Trees and Graphs: Interactive Learning Quizzes for Computer Science Students

Question 1

A tree where each vertex is connected to exactly one other vertex is known as a:

Accepted Answer

Star graph

Answer

Connected graph

Answer

Complete graph

Answer

Binary tree

Question 2

Which data structure is typically used to implement a binary search tree?

Accepted Answer

Linked list

Answer

Array

Answer

Queue

Answer

Stack

Question 3

The maximum number of edges in a simple graph with n vertices is:

Accepted Answer

n(n-1)/2

Answer

n-1

Answer

n^2

Answer

2n

Question 4

Which graph search algorithm utilizes a queue to explore the graph?

Accepted Answer

Breadth-first search

Answer

Depth-first search

Answer

Dijkstra's algorithm

Answer

Prim's algorithm

Question 5

A directed graph representing the relationships between individuals is known as a(n):

Accepted Answer

Network

Answer

Tree

Answer

Grid

Answer

Matrix

Question 6

Which tree data structure is specifically designed for storing hierarchical data?

Accepted Answer

Trie

Answer

Suffix tree

Answer

B-tree

Answer

AVL tree

Question 7

A graph that represents the layout of a computer network is known as a(n):

Accepted Answer

Network topology

Answer

Data center

Answer

Data structure

Answer

Database

Question 8

Which of the following is NOT a defining property of a tree?

Accepted Answer

A tree can have cycles

Answer

A tree has exactly one root node

Answer

Every node, except the root, has exactly one parent node

Answer

A tree is a connected graph

Question 9

What is the minimum number of edges required to connect n nodes in a tree?

Accepted Answer

n - 1

Answer

n

Answer

n + 1

Answer

2n

Question 10

Which of the following sorting algorithms has the best average-case time complexity?

Accepted Answer

Merge sort

Answer

Bubble sort

Answer

Insertion sort

Answer

Selection sort

Question 11

What is the role of a compiler in software development?

Accepted Answer

To convert high-level code into machine code

Answer

To execute the program directly

Answer

To debug the program

Answer

To create the user interface

Question 12

What is the difference between a primary key and a foreign key in a relational database?

Accepted Answer

A primary key uniquely identifies a row, while a foreign key references another table

Answer

A foreign key uniquely identifies a row, while a primary key references another table

Answer

Both primary keys and foreign keys uniquely identify rows

Answer

There is no difference between a primary key and a foreign key

Question 13

Which of the following is a defining property of a binary tree?

Accepted Answer

Each node has at most two children.

Answer

The left child is always smaller than the parent.

Answer

The tree is always balanced.

Answer

The height of the tree is always logarithmic.

Question 14

In a graph, what is the time complexity of locating a vertex using breadth-first search?

Accepted Answer

O(V)

Answer

O(V^2)

Answer

O(E)

Answer

O(E^2)

Question 15

When inserting a node into a balanced binary search tree, what is the time complexity?

Accepted Answer

O(log V)

Answer

O(V)

Answer

O(V^2)

Answer

O(E)

Question 16

Which of the following is NOT an application of graphs?

Accepted Answer

Solving linear equations using matrices

Answer

Social network analysis

Answer

Routing in computer networks

Answer

Representing molecular structures

Question 17

What is the time complexity of a 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 18

What is the primary purpose of a minimum spanning tree (MST) algorithm?

Accepted Answer

To find the smallest set of edges that connect all vertices in a graph

Answer

To find the shortest path between two vertices in a graph

Answer

To find the maximum flow through a network

Answer

To sort a list of numbers

Question 19

Which property is NOT characteristic of a tree data structure?

Accepted Answer

Each node has exactly two parent nodes

Answer

A single root node

Answer

A connected graph

Answer

Height less than or equal to the number of nodes

Question 20

Which traversal method visits nodes in the sequence they are stored in memory for a tree?

Accepted Answer

Preorder traversal

Answer

Inorder traversal

Answer

Postorder traversal

Answer

Level-order traversal

Question 21

What is the time complexity of searching for a node using a key in a balanced binary search tree?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 22

Which of the following is NOT an application of graphs in computer science?

Accepted Answer

Facial recognition

Answer

Modeling social networks

Answer

Routing algorithms

Answer

Image processing

Question 23

Which algorithm is used to find the shortest path between two nodes in a weighted graph?

Accepted Answer

Dijkstra's algorithm

Answer

Breadth-first search

Answer

Depth-first search

Answer

Kruskal's algorithm

Question 24

Which of the following is a fundamental data structure that resembles a hierarchical tree structure?

Accepted Answer

Binary tree

Answer

Linked list

Answer

Queue

Answer

Hash table

Question 25

Balanced binary search trees, commonly used in computer science, offer optimized search performance. What is the time complexity of searching for an element in such a tree?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 26

In the context of binary trees, which traversal method prints the nodes in a logical sequential order?

Accepted Answer

In-order

Answer

Pre-order

Answer

Post-order

Answer

Level-order

Question 27

Graph theory utilizes a specific algorithm to identify groups of interconnected nodes. What is the primary purpose of this algorithm?

Accepted Answer

To identify connected components

Answer

To find the shortest path between nodes

Answer

To determine the diameter of a graph

Answer

To construct a minimum spanning tree

Question 28

In the realm of graph theory, which of the following is not a recognized type of graph?

Accepted Answer

Binary

Answer

Directed

Answer

Undirected

Answer

Weighted

Question 29

Consider a complete graph with 'n' nodes. This type of graph exhibits a specific property. What is the maximum number of edges in such a graph?

Accepted Answer

n(n-1)/2

Answer

n

Answer

n-1

Answer

n^2

Question 30

Kruskal's algorithm is employed to find the minimum spanning tree in a graph. What is the established time complexity of this algorithm?

Accepted Answer

O(n log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(2^n)

Question 31

When comparing trees and arrays, a key advantage of using trees emerges. Which of the following best describes this advantage?

Accepted Answer

Efficient insertion and deletion operations

Answer

Faster searching

Answer

Reduced memory consumption

Answer

Lower overall time complexity

Question 32

Binary search trees (BSTs) are commonly used in computer science. What is the primary purpose of a BST?

Accepted Answer

Efficient storage and searching of data

Answer

Graph data structure creation

Answer

Linked list representation

Answer

Matrix operation execution

Question 33

Evaluate the advantages and disadvantages of representing graphs using adjacency lists versus adjacency matrices. Provide specific examples to illustrate your analysis.

Accepted Answer

Adjacency lists are more space-efficient for sparse graphs, while adjacency matrices excel for dense graphs.

Accepted Answer

Adjacency lists enable efficient traversal, iterating through a vertex's neighbors, while adjacency matrices facilitate faster lookups, determining if two vertices are connected.

Accepted Answer

Adjacency matrices are inherently more space-intensive than adjacency lists.

Answer

Adjacency matrices are used for both directed and undirected graphs, while adjacency lists are suitable for both types.

Question 34

In a rooted tree, which of these is a defining characteristic?

Accepted Answer

It has a single root node.

Answer

It always has both a left and a right subtree.

Answer

It can have multiple root nodes.

Answer

It is always a complete binary tree.

Question 35

Which of the following statements about a tree data structure is NOT true?

Accepted Answer

A tree can contain cycles.

Answer

A tree has a hierarchical structure.

Answer

A tree has a non-linear storage structure.

Answer

A tree has a unique root node.

Question 36

In a binary tree, which traversal algorithm visits nodes in the order of left subtree, root, right subtree?

Accepted Answer

In-order traversal

Answer

Pre-order traversal

Answer

Post-order traversal

Answer

Breadth-first search

Question 37

In a graph with n vertices and no loops, what is the maximum possible number of edges?

Accepted Answer

n * (n - 1) / 2

Answer

n * (n - 2) / 2

Answer

n * (n + 1) / 2

Answer

n * n

Question 38

Which data structure is a specialized tree used to represent disjoint sets?

Accepted Answer

Disjoint-set data structure

Answer

AVL tree

Answer

Binary search tree

Answer

Red-black tree

Question 39

What is the time complexity of searching for a node in a balanced binary search tree with n nodes?

Accepted Answer

O(log(n))

Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Question 40

What is the primary purpose of finding a minimum spanning tree in a weighted graph?

Accepted Answer

To find a subgraph with the minimum total edge weight connecting all vertices

Answer

To find the shortest path between two specific vertices

Answer

To determine the number of cycles in a graph

Question 41

Which of the following uniquely characterizes a complete binary tree?

Accepted Answer

Every internal node has exactly two children.

Answer

The tree is perfectly balanced.

Answer

The difference in depths between any two leaves is at most one.

Answer

The number of nodes at each level forms an arithmetic progression.

Question 42

Which of the following is not a recognized method for traversing a tree?

Accepted Answer

Circular Traversal

Answer

Depth-first Search (DFS)

Answer

Post-order Traversal

Answer

Breadth-first Search (BFS)

Question 43

What is the primary purpose of finding a spanning tree for an undirected graph?

Accepted Answer

To connect all vertices without introducing any cycles.

Answer

To identify the shortest path between a pair of vertices.

Answer

To determine whether or not the graph is connected.

Question 44

What is the definition of the diameter of a graph?

Accepted Answer

The length of the longest path between any two nodes in the graph.

Answer

The average shortest path length between all pairs of nodes in the graph.

Answer

The number of edges in the minimum spanning tree of the graph.

Question 45

What is a fundamental distinction between undirected and directed graphs?

Accepted Answer

In an undirected graph, edges have no inherent direction, while in a directed graph, edges have a specified direction.

Answer

Directed graphs are more efficient for representing relationships.

Answer

Undirected graphs are simpler than directed graphs.

Question 46

Which algorithm is commonly used to find the shortest path between two vertices in a graph?

Accepted Answer

Dijkstra's algorithm

Answer

Depth-First Search (DFS)

Answer

Breadth-First Search (BFS)

Answer

A* Search

Question 47

What is the computational complexity of finding the minimum spanning tree of a graph using Kruskal's algorithm?

Accepted Answer

O(E log V)

Answer

O(E)

Answer

O(V log E)

Answer

O(V^2)

Question 48

Which of the following is NOT a property of a binary search tree?

Accepted Answer

The left subtree of any node contains values greater than the node's value.

Answer

Every node has at most two children.

Answer

The left subtree of any node contains values less than the node's value.

Question 49

What is the time complexity of searching for a specific value in a balanced binary search tree?

Accepted Answer

O(log n)

Answer

O(n log n)

Answer

O(1)

Answer

O(n)

Question 50

In a directed graph, what does an edge represent?

Accepted Answer

A one-way relationship between two vertices.

Answer

A two-way relationship between two vertices.

Answer

A connection that can be traversed in both directions.

Answer

The distance between two vertices.

Question 51

Which graph traversal algorithm uses a queue to explore vertices?

Accepted Answer

Breadth-first search (BFS)

Answer

Dijkstra's algorithm

Answer

Bellman-Ford algorithm

Answer

Depth-first search (DFS)

Question 52

What is the primary difference between a tree and a graph?

Accepted Answer

A tree has a single root node, while a graph can have multiple starting points.

Answer

A tree is directed, while a graph is undirected.

Answer

A tree has cycles, while a graph does not.

Question 53

Which data structure is most suitable for representing a hierarchical relationship, like a family tree?

Accepted Answer

Tree

Answer

Linked List

Answer

Stack

Answer

Queue

Question 54

What is the purpose of a topological sort?

Accepted Answer

To order the vertices of a directed acyclic graph (DAG) such that all dependencies are satisfied.

Answer

To determine the minimum spanning tree of a graph.

Answer

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

Question 55

In a weighted graph, what does the weight of an edge represent?

Accepted Answer

The cost or distance associated with traversing that edge.

Answer

The direction of the edge.

Answer

The number of nodes connected to the edge.

Question 56

Which of the following is NOT a common use case for graphs in computer science?

Accepted Answer

Representing the structure of a linked list.

Answer

Analyzing website traffic patterns.

Answer

Modeling social networks.

Answer

Optimizing routing in GPS systems.