How does an AVL tree maintain balance after an insertion?

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Question: How does an AVL tree maintain balance after an insertion?

Options:

Correct Answer: By performing rotations.

Solution:

An AVL tree maintains balance after an insertion by performing rotations (single or double) to ensure the height difference property is satisfied.

How does an AVL tree maintain balance after an insertion?

How does an AVL tree maintain balance after an insertion?

Step 1: Insert the new node into the AVL tree just like you would in a regular binary search tree.
Step 2: After the insertion, 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 means the tree is unbalanced.
Step 4: Determine the type of imbalance: Left-Left, Left-Right, Right-Right, or Right-Left based on the balance factors of the affected nodes.
Step 5: Perform the appropriate rotation to restore balance: a single rotation (left or right) or a double rotation (left-right or right-left) depending on the type of imbalance.
Step 6: After performing the rotation, the tree is now balanced, and you can stop checking further.

AVL Tree Balance Maintenance – An AVL tree maintains balance by ensuring that the heights of the two child subtrees of any node differ by no more than one, using rotations to restore balance after insertions.
Rotations – Single and double rotations are techniques used to adjust the tree structure and maintain the AVL property after an insertion.
Height Difference Property – The property that defines the balance of an AVL tree, which states that for any node, the height of the left and right subtrees can differ by at most one.