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