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What happens to the balance factor of an AVL tree after a node is deleted?

Practice Questions

Q1
What happens to the balance factor of an AVL tree after a node is deleted?
  1. It remains unchanged.
  2. It can become unbalanced.
  3. It always becomes 0.
  4. It can only increase.

Questions & Step-by-Step Solutions

What happens to the balance factor of an AVL tree after a node is deleted?
  • Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains a balance factor for each node.
  • Step 2: Know what a balance factor is. The balance factor is the difference between the heights of the left and right subtrees of a node.
  • Step 3: When a node is deleted from the AVL tree, the structure of the tree changes.
  • Step 4: After deletion, check the balance factor of the affected nodes starting from the parent of the deleted node up to the root.
  • Step 5: If any node has a balance factor of -2 or +2, it means the tree is unbalanced.
  • Step 6: To fix the unbalance, perform rotations (single or double) on the affected nodes to restore the AVL property.
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