What is the worst-case time complexity for balancing an AVL tree after insertion

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Question: What is the worst-case time complexity for balancing an AVL tree after insertion?

Options:

Correct Answer: O(log n)

Solution:

The worst-case time complexity for balancing an AVL tree after insertion is O(log n).

What is the worst-case time complexity for balancing an AVL tree after insertion?

What is the worst-case time complexity for balancing an AVL tree after insertion?

Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains balance to ensure efficient operations.
Step 2: Know that after inserting a new node into an AVL tree, the tree may become unbalanced.
Step 3: Recognize that balancing the tree involves checking the heights of the nodes and performing rotations if necessary.
Step 4: Realize that the height of an AVL tree is always O(log n), where n is the number of nodes in the tree.
Step 5: Understand that checking the balance and performing rotations takes time proportional to the height of the tree.
Step 6: Conclude that since the height of the tree is O(log n), the worst-case time complexity for balancing the AVL tree after insertion is O(log n).

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