Which of the following operations is guaranteed to be O(log n) in an AVL tree?

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Question: Which of the following operations is guaranteed to be O(log n) in an AVL tree?

Options:

Correct Answer: All of the above

Solution:

All operations (insertion, deletion, and searching) in an AVL tree are guaranteed to be O(log n) due to the tree\'s balanced nature.

Which of the following operations is guaranteed to be O(log n) in an AVL tree?

Which of the following operations is guaranteed to be O(log n) in an AVL tree?

Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains balance, meaning the heights of the two child subtrees of any node differ by at most one.
Step 2: Know what O(log n) means. O(log n) indicates that the time it takes to perform an operation grows logarithmically as the number of elements (n) increases. This is efficient for large datasets.
Step 3: Recognize the operations in an AVL tree. The main operations are insertion, deletion, and searching for a value.
Step 4: Learn how AVL trees maintain balance. After each insertion or deletion, the tree checks if it is balanced and performs rotations if necessary to maintain the AVL property.
Step 5: Conclude that because AVL trees are balanced, the height of the tree is always kept to O(log n). Therefore, all operations (insertion, deletion, and searching) can be performed in O(log n) time.

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