What is the time complexity for searching an element in a balanced AVL tree?
Practice Questions
Q1
What is the time complexity for searching an element in a balanced AVL tree?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the time complexity for searching an element in a balanced 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 in a binary search tree, searching for an element involves comparing the target value with the values of the nodes, starting from the root and moving left or right based on the comparison.
Step 3: Realize that because the AVL tree is balanced, the maximum height of the tree is kept to a minimum, specifically around log base 2 of the number of nodes (n).
Step 4: Understand that the time it takes to search for an element is proportional to the height of the tree. Since the height of a balanced AVL tree is O(log n), the search operation will also take O(log n) time.
Step 5: Conclude that the time complexity for searching an element in a balanced AVL tree is O(log n).
