Which operation is guaranteed to be O(log n) in an AVL tree?
Practice Questions
Q1
Which operation is guaranteed to be O(log n) in an AVL tree?
Insertion
Deletion
Searching
All of the above
Questions & Step-by-Step Solutions
Which operation is guaranteed to be O(log n) in an AVL tree?
Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains balance, meaning the heights of the two child subtrees of any node differ by at most one.
Step 2: Know what O(log n) means. O(log n) indicates that the time it takes to perform an operation grows logarithmically as the number of elements (n) increases. This is efficient for large datasets.
Step 3: Recognize the operations in an AVL tree. The main operations are insertion, deletion, and searching for a value.
Step 4: Learn how AVL trees maintain balance. After each insertion or deletion, the tree checks its balance and performs rotations if necessary to keep it balanced.
Step 5: Conclude that because AVL trees are balanced, the height of the tree is always kept to log(n), which means all operations (insertion, deletion, searching) can be performed in O(log n) time.
