What is the maximum height of an AVL tree with n nodes?
Practice Questions
Q1
What is the maximum height of an AVL tree with n nodes?
O(log n)
O(n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the maximum height of an AVL tree with n nodes?
Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains balance to ensure efficient operations.
Step 2: Know that the height of a tree is the number of edges on the longest path from the root to a leaf.
Step 3: Realize that an AVL tree is balanced, meaning the heights of the two child subtrees of any node differ by at most one.
Step 4: Learn that the maximum height of an AVL tree with n nodes can be derived from the properties of Fibonacci numbers.
Step 5: The maximum height (h) of an AVL tree with n nodes is approximately 1.44 * log2(n + 2) - 0.328, which simplifies to O(log n).
Step 6: Conclude that the maximum height of an AVL tree grows logarithmically with the number of nodes, ensuring efficient operations like insertion, deletion, and lookup.
