What is the worst-case time complexity of the depth-first search (DFS) algorithm
Practice Questions
Q1
What is the worst-case time complexity of the depth-first search (DFS) algorithm on a binary tree?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the worst-case time complexity of the depth-first search (DFS) algorithm on a binary tree?
Step 1: Understand what depth-first search (DFS) is. It is an algorithm used to explore nodes and edges of a tree or graph by going as deep as possible down one branch before backtracking.
Step 2: Recognize that a binary tree is a tree data structure where each node has at most two children.
Step 3: Identify that in the worst-case scenario, DFS will need to visit every node in the binary tree to ensure it has explored all possible paths.
Step 4: Count the number of nodes in the binary tree. Let's say there are 'n' nodes.
Step 5: Since DFS visits each node once, the time taken to visit all nodes is proportional to 'n'.
Step 6: Conclude that the worst-case time complexity of DFS on a binary tree is O(n), meaning it grows linearly with the number of nodes.
