What is the worst-case time complexity for deleting a node from an AVL tree?

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Question: What is the worst-case time complexity for deleting a node from an AVL tree?

Options:

Correct Answer: O(log n)

Solution:

The worst-case time complexity for deleting a node from an AVL tree is O(log n) due to the need to maintain balance.

What is the worst-case time complexity for deleting a node from an AVL tree?

What is the worst-case time complexity for deleting a node from an AVL tree?

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 deleting a node from a binary search tree involves finding the node and removing it.
Step 3: Realize that after deleting a node, the AVL tree may become unbalanced.
Step 4: Understand that to maintain the AVL tree's balance, we may need to perform rotations after the deletion.
Step 5: Recognize that both finding the node to delete and performing any necessary rotations take time proportional to the height of the tree.
Step 6: Since an AVL tree is balanced, its height is logarithmic in relation to the number of nodes, specifically O(log n).
Step 7: Conclude that the worst-case time complexity for deleting a node from an AVL tree is O(log n).

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