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- 9.1 Objectives
- 9.2 Vocabulary and Definitions
- 9.3 The Graph Abstract Data Type
- 9.4 An Adjacency Matrix
- 9.5 An Adjacency List
- 9.6 Implementation
- 9.7 The Word Ladder Problem
- 9.8 Building the Word Ladder Graph
- 9.9 Implementing Breadth First Search
- 9.10 Breadth First Search Analysis
- 9.11 The Knight’s Tour Problem
- 9.12 Building the Knight’s Tour Graph
- 9.13 Implementing Knight’s Tour
- 9.14 Knight’s Tour Analysis
- 9.15 General Depth First Search
- 9.16 Depth First Search Analysis
- 9.17 Topological Sorting
- 9.18 Strongly Connected Components
- 9.19 Shortest Path Problems
- 9.20 Dijkstra’s Algorithm
- 9.21 Analysis of Dijkstra’s Algorithm
- 9.22 Prim’s Spanning Tree Algorithm
- 9.23 Summary
- 9.24 Discussion Questions
- 9.25 Programming Exercises
- 9.26 Glossary
- 9.2. Vocabulary and Definitions" data-toggle="tooltip">
- 9.4. An Adjacency Matrix' data-toggle="tooltip" >
9.3. The Graph Abstract Data Type ¶
The graph abstract data type (ADT) is defined as follows:
Graph() creates a new, empty graph.
addVertex(vert) adds an instance of Vertex to the graph.
addEdge(fromVert, toVert) Adds a new, directed edge to the graph that connects two vertices.
addEdge(fromVert, toVert, weight) Adds a new, weighted, directed edge to the graph that connects two vertices.
getVertex(vertKey) finds the vertex in the graph named vertKey .
getVertices() returns the list of all vertices in the graph.
in returns True for a statement of the form vertex in graph , if the given vertex is in the graph, False otherwise.
Beginning with the formal definition for a graph there are several ways we can implement the graph ADT in Python. We will see that there are trade-offs in using different representations to implement the ADT described above. There are two well-known implementations of a graph, the adjacency matrix and the adjacency list . We will explain both of these options, and then implement one as a Python class.
- creates a new, empty graph.
- addVertex(vert)
- adds an instance of Vertex to the graph.
- addEdge(fromVert, toVert)
- Adds a new, directed edge to the graph that connects two vertices.
- addEdge(fromVert, toVert, weight)
- Adds a new, weighted, directed edge to the graph that connects two vertices.
- getVertex(vertKey)
- finds the vertex in the graph named vertKey.
- getVertices()
- returns the list of all vertices in the graph.
- returns True for a statement of the form vertex in graph, if the given vertex is in the graph, False otherwise.
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The text Explores problem solving and the efficient access and manipulation of data and is intended for readers who already have a basic understanding of C++. The "walls and mirrors" mentioned in the title represent problem-solving techniques that appear throughout the text. Data abstraction hides the details of a module from the rest of ...
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•To review the ideas of computer science, programming, and problem-solving. •To understand abstraction and the role it plays in the problem-solving process. •To understand and implement the notion of an abstract data type. •To review the Python programming language. 1.2Getting Started
The text explores problem solving and the efficient access and manipulation of data and is intended for students who already have a basic understanding of programming, preferably in C++. The "walls and mirrors" mentioned in the title represent problem-solving techniques that appear throughout the text. Data abstraction hides the details of ...
The Graph Abstract Data Type — Problem Solving with Algorithms and Data Structures using C++. 9.3. The Graph Abstract Data Type ¶. The graph abstract data type (ADT) is defined as follows: Graph() creates a new, empty graph. addVertex(vert) adds an instance of Vertex to the graph. addEdge(fromVert, toVert) Adds a new, directed edge to the ...
From the Publisher: Focusing on data abstraction and data structures, the second edition of this very successful book continues to emphasize the needs of both the instructor and the student. The book illustrates the role of classes and abstract data types (ADTs) in the problem-solving process as the foundation for an object-oriented approach.
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