How many rotations are needed in the worst case when inserting a node in an AVL tree?
Practice Questions
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How many rotations are needed in the worst case when inserting a node in an AVL tree?
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In the worst case, at most 2 rotations are needed 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 needed in the worst case when inserting a node in an AVL tree?
Solution: In the worst case, at most 2 rotations are needed to maintain the balance of an AVL tree after 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 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: Learn that to fix these imbalances, we use rotations. A rotation is a local operation that changes the structure of the tree to restore balance.
Step 5: Realize that in the worst-case scenario, you may need to perform two rotations to restore balance after an insertion. This can happen in cases like Left-Right or Right-Left imbalances.
Step 6: Conclude that the maximum number of rotations needed in the worst case when inserting a node in an AVL tree is 2.
