What is the worst-case time complexity for insertion in an AVL tree?
Practice Questions
Q1
What is the worst-case time complexity for insertion 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 insertion in an AVL tree?
Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that automatically keeps itself balanced after insertions and deletions.
Step 2: Know what 'worst-case time complexity' means. It refers to the maximum amount of time an operation could take in the worst scenario.
Step 3: Recognize that when you insert a new node into an AVL tree, you first need to find the correct position for that node, just like in a regular binary search tree.
Step 4: Understand that finding the correct position in a balanced binary search tree takes O(log n) time, where n is the number of nodes in the tree.
Step 5: After inserting the node, the AVL tree may need to perform rotations to maintain its balance. However, the number of rotations needed is limited and also takes O(log n) time.
Step 6: Combine the time taken to find the position and the time taken for rotations. Both are O(log n), so the total time complexity for insertion remains O(log n).
Step 7: Conclude that the worst-case time complexity for insertion in an AVL tree is O(log n) because the tree stays balanced.
