What is the time complexity of inserting an element in an AVL tree?
Practice Questions
Q1
What is the time complexity of inserting an element in 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 in an AVL tree?
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 inserting an element in a binary search tree generally takes O(h) time, where h is the height of the tree.
Step 3: Realize that the height of an AVL tree is always O(log n), where n is the number of nodes in the tree, because it is balanced.
Step 4: Therefore, when you insert an element into an AVL tree, you first find the correct position for the new element, which takes O(log n) time.
Step 5: After inserting the element, you may need to perform rotations to maintain the balance of the tree, but this also takes O(log n) time.
Step 6: Combine the time taken for finding the position and the time for balancing, which results in a total time complexity of O(log n) for the insertion operation.
