This set of Data Structure Multiple Choice Questions & Answers (MCQs) focuses on “Depth First Search”.

1. Depth First Search is equivalent to which of the traversal in the Binary Trees?

a) Pre-order Traversal

b) Post-order Traversal

c) Level-order Traversal

d) In-order Traversal

View Answer

Explanation: In Depth First Search, we explore all the nodes aggressively to one path and then backtrack to the node. Hence, it is equivalent to the pre-order traversal of a Binary Tree.

2. Time Complexity of DFS is? (V – number of vertices, E – number of edges)

a) O(V + E)

b) O(V)

c) O(E)

d) None of the mentioned

View Answer

Explanation: The Depth First Search explores every node once and every edge once (in worst case), so it’s time complexity is O(V + E).

3. The Data structure used in standard implementation of Breadth First Search is?

a) Stack

b) Queue

c) Linked List

d) None of the mentioned

View Answer

Explanation: The Depth First Search is implemented using recursion. So, stack can be used as data structure to implement depth first search.

4. The Depth First Search traversal of a graph will result into?

a) Linked List

b) Tree

c) Graph with back edges

d) None of the mentioned

View Answer

Explanation: The Depth First Search will make a graph which don’t have back edges (a tree) which is known as Depth First Tree.

5. A person wants to visit some places. He starts from a vertex and then wants to visit every vertex till it finishes from one vertex, backtracks and then explore other vertex from same vertex. What algorithm he should use?

a) Depth First Search

b) Breadth First Search

c) Trim’s algorithm

d) None of the mentioned

View Answer

Explanation: This is the definition of the Depth First Search. Exploring a node, then aggressively finding nodes till it is not able to find any node.

6. What can be the applications of Depth First Search?

a) For generating topological sort of a graph

b) For generating Strongly Connected Components of a directed graph

c) Detecting cycles in the graph

d) All of the mentioned

View Answer

Explanation: Depth First Search can be applied to all of the mentioned problems.

7. When the Depth First Search of a graph is unique?

a) When the graph is a Binary Tree

b) When the graph is a Linked List

c) When the graph is a n-ary Tree

d) None of the mentioned

View Answer

Explanation: When Every node will have one successor then the Depth First Search is unique. In all other cases, when it will have more than one successor, it can choose any of them in arbitrary order.

8. Regarding implementation of Depth First Search using stacks, what is the maximum distance between two nodes present in the stack? (considering each edge length 1)

a) Can be anything

b) 0

c) At most 1

d) Insufficient Information

View Answer

Explanation: In the stack, at a time, there can be nodes which can differ in many levels. So, it can be the maximum distance between two nodes in the graph.

9. In Depth First Search, how many times a node is visited?

a) Once

b) Twice

c) Equivalent to number of indegree of the node

d) None of the mentioned

View Answer

Explanation: In Depth First Search, we have to see whether the node is visited or not by it’s ancestor. If it is visited, we won’t let it enter it in the stack.

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