Transcript Chapter 20: Graph Implementation

Graph Implementations
Chapter 29
Copyright ©2012 by Pearson Education, Inc. All rights reserved
Contents
• An Overview of Two Implementations
 The Adjacency Matrix
 The Adjacency List
• Vertices and Edges
 Specifying the Class Vertex
 The Inner Class Edge
 Implementing the Class Vertex
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Contents
• An Implementation of the ADT Graph
 Basic Operations
 Graph Algorithms
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Objectives
• Describe adjacency matrix
• Describe adjacency list
• Specify and implement classes that
represent vertices and edges of a graph
• Implement ADT graph by using adjacency
lists
Copyright ©2012 by Pearson Education, Inc. All rights reserved
Adjacency Matrix
•
•
•
•
For a graph of n vertices
Has n rows, n columns
Rows and columns numbered 0 to n -1
Each row and column corresponds to
vertex of graph
• Note:
 Sparse graph wastes space
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Figure 29-1 (a) An unweighted, directed graph and
(b) its adjacency matrix
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The Adjacency List
• Represents only those edges that
originate from vertex
• Space not reserved for edges that do not
exist
• Use less memory than corresponding
adjacency matrix
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Figure 29-2 Adjacency lists for the directed
graph in Figure 29-1a
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Figure 29-2 Adjacency lists for the directed
graph in Figure 29-1a
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Specifying the Class Vertex
•
•
•
•
Need a way to identify vertices
Operations that mark a vertex as visited
Adjacency list indicates its neighbors
Path operations:
 Get
 Set
 Test
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Specifying the Class Vertex
•
•
•
•
Note interface, Listing 29-1
Inner class Edge, Listing 29-2
Class Vertex, Listing 29-3
Private class neighborIterator,
Listing 29-4
Note: Code listing files
must be in same folder
as PowerPoint files
for links to work
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Implementation
of the ADT Graph
• With either implementation
 Need container for the graph’s vertices
• Could be list or dictionary
 Depending on how object is identified
• We will use dictionary
 Identify objects with a string
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Class DirectedGraph, Listing 29-5
Figure 29-3 (a) A directed graph and
(b) its implementation using adjacency lists
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Figure 29-4 The performance of basic operations of the ADT
graph when implemented by using adjacency lists
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Graph Algorithms
• Breadth-first traversal, Listing 29-A
 Depth-first traversal left as exercise
• Shortest path, Listing 29-B
 Implementation of method
getCheapestPath for weighted graph left as
an exercise
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End
Chapter 29
Copyright ©2012 by Pearson Education, Inc. All rights reserved