By Robert Sedgewick

ISBN-10: 0201361213

ISBN-13: 9780201361216

Textual content presents a device set for programmers to enforce, debug, and use graph algorithms throughout quite a lot of desktop purposes. Covers graph houses and kinds; digraphs and DAGs; minimal spanning timber; shortest paths; community flows; and diagrams, pattern Java code, and particular set of rules descriptions. Softcover.

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Additional info for Algorithms in Java, Part 5: Graph Algorithms

Sample text

11. 6, top). Part V: Graph Algorithms 47 48 Part V: Graph Algorithms For weighted graphs and networks, we fill the adjacency matrix with structures containing information about edges (including their presence or absence) instead of Boolean values; in the adjacency-lists representation, we include this information in adjacency-list elements. It is often necessary to associate still more information with the vertices or edges of a graph to allow that graph to model more complicated objects. We can associate extra information with each edge by extending our Edge class as appropriate, then using Edge objects in the adjacency matrix, or in the list nodes in the adjacency lists.

We use vertex-indexed array in numerous implementations throughout the book. As an example, suppose that we wish to know whether a vertex v in a graph is isolated. Is v of degree 0? For the adjacency-lists representation, we can find this information immediately, simply by checking whether adj[v] is null. But for the adjacency-matrix representation, we need to check all V entries in the row or column corresponding to v to know that each one is not connected to any other vertex; and for the array-of-edges representation, we have no better approach than to check all E edges to see whether there are any that involve v.

The output produced by these programs are themselves graph representations that clearly illustrate a basic performance tradeoff. To print out the matrix, we need room on the page for all V2 entries; to print out the lists, we need room for just V + E numbers. For sparse graphs, when V2 is huge compared to V + E, we prefer the lists; for dense graphs, when E and V2 are comparable, we prefer the matrix. As we shall soon see, we make the same basic tradeoff when we compare the adjacency-matrix representation with its primary alternative: an explicit representation of the lists.

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