What is the time complexity of balancing an AVL tree after an insertion?
Practice Questions
1 question
Q1
What is the time complexity of balancing an AVL tree after an insertion?
O(log n)
O(n)
O(1)
O(n log n)
Balancing an AVL tree after an insertion takes O(log n) time due to the height of the tree.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the time complexity of balancing an AVL tree after an insertion?
Solution: Balancing an AVL tree after an insertion takes O(log n) time due to the height of the tree.
Steps: 5
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 that balancing is necessary when the tree becomes unbalanced after an insertion. An AVL tree is considered unbalanced if the heights of the two child subtrees of any node differ by more than one.
Step 3: After inserting a new node, check the balance factor of each node starting from the newly inserted node up to the root. The balance factor is calculated as the height of the left subtree minus the height of the right subtree.
Step 4: If any node is found to be unbalanced (balance factor is not -1, 0, or 1), perform rotations to restore balance. There are four types of rotations: left rotation, right rotation, left-right rotation, and right-left rotation.
Step 5: The height of an AVL tree is logarithmic in relation to the number of nodes (n), specifically O(log n). Since we may need to check the balance of nodes up to the height of the tree, the time taken to balance the tree after an insertion is O(log n).
