How does an AVL tree maintain balance after insertion?

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

Options:

Correct Answer: By performing rotations.

Solution:

AVL trees maintain balance by performing rotations (single or double) after insertions to ensure the balance factor remains within the allowed range.

How does an AVL tree maintain balance after insertion?

How does an AVL tree maintain balance after insertion?

Step 1: Understand that an AVL tree is a type of binary search tree that keeps itself balanced.
Step 2: Know that each node in an AVL tree has a balance factor, which is the difference between the heights of its left and right subtrees.
Step 3: After inserting a new node, calculate the balance factor for each node starting from the newly inserted node up to the root.
Step 4: If the balance factor of any node becomes less than -1 or greater than 1, the tree is unbalanced.
Step 5: Identify the type of imbalance (Left-Left, Left-Right, Right-Right, or Right-Left) based on the balance factors of the affected nodes.
Step 6: Perform the appropriate rotation (single or double) to restore balance. A single rotation is used for Left-Left or Right-Right imbalances, while a double rotation is used for Left-Right or Right-Left imbalances.
Step 7: After performing the rotation, the tree is balanced again, and the insertion process is complete.

AVL Tree Balance Maintenance – AVL trees maintain balance by ensuring that the heights of the two child subtrees of any node differ by no more than one, using rotations after insertions.