Approach
To design and implement a binary search tree (BST) class from scratch, we will follow a structured framework that includes:
Defining the Tree Node Structure
Create a class for the nodes of the tree.
Each node will hold a value, pointers to left and right children, and maintain a count of nodes for random selection.
Implementing the Binary Search Tree Class
Create a class for the BST.
Implement methods for insertion, searching, deletion, and retrieving a random node.
Detailing Each Method's Functionality
Break down the logic of each method to ensure clarity and efficiency.
Key Points
Understand the BST Properties: A binary search tree maintains order; for any node, values in the left subtree are less, and values in the right subtree are greater.
Insertion Logic: Properly placing the new node while maintaining the order.
Search Logic: Efficiently locating a node based on value comparisons.
Deletion Logic: Handling three cases—leaf node, node with one child, and node with two children.
Random Node Selection: Utilizing the size of the tree to select a node uniformly at random.
Standard Response
Here's a detailed example of how to implement a BST class in Python, including the essential methods.