What is the worst-case time complexity for deleting an element from an AVL tree?

Practice Questions

Q1
What is the worst-case time complexity for deleting an element from an AVL tree?
  1. O(1)
  2. O(log n)
  3. O(n)
  4. O(n log n)

Questions & Step-by-Step Solutions

What is the worst-case time complexity for deleting an element from an AVL tree?
  • Step 1: Understand what an AVL tree is. It is a type of binary search tree that keeps itself balanced.
  • Step 2: Know that in a binary search tree, deleting an element may require finding the element first.
  • Step 3: Realize that finding an element in an AVL tree takes O(log n) time because the tree is balanced.
  • Step 4: After finding the element, you need to delete it. This also takes O(log n) time in an AVL tree.
  • Step 5: After deletion, the tree may become unbalanced, so you need to perform rotations to restore balance.
  • Step 6: The rotations also take O(log n) time because they involve a limited number of tree nodes.
  • Step 7: Combine the times: finding the element, deleting it, and balancing the tree all take O(log n) time.
  • Step 8: Conclude that the worst-case time complexity for deleting an element from an AVL tree is O(log n).
No concepts available.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely