Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The AVL trees are more balanced as compared to Red Black trees, but they may cause more rotations during insertion and deletion
Reason R: A Red Black tree with n nodes has height that is greater than 2 log₂ (n + 1) and the AVL tree with n nodes has height less than log_Φ (√5 (n+2)) -2 (where Φ is golden ratio)
In the light of the above statements, choose the correct answer from the options given below.

Question

Question

This question was previously asked in

UGC NET Computer Science (Paper 2) 17 June 2023 Official Paper

Answer 1

The correct answer is A is true but R is false

EXPLANATION:

Assertion A: "AVL trees are more balanced as compared to Red Black trees, but they may cause more rotations during insertion and deletion."
- This assertion is correct. AVL trees are more strictly balanced than Red-Black trees, meaning that the height difference between the left and right subtrees of any node (called the balance factor) is at most 1 in AVL trees, whereas it can be up to 2 in Red-Black trees.
- However, this strict balancing in AVL trees can lead to more rotations during insertion and deletion operations compared to Red-Black trees.
Reason R: "A Red-Black tree with n nodes has a height that is greater than 2 log₂ (n + 1), and the AVL tree with n nodes has a height less than logΦ (√5 (n+2)) - 2 (where Φ is the golden ratio)."
- This reason is incorrect. The correct upper bound for the height of a Red-Black tree with n nodes is 2 log₂ (n + 1), not greater than.
- The statement for AVL trees is also incorrect; the correct upper bound for the height of an AVL tree with n nodes is approximately 1.44 * log₂(n+2) - 1.329.

Therefore, Assertion A is correct, but Reason R is incorrect. The correct answer is option 3: "A is true but R is false."