Graph Implementations Chapter 29 Copyright ©2012 by Pearson Education, Inc. All rights reserved.

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


Contents

• An Implementation of the ADT Graph Basic Operations Graph Algorithms


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


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


Figure 29-1 (a) An unweighted, directed graph and (b) its adjacency matrix


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


Figure 29-2 Adjacency lists for the directed graph in Figure 29-1a


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


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 filesmust be in same folder

as PowerPoint filesfor links to work

Note: Code listing filesmust be in same folder

as PowerPoint filesfor links to work

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


Figure 29-3 (a) A directed graph and (b) its implementation using adjacency lists


Class DirectedGraph, Listing 29-5

Figure 29-4 The performance of basic operations of the ADT graph when implemented by using adjacency lists


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


End

Chapter 29


Graph Implementations Chapter 29 Copyright ©2012 by Pearson Education, Inc. All rights reserved.

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