Explain the difference between Binary Tree and Binary Search Tree with an example?

Difference Between Binary Tree and Binary Search Tree

Binary Tree

A Binary Tree is a non-linear data structure where each node can have at most two children, referred to as the left child and the right child. The primary characteristics of a binary tree are:

• Structure: Each node in a binary tree consists of three components: a data element, a pointer to the left child, and a pointer to the right child.
• Hierarchy: The topmost node is called the root, and nodes with no children are called leaves.
• Flexibility: There is no specific order in which the nodes are arranged. This means that the left and right children of a node can have any value relative to the parent node.

Example:

      1
     / \
    2   3
   / \
  4   5

In this example, node 1 is the root, nodes 2 and 3 are its children, and nodes 4 and 5 are the children of node 2. There is no specific ordering of the values.

Binary Search Tree (BST)

A Binary Search Tree (BST) is a specialized type of binary tree that maintains a specific order among its elements. The key properties of a BST are:

• Ordered Structure: For each node, all elements in its left subtree are less than the node's key, and all elements in its right subtree are greater than the node's key.
• No Duplicates: BSTs do not allow duplicate values.
• Efficient Operations: Due to its ordered nature, operations like search, insertion, and deletion are more efficient, typically taking $$O(\log n)$$ time in a balanced BST.

Example:

      8
     / \
    3   10
   / \    \
  1   6    14
     / \   /
    4   7 13

In this example, node 8 is the root. The left subtree of 8 contains nodes with values less than 8, and the right subtree contains nodes with values greater than 8. This ordering property is maintained throughout the tree.

Key Differences

1. Structure:

   • Binary Tree: No specific order; nodes can have any value.
   • BST: Nodes are ordered such that left child values are less than the parent, and right child values are greater.

2. Operations:

   • Binary Tree: Operations like insertion, deletion, and search take $$O(n)$$ time in the worst case.
   • BST: Operations are more efficient,...