Welcome to a deep dive into the fascinating world of Binary Search Trees (BST)! In this lesson, we'll explore the key properties that make BSTs a valuable data structure in real-world programming scenarios. Let's get started!
A Binary Search Tree is a tree data structure where each node has at most two children (left and right). This structure allows for efficient searching, insertion, and deletion of elements.
In a BST, the key at any node is greater than (>) all keys in its left subtree and smaller than (<) all keys in its right subtree. This property ensures that a BST maintains a sorted order of the elements.
A BST does not allow duplicate keys. If we try to insert a duplicate, it will violate the ordered property.
A BST is a binary tree, meaning each node has at most two children: left and right.
Let's look at a simple BST implementation in Python:
class Node:
def __init__(self, key):
self.left = None
self.right = None
self.key = key
def insert(root, key):
if root is None:
return Node(key)
else:
if root.key < key:
root.right = insert(root.right, key)
else:
root.left = insert(root.left, key)
return root
# Example usage
tree = None
tree = insert(tree, 50)
tree = insert(tree, 30)
tree = insert(tree, 20)
tree = insert(tree, 40)
tree = insert(tree, 70)
tree = insert(tree, 60)
tree = insert(tree, 80)Now that you've seen how to implement a BST, let's test your understanding!
Which of the following is a valid BST property?
Stay tuned for more lessons on BSTs, where we'll dive deeper into traversals, balancing, and advanced techniques! š