What is the time complexity for deleting an element from an AVL tree?

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Question: What is the time complexity for deleting an element from an AVL tree?

Options:

Correct Answer: O(log n)

Solution:

Deleting an element from an AVL tree also takes O(log n) time, as it may require rebalancing.

What is the time complexity for deleting an element from an AVL tree?

What is the time complexity for deleting an element from an AVL tree?

Step 1: Understand what an AVL tree is. It is a type of binary search tree that keeps itself balanced.
Step 2: Know that deleting an element from a binary search tree usually takes O(h) time, where h is the height of the tree.
Step 3: In an AVL tree, the height is always kept to O(log n) because it is balanced.
Step 4: When you delete an element, you first find the element, which takes O(log n) time.
Step 5: After deleting the element, you may need to rebalance the tree to maintain the AVL property.
Step 6: Rebalancing also takes O(log n) time because it involves checking the heights of the nodes and performing rotations if necessary.
Step 7: Combine the time for finding the element and the time for rebalancing, which both take O(log n).
Step 8: Conclude that the total time complexity for deleting an element from an AVL tree is O(log n).

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