AVL Deletion 🎯

Welcome to our comprehensive guide on AVL Deletion! In this lesson, we'll dive deep into understanding AVL trees, their importance, and the process of deleting a node from an AVL tree.

What are AVL Trees? 📝

AVL trees are self-balancing binary search trees, named after their inventors Adelson-Velsky and Landis. They maintain a balance by adjusting the height of the tree during insertions and deletions. This balance ensures that the height of the left and right subtrees of every node differs by at most one.

Importance of AVL Trees 💡

AVL trees are useful in scenarios where the order of insertion and deletion of elements is important, and the tree needs to be kept balanced. They provide faster search, insert, and delete operations compared to ordinary binary search trees.

AVL Deletion Process 🎯

The AVL deletion process involves the following steps:

1. Locate the Node to be Deleted

   • First, we find the node to be deleted within the tree.

2. Case 1: Deleting a Leaf Node

   • If the node to be deleted is a leaf node (i.e., it doesn't have any child nodes), we simply remove it.
   python

   Try it YourselfCopy

   def delete_leaf_node(root, key): if root is None: return root if root.key > key: root.left = delete_leaf_node(root.left, key) elif root.key < key: root.right = delete_leaf_node(root.right, key) else: if root.left is None: return root.right elif root.right is None: return root.left # ... (Handle cases where the node has children)

3. Case 2: Deleting an Internal Node with One Child

   • If the node to be deleted has one child, we simply replace the node with its child.
   python

   Try it YourselfCopy

   def delete_node_with_one_child(root, key): if root is None: return root if root.key > key: root.left = delete_node_with_one_child(root.left, key) elif root.key < key: root.right = delete_node_with_one_child(root.right, key) else: if root.left is None: return root.right elif root.right is None: return root.left # ... (Handle cases where the node has children)

4. Case 3: Deleting an Internal Node with Two Children

   • If the node to be deleted has two children, we first find its successor (the smallest node in the right subtree) and replace the node with its successor. Then, we adjust the balance factor of the tree.
   python

   Try it YourselfCopy

   def find_successor(node): if node.right is not None: return find_min(node.right) parent, current = node.parent, node while current is not node.left: parent = current current = current.parent parent.left = current.right if current.right is not None: current.right.parent = parent return node def delete_node_with_two_children(root, key): if root is None: return root if root.key > key: root.left = delete_node_with_two_children(root.left, key) elif root.key < key: root.right = delete_node_with_two_children(root.right, key) else: if root.left is None: return root.right elif root.right is None: return root.left # ... (Handle cases where the node has children) def rebalance_tree(node): if node.balance_factor > 1 and node.right.balance_factor >= 0: node.balance_factor -= 1 node.right.balance_factor += 1 node = rotate_right(node) if node.balance_factor > 1 and node.right.balance_factor < 0: node.balance_factor -= 1 node.right = rotate_left(node.right) node = rotate_right(node) if node.balance_factor < -1 and node.left.balance_factor <= 0: node.balance_factor += 1 node.left.balance_factor -= 1 node = rotate_left(node) if node.balance_factor < -1 and node.left.balance_factor > 0: node.balance_factor += 1 node.left = rotate_right(node.left) node = rotate_left(node)

Quiz 🎯

That's it for our AVL Deletion guide! Now you have a good understanding of AVL trees and the process of deleting nodes from them. Happy coding! 💡🎯📝