Graph Traversal: BFS and DFS for Competitive Exams

Graph Traversal: BFS and DFS - Complexity Analysis - Higher Difficulty Problems

Q. If a graph has a cycle, which traversal method can detect it?

Solution

DFS can detect cycles in a graph by keeping track of visited nodes and checking for back edges.

Correct Answer: B — Only DFS

Q. In DFS, what is the maximum depth of recursion for a graph with V vertices?

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.

Correct Answer: A — O(V)

Q. In which scenario would DFS be preferred over BFS?

Solution

DFS is preferred when memory is limited, as it can use less space than BFS in certain cases.

Correct Answer: C — When memory is limited

Q. What is the space complexity of BFS using an adjacency list representation?

Solution

BFS requires space for the queue and visited list, leading to a space complexity of O(V) for the vertices.

Correct Answer: A — O(V)

Q. What is the space complexity of DFS using a recursive approach?

Solution

The space complexity of DFS using recursion is O(V) due to the call stack used for recursion.

Correct Answer: A — O(V)

Q. What is the worst-case time complexity of DFS for a graph represented as an adjacency matrix?

Solution

In the worst case, DFS will check all entries in the adjacency matrix, leading to a time complexity of O(V^2).

Correct Answer: C — O(V^2)

Q. Which traversal method is generally faster for large graphs?

Solution

The speed of BFS or DFS can depend on the graph structure; for some graphs, one may be faster than the other.

Correct Answer: D — Depends on the graph structure

Q. Which traversal method is more memory efficient for a sparse graph?

Solution

DFS can be more memory efficient than BFS for sparse graphs because it uses a stack (or recursion) instead of a queue, which can grow larger in BFS.

Correct Answer: B — DFS

Showing 1 to 8 of 8 (1 Pages)