How many rotations are required in the worst case to balance an AVL tree after a
Practice Questions
Q1
How many rotations are required in the worst case to balance an AVL tree after an insertion?
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Questions & Step-by-Step Solutions
How many rotations are required in the worst case to balance an AVL tree after an insertion?
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 it means for an AVL tree to be unbalanced. 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: In the worst-case scenario, after an insertion, the tree may require two rotations to restore balance. This can happen in cases where a node is inserted into the subtree of a child node, causing the imbalance to propagate up.
Step 6: Conclude that in the worst case, 2 rotations are needed to balance the AVL tree after an insertion.
AVL Tree Balancing – AVL trees are self-balancing binary search trees where the difference in heights between the left and right subtrees (balance factor) is at most 1. After an insertion, the tree may become unbalanced, requiring rotations to restore balance.
Rotations in AVL Trees – There are four types of rotations (single and double) used to balance an AVL tree: left rotation, right rotation, left-right rotation, and right-left rotation. In the worst case, two rotations may be needed to restore balance.
