enqueue the root node into the queue.
- While the queue is not empty, do the following:
- Dequeue a node from the front of the queue.
- Print the value of the dequeued node.
- Enqueue its left child if it exists.
- Enqueue its right child if it exists.
- Repeat steps 3 until the queue is empty, which ensures that all nodes are processed in a level order manner.
Here is the pseudocode for binary tree Level Order Traversal using queue:
levelOrderQueue(root):
if root is null:
return
queue = new Queue()
queue.enqueue(root)
while queue is not empty:
current = queue.dequeue()
print(current.value)
if current.left is not null:
queue.enqueue(current.left)
if current.right is not null:
queue.enqueue(current.right)
Implementation
Code:
import java.util.LinkedList;
import java.util.Queue;
class TreeNode {
int value;
TreeNode left;
TreeNode right;
TreeNode(int val) {
value = val;
left = null;
right = null;
}
}
public class BinaryTree {
TreeNode root;
public void levelOrderQueue(TreeNode root) {
if (root == null) {
return;
}
Queue<TreeNode> queue = new LinkedList<>();
queue.add(root);
while (!queue.isEmpty()) {
TreeNode current = queue.poll();
System.out.print(current.value + " ");
if (current.left != null) {
queue.add(current.left);
}
if (current.right != null) {
queue.add(current.right);
}
}
}
public static void main(String[] args) {
BinaryTree tree = new BinaryTree();
tree.levelOrderQueue(tree.root);
}
}
The code begins by defining the TreeNode class with integer valus and references to its left and right child nodes. The constructor initializes these properties.The BinaryTree class includes a method named levelOrderQueue responsible for performing level order traversal using a queue-based approach.
Inside the levelOrderQueue method, it starts by checking if the root node is null. If it is, there's no tree to traverse, so the method returns. A Queue<TreeNode> named queue is created using LinkedList and this queue will facilitate the orderly traversal of nodes. A while loop is employed to iterate through the queue.
Comparison of Both Approaches
Depth-First Traversal and Level Order Traversal (Breadth-First Traversal) are two different approaches for exploring nodes in a tree data structure. While both have their advantages and applications, the choice of which to use depends on the specific problem and the desired output. Let us compare the two approaches to understand them in detail:
Aspect | Depth-First Traversal | Level Order Traversal (Breadth-First Traversal) |
Processing Order | Top-Down | Left to Right |
Data Structure | Uses Stack | Uses Queue |
Memory Usage | Requires less memory | Requires more memory |
Implementation Complexity | Typically simpler to implement | Slightly more complex |
Usage | Useful for specific tree-related problems | Ideal for searching, shortest path, and processing hierarchical data |
Application | In-order, pre-order, and post-order traversals | Level-by-level exploration |
Algorithm Type | Depth-First Search (DFS) | Breadth-First Search (BFS) |
Conclusion
To wrap up, Level Order Traversal provides a powerful and systematic way to explore nodes level by level, just like exploring a building one floor at a time.
Whether you use an iterative queue-based approach or recursion, mastering the Level Order Traversal of Tree is fundamental for solving a wide range of problems, from searching hierarchical data to finding the shortest path in a graph. This breadth-first technique is an essential tool in any programmer's problem-solving toolkit.
FAQs
1. What do you mean by Level Order Traversal in a binary tree?
Level Order Traversal of Tree, also known as Breadth-First Traversal, is an algorithm to visit and process nodes in a tree data structure. This Level Order Traversal method explores the tree layer by layer, starting from the root node. It first visits all the nodes at the current depth (level) before moving on to the nodes at the next depth.
2. How is Level Order Traversal different from DFS traversals like Pre-order, In-order, and Post-order?
The main difference is the order of node exploration. Depth-First Search (DFS) traversals like Pre-order, In-order, and Post-order explore as far down a path as possible before backtracking. In contrast, a Level Order Traversal explores nodes broadly, visiting all neighbors at the current level before going deeper. This makes the Level Order Traversal of Tree fundamentally a breadth-first approach, whereas the others are depth-first.
3. What are the main real-world applications of the Level Order Traversal of Tree algorithm?
The Level Order Traversal of Tree algorithm is not just a theoretical concept; it has many practical applications. One of the most significant is finding the shortest path between two nodes in an unweighted graph, as it always explores the nearest nodes first. A Level Order Traversal is also used in algorithms like Cheney's algorithm for garbage collection and to find all connected components in a graph.
4. What is the primary data structure used for an iterative Level Order Traversal?
The primary data structure used to implement an iterative Level Order Traversal is the Queue. A queue follows a First-In, First-Out (FIFO) principle, which is perfect for exploring a tree level by level. When performing a Level Order Traversal of Tree, nodes are added to the back of the queue, and processed from the front, ensuring that all nodes at a given level are visited before their children.
5. What is Level Order Traversal in queue?
A Level Order Traversal using a queue is the standard iterative method for implementing this algorithm. This approach to the Level Order Traversal of Tree involves using a queue data structure to temporarily store and process nodes. The algorithm starts by enqueuing the root node. Then, in a loop, it dequeues a node, processes it, and enqueues its children, ensuring a breadth-first exploration.
6. Can you provide a code example for the Level Order Traversal of Tree using a queue?
Certainly. Here is a high-level pseudocode example for a Level Order Traversal of Tree. This demonstrates the queue-based approach to a Level Order Traversal.
function levelOrderTraversal(root):
if root is null, return
Queue q
q.enqueue(root)
while q is not empty:
Node current = q.dequeue()
print(current.data)
if current.left is not null:
q.enqueue(current.left)
if current.right is not null:
q.enqueue(current.right)
7. How do you handle a null or empty tree in a Level Order Traversal implementation?
Handling a null or empty tree is the crucial first step in any robust Level Order Traversal implementation. Before starting the process, you should always check if the root node is null. If it is, the Level Order Traversal of Tree should simply terminate and return an empty result. This initial check prevents null pointer errors and ensures the algorithm behaves correctly for edge cases.
8. What is the time complexity of a Level Order Traversal of Tree?
The time complexity of a Level Order Traversal of Tree is O(n), where 'n' is the number of nodes in the tree. This is because the algorithm must visit and process every single node exactly once. Each node is enqueued and dequeued one time. Therefore, the time taken by the Level Order Traversal is directly proportional to the number of nodes.
9. What is the space complexity of a Level Order Traversal?
The space complexity of a Level Order Traversal is O(w) or O(n) in the worst case, where 'w' is the maximum width of the tree and 'n' is the total number of nodes. The space is determined by the maximum number of nodes stored in the queue at any given time. For a complete binary tree, the last level can contain up to n/2 nodes, making the worst-case space complexity for a Level Order Traversal of Tree proportional to O(n).
10. Is it possible to implement a Level Order Traversal of Tree recursively?
While the iterative queue-based method is standard for a Level Order Traversal, a recursive implementation is also possible, though it is less intuitive and often less efficient. A recursive Level Order Traversal of Tree would typically involve a helper function that prints all nodes at a given level. You would first need to calculate the height of the tree and then call this helper function for each level from the root down.
11. How can you modify the Level Order Traversal to print each level on a new line?
To modify the Level Order Traversal to print each level on a new line, you need to know how many nodes are in the current level. A common technique is to use a nested loop. The outer loop iterates as long as the queue is not empty, and the inner loop runs for the number of nodes currently in the queue (the size of the current level). This modification to the Level Order Traversal of Tree algorithm is a very popular interview question.
12. What is a Reverse Level Order Traversal of Tree?
A Reverse Level Order Traversal of Tree is a variation where you visit the nodes from the bottom level up, and within each level, you visit them from right to left (or left to right). To implement this Level Order Traversal, you can modify the standard algorithm to use a stack in addition to a queue. You would perform a regular traversal but push the dequeued nodes onto a stack. After the traversal is complete, popping all elements from the stack gives you the nodes in reverse level order.
13. How can you find the height of a binary tree using a Level Order Traversal?
You can find the height of a binary tree by adapting the Level Order Traversal algorithm. The height is essentially the number of levels in the tree. You can keep a height counter that you increment after you have processed all the nodes of a given level. This approach to the Level Order Traversal of Tree is an efficient way to calculate the height iteratively.
14. How does the concept of Level Order Traversal apply to graphs?
The concept of Level Order Traversal is directly applicable to graphs, where it is known as Breadth-First Search (BFS). BFS is a graph traversal algorithm that explores vertices "layer by layer" starting from a source vertex. Just like the Level Order Traversal of Tree, BFS uses a queue to explore the nearest neighbors first before moving on to their neighbors, making it ideal for finding the shortest path in an unweighted graph.
15. How can you use the Level Order Traversal of Tree to find the maximum width?
The maximum width of a binary tree is the maximum number of nodes at any single level. You can find this by modifying the Level Order Traversal of Tree algorithm. At each level of the traversal, you can calculate the number of nodes currently in the queue. You then keep track of the maximum size the queue reaches during the entire Level Order Traversal. This maximum size will be the maximum width of the tree.
16. What are common mistakes to avoid when implementing a Level Order Traversal?
When implementing a Level Order Traversal, a common mistake is forgetting to handle the case of a null root node. Another frequent error is incorrectly managing the queue, such as adding children to the queue before checking if they are null. Forgetting to dequeue a node inside the loop can lead to an infinite loop. A robust Level Order Traversal of Tree implementation must handle these edge cases correctly.
17. What is the significance of Level Order Traversal Hackerrank problems for interviews?
Problems on platforms like Hackerrank that are related to Level Order Traversal are significant for technical interviews because they test a candidate's fundamental understanding of trees, graphs, and data structures like queues. Solving these challenges demonstrates your ability to implement the Level Order Traversal of Tree algorithm and adapt it to solve various problems, which is a key skill for a software developer.
18. In what scenarios is a Level Order Traversal of Tree more advantageous than a Depth-First Traversal?
A Level Order Traversal of Tree is more advantageous than a Depth-First Traversal (DFS) in specific scenarios. The most prominent case is finding the shortest path from a source node to a target node in an unweighted graph or tree. Because Level Order Traversal explores level by level, the first time it reaches the target node, it is guaranteed to have found the shortest path. DFS, in contrast, might explore a very long path before finding a shorter one.
19. Can the Level Order Traversal algorithm be used on trees that are not binary?
Yes, the Level Order Traversal algorithm is not limited to binary trees. It can be easily adapted to work on any type of tree, such as an N-ary tree, where a node can have any number of children. The logic for the Level Order Traversal of Tree remains the same: you start with the root, and for each dequeued node, you enqueue all of its children. This makes it a very versatile traversal algorithm.
20. Why is mastering the Level Order Traversal of Tree important for a software engineering career?
Mastering the Level Order Traversal of Tree is crucial for a software engineering career because it is a foundational algorithm that appears frequently in technical interviews and real-world problem-solving. A deep understanding of Level Order Traversal demonstrates a strong grasp of data structures (trees, graphs, queues) and algorithmic thinking. At upGrad, our software engineering programs focus on these core computer science principles to ensure students are well-prepared to tackle complex challenges in their careers.
