Binary Search Tree

Binary Search Tree

  • A binary search tree (BST) is a data structure that is commonly used in computer science to store and retrieve data efficiently. It is called a "binary" search tree because each node has at most two children, and it is called a "search" tree because it allows for efficient search and retrieval of data.

  • All elements on left are less than the root and all elements on right are greater than the root!

  • Time Complexity:

    • Access -> O(n).

    • Deletion -> O(n).

    • Searching -> O(n)

    • Insertion -> O(n)

  • Inorder traversal is sorted!

public class BinarySearchTree {

  // Node class represents a node in the binary tree
  static class Node {
    int value;
    Node left;
    Node right;

    // Constructor to create a new node
    Node(int value) {
      this.value = value;
      left = null;
      right = null;

  // Root of the binary tree
  Node root;

  // Constructor to create a binary search tree
  BinarySearchTree() {
    root = null;

  // Method to search a value in the binary tree
  boolean search(int value) {
    return search(root, value);

  // Helper method to search a value in the binary tree
  boolean search(Node node, int value) {
    // If the tree is empty, return false
    if (node == null) {
      return false;

    // If the value is found at the root, return true
    if (node.value == value) {
      return true;

    // Recursively search in the left or right subtree
    if (value < node.value) {
      return search(node.left, value);
    } else {
      return search(node.right, value);

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