Which operation is guaranteed to be O(log n) in both AVL and Red-Black trees?

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Question: Which operation is guaranteed to be O(log n) in both AVL and Red-Black trees?

Options:

Correct Answer: All of the above

Solution:

All of the operations (insertion, deletion, and searching) are guaranteed to be O(log n) in both AVL and Red-Black trees.

Which operation is guaranteed to be O(log n) in both AVL and Red-Black trees?

Which operation is guaranteed to be O(log n) in both AVL and Red-Black trees?

Step 1: Understand what O(log n) means. It refers to the time complexity of an operation, indicating that the time taken grows logarithmically as the size of the data (n) increases.
Step 2: Know that AVL trees and Red-Black trees are types of self-balancing binary search trees. They keep their height balanced to ensure efficient operations.
Step 3: Recognize that in both AVL and Red-Black trees, the height of the tree is kept to a minimum, specifically O(log n). This is crucial for the efficiency of operations.
Step 4: Identify the main operations performed on these trees: insertion, deletion, and searching.
Step 5: Realize that because the height of both AVL and Red-Black trees is O(log n), all three operations (insertion, deletion, and searching) can be performed in O(log n) time.
Step 6: Conclude that all operations (insertion, deletion, and searching) are guaranteed to be O(log n) in both AVL and Red-Black trees.

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