Question

Convert classes TreeNode and Tree trom Fig. 17.17 into generic classes. Io insert an object in a Tree, the object must be compared to the objects in existing TreeNodes. For this reason, classes TreeNode and Tree should specify Comparable \(<\mathrm{E}>\) as the upper bound of each class's type parameter. After modifying classes TreeNode and Tree, write a test application that creates three Tree objects - one that stores Integers, one that stores Doubles and one that stores Strings. Insert 10 values into each tree. Then output the preorder, inorder and postorder traversals for each Tree.

Short answer

Convert TreeNode and Tree to generic classes using Comparable. Implement insertion and traversal methods. Test with Trees for Integers, Doubles, and Strings.

Step-by-step solution

Convert TreeNode to a Generic Class

Modify the `TreeNode` class so it has a type parameter `E` that extends `Comparable`. This will ensure that all elements stored in a `TreeNode` can be compared to one another. The class definition should look like this: ```java public class TreeNode> { E element; TreeNode left; TreeNode right; // Constructor and other methods... } ```

Convert Tree to a Generic Class

Modify the `Tree` class to include a type parameter `E` that extends `Comparable`. This ensures the `Tree` can handle elements that are comparable as required for ordering and organizing in the Binary Search Tree. The class definition should be similar to this: ```java public class Tree> { private TreeNode root; // Constructor and other methods for insertion and traversal... } ```

Implement Insertion Method

Implement a method to add an element to the `Tree`. Since each element is an instance of `Comparable`, use the compareTo method to decide whether to move down the left or right subtree. For example: ```java public void insert(E element) { root = insertNode(root, element); } private TreeNode insertNode(TreeNode node, E element) { // Implementation logic... } ```

Implement Tree Traversals

Extend the `Tree` class with methods for preorder, inorder, and postorder traversals. These methods should recursively process the nodes in the respective order while collecting or printing the node values: ```java public void inorderTraversal() { inorderHelper(root); } private void inorderHelper(TreeNode node) { // Recursive calls for traversals... } // Similar methods for preorder and postorder. ```

Write Test Application

Create a test application that initializes three different `Tree` instances for `Integer`, `Double`, and `String`. Populate each tree with 10 values using the insert method. Finally, perform and print the results of preorder, inorder, and postorder traversals for each tree. The test code might include: ```java public class TreeTest { public static void main(String[] args) { Tree intTree = new Tree<>(); Tree doubleTree = new Tree<>(); Tree strTree = new Tree<>(); // Insert values and perform traversals... } } ```

Key concepts

Generic Classes

In programming, a **generic class** is a way to create classes that work with different data types without sacrificing type safety. In Java, this is done using type parameters. A type parameter is a placeholder for a data type, allowing for flexibility and reusability.
When we say `TreeNode` or `Tree>`, the `` represents a type parameter. The `extends Comparable` constraint ensures that any specified type implements the `Comparable` interface, which allows objects to be compared with each other.
This is particularly useful in data structures like trees, where elements need to be ordered. Generic classes bring the benefits of readability by reducing redundancy and maintaining the code’s integrity by ensuring type correctness. They help in building efficient algorithms that do not rely on specific data types.

Binary Search Tree

A **Binary Search Tree (BST)** is a particular type of binary tree that maintains order. Each node in a BST contains a key greater than all keys in the left subtree and smaller than those in the right subtree. This property makes it efficient for operations like insertions, deletions, and searches.
When you insert an element in a BST, you compare the element with the current node's key. If it's smaller, you move to the left child; if larger, you move to the right child. This process continues until you find the right spot for the new node. This ordered structure allows for efficient data retrieval with a time complexity of average \(O(\log n)\) for these operations.
BSTs are dynamically changing data structures, allowing you to maintain a sorted list of elements, ideal for applications requiring frequent insertions and lookups.

Tree Traversals

Tree traversal is essential for processing each node in a data structure like a Binary Search Tree. There are three common types of tree traversal methods, namely inorder, preorder, and postorder, each with its processing order:

• **Inorder Traversal**: This visits nodes in ascending order when performed on a BST. It processes the left subtree, then the root node, and finally the right subtree.
• **Preorder Traversal**: Here, processing begins with the root node, followed by the left subtree, and lastly, the right subtree. It's used in creating a copy of the tree and in prefix expression evaluation.
• **Postorder Traversal**: This traversal processes the left subtree, then the right subtree, and ends with the root node. It's typically used for deleting the tree because each parent node is processed after its child nodes.

These traversals enable comprehensive access and manipulation of each tree node, achieving different results based on the needs of your application.

Comparable Interface

The **Comparable** interface in Java provides a way to define a natural ordering for objects, which is essential for many sorted data structures, like the Binary Search Tree. By implementing this interface, you can determine how objects of a class will be compared and subsequently ordered.
The `Comparable` interface consists of the `compareTo` method. This method returns:

• A negative number if the current object is less than the specified object.
• Zero if they are equal.
• A positive number if the current object is greater than the specified object.

The `compareTo` method is crucial for ordering operations, such as maintaining an ordered sequence of elements within data structures like trees or handling search functionalities efficiently.
Using `Comparable`, we can ensure a consistent strategy for comparing objects, which is foundational for executing tree operations like the insertion in the correct order. Hence, `Comparable` is indispensable for generic and flexible data structure implementations.