Graph Theory and Data Structures Quiz

A set of sequences of machine symbols with a specific representation and manipulation interface.

How machine symbols represent specific data (e.g., ASCII for text).

Procedures used to manipulate a data type (e.g., resizing an image).

Representing data using machine symbols (e.g., ASCII for characters).

Reading data from machine symbols.

Basic data types supported directly by programming languages (e.g., integers, booleans).

Created by combining primitive data types (e.g., records, arrays, variants).

Contain multiple fields with different data types.

Store a sequence of items of the same data type.

Contain a single field that can hold different data types.

Specification of a data type, focusing on its operations and behavior, regardless of its internal representation.

Set of values allowed in an ADT (e.g., True or False for a Boolean ADT).

Procedures to manipulate data within an ADT (e.g., AND, OR, and NOT for Boolean).

Rules defining the relationships between operations within an ADT.

Transformation of data from input to output.

Specifies the mapping between valid inputs and outputs.

Finite sequence of instructions to solve a computational problem.

Method of organizing data to efficiently support algorithms.

Set of vertices connected by edges.

Graph where edges have a direction.

Graph where edges have associated weights (e.g., distances).

Matrix representation of a graph, with values showing connections.

Abstract data type defining operations on graphs.

Variants, also known as unions, are data structures that hold a single value but its data type can change. Imagine a container that can hold either an integer, a float, or a string, but only one at a time.

In C, we use the union keyword to define a variant. For example, union Number { int asInteger; float asFloat; }; allows storing an integer or a float, but not both at the same time.

Variants are used when we need a single variable to hold various types of data. For example, you might use a variant to store a username or an email address, where the actual value can be either a string or a number.

The programming interface of a data type defines how you interact with it, including the operations you can perform on it, like adding numbers or comparing strings.

An abstract data type (ADT) is defined by its operations and behavior, not its internal representation. It focuses on what a data type does, not how it's implemented.

ADTs help us design algorithms that are independent of the specific data representation, making the algorithms more reusable and adaptable to different data structures.

Procedures in a character data type must behave logically and predictably. For example, converting a character to uppercase and then back to lowercase should result in the original character.

A branch of mathematics that studies the relationships between objects, represented as vertices connected by edges.

A point or node in a graph, representing an individual entity.

A line connecting two vertices in a graph, representing a relationship between entities.

An algorithm that explores a graph by visiting vertices in a depth-first manner, exploring an entire branch before moving to the next.

A simple graph is a basic type of graph where edges are undirected, meaning they connect two vertices without a specific direction.

Vertices represent the objects in a graph, like cities, people, or species. Edges represent the connections between them, like roads, relationships, or who eats whom.

A food web can be represented as a directed graph, where vertices represent species and arrows represent who eats whom. This shows the flow of energy in an ecosystem.

A directed graph is illustrated by a food web where vertices represent species (e.g., Hawk, Snake, Rabbit) and edges represent who eats whom. This gives a clear direction to the relationships.

A weighted graph is represented by a transportation system where vertices represent locations (cities) and edges represent roads between them, with weights representing distances.

This notation defines a graph where G represents the graph itself, V is the set of vertices, and E is the set of edges. Edges are either pairs of vertices in an undirected graph or ordered pairs (for directed graphs).

A way to represent a graph using a matrix where rows represent vertices and columns represent edges. A cell value is 1 if the vertex is incident to the edge, and 0 otherwise.

In a directed graph, the incidence matrix can have negative values. A 1 indicates the vertex is the head (start) of the edge, while a -1 indicates the vertex is the tail (end) of the edge.

A graph where multiple edges can exist between the same pair of vertices.

A graph where an edge can connect more than two vertices.

Challenges arising from the structure of a graph, focusing on properties like connectivity, shortest paths, or finding specific vertex configurations.

A point or node in a graph representing an object or entity.

A line connecting two vertices in a graph, representing a relationship or connection.

A '1' in an incidence matrix cell indicates that the corresponding vertex is incident to the corresponding edge.

A '0' in an incidence matrix cell indicates that the corresponding vertex is not incident to the corresponding edge.

A collection of vertices (nodes) and edges (connections) that represent relationships between objects or entities.

An incidence matrix is used to represent a graph by showing the connections between its vertices and edges.

A graph where each edge has a numerical value (weight) associated with it, representing a cost, distance, or other relevant measure.

An adjacency matrix represents connections between vertices, while an incidence matrix represents connections between vertices and edges.

A way to represent a graph using two separate lists: one for vertices and one for edges, where each edge record contains information about its source and target vertices.

A data structure that stores information about an edge, including its source and target vertices, as well as any associated data like weight or label.

A list of all edges in a graph, where each edge is represented by an edge record.