Graph Traversal Algorithms: Master Depth-First and Breadth-First Search

Question 1

Which data structure is typically used to implement a Depth-First Search (DFS) traversal?

Accepted Answer

Stack

Answer

Array

Answer

Linked list

Answer

Queue

Question 2

What is the primary distinction between Depth-First Search (DFS) and Breadth-First Search (BFS) traversal?

Accepted Answer

DFS explores a node's neighbors before continuing deeper, while BFS explores all nodes at a given level first.

Answer

BFS is an iterative algorithm, while DFS is a recursive one.

Answer

DFS can detect cycles, while BFS cannot.

Answer

DFS is best suited for sparse graphs, while BFS is best for dense graphs.

Question 3

What is the time complexity of a DFS traversal on a graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(V * E)

Answer

O(E)

Answer

O(V)

Question 4

What is the primary purpose of a 'visited' array in a DFS traversal?

Accepted Answer

To track visited nodes and prevent revisiting

Answer

To record the order in which nodes are visited

Answer

To calculate the distance from the source node

Answer

To determine if the graph contains a cycle

Question 5

Which of the following is a potential drawback of DFS traversal?

Accepted Answer

DFS can run indefinitely on graphs with cycles

Answer

DFS does not guarantee finding the shortest path

Answer

DFS is more complex to implement than BFS

Answer

DFS is not suitable for sparse graphs

Question 6

Consider a graph with vertices labeled A, B, C, D, E, and F, and edges (A, B), (B, C), (C, D), (D, E), (E, F), (A, F). What is the output of a BFS traversal starting from vertex A?

Accepted Answer

A, B, C, D, E, F

Answer

A, B, F, C, D, E

Answer

A, F, B, C, D, E

Answer

A, B, F, C, E, D

Question 7

Which of the following is NOT a characteristic of a topological sort?

Accepted Answer

It is used to find cycles in a graph

Answer

It produces a linear ordering of vertices

Answer

All edges in the graph are respected in the ordering

Answer

It can only be performed on directed acyclic graphs

Question 8

Which of the following algorithms is most efficient for performing topological sort?

Accepted Answer

Depth-first search

Answer

Breadth-first search

Answer

Dijkstra's algorithm

Answer

Floyd-Warshall algorithm

Question 9

Which of the following is a necessary condition for applying DFS or BFS algorithms on a graph?

Accepted Answer

Graph must have a designated starting vertex

Answer

Graph must be a directed graph

Answer

Graph must be an undirected graph

Answer

Graph must have equal weights on all edges

Question 10

What is the time complexity of performing a DFS or BFS traversal on a graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(V)

Answer

O(E)

Answer

O(V^2)

Question 11

Which of the following algorithms is guaranteed to find the shortest path between two vertices in a weighted graph?

Accepted Answer

Dijkstra's algorithm

Answer

Depth-first search

Answer

Breadth-first search

Answer

Prim's algorithm

Question 12

Which data structure is commonly used to implement the stack required for DFS?

Accepted Answer

Stack

Answer

Queue

Answer

Array

Answer

Linked list

Question 13

Which traversal strategy explores nodes at the same level before proceeding to the next level?

Accepted Answer

Breadth-first search

Answer

Depth-first search

Answer

In-order traversal

Answer

Post-order traversal

Question 14

What is the key purpose of using a visited array in graph traversal algorithms?

Accepted Answer

To prevent revisiting previously visited nodes

Answer

To store the distance from the starting vertex

Answer

To keep track of the order of node visits

Answer

To represent the adjacency list of the graph

Question 15

Which modification to DFS can effectively detect cycles in a graph?

Accepted Answer

Adding a loop to check for back edges

Answer

Using a queue instead of a stack

Answer

Marking visited nodes with different colors

Answer

Reversing the order of node traversal

Question 16

Depth-First Search (DFS) is a graph traversal algorithm that explores nodes based on which order?

Accepted Answer

Depth-first

Answer

Breadth-first

Answer

Random

Answer

Height-first

Question 17

In a directed graph, which algorithm can be used to detect cycles?

Accepted Answer

DFS

Answer

BFS

Answer

Dijkstra's Algorithm

Answer

A* Algorithm

Question 18

Which of the following is a recursive implementation of DFS?

Accepted Answer

Recursive function that marks nodes as visited and explores neighbors

Answer

Function that uses a stack to keep track of nodes to visit

Answer

Function that uses a loop to traverse nodes

Answer

Function that uses a queue to traverse nodes

Question 19

When implementing BFS, which data structure is typically used to keep track of nodes to be visited?

Accepted Answer

Queue

Answer

Stack

Answer

List

Answer

Set

Question 20

In a graph with 'V' vertices and 'E' edges, what is the time complexity associated with DFS?

Accepted Answer

O(V+E)

Answer

O(V)

Answer

O(E)

Answer

O(V^2)

Question 21

Identify an application where Depth-First Search (DFS) is commonly utilized:

Accepted Answer

All of the aforementioned applications

Answer

Discovering connected components within a graph structure

Answer

Detecting the presence of cycles in a graph

Answer

Performing topological sorting of directed acyclic graphs

Question 22

What is the definition of topological sorting?

Accepted Answer

An ordering of vertices in a directed acyclic graph ensuring that for any directed edge (u, v), vertex u precedes vertex v in the ordering.

Answer

A sorting algorithm applicable to any type of graph

Answer

A method for representing a graph as a tree structure

Answer

An algorithm designed to find the shortest path between two specified nodes in a graph

Question 23

Which algorithm is commonly employed for topological sorting of directed acyclic graphs?

Accepted Answer

Depth-First Search (DFS)

Answer

Breadth-First Search (BFS)

Answer

Prim's algorithm for Minimum Spanning Trees

Answer

Kruskal's algorithm for Minimum Spanning Trees

Question 24

In the context of DFS, what is the primary purpose of utilizing a visited array?

Accepted Answer

To prevent revisiting nodes, thus avoiding infinite loops during traversal

Answer

To maintain a record of the sequence in which nodes are visited

Answer

To determine the total number of nodes in the graph

Answer

To calculate the distance from the starting node to each visited node

Question 25

Distinguish between directed and undirected graphs?

Accepted Answer

In directed graphs, edges possess a specific direction, whereas in undirected graphs, edges do not have a defined direction.

Answer

In directed graphs, vertices can receive multiple incoming edges, while in undirected graphs, vertices receive at most one incoming edge.

Answer

In directed graphs, edges are assigned weights, while in undirected graphs, edges remain unweighted.

Answer

Directed and undirected graphs do not differ in any significant way.

Question 26

What is the outcome of performing DFS on a connected graph with a single source node?

Accepted Answer

The result is a tree rooted at the source node

Answer

The result is a list encompassing all nodes in the graph

Answer

The result is a list containing all edges in the graph

Answer

The result is a sorted list of nodes based on their respective distances from the source node

Question 27

Which of the following is NOT a fundamental property of depth-first search (DFS)?

Accepted Answer

It finds the shortest path between two nodes.

Answer

It traverses the graph in a stack-like manner.

Answer

It guarantees that each node is visited exactly once.

Answer

It is a recursive algorithm.

Question 28

Consider a graph with n nodes and m edges. Determine the time complexity of a DFS traversal on this graph.

Accepted Answer

O(n + m)

Answer

O(n)

Answer

O(n^2)

Answer

O(m)

Question 29

Identify an invalid application of a topological sort.

Accepted Answer

Finding the shortest path in a graph

Answer

Scheduling tasks without dependencies

Answer

Analyzing program flow

Answer

Detecting cycles in a graph

Question 30

Determine the time complexity of a topological sort on a directed acyclic graph (DAG) with n nodes and m edges.

Accepted Answer

O(n + m)

Answer

O(n)

Answer

O(n^2)

Answer

O(m)

Question 31

Which data structure is typically employed to implement the queue in a BFS algorithm?

Accepted Answer

Queue

Answer

Stack

Answer

Tree

Answer

Heap

Question 32

In DFS, why is a stack utilized?

Accepted Answer

To monitor nodes visited but not yet fully explored

Answer

To monitor nodes explored but not yet visited

Answer

To track the shortest path from the origin node

Answer

To track the longest path from the origin node

Question 33

Which traversal technique is guaranteed to find the shortest path between two nodes in a weighted graph?

Accepted Answer

Dijkstra's algorithm

Answer

DFS

Answer

BFS

Answer

Prim's algorithm

Question 34

Which search strategy can be effectively used to detect cycles within a graph?

Accepted Answer

DFS

Answer

BFS

Answer

Dijkstra's algorithm

Answer

Kruskal's algorithm

Question 35

In a graph with N nodes and E edges, what is the time complexity of performing a BFS traversal?

Accepted Answer

O(V + E)

Answer

O(V)

Answer

O(E)

Answer

O(V^2)

Question 36

Which of the following is a defining characteristic of a Depth-First Search (DFS) algorithm?

Accepted Answer

It typically utilizes a stack data structure for efficient implementation.

Answer

It systematically explores all nodes at a given level before moving to the next level.

Answer

It is guaranteed to find the shortest path between two nodes in the graph.

Answer

It can only be applied to graphs that are connected.

Question 37

Among the following data structures, which one is NOT typically used in the implementation of Depth-First Search?

Accepted Answer

Queue

Answer

Stack

Answer

Adjacency list

Answer

Set to track visited nodes

Question 38

Which of the following statements accurately describes the behavior of BFS?

Accepted Answer

It assigns distinct levels to nodes in the graph, starting from the source node.

Answer

It can be employed to determine the diameter of a tree, i.e., the longest path between any two nodes.

Answer

It always finds the shortest path between two specified nodes in the graph.

Answer

It requires the input graph to be acyclic, meaning it contains no cycles.

Question 39

Which of the following potential time complexities accurately reflects the performance of BFS?

Accepted Answer

O(V + E)

Answer

O(V)

Answer

O(E)

Answer

O(V^2)

Question 40

Compared to BFS, a potential disadvantage of using DFS is that it:

Accepted Answer

Has a higher risk of getting trapped in cycles within the graph.

Answer

May not always find the shortest path between two nodes.

Answer

Requires a larger amount of memory for its implementation.

Answer

Is inherently more complex and difficult to implement.

Question 41

Which of the following algorithms is primarily used to establish topological ordering in a directed acyclic graph (DAG)?

Accepted Answer

Depth-First Search (DFS)

Answer

Breadth-First Search (BFS)

Answer

Dijkstra's algorithm

Answer

Kruskal's algorithm

Question 42

Which graph traversal algorithm systematically explores the nodes at each level, starting from the root node?

Accepted Answer

Breadth-first search (BFS)

Answer

Dijkstra's algorithm

Answer

Bellman-Ford algorithm

Answer

Depth-first search (DFS)

Question 43

In the implementation of depth-first search (DFS), which data structure is commonly employed to keep track of the nodes to be visited?

Accepted Answer

Stack

Answer

List

Answer

Tree

Answer

Queue

Question 44

Which of the following tasks is NOT an application of graph traversal algorithms?

Accepted Answer

Prim's algorithm for finding minimum spanning trees

Answer

Topological sorting

Answer

Detecting cycles in a graph

Answer

Identifying connected components

Question 45

Consider a graph with V vertices and E edges. What is the time complexity of traversing this graph using DFS?

Accepted Answer

O(V + E)

Answer

O(V^2)

Answer

O(E)

Question 46

Which limitation of depth-first search (DFS) can lead to inefficient or incorrect traversal results?

Accepted Answer

DFS may get trapped in infinite loops in graphs with cycles

Answer

DFS requires excessive memory

Answer

DFS always finds the shortest path

Answer

DFS cannot be used to find connected components

Question 47

What is the fundamental distinction between pre-order and post-order traversals in a graph?

Accepted Answer

In pre-order traversal, the root is visited before its children, while in post-order traversal, it is visited after its children

Answer

Pre-order is used for topological sorting, while post-order is used for finding Eulerian paths

Answer

Pre-order uses a stack, while post-order uses a queue

Question 48

Which graph traversal algorithm is specifically designed to construct the minimum spanning tree of a weighted graph?

Accepted Answer

Kruskal's algorithm

Answer

Depth-first search

Answer

A-star algorithm

Question 49

In the context of graph theory, what is a spanning tree?

Accepted Answer

A subset of edges that connects all the vertices in a graph without creating any cycles

Answer

A set of vertices that are not connected to each other

Answer

A path that visits all the vertices in a graph exactly once

Question 50

Which graph traversal algorithm can be employed to identify strongly connected components in a directed graph?

Accepted Answer

Tarjan's strongly connected components algorithm

Answer

Dijkstra's algorithm

Answer

Depth-first search

Answer

Breadth-first search

Question 51

What is the key difference between strongly connected components and weakly connected components in a graph?

Accepted Answer

Strongly connected components are groups of vertices where every vertex can reach every other vertex, while weakly connected components are groups of vertices where some vertices can reach each other but not all

Answer

Strongly connected components are used for topological sorting, while weakly connected components are not