What happens to the balance factor of an AVL tree after an insertion?

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Question: What happens to the balance factor of an AVL tree after an insertion?

Options:

Correct Answer: It can become -2 or 2.

Solution:

After an insertion, the balance factor of an AVL tree can become -2 or 2, indicating that rebalancing is needed.

What happens to the balance factor of an AVL tree after an insertion?

What happens to the balance factor of an AVL tree after an insertion?

Step 1: Understand what an AVL tree is. It is a type of binary search tree that maintains balance.
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: The balance factor can be -1, 0, or 1 for a balanced AVL tree.
Step 4: When you insert a new node, the height of the tree may change, affecting the balance factors of the nodes.
Step 5: After the insertion, check the balance factors of the affected nodes starting from the inserted node up to the root.
Step 6: If any node has a balance factor of -2 or 2, it means the tree is unbalanced and needs rebalancing.
Step 7: Rebalancing can be done using rotations (single or double) to restore the balance of the tree.

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 any node is maintained to ensure logarithmic height.
Rebalancing – When the balance factor of a node becomes -2 or 2 after an insertion, it indicates that the tree is unbalanced and requires rebalancing through rotations.