Binary Search Tree

A binary search tree (BST) is a binary tree data structure in which each node has a key (a value) and two sub-nodes, referred to as the left child and right child. The key in each node must satisfy the following condition: the key in the left child is less than the key in the parent node, and the key in the right child is greater than the key in the parent node.

Binary search trees are efficient for searching, inserting, and deleting elements. The structure of a binary search tree allows for fast search and retrieval operations by using the property of binary search, which narrows down the search space at each step.

The implementation of a binary search tree typically involves operations such as:

• Insertion: Adding a new key into the tree while maintaining the binary search tree property.
• Deletion: Removing a key from the tree while maintaining the binary search tree property.
• Search: Finding a specific key in the tree.

Here is an example of a basic binary search tree implementation in Java:

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In this example, we have a BinarySearchTree class that represents a binary search tree. It has a Node class as a nested class, which represents a node in the tree. The BinarySearchTree class maintains a reference to the root node of the tree.

The insert method is used to insert a new key into the binary search tree. It uses a recursive approach to traverse the tree and find the correct position for the new key based on the binary search property. The search method is used to search for a specific key in the binary search tree. It also uses a recursive approach to traverse the tree and find the key.

Binary search trees are a fundamental data structure that is widely used in various algorithms and applications. They provide an efficient way to store and retrieve data in a sorted order, making them suitable for tasks such as searching, indexing, and maintaining a sorted collection of elements.

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class BinarySearchTree {

    private Node root;

    private class Node {

        int key;

        Node left;

        Node right;

    }

    public BinarySearchTree() {

        root = null;

    }

    public void insert(int key) {

        root = insertRecursive(root, key);

    }

    private Node insertRecursive(Node root, int key) {

        if (root == null) {

            root = new Node();

            root.key = key;

        } else {

            if (key < root.key) {

                root.left = insertRecursive(root.left, key);

            } else if (key > root.key) {

                root.right = insertRecursive(root.right, key);

            }

        }