Graphs: Implementation and Algorithms - Interactive Learning Quizzes

Question 1

Which of the following is NOT a common implementation of graphs?

Accepted Answer

Binary Search Tree

Answer

Adjacency List

Answer

Adjacency Matrix

Answer

Edge List

Question 2

What is the primary purpose of a Breadth-First Search (BFS) algorithm?

Accepted Answer

To find all nodes reachable from a starting node.

Answer

To find the shortest path between two nodes.

Answer

To find the minimum spanning tree of a graph.

Answer

To detect cycles in a graph.

Question 3

What is the time complexity of a Depth-First Search (DFS) on an undirected graph?

Accepted Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Answer

O(n log n)

Question 4

Which of the following is the function of Kruskal's algorithm in graphs?

Accepted Answer

Finds the minimum spanning tree of a weighted graph.

Answer

Finds the shortest path between two nodes.

Answer

Detects cycles in a graph.

Answer

Finds all strongly connected components in a graph.

Question 5

What is the time complexity of checking for a path between two nodes in a graph using BFS?

Accepted Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Answer

O(n log n)

Question 6

What is the main purpose of topological sorting in a directed graph?

Accepted Answer

To arrange the vertices such that there are no directed edges from a vertex to a vertex that precedes it.

Answer

To find the shortest path between two nodes.

Answer

To detect cycles in a graph.

Answer

To find the minimum spanning tree of a graph.

Question 7

Which of the following is a disadvantage of using an adjacency list to represent a graph?

Accepted Answer

Efficient for dense graphs.

Answer

Can represent weighted graphs.

Answer

Uses less space than an adjacency matrix.

Answer

Can handle graphs with cycles.

Question 8

How does Depth-First Search (DFS) efficiently detect cycles in a graph?

Accepted Answer

Maintain a stack of visited nodes and check for revisits.

Answer

Calculate the number of edges and nodes in the graph.

Answer

Find the shortest path between two nodes.

Answer

Identify bridges or articulation points in the graph.

Question 9

How does Kruskal's algorithm ensure the created tree is a minimum spanning tree?

Accepted Answer

It adds edges with the lowest weight that connect separate vertex sets, ensuring minimum weight selection.

Answer

It removes edges that create cycles, ensuring only acyclic edges are included.

Answer

It compares the constructed tree's weight to the original graph's edge weights.

Question 10

How can graphs be used to optimize task completion in a construction project?

Accepted Answer

Visualizing task dependencies and identifying critical paths for efficient resource allocation

Answer

Monitoring employee availability to ensure proper staffing levels

Answer

Storing financial data for project accounting and cost analysis

Question 11

Which of the following is NOT a valid data structure representation for a graph?

Accepted Answer

Linked list

Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incident matrix

Question 12

What is the time complexity of depth-first search (DFS) on a graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(V^2)

Answer

O(E^2)

Answer

O(V log V)

Question 13

What is the primary purpose of a topological sort?

Accepted Answer

Ordering vertices in a directed acyclic graph (DAG) based on their dependencies

Answer

Identifying the shortest path between two vertices in a graph

Answer

Determining if a graph is bipartite

Answer

Detecting cycles within a graph

Question 14

Which property uniquely defines a connected graph?

Accepted Answer

Every pair of vertices is connected by at least one path

Answer

The graph can be partitioned into isolated subgraphs

Answer

Each vertex is connected to itself by a loop

Answer

The graph has no cycles

Question 15

What fundamental distinction separates directed graphs from undirected graphs?

Accepted Answer

Directed graphs have edges with specified orientations, unlike undirected graphs

Answer

Undirected graphs have weighted edges, whereas directed graphs do not

Answer

Directed graphs allow cycles, but undirected graphs do not

Answer

Undirected graphs can represent relationships, while directed graphs cannot

Question 16

Which data structure is typically used in the implementation of an adjacency list representation for graphs?

Accepted Answer

An array of linked lists

Answer

An array of arrays

Answer

A hash table

Answer

A binary tree

Question 17

In an undirected graph G with positive edge weights and n vertices, what is the minimum number of edges that must be added to make the graph connected?

Accepted Answer

n - 1

Answer

n - 2

Answer

n + 1

Answer

E

Question 18

In a connected, undirected graph, how does the **diameter** of the graph impact the worst-case time complexity of BFS and DFS graph traversal algorithms?

Accepted Answer

The worst-case time complexity increases as the diameter increases.

Answer

The worst-case time complexity decreases as the diameter increases.

Answer

The worst-case time complexity remains unaffected by the diameter of the graph.

Question 19

For a graph with many vertices and few edges, which data structure is more efficient: an adjacency list or an adjacency matrix?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Hash table

Answer

Tree

Question 20

Which of the following algorithms can be used to traverse a graph in a depth-first manner?

Accepted Answer

Depth-first search (DFS)

Answer

Breadth-first search (BFS)

Answer

Dijkstra's algorithm

Answer

Kruskal's algorithm

Question 21

What is the primary purpose of applying a topological sort to a directed acyclic graph (DAG)?

Accepted Answer

To order the vertices in a linear sequence without creating cycles.

Answer

To determine the shortest path between two vertices.

Answer

To find the minimum spanning tree of the graph.

Answer

To identify strongly connected components of the graph.

Question 22

Which data structure is commonly used to implement a priority queue in a graph algorithm?

Accepted Answer

Heap

Answer

Stack

Answer

Queue

Answer

Linked list

Question 23

What is the key distinction between a strongly connected graph and a weakly connected graph?

Accepted Answer

A strongly connected graph has at least one path from every vertex to every other vertex, while a weakly connected graph does not.

Answer

A weakly connected graph has at least one path from every vertex to every other vertex, while a strongly connected graph does not.

Answer

A strongly connected graph has a spanning tree, while a weakly connected graph does not.

Answer

There is no distinction between strongly connected graphs and weakly connected graphs.

Question 24

In the realm of social network analysis, which of the following best illustrates a practical application of graphs?

Accepted Answer

Modeling the dissemination of information through a network

Answer

Identifying the shortest route between two points on a map

Answer

Optimizing the design of a computer network to reduce latency

Question 25

What is the main purpose of using the Breadth-First Search (BFS) algorithm?

Accepted Answer

To find all nodes in a graph that can be reached from a given starting node.

Answer

To find the shortest path between two nodes in a weighted graph.

Answer

To traverse the graph depth-first, exploring all nodes level by level.

Question 26

Which of the following is NOT a valid representation of a graph?

Accepted Answer

Hash table

Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 27

Which of the following data structures is primarily utilized for the representation of graphs?

Accepted Answer

Adjacency list

Answer

Array

Answer

Hash table

Question 28

Which graph traversal methods guarantee that all vertices in a connected graph will be visited?

Accepted Answer

Depth-First Search (DFS)

Accepted Answer

Breadth-First Search (BFS)

Answer

Prim's algorithm

Answer

Kruskal's algorithm

Question 29

Which traversal algorithm explores a graph by visiting nodes in a depth-first manner?

Accepted Answer

Depth-first search (DFS)

Answer

Kruskal's algorithm

Answer

Breadth-first search (BFS)

Answer

Dijkstra's algorithm

Question 30

What is the time complexity of Breadth-first search (BFS) algorithm for an unweighted graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(E * V)

Answer

O(2^V)

Answer

O(V * E)

Question 31

What is the primary purpose of a topological sort in a directed acyclic graph (DAG)?

Accepted Answer

To compute a linear ordering of vertices such that all edges go from a lower-numbered vertex to a higher-numbered one.

Answer

To find the shortest path between two vertices

Question 32

What is the time complexity of finding the shortest path between two vertices in a weighted directed graph using Dijkstra's algorithm?

Accepted Answer

O((V + E) * log V)

Answer

O(E^2)

Answer

O(2^V)

Answer

O(V^2)

Question 33

What is the purpose of finding a maximum matching in a graph?

Accepted Answer

To determine the largest set of non-overlapping edges in a graph

Answer

To detect cycles in the graph

Answer

To find the shortest path between two vertices

Question 34

Which of the following is the time complexity of a depth-first search (DFS) traversal on a connected graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(E^2)

Answer

O(V log E)

Answer

O(V^2)

Question 35

Which of the following algorithms is used to find the shortest path between two specified vertices in a weighted, non-negative graph?

Accepted Answer

Dijkstra's algorithm

Answer

Bellman-Ford algorithm

Answer

Kruskal's algorithm

Answer

Prim's algorithm

Question 36

What is the difference between a directed and an undirected graph?

Accepted Answer

In a directed graph, edges have a specified direction, while in an undirected graph, edges do not have a specified direction.

Answer

Undirected graphs can be represented using adjacency matrices, while directed graphs cannot.

Answer

Directed graphs have more edges than undirected graphs.

Question 37

What is the purpose of a topological sort?

Accepted Answer

To order vertices in a directed acyclic graph (DAG) such that for every directed edge from vertex u to vertex v, u appears before v in the ordering.

Answer

To find the shortest path between two vertices in a graph.

Question 38

What is the worst-case time complexity of Prim's algorithm for finding the minimum spanning tree of a connected graph with V vertices and E edges?

Accepted Answer

O(E log V)

Answer

O(E^2)

Answer

O(V^2)

Answer

O(V + E)

Question 39

What is a Hamiltonian path?

Accepted Answer

A path in a graph that visits each vertex exactly once.

Answer

A path in a graph that visits each edge exactly once.

Answer

A path in a graph that starts and ends at the same vertex.

Question 40

What is the time complexity of a breadth-first search (BFS) algorithm on a graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(E log V)

Answer

O(V^2)

Answer

O(E^2)

Question 41

What is the purpose of using weighted edges in a graph?

Accepted Answer

To represent the cost or weight associated with traversing edges.

Answer

To store additional information about nodes.

Answer

To improve search efficiency.

Question 42

Which of the following is a real-world application of graph theory?

Accepted Answer

Network routing

Answer

Linear algebra

Answer

Statistics

Answer

Calculus

Question 43

What is the key difference between a directed graph and an undirected graph?

Accepted Answer

In a directed graph, edges have a direction, while in an undirected graph, they do not.

Answer

Undirected graphs have a lower computational complexity.

Answer

Directed graphs can only be represented using adjacency matrices.

Question 44

What is the advantage of using an adjacency list to represent a sparse graph?

Accepted Answer

It requires less space than an adjacency matrix.

Answer

It can handle graphs with negative edge weights.

Answer

It supports faster search operations.

Answer

It is more flexible for adding and removing nodes and edges.

Question 45

What is the purpose of a topological sort in a directed acyclic graph (DAG)?

Accepted Answer

To order the nodes such that each node precedes all nodes that depend on it.

Answer

To find the shortest path between two nodes.

Answer

To detect cycles in the graph.

Question 46

Which of the following is NOT a common way to represent a graph?

Accepted Answer

Binary Search Tree

Answer

Adjacency Matrix

Answer

Edge List

Answer

Adjacency List

Question 47

In an undirected graph with n vertices, what is the maximum number of edges possible?

Accepted Answer

n * (n - 1) / 2

Answer

n * (n + 1) / 2

Answer

n - 1

Answer

n

Question 48

Which algorithm is best suited for finding the shortest path in a weighted graph where all edge weights are positive?

Accepted Answer

Dijkstra's Algorithm

Answer

Bellman-Ford Algorithm

Answer

Breadth-First Search

Answer

Depth-First Search

Question 49

What is the time complexity of Depth-First Search (DFS) on a graph represented using an adjacency list?

Accepted Answer

O(V + E)

Answer

O(V^2)

Answer

O(E log V)

Answer

O(V)

Question 50

Which of the following is NOT a characteristic of a minimum spanning tree (MST) in a weighted graph?

Accepted Answer

It may not be unique

Answer

It has no cycles

Answer

It has the minimum total edge weight

Answer

It connects all vertices

Question 51

What data structure is commonly used to implement Breadth-First Search (BFS)?

Accepted Answer

Queue

Answer

Heap

Answer

Stack

Answer

Binary Search Tree

Question 52

Which algorithm is typically used to detect cycles in a graph?

Accepted Answer

Depth-First Search (DFS)

Answer

Breadth-First Search (BFS)

Answer

Dijkstra's Algorithm

Question 53

What is an advantage of using an adjacency list over an adjacency matrix for representing a sparse graph?

Accepted Answer

Lower space complexity

Answer

Faster edge lookup

Answer

Easier implementation

Answer

Better for dense graphs

Question 54

In Kruskal's algorithm for finding the minimum spanning tree, what data structure is often used to efficiently check for cycles?

Accepted Answer

Disjoint Set Union (DSU)

Answer

Queue

Answer

Stack

Answer

Binary Heap

Question 55

What is the primary difference between Prim's and Kruskal's algorithms for finding the Minimum Spanning Tree?

Accepted Answer

Prim's algorithm builds the MST one vertex at a time, while Kruskal's algorithm builds it one edge at a time.

Answer

Prim's algorithm works only on undirected graphs, while Kruskal's algorithm works on both directed and undirected graphs.