Question: In DFS, what is the maximum depth of recursion for a graph with V vertices?
Options:
O(V)
O(E)
O(V + E)
O(log V)
Correct Answer: O(V)
Solution:
The maximum depth of recursion in DFS can go up to O(V) in the worst case, where V is the number of vertices.
In DFS, what is the maximum depth of recursion for a graph with V vertices?
Practice Questions
Q1
In DFS, what is the maximum depth of recursion for a graph with V vertices?
O(V)
O(E)
O(V + E)
O(log V)
Questions & Step-by-Step Solutions
In DFS, what is the maximum depth of recursion for a graph with V vertices?
Step 1: Understand what DFS (Depth-First Search) is. It is a method for exploring a graph by going as deep as possible along each branch before backtracking.
Step 2: Recognize that in DFS, we use a stack (either explicitly or through recursion) to keep track of the vertices we are visiting.
Step 3: Note that each time we visit a new vertex, we go one level deeper in the recursion.
Step 4: Consider the worst-case scenario where the graph is a long chain (like a linked list) with V vertices.
Step 5: In this worst-case scenario, we would visit each vertex one after the other, leading to a maximum depth of recursion equal to the number of vertices, V.
Step 6: Therefore, we conclude that the maximum depth of recursion in DFS can be O(V) in the worst case.
Depth-First Search (DFS) – DFS is an algorithm for traversing or searching tree or graph data structures, where it explores as far as possible along each branch before backtracking.
Recursion Depth – The maximum depth of recursion refers to the maximum number of recursive calls that can be made before reaching a base case or exhausting the graph's vertices.
Graph Vertices (V) – In graph theory, V represents the number of vertices in a graph, which can affect the performance and behavior of graph algorithms like DFS.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
