How many rotations are needed in the worst case for balancing an AVL tree after an insertion?
Practice Questions
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How many rotations are needed in the worst case for balancing an AVL tree after an insertion?
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In the worst case, 2 rotations may be needed to balance an AVL tree after an insertion.
Questions & Step-by-step Solutions
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Q
Q: How many rotations are needed in the worst case for balancing an AVL tree after an insertion?
Solution: In the worst case, 2 rotations may be needed to balance an AVL tree after an insertion.
Steps: 6
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.
