How do AVL trees maintain balance after insertion?
Practice Questions
Q1
How do AVL trees maintain balance after insertion?
By performing rotations.
By deleting nodes.
By increasing the height of the tree.
By changing node colors.
Questions & Step-by-Step Solutions
How do AVL trees maintain balance after insertion?
Step 1: Understand that an AVL tree is a type of binary search tree that keeps itself balanced.
Step 2: Know that each node in an AVL tree has a balance factor, which is the difference between the heights of its left and right subtrees.
Step 3: After inserting a new node, check the balance factor of each node starting from the newly inserted node up to the root.
Step 4: If the balance factor of any node becomes +2 or -2, it means the tree is unbalanced.
Step 5: Determine the type of imbalance: Left-Left, Left-Right, Right-Right, or Right-Left based on the structure of the tree.
Step 6: Perform the appropriate rotation to restore balance: a single rotation for Left-Left or Right-Right, and a double rotation for Left-Right or Right-Left.
Step 7: After performing the rotation, the tree is now balanced again.
AVL Tree Balance Maintenance – AVL trees maintain balance by ensuring that the heights of the two child subtrees of any node differ by no more than one, using rotations to restore balance after insertions.
