What happens when a node is inserted into an AVL tree and it causes an imbalance

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Question: What happens when a node is inserted into an AVL tree and it causes an imbalance?

Options:

Correct Answer: The tree is restructured using rotations.

Solution:

When an imbalance occurs after insertion in an AVL tree, the tree is restructured using rotations to restore balance.

What happens when a node is inserted into an AVL tree and it causes an imbalance?

What happens when a node is inserted into an AVL tree and it causes an imbalance?

Step 1: Insert the new node into the AVL tree like you would in a regular binary search tree.
Step 2: After inserting, check the balance factor of each node starting from the newly inserted node up to the root. The balance factor is calculated as the height of the left subtree minus the height of the right subtree.
Step 3: If the balance factor of any node is greater than 1 or less than -1, it indicates an imbalance.
Step 4: Determine the type of imbalance: Left-Left, Left-Right, Right-Right, or Right-Left based on the position of the newly inserted node.
Step 5: Perform the appropriate rotation to restore balance: a single right rotation for Left-Left, a single left rotation for Right-Right, a left-right rotation for Left-Right, and a right-left rotation for Right-Left.
Step 6: After performing the rotation, the AVL tree is now balanced again.

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.
Rotations – To restore balance after an insertion, AVL trees use rotations (single or double) to rearrange the nodes.
Imbalance Types – There are four types of imbalances that can occur: Left-Left, Left-Right, Right-Right, and Right-Left, each requiring a specific rotation.