What is the worst-case time complexity for inserting a node in an AVL tree?
Practice Questions
1 question
Q1
What is the worst-case time complexity for inserting a node in an AVL tree?
O(n)
O(log n)
O(n log n)
O(1)
The worst-case time complexity for inserting a node in an AVL tree is O(log n) due to the tree's balanced nature.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the worst-case time complexity for inserting a node in an AVL tree?
Solution: The worst-case time complexity for inserting a node in an AVL tree is O(log n) due to the tree's balanced nature.
Steps: 5
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 when you insert a node into an AVL tree, you first perform a standard binary search tree insertion. This takes O(h) time, where h is the height of the tree.
Step 3: Realize that the height of an AVL tree is always logarithmic in relation to the number of nodes (n) because it is balanced. Specifically, h = O(log n).
Step 4: After inserting the node, you may need to perform rotations to maintain the balance of the tree. The number of rotations needed is also limited by the height of the tree, which is O(log n).
Step 5: Combine the time for insertion and the time for balancing. Since both operations take O(log n) time, the overall worst-case time complexity for inserting a node in an AVL tree is O(log n).
