How many rotations are needed in the worst case when inserting a node into an AV
Practice Questions
Q1
How many rotations are needed in the worst case when inserting a node into an AVL tree?
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Questions & Step-by-Step Solutions
How many rotations are needed in the worst case when inserting a node into 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 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 what it means for a tree to be unbalanced. If the balance factor (the difference in height between the left and right subtrees) of any node becomes greater than 1 or less than -1, the tree is unbalanced.
Step 4: Learn about rotations. Rotations are operations that help restore balance to the AVL tree. There are four types of rotations: left rotation, right rotation, left-right rotation, and right-left rotation.
Step 5: In the worst-case scenario, inserting a node can cause an imbalance that requires two rotations to fix. This can happen in cases where the tree becomes unbalanced after the insertion of a node in a specific pattern.
Step 6: Conclude that in the worst case, you may need up to 2 rotations to restore balance after inserting a node into an AVL tree.
AVL Tree Rotations – AVL trees are self-balancing binary search trees that require rotations to maintain balance after insertions or deletions.
Balance Factor – The balance factor of a node in an AVL tree is the difference in heights between its left and right subtrees, which must be -1, 0, or 1 for the tree to remain balanced.
Types of Rotations – There are four types of rotations (single right, single left, double right-left, and double left-right) that can be performed to restore balance in an AVL tree.
