How many rotations are required in the worst case for balancing an AVL tree afte
Practice Questions
Q1
How many rotations are required in the worst case for balancing an AVL tree after an insertion?
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Questions & Step-by-Step Solutions
How many rotations are required in the worst case for balancing an AVL tree after an insertion?
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 after inserting a new node into an AVL tree, the tree may become unbalanced.
Step 3: Identify the types of imbalances that can occur after an insertion: Left-Left, Left-Right, Right-Right, and Right-Left.
Step 4: Realize that each type of imbalance can be corrected using rotations.
Step 5: Understand that in the worst-case scenario, two rotations may be needed to restore balance. This can happen in cases like Left-Right or Right-Left imbalances.
Step 6: Conclude that the maximum number of rotations required to balance an AVL tree after an insertion is 2.
AVL Tree Balancing – AVL trees are self-balancing binary search trees where the difference in heights between the left and right subtrees (balance factor) is at most 1. After an insertion, the tree may become unbalanced, requiring rotations to restore balance.
Rotations in AVL Trees – There are four types of rotations used to balance an AVL tree: single right rotation, single left rotation, double right-left rotation, and double left-right rotation. In the worst case, two rotations may be needed to restore balance.
