What is the average time complexity of searching for an element in a balanced bi
Practice Questions
Q1
What is the average time complexity of searching for an element in a balanced binary search tree?
O(1)
O(log n)
O(n)
O(n log n)
Questions & Step-by-Step Solutions
What is the average time complexity of searching for an element in a balanced binary search tree?
Step 1: Understand what a balanced binary search tree is. It is a type of data structure that keeps its elements in a sorted order and maintains balance to ensure efficient operations.
Step 2: Know that in a binary search tree, each node has at most two children, and for any given node, all elements in the left subtree are smaller, and all elements in the right subtree are larger.
Step 3: Realize that searching for an element involves comparing the target value with the current node's value and deciding whether to go left or right based on the comparison.
Step 4: In a balanced binary search tree, the height of the tree is kept to a minimum, which means the number of comparisons needed to find an element is reduced.
Step 5: The height of a balanced binary search tree is approximately log base 2 of the number of elements (n) in the tree, which is written as log(n).
Step 6: Therefore, the average time complexity for searching for an element in a balanced binary search tree is O(log n).
