How many rotations are needed to balance an AVL tree after an insertion?
Practice Questions
1 question
Q1
How many rotations are needed to balance an AVL tree after an insertion?
At most one.
At most two.
At most three.
No rotations are needed.
At most two rotations are needed to balance an AVL tree after an insertion, depending on the case of imbalance.
Questions & Step-by-step Solutions
1 item
Q
Q: How many rotations are needed to balance an AVL tree after an insertion?
Solution: At most two rotations are needed to balance an AVL tree after an insertion, depending on the case of imbalance.
Steps: 6
Step 1: Understand that 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: After inserting a new node into the AVL tree, check the balance factor of the affected nodes. The balance factor is calculated as the height of the left subtree minus the height of the right subtree.
Step 3: If the balance factor of any node becomes greater than 1 or less than -1, it indicates that the tree is unbalanced.
Step 4: Identify the type of imbalance based on the balance factors of the nodes involved. There are four cases: Left-Left, Left-Right, Right-Right, and Right-Left.
Step 5: Depending on the type of imbalance, perform the appropriate rotations to restore balance. Each case can be resolved with either one or two rotations.
Step 6: Conclude that at most two rotations are needed to balance the AVL tree after an insertion.
