How many rotations are needed in the worst case for balancing an AVL tree after
Practice Questions
Q1
How many rotations are needed 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 needed 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 to ensure efficient operations.
Step 2: Know that after inserting a new node into an AVL tree, the tree may become unbalanced.
Step 3: Identify what 'unbalanced' means. An AVL tree is unbalanced if the heights of the two child subtrees of any node differ by more than one.
Step 4: Learn about the types of rotations used to balance an AVL tree: single rotations (left or right) and double rotations (left-right or right-left).
Step 5: Realize that in the worst-case scenario, two rotations may be required to restore balance after an insertion.
Step 6: Conclude that the maximum number of rotations needed 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 necessary.
