Question: What is the time complexity of inserting an element into an AVL tree?
Options:
O(n)
O(log n)
O(n log n)
O(1)
Correct Answer: O(log n)
Solution:
Inserting an element into an AVL tree takes O(log n) time due to the need to maintain balance after insertion.
What is the time complexity of inserting an element into an AVL tree?
Practice Questions
Q1
What is the time complexity of inserting an element into an AVL tree?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the time complexity of inserting an element into 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.
Step 2: Know that when you insert an element into a binary search tree, you first find the correct position for the new element. This takes O(log n) time because the tree is balanced.
Step 3: After inserting the new element, check if the tree is still balanced. This involves looking at the heights of the nodes and their children.
Step 4: If the tree is unbalanced, perform rotations to restore balance. The number of rotations needed is limited, so this also takes O(log n) time.
Step 5: Combine the time taken for insertion and balancing. Since both steps take O(log n) time, the overall time complexity for inserting an element into an AVL tree is O(log n).
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