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

Balanced Trees: AVL and Red-Black Trees - Complexity Analysis - Case Studies

Q. How does the insertion operation in a Red-Black Tree differ from that in an AVL Tree?

Solution

Insertion in Red-Black Trees typically requires fewer rotations compared to AVL Trees.

Correct Answer: A — Red-Black Trees require fewer rotations

Q. In a Red-Black Tree, what property must be maintained after an insertion?

A. The tree must be a complete binary tree
B. The root must always be red
C. Every path from a node to its descendant leaves must have the same number of black nodes
D. All leaves must be red

Solution

In a Red-Black Tree, every path from a node to its descendant leaves must have the same number of black nodes.

Correct Answer: C — Every path from a node to its descendant leaves must have the same number of black nodes

Q. What is the time complexity of deleting a node from an AVL tree?

Solution

The time complexity of deleting a node from an AVL 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 balancing an AVL tree after insertion?

Solution

The worst-case time complexity for balancing an AVL tree after insertion is O(log n).

Correct Answer: B — O(log n)

Q. Which of the following operations is more efficient in AVL trees compared to Red-Black trees?

Solution

Search operations are generally more efficient in AVL trees due to their stricter balancing.

Correct Answer: A — Search

Q. Which tree structure guarantees that no path from the root to a leaf is more than twice as long as any other such path?

Solution

Red-Black Trees guarantee that no path from the root to a leaf is more than twice as long as any other such path.

Correct Answer: B — Red-Black Tree

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