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

2. 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 Copyright ©2012 by Pearson Education, Inc. All rights reserved

3. Contents An Implementation of the ADT Graph  Basic Operations  Graph Algorithms Copyright ©2012 by Pearson Education, Inc. All rights reserved

4. 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

5. 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 Copyright ©2012 by Pearson Education, Inc. All rights reserved

6. Figure 29-1 (a) An unweighted, directed graph and (b) its adjacency matrix Copyright ©2012 by Pearson Education, Inc. All rights reserved

7. 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 Copyright ©2012 by Pearson Education, Inc. All rights reserved

8. Figure 29-2 Adjacency lists for the directed graph in Figure 29-1aFigure 29-1a Copyright ©2012 by Pearson Education, Inc. All rights reserved

9. Figure 29-2 Adjacency lists for the directed graph in Figure 29-1aFigure 29-1a Copyright ©2012 by Pearson Education, Inc. All rights reserved

10. 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 Copyright ©2012 by Pearson Education, Inc. All rights reserved

11. Specifying the Class Vertex Note interface, Listing 29-1Listing 29-1 Inner class Edge, Listing 29-2Listing 29-2 Class Vertex, Listing 29-3Listing 29-3 Private class neighborIterator, Listing 29-4 Listing 29-4 Copyright ©2012 by Pearson Education, Inc. All rights reserved Note: Code listing files must be in same folder as PowerPoint files for links to work Note: Code listing files must be in same folder as PowerPoint files for links to work

12. 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 Copyright ©2012 by Pearson Education, Inc. All rights reserved

13. Figure 29-3 (a) A directed graph and (b) its implementation using adjacency lists Copyright ©2012 by Pearson Education, Inc. All rights reserved Class DirectedGraph, Listing 29-5Listing 29-5

14. Figure 29-4 The performance of basic operations of the ADT graph when implemented by using adjacency lists Copyright ©2012 by Pearson Education, Inc. All rights reserved

15. Graph Algorithms Breadth-first traversal, Listing 29-AListing 29-A  Depth-first traversal left as exercise Shortest path, Listing 29-BListing 29-B  Implementation of method getCheapestPath for weighted graph left as an exercise Copyright ©2012 by Pearson Education, Inc. All rights reserved

16. End Chapter 29 Copyright ©2012 by Pearson Education, Inc. All rights reserved