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How do AVL trees ensure balance after insertion?

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Question: How do AVL trees ensure balance after insertion?

Options:

  1. By performing a single rotation
  2. By performing multiple rotations
  3. By ignoring balance factors
  4. By using a hash table

Correct Answer: By performing multiple rotations

Solution: 

AVL trees ensure balance after insertion by performing multiple rotations as needed based on the balance factors of the nodes.

How do AVL trees ensure balance after insertion?

Practice Questions

Q1
How do AVL trees ensure balance after insertion?
  1. By performing a single rotation
  2. By performing multiple rotations
  3. By ignoring balance factors
  4. By using a hash table

Questions & Step-by-Step Solutions

How do AVL trees ensure balance after insertion?
  • Step 1: Insert the new node into the AVL tree just like you would in a regular binary search tree.
  • Step 2: After inserting the new node, 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 is greater than 1 or less than -1, it means the tree is unbalanced.
  • Step 4: Determine the type of imbalance (Left-Left, Left-Right, Right-Right, or Right-Left) based on the balance factors of the affected nodes.
  • Step 5: Perform the appropriate rotation(s) to restore balance. This could be a single rotation (left or right) or a double rotation (left-right or right-left).
  • Step 6: After performing the rotations, the tree will be balanced again, and you can continue using it.
  • AVL Tree Balancing – AVL trees maintain balance by calculating the balance factor (height difference between left and right subtrees) and performing rotations (single or double) to restore balance after insertions.
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