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

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Q: What is the worst-case time complexity for deleting an element from an AVL tree?

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

Steps: 8

Step 1: Understand what an AVL tree is. It is a type of binary search tree that keeps itself balanced.
Step 2: Know that in a binary search tree, deleting an element may require finding the element first.
Step 3: Realize that finding an element in an AVL tree takes O(log n) time because the tree is balanced.
Step 4: After finding the element, you need to delete it. This also takes O(log n) time in an AVL tree.
Step 5: After deletion, the tree may become unbalanced, so you need to perform rotations to restore balance.
Step 6: The rotations also take O(log n) time because they involve a limited number of tree nodes.
Step 7: Combine the times: finding the element, deleting it, and balancing the tree all take O(log n) time.
Step 8: Conclude that the worst-case time complexity for deleting an element from an AVL tree is O(log n).