How do AVL trees handle insertion that causes imbalance?
Practice Questions
Q1
How do AVL trees handle insertion that causes imbalance?
By performing a single rotation
By performing a double rotation
By ignoring the new node
By deleting the node causing imbalance
Questions & Step-by-Step Solutions
How do AVL trees handle insertion that causes imbalance?
Step 1: Insert the new node into the AVL tree like you would in a regular binary search tree.
Step 2: After insertion, check the balance factor of each node starting from the newly inserted node up to the root. 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 an imbalance.
Step 4: Determine 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: Perform the appropriate rotation to fix the imbalance: a single rotation for Left-Left or Right-Right cases, and a double rotation for Left-Right or Right-Left cases.
Step 6: After performing the rotation, the tree will be balanced again.
AVL Tree Insertion – AVL trees maintain balance through rotations after insertions that cause height imbalances.
Rotations – Single and double rotations are techniques used to restore balance in AVL trees.
Imbalance Cases – Different cases of imbalance (left-left, left-right, right-left, right-right) determine the type of rotation needed.
