What is the time complexity of balancing an AVL tree after a deletion?
Practice Questions
Q1
What is the time complexity of balancing an AVL tree after a deletion?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the time complexity of balancing an AVL tree after a deletion?
Step 1: Understand that an AVL tree is a type of binary search tree that maintains balance after insertions and deletions.
Step 2: When a node is deleted from an AVL tree, the tree may become unbalanced.
Step 3: To restore balance, we need to check the balance factor of the affected nodes starting from the node where the deletion occurred up to the root.
Step 4: The balance factor is calculated as the height of the left subtree minus the height of the right subtree.
Step 5: If the balance factor is not within the range of -1 to 1, we perform rotations (single or double) to restore balance.
Step 6: The height of an AVL tree is logarithmic in relation to the number of nodes, which means it is O(log n).
Step 7: Since we may need to check and possibly rotate nodes up to the height of the tree, the time complexity for balancing the tree after a deletion is O(log n).
