What is the worst-case time complexity for deletion in an AVL tree?
Practice Questions
Q1
What is the worst-case time complexity for deletion in an AVL tree?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the worst-case time complexity for deletion in an AVL tree?
Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that is balanced, meaning the heights of the two child subtrees of any node differ by at most one.
Step 2: Know that in a binary search tree, deletion involves finding the node to delete and then removing it while maintaining the tree's properties.
Step 3: Realize that after deleting a node, the AVL tree may become unbalanced, so we need to perform rotations to restore balance.
Step 4: Understand that finding a node in a balanced binary search tree takes O(log n) time, where n is the number of nodes in the tree.
Step 5: Know that performing rotations to maintain balance also takes O(log n) time in the worst case.
Step 6: Combine these two points: the time to find the node and the time to restore balance both take O(log n).
Step 7: Conclude that the worst-case time complexity for deletion in an AVL tree is O(log n).
