data abstraction & problem solving with c chegg

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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" >

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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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[Available] [TestBank] Data Abstraction & Problem Solving with C: Walls and Mirrors, 7th Edition

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by Frank M. Carrano; Timothy M. Henry

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