How many rotations are required in the worst case when inserting a node in an AVL tree?
Practice Questions
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How many rotations are required in the worst case when inserting a node in an AVL tree?
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In the worst case, only 1 or 2 rotations are required to maintain the balance of an AVL tree after insertion.
Questions & Step-by-step Solutions
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Q
Q: How many rotations are required in the worst case when inserting a node in an AVL tree?
Solution: In the worst case, only 1 or 2 rotations are required to maintain the balance of an AVL tree after insertion.
Steps: 7
Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains balance by ensuring that the heights of the two child subtrees of any node differ by at most 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: For each type of imbalance, determine how many rotations are needed to restore balance.
Step 5: Realize that for Left-Left and Right-Right imbalances, only 1 rotation is needed.
Step 6: For Left-Right and Right-Left imbalances, 2 rotations are needed to restore balance.
Step 7: Conclude that in the worst case, you will need either 1 or 2 rotations to maintain the balance of the AVL tree after an insertion.
