What is the worst-case time complexity for searching an element in a binary sear
Practice Questions
Q1
What is the worst-case time complexity for searching an element in a binary search tree (BST) using DFS?
O(log V)
O(V)
O(E)
O(V^2)
Questions & Step-by-Step Solutions
What is the worst-case time complexity for searching an element in a binary search tree (BST) using DFS?
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 what Depth-First Search (DFS) means. DFS is a method for exploring nodes and edges of a tree or graph by going as deep as possible down one branch before backtracking.
Step 3: Consider the worst-case scenario for a BST. In the worst case, the BST can become unbalanced and look like a linked list, where each node has only one child.
Step 4: In this unbalanced case, to find an element, you may have to check every node in the tree, which means you will visit all nodes one by one.
Step 5: Count the number of nodes in the tree. If there are V nodes, you will have to check all V nodes in the worst case.
Step 6: Conclude that the worst-case time complexity for searching an element in a BST using DFS is O(V), where V is the number of nodes.
