What happens to the balance factor of an AVL tree after a node is deleted?

₹0.0

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

Options:

Correct Answer: It can become unbalanced.

Solution:

After a node is deleted from an AVL tree, the balance factor can become unbalanced, requiring rebalancing operations.

What happens to the balance factor of an AVL tree after a node is deleted?

What happens to the balance factor of an AVL tree after a node is deleted?

Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains a balance factor for each node.
Step 2: Know what a balance factor is. The balance factor is the difference between the heights of the left and right subtrees of a node.
Step 3: When a node is deleted from the AVL tree, the structure of the tree changes.
Step 4: After deletion, check the balance factor of the affected nodes starting from the parent of the deleted node up to the root.
Step 5: If any node has a balance factor of -2 or +2, it means the tree is unbalanced.
Step 6: To fix the unbalance, perform rotations (single or double) on the affected nodes to restore the AVL property.

Balance Factor – The balance factor of a node in an AVL tree is the difference between the heights of its left and right subtrees, which should be -1, 0, or 1 for the tree to remain balanced.
AVL Tree Properties – An AVL tree is a self-balancing binary search tree where the balance factor of each node is maintained to ensure logarithmic height.
Rebalancing Operations – After deletion, if the balance factor of any node becomes less than -1 or greater than 1, rotations (single or double) are performed to restore balance.