1. Introduction

A Binary Search Tree (BST) is a node-based binary tree data structure where each node contains a value. The left child contains only nodes with values less than the parent node, and the right child only nodes with values greater than the parent node. This blog post will demonstrate how to implement a BST in Java and cover common operations such as insertion, search, and inorder traversal.

2. Program Steps

1. Define the Node class which will represent individual elements of the BST.

2. Create a BinarySearchTree class that includes methods for various operations.

3. Implement the different operations and test the BinarySearchTree.

3. Code Program

// Step 1: Define the Node class
class Node {
    int data;
    Node left, right;

    Node(int item) {
        data = item;
        left = right = null;
    }
}

// Step 2: Define the BinarySearchTree class
class BinarySearchTree {
    Node root;

    BinarySearchTree() {
        root = null;
    }

    // Insert a new node
    void insert(int data) {
        root = insertRec(root, data);
    }

    Node insertRec(Node root, int data) {
        if (root == null) {
            root = new Node(data);
            return root;
        }

        if (data < root.data) {
            root.left = insertRec(root.left, data);
        } else if (data > root.data) {
            root.right = insertRec(root.right, data);
        }

        return root;
    }

    // This method mainly calls InorderRec()
    void inorder() {
        inorderRec(root);
    }

    // A utility function to do inorder traversal of BST
    void inorderRec(Node root) {
        if (root != null) {
            inorderRec(root.left);
            System.out.print(root.data + " ");
            inorderRec(root.right);
        }
    }

    // Search a node
    boolean search(int data) {
        return searchRec(root, data) != null;
    }

    Node searchRec(Node root, int data) {
        if (root == null || root.data == data) {
            return root;
        }

        if (root.data > data) {
            return searchRec(root.left, data);
        }

        return searchRec(root.right, data);
    }
}

public class Main {
    public static void main(String[] args) {
        // Step 3: Implement and test the BinarySearchTree
        BinarySearchTree tree = new BinarySearchTree();

        tree.insert(50);
        tree.insert(30);
        tree.insert(20);
        tree.insert(40);
        tree.insert(70);
        tree.insert(60);
        tree.insert(80);

        tree.inorder();
        System.out.println();

        System.out.println(tree.search(25) ? "Found" : "Not Found");
        System.out.println(tree.search(70) ? "Found" : "Not Found");
    }
}

Output:

20 30 40 50 60 70 80
Not Found
Found

4. Step By Step Explanation

Step 1: The Node class represents individual elements of the BST. Each node has a data value, a left child, and a right child.

Step 2: The BinarySearchTree class provides:

1. insert: Inserts a new node into the BST.

2. inorder: This is an inorder tree traversal which gives nodes in non-decreasing order.

3. search: Searches for a node with a given value and returns a boolean indicating its presence.

Step 3: In the Main class, we test the BinarySearchTree. We insert several nodes, perform an inorder traversal to print the nodes in ascending order, and then search for specific nodes.

The output displays the nodes of the BST in non-decreasing order (thanks to the inorder traversal) followed by results of two search operations.