What is the time complexity of inserting a node in an AVL tree?
Practice Questions
Q1
What is the time complexity of inserting a node in an AVL tree?
O(1)
O(log n)
O(n)
O(n log n)
Questions & Step-by-Step Solutions
What is the time complexity of inserting a node in an AVL tree?
Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that keeps itself balanced.
Step 2: Know that when you insert a node into an AVL tree, you first perform a regular binary search tree insertion.
Step 3: After inserting the node, check if the tree is still balanced. This involves looking at the heights of the nodes.
Step 4: If the tree is unbalanced, perform rotations to rebalance it. There are four types of rotations: left, right, left-right, and right-left.
Step 5: The height of an AVL tree is always logarithmic in relation to the number of nodes, which means it grows slowly as more nodes are added.
Step 6: Since both the insertion and the rebalancing operations take time proportional to the height of the tree, the overall time complexity for inserting a node is O(log n).
