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

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

Options:

Correct Answer: It decreases.

Solution:

After a right rotation, the balance factor of the affected nodes decreases, helping to restore balance in the AVL tree.

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

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

Step 1: Understand what a balance factor is. The balance factor of a node in an AVL tree is calculated as the height of the left subtree minus the height of the right subtree.
Step 2: Identify the nodes affected by a right rotation. In a right rotation, the node that becomes the new root of the subtree and its children are the ones affected.
Step 3: Perform the right rotation. This involves moving the left child of the node up to become the new root of the subtree, and the original root becomes the right child of the new root.
Step 4: Calculate the new heights of the affected nodes. After the rotation, the heights of the nodes will change, which affects their balance factors.
Step 5: Update the balance factors of the affected nodes. The balance factors of the nodes that were involved in the rotation will decrease, indicating that the tree is becoming more balanced.

Balance Factor – The balance factor of a node in an AVL tree is the difference between the heights of its left and right subtrees, used to determine if the tree is balanced.
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.
AVL Tree Properties – An AVL tree is a self-balancing binary search tree where the difference in heights between the left and right subtrees (balance factor) is at most 1.