How many rotations are required in the worst case when inserting a node into an

How many rotations are required in the worst case when inserting a node into an AVL tree?

How many rotations are required in the worst case when inserting a node into an AVL tree?

Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains balance by ensuring the heights of the two child subtrees of any node differ by no more than one.
Step 2: Know that when you insert a new node into an AVL tree, it may cause the tree to become unbalanced.
Step 3: Identify the types of imbalances that can occur after an insertion. There are four types: Left-Left, Left-Right, Right-Right, and Right-Left.
Step 4: Realize that to fix an imbalance, you may need to perform rotations. A rotation is a local operation that changes the structure of the tree to restore balance.
Step 5: Understand that in the worst-case scenario, you may need to perform two rotations to restore balance after an insertion. This can happen in cases like Left-Right or Right-Left imbalances.
Step 6: Conclude that the maximum number of rotations required in the worst case when inserting a node into an AVL tree is 2.

AVL Tree Rotations – AVL trees are self-balancing binary search trees that require rotations to maintain balance after insertions or deletions.
Balance Factor – The balance factor of a node in an AVL tree is the difference in heights between its left and right subtrees, which must be -1, 0, or 1 for the tree to remain balanced.
Types of Rotations – There are four types of rotations in AVL trees: single right rotation, single left rotation, double right-left rotation, and double left-right rotation.