Level Order Traversal of Binary Tree
Introduction
Level Order Traversal of Binary Tree provides a structured approach to explore and analyze binary trees, offering insights into their hierarchical organization and facilitating various computational tasks. In this article, we will embark on a journey to unravel the complexity of Level Order Traversal, uncover its significance, and uncover how to employ this method for both basic and advanced computing tasks.
Let’s learn more about Level Order Traversal along with its working and implementation.
What is Level Order Traversal of Binary Tree?
Level Order Traversal, also known as Breadth-First Traversal, is a method for systematically visiting the nodes of a binary tree in a level-wise order, from top to bottom and from left to right.
- In this traversal, you start at the root node and visit all the nodes at the current level before moving on to the next level.
- It follows a systematic pattern where nodes at the same level are visited in the order they appear from left to right.
Level Order Traversal Example
Visualization of Level Order Traversal of Binary Tree
The fundamental concept behind level order traversal is to visit all nodes within a lower level before progressing to nodes at higher levels.
- Achieving this can be approached using either a more straightforward method, which involves determining the tree’s height and visiting each level sequentially,
- Or a more efficient technique that utilizes a queue to systematically explore the levels.
Level Order Traversal Algorithm:
The algorithm for level order traversal is as follows:
- Start at the root node and enqueue it into a queue (usually a First-In-First-Out, or FIFO, data structure).
- While the queue is not empty, do the following: a. Dequeue a node from the front of the queue and visit (or process) it. b. Enqueue its left child (if it exists). c. Enqueue its right child (if it exists).
The process continues until all nodes have been visited in the order dictated by their levels.
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Implementation of Level Order Traversal using Naive approach
Here’s a Python implementation of Level Order Traversal using a naive approach that calculates the height of the tree and then traverses each level, printing the nodes of each level.
Code :
class TreeNode:
def __init__(self, value):
self.val = value
self.left = None
self.right = None
def height(root):
if root is None:
return 0
left_height = height(root.left)
right_height = height(root.right)
return max(left_height, right_height) + 1
def printLevel(root, level):
if root is None:
return
if level == 1:
print(root.val, end=' ')
elif level > 1:
printLevel(root.left, level - 1)
printLevel(root.right, level - 1)
def levelOrderTraversal(root):
h = height(root)
for i in range(1, h + 1):
printLevel(root, i)
# Construct your binary tree
root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)
root.left.left = TreeNode(4)
root.left.right = TreeNode(5)
# Perform the level order traversal using the naive approach
levelOrderTraversal(root)
Output :
Level Order Traversal using Naive approach :
1 2 3 4 5
Explanation :
Level Order Traversal, using a naive approach, systematically visits the nodes of a binary tree from top to bottom and left to right. It first calculates the tree’s height, then traverses each level, printing nodes at each level. This approach ensures nodes at higher levels are visited before those at lower levels, providing an organized representation of the tree’s structure.
Level Order Traversal using Queue
Here’s a Python implementation of Level Order Traversal using a queue for efficiently visiting nodes in a binary tree.
Code :
class TreeNode:
def __init__(self, value):
self.val = value
self.left = None
self.right = None
def levelOrderTraversal(root):
if root is None:
return
queue = []
queue.append(root)
while queue:
current = queue.pop(0)
print(current.val, end=' ')
if current.left is not None:
queue.append(current.left)
if current.right is not None:
queue.append(current.right)
# Construct your binary tree
root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)
root.left.left = TreeNode(4)
root.left.right = TreeNode(5)
# Perform the level order traversal using a queue
levelOrderTraversal(root)
Output :
Level Order Traversal using Queue :
1 2 3 4 5
Explanation :
Level Order Traversal using a queue efficiently explores a binary tree in a level-wise manner. It begins at the root, enqueues it, and then dequeues and prints each node while enqueuing its left and right children. This approach ensures nodes at the same level are visited before moving to the next level, providing a structured representation of the tree’s layout.
Complexity analysis of Level Order Traversal of Binary Tree
The complexity analysis of Level Order Traversal of a binary tree is as follows:
Time Complexity:
- In the worst case, the time complexity is O(n), where n is the number of nodes in the binary tree. This is because the algorithm must visit all nodes in the tree.
- Level Order Traversal processes each node once, and it covers all levels, so the time complexity remains linear in relation to the number of nodes.
Space Complexity:
- The space complexity is O(w), where w is the width of the binary tree’s widest level. The width is the number of nodes at the widest level.
- In the worst case, when the tree is completely skewed (all nodes on one level), the width becomes n, and the space complexity is O(n).
- In balanced trees, such as a complete binary tree, the space complexity is O(2^(h-1)), where h is the height of the tree. In this case, the space used by the queue is proportional to the number of nodes at the maximum level.
Applications of Level Order Traversal
Following are the applications of Inorder traversal :
To Wrap it up:
In conclusion, Level Order Traversal, also known as Breadth-First Traversal, is a method for systematically visiting the nodes of a binary tree in a level-wise order, offering a comprehensive understanding of their structure. Its applications extend beyond binary trees to graph theory and hierarchical data representation. Implementing level order traversal equips programmers and computer scientists with a powerful tool for various real-world problems, ensuring a systematic exploration of hierarchical structures.
Question 1.
Is Level Order Traversal Suitable for Binary Search Trees (BSTs) Only?
Level Order Traversal can be applied to both binary search trees (BSTs) and general binary trees. It works with any hierarchical tree structure.
Question 2.
How Does Level Order Traversal Help in Finding the Shortest Path?
Level Order Traversal explores nodes level by level, making it ideal for finding the shortest path between two nodes as it ensures that the shortest path is found before longer paths are considered.
Question 3.
What Are the Key Characteristics of Level Order Traversal?
Level Order Traversal is characterized by visiting nodes from top to bottom, left to right, ensuring that nodes at the same level are visited before progressing to the next level.
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