Binary Trees

In computer science, a binary tree is a type of hierarchical data structure where each node has at most two children - a left child and a right child. These children are unordered, meaning there is no specific order in which they are arranged.

Binary trees are widely used in various applications, including:

• Binary search trees, which allow efficient searching, insertion, and deletion of elements.
• Expression trees, which are used to represent mathematical expressions.
• Huffman trees, which are used in data compression algorithms.

The nodes of a binary tree can be represented using a class, such as the following Java code snippet:

1// Define a node class
2class Node {
3  int value;
4  Node left;
5  Node right;
6
7  public Node(int value) {
8    this.value = value;
9    left = null;
10    right = null;
11  }
12}
13
14// Create a binary tree
15Node root = new Node(1);
16root.left = new Node(2);
17root.right = new Node(3);

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}

class Node {

  int value;

  Node left;

  Node right;

​

  public Node(int value) {

    this.value = value;

    left = null;

    right = null;

  }

}

​

public class BinaryTree {

  Node root;

​

  public BinaryTree() {

    root = null;

  }

​

  public void insert(int value) {

    root = insertRecursive(root, value);

  }

​

  private Node insertRecursive(Node current, int value) {

    if (current == null) {

      return new Node(value);

    }

​

    if (value < current.value) {