A Class Of Binary Search Tree: MyTree Definition

A Class Of Binary Search Tree Mytree Is Defined In Which the Following

A class of binary search tree MyTree is defined in which the following methods are implemented. MyTree() // constructor: an empty tree is created addNode(int v) //Value v is added to the tree following the rule for a binary search tree print() //The values in the tree are printed following in-order traversal. The method that you are asked to implement is a method called “printByLevel” public void printByLevel() This method prints the values in the tree by the levels. For example, if the tree is as below, the method prints 8, 3, 10, 1, 6, 14, 4, 7, 13 Note: You can use class ArrayDeque in JAVA API. Only two methods from this class are needed: To add an object into the end of the queue, use add method; to remove an object from the front of the queue, use remove method.

Paper For Above instruction

A Class Of Binary Search Tree Mytree Is Defined In Which the Following

Introduction

The binary search tree (BST) is a fundamental data structure used extensively in computer science for efficient data retrieval, insertion, and deletion operations. The class MyTree encapsulates the properties and methods of a BST, including key operations such as adding nodes and printing tree values in different traversal orders. Among these, the "printByLevel" method provides a level-order (breadth-first) traversal, which visits nodes level by level from the root downward. This paper discusses the implementation of the "printByLevel" method in Java, emphasizing its importance, methodology, and practical applications.

Understanding the Existing MyTree Class

The MyTree class offers a constructor to create an empty BST, an addNode method that inserts values according to BST rules, and a print method for in-order traversal. The in-order traversal prints the nodes in ascending order, which is essential for operations needing sorted data. However, to visualize the structure of the tree more intuitively, especially for balanced trees, a level-order traversal like "printByLevel" is highly valuable.

The Need for Level-Order Traversal

Level-order traversal is crucial in scenarios such as printing the hierarchy of organizational structures, evaluating the shortest path in unweighted graphs, and visualizing the shape of the tree. Unlike in-order, pre-order, or post-order traversals, level-order visits nodes across the same depth before proceeding deeper, thus giving a broader overview of the tree's structure. Implementing this method enhances the usability of the MyTree class, making it more versatile for different applications.

Implementing the printByLevel Method

The core concept behind the "printByLevel" method is to utilize a queue data structure—specifically, the ArrayDeque class in Java—aligned with the FIFO (First-In-First-Out) principle. The method begins by checking if the root node exists. If the root is null, the method terminates as there are no nodes to print.

Next, the root node is added to the queue. Inside a loop, nodes are dequeued one by one, their values are printed or stored, and their children (left and right) are enqueued. This process continues until the queue is empty, indicating all nodes have been visited.

By leveraging the add method for enqueuing and remove method for dequeuing, the implementation remains straightforward and efficient, allowing for a clear breadth-first traversal of the BST.

Sample Implementation in Java



public void printByLevel() {


if (root == null) {


return; // Tree is empty


}


ArrayDeque queue = new ArrayDeque();


queue.add(root);


while (!queue.isEmpty()) {


Node current = queue.remove();


System.out.print(current.value + ", "); // Print current node's value


if (current.left != null) {


queue.add(current.left);


}


if (current.right != null) {


queue.add(current.right);


}


}


}

This implementation ensures that all nodes are visited in level order, and their values are printed accordingly, separated by commas for clarity.

Practical Applications and Benefits

Implementing "printByLevel" provides a comprehensive view of the binary search tree's structure, which is particularly useful in debugging, visualization, and algorithms requiring level-based processing. It allows developers and users to understand the shape and balance of the tree more effectively.

Furthermore, this traversal technique aids in serializing trees for storage or transmission, facilitating operations like tree reconstruction or network data exchange.

Conclusion

The "printByLevel" method constitutes a significant enhancement to the MyTree class, offering a level-order perspective that complements existing traversal methods. Its implementation using Java's ArrayDeque exemplifies efficient and readable code, leveraging the queue's FIFO nature. By understanding and applying this traversal, developers can better visualize, analyze, and utilize binary search trees across various applications, reinforcing their importance in computer science.

References

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  • Java API Documentation. (2020). ArrayDeque Class. Retrieved from https://docs.oracle.com/en/java/javase/16/docs/api/java/util/ArrayDeque.html
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