Which of the following operations is guaranteed to be O(log n) in both AVL and R
Practice Questions
Q1
Which of the following operations is guaranteed to be O(log n) in both AVL and Red-Black trees?
Insertion
Deletion
Searching
All of the above
Questions & Step-by-Step Solutions
Which of the following operations 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 input (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: Learn that in both AVL and Red-Black trees, the height of the tree is kept to O(log n). This means that any operation that depends on the height of the tree will also be O(log n).
Step 4: Identify the common operations performed on these trees: insertion, deletion, and searching.
Step 5: Realize that all three operations (insertion, deletion, and searching) require traversing the height of the tree, which is O(log n) in both AVL and Red-Black trees.
Step 6: Conclude that since all three operations are performed in O(log n) time, they are guaranteed to be O(log n) in both AVL and Red-Black trees.
