How do I implement AVL trees in Python?

How do I implement AVL trees in Python?

To implement AVL trees in Python, you need to create a class for the tree and define methods for insertion, deletion, and balancing.

Can you show me the code for inserting a node?

Sure! Here's a basic implementation of the insert method:

class AVLTree:
    class Node:
        def __init__(self, key):
            self.key = key
            self.left = None
            self.right = None
            self.height = 1

    def insert(self, root, key):
        if not root:
            return self.Node(key)
        elif key < root.key:
            root.left = self.insert(root.left, key)
        else:
            root.right = self.insert(root.right, key)

        root.height = 1 + max(self.get_height(root.left), self.get_height(root.right))
        return self.balance(root)

This method inserts a node and then balances the tree.

What about the balancing part?

The balancing part involves checking the balance factor and performing rotations if necessary. Here's how you can implement it:

def balance(self, root):
    balance_factor = self.get_balance(root)
    
    # Left Left Case
    if balance_factor > 1 and key < root.left.key:
        return self.rotate_right(root)
    
    # Right Right Case
    if balance_factor < -1 and key > root.right.key:
        return self.rotate_left(root)
    
    # Left Right Case
    if balance_factor > 1 and key > root.left.key:
        root.left = self.rotate_left(root.left)
        return self.rotate_right(root)
    
    # Right Left Case
    if balance_factor < -1 and key < root.right.key:
        root.right = self.rotate_right(root.right)
        return self.rotate_left(root)
    
    return root

This ensures the tree remains balanced after every insertion.