Balanced Trees: AVL and Red-Black Trees for Exam Prep

Balanced Trees: AVL and Red-Black Trees - Complexity Analysis - Applications

Q. What is a primary application of AVL trees?

Solution

AVL trees are commonly used in database indexing due to their efficient search, insert, and delete operations.

Correct Answer: A — Database indexing

Q. What is the time complexity for searching an element in a Red-Black tree?

Solution

Searching for an element in a Red-Black tree takes O(log n) time due to its balanced nature.

Correct Answer: B — O(log n)

Q. What is the worst-case time complexity for deleting a node from a Red-Black tree?

Solution

The worst-case time complexity for deleting a node from a Red-Black tree is O(log n) due to its balanced structure.

Correct Answer: B — O(log n)

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

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.

Correct Answer: B — O(log n)

Q. Which of the following is a characteristic of a Red-Black tree?

Solution

In a Red-Black tree, every path from the root to the leaves must have the same number of black nodes, ensuring balanced height.

Correct Answer: B — Every path from root to leaf has the same number of black nodes

Q. Which operation is guaranteed to be O(log n) in an AVL tree?

Solution

All of the operations (insertion, deletion, and searching) in an AVL tree are guaranteed to be O(log n) due to its balanced structure.

Correct Answer: D — All of the above

Q. Which operation is not allowed in an AVL tree?

Solution

Duplicate insertion is not allowed in an AVL tree as it must maintain unique keys.

Correct Answer: D — Duplicate insertion

Q. Which tree structure is more rigidly balanced, AVL or Red-Black?

Solution

AVL trees are more rigidly balanced than Red-Black trees, which allows for faster lookups at the cost of slower insertions and deletions.

Correct Answer: A — AVL tree

Showing 1 to 8 of 8 (1 Pages)