How many rotations are needed in the worst case for a single insertion in an AVL
Practice Questions
Q1
How many rotations are needed in the worst case for a single insertion in an AVL tree?
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Questions & Step-by-Step Solutions
How many rotations are needed in the worst case for a single insertion in an AVL tree?
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: Realize that to fix an imbalance, you may need to perform rotations. A rotation is a local operation that changes the structure of the tree to restore balance.
Step 5: Understand that in the worst-case scenario, fixing an imbalance may require two rotations. This can happen in cases like Left-Right or Right-Left imbalances.
Step 6: Conclude that therefore, in the worst case, a single insertion in an AVL tree may require up to 2 rotations to maintain balance.
AVL Tree Rotations – AVL trees are self-balancing binary search trees that require rotations to maintain balance after insertions or deletions.
Worst Case Analysis – Understanding the worst-case scenario for AVL tree operations is crucial for analyzing their performance.
