What is the time complexity of searching for a value in a binary search tree (BS
Practice Questions
Q1
What is the time complexity of searching for a value in a binary search tree (BST) with n nodes?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the time complexity of searching for a value in a binary search tree (BST) with n nodes?
Step 1: Understand what a binary search tree (BST) is. A BST is a data structure where each node has at most two children, and the left child is less than the parent node, while the right child is greater.
Step 2: Know that searching in a BST involves comparing the value you are looking for with the values in the nodes, starting from the root.
Step 3: In a balanced BST, the height of the tree is log(n), where n is the number of nodes. This means you can find the value by going down the tree, making at most log(n) comparisons.
Step 4: In the worst case, if the BST is unbalanced (like a linked list), the height can be n. This means you may have to check every node, resulting in n comparisons.
Step 5: Therefore, the average time complexity for searching in a balanced BST is O(log n), while in the worst case (unbalanced), it is O(n).
