Which of the following statements is true about the height of an AVL tree?
Practice Questions
Q1
Which of the following statements is true about the height of an AVL tree?
It can be greater than log(n)
It is always less than or equal to 1.44 log(n)
It is always equal to log(n)
It can be less than log(n)
Questions & Step-by-Step Solutions
Which of the following statements is true about the height of an AVL tree?
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 what 'height' means. The height of a tree is the number of edges on the longest path from the root to a leaf.
Step 3: Learn about the balance factor. In an AVL tree, the balance factor (the difference in height between the left and right subtrees) must be -1, 0, or 1.
Step 4: Recognize the logarithmic relationship. The height of an AVL tree is related to the number of nodes (n) in the tree, specifically it is less than or equal to 1.44 times the logarithm of n.
Step 5: Conclude that this height limit ensures that operations like insertion, deletion, and searching can be done efficiently, typically in O(log n) time.
