How does a binary tree function?

A binary tree is a tree data structure where each node has at most two children: left and right.

Principles of operation:

• Root: The top node of the tree.
• Nodes: Contain data and references to child nodes.
• Leaves: Nodes without children.
• Connections: Directed from parent node to child nodes.

Main operations:

• Insertion: New nodes are added to a specific location in the tree, maintaining its structure and rules (for example, in a binary search tree: smaller values go to the left, larger to the right).
• Search: Traversing nodes to find a specific element. In a binary search tree, search is efficient due to data ordering.
• Deletion: Removing a node with restructuring of the tree.
• Traversal: Visiting all nodes of the tree in a specific order:
  • Pre-order: Root, left subtree, right subtree.
  • Post-order: Left subtree, right subtree, root.
  • In-order: Left subtree, root, right subtree (provides a sorted list of elements for a binary search tree).

Advantages:

• Efficient search, insertion, and deletion (in balanced trees).
• Used for representing hierarchical data.

Example of a node structure in PHP:

<?php

class Node {
    public $data; // Node data
    public $left; // Left child node
    public $right; // Right child node

    public function __construct($data) {
        $this->data = $data;
        $this->left = null;
        $this->right = null;
    }
}