In this assignment, you will explore the Binary Tree data structure. A binary tree is a hierarchical data structure where each node has at most two children, referred to as the left child and the right child. Binary trees are fundamental in computer science and are used in various applications including searching, sorting, and representing hierarchical data.
This assignment focuses on understanding a basic implementation of a Binary Search Tree (BST), which is a special type of binary tree where for each node: - All elements in the left subtree are less than the node’s value - All elements in the right subtree are greater than or equal to the node’s value
The key learning objective is to understand how recursion is used to solve tree-related problems.
You are designing h a BinaryTree
class that contains the
following components:
Node
class that represents each node in the
treepublic class BinaryTree {
protected class Node {
int data;
Node left;
Node right;
public Node(int data) {
this.data = data;
}
}
protected Node root;
// Constructors and methods...
}
public BinaryTree()
public BinaryTree(int data)
public void insert(int data)
private Node insert_recursive(Node root, int data)
public String in_order_traversal()
private String in_order_traversal(Node root, String s)
public int count_nodes()
private int count_nodes_recursive(Node root)
public int depth()
private int depth_recursive(Node root)
BinaryTree
class.Here’s an example of creating a binary tree and using its methods:
public class BinaryTreeDemo {
public static void main(String[] args) {
= new BinaryTree();
BinaryTree tree
// Insert values
.insert(50);
tree.insert(30);
tree.insert(70);
tree.insert(20);
tree.insert(40);
tree.insert(60);
tree.insert(80);
tree
// Display in-order traversal
System.out.println("In-order traversal:");
.in_order_traversal();
tree
// Count nodes
System.out.println("\nNumber of nodes: " + tree.count_nodes());
// Calculate depth
System.out.println("Tree depth: " + tree.depth());
}
}
Expected output:
In-order traversal:
20 30 40 50 60 70 80
Number of nodes: 7
Tree depth: 3
For each recursive method in the BinaryTree
class,
consider: 1. What is the base case? (When does the recursion stop?) 2.
How does the method break down the problem into smaller subproblems? 3.
How does the method combine the results of the subproblems to solve the
original problem?
Understanding these aspects of recursion is crucial for working with tree structures.