What happens to the balance factor of an AVL tree node after a right rotation?

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Question: What happens to the balance factor of an AVL tree node after a right rotation?

Options:

Correct Answer: It decreases by 1.

Solution:

After a right rotation, the balance factor of the node that was rotated down decreases by 1.

What happens to the balance factor of an AVL tree node after a right rotation?

What happens to the balance factor of an AVL tree node after a right rotation?

Step 1: Understand what an AVL tree is. It is a type of binary search tree that maintains balance to ensure efficient operations.
Step 2: Know what a balance factor is. The balance factor of a node is calculated as the height of the left subtree minus the height of the right subtree.
Step 3: Identify the node that will be rotated down during a right rotation. This is the node that has become unbalanced.
Step 4: Perform the right rotation. This means the node that is currently unbalanced will move down, and its right child will move up to take its place.
Step 5: After the rotation, check the heights of the left and right subtrees of the node that was rotated down.
Step 6: Since the right child has moved up, the height of the left subtree remains the same, but the height of the right subtree decreases by 1.
Step 7: Calculate the new balance factor for the node that was rotated down. It will now be 1 less than it was before the rotation.

Balance Factor in AVL Trees – The balance factor of a node in an AVL tree is the difference between the heights of its left and right subtrees, which helps maintain the tree's balance.
Right Rotation – A right rotation is a tree restructuring operation that is performed to maintain the balance of an AVL tree when a node becomes unbalanced due to insertions or deletions.