What is a binary search tree, and how does it differ from a regular binary tree?

Binary Search Tree (BST):

A Binary Search Tree (BST) is a type of binary tree where nodes are organized based on their key values to maintain a specific order. It adheres to the following properties:

Left Subtree Rule: For any node, all values in its left subtree are less than the value of the node.
Right Subtree Rule: For any node, all values in its right subtree are greater than the value of the node.
Uniqueness: Typically, BSTs do not allow duplicate values (though this can vary depending on implementation).

These properties ensure that a BST is sorted, which allows for efficient searching, insertion, and deletion operations.

Binary Tree (General Definition):

A Binary Tree is a tree data structure where each node has at most two children. It does not impose any ordering constraints on the values of the nodes.

Structure: Each node can have a left child, a right child, or both (or no children).
No Value Order: The values in a binary tree are not arranged in any specific order.

Key Differences Between Binary Tree and Binary Search Tree:

Aspect	Binary Tree	Binary Search Tree
Node Value Order	No specific order for node values.	Nodes are organized by the BST property (left < root < right).
Searching Efficiency	Searching is linear in worst case (O(n)).	Searching is efficient (O(log n)) if balanced.
Insertion Rule	Nodes can be added in any order.	Nodes are inserted based on their value to maintain the BST property.
Duplicates	Allows duplicates freely.	May or may not allow duplicates, depending on implementation.
Applications	Used for general tree structures.	Used for sorted collections or when efficient searching is required.

Example:

Binary Tree:

A binary tree with no ordering constraints:

Node values are not in any specific order.

Binary Search Tree:

A binary search tree:

		10
       /  \
      5    20
     / \   / \
    2   7 15  25

For every node:
- Left subtree values < Node value.
- Right subtree values > Node value.

Advantages of BST Over a General Binary Tree:

Efficient Searching: Searching in a BST takes O(h), where h is the height of the tree. In a balanced BST, h=O(log⁡n).
Ordered Traversal: In-order traversal of a BST produces the nodes in sorted order.
Efficient Range Queries: BSTs can efficiently find all elements within a specific range.

Disadvantages of BST:

If unbalanced (e.g., when nodes are inserted in sorted order), the BST can degrade to a linked list, resulting in O(n) time for operations.
Maintaining balance (e.g., in AVL or Red-Black Trees) adds complexity.

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