By Robert Sedgewick

ISBN-10: 0201361213

ISBN-13: 9780201361216

Textual content offers a device set for programmers to enforce, debug, and use graph algorithms throughout a variety of machine functions. Covers graph homes and kinds; digraphs and DAGs; minimal spanning bushes; shortest paths; community flows; and diagrams, pattern Java code, and precise set of rules descriptions. Softcover.

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**Extra resources for Algorithms in Java, Part 5: Graph Algorithms**

**Sample text**

W 46 Part V: Graph Algorithms Part V: Graph Algorithms 47 where u and w are either equal or not of degree 2. 36. Note: This operation may introduce self-loops and parallel edges, but it preserves the degrees of vertices that are not removed. 1. 4. The topics fall into one of three categories. First, the basic adjacency-matrix and adjacency-lists mechanisms extend readily to allow us to represent other types of graphs. In the relevant chapters, we consider these extensions in detail and give examples; here, we look at them briefly.

Duplicate edge insert requests are silently ignored, but clients can use edge to test whether an edge exists. Constructing the graph takes time proportional to V2. 7 uses an index i to scan past false entries in row v of the adjacency matrix (adj[v]). An invocation of beg() followed by a sequence of invocations of nxt() (checking that end() is false before each invocation) gives a sequence of the vertices adjacent to v in G in order of their vertex index. v = v; i = -1;} public int beg() { i = -1; return nxt(); } public int nxt() { for (i++; i < V(); i++) if (edge(v, i) == true) return i; return -1; } public boolean end() { return i >= V(); } } In the adjacency matrix that represents a graph G, row v is an array that is an existence table whose ith entry is true if vertex i is adjacent to v (the edge v-i is in G).

4. 4 uses the graph ADT to print a table of the vertices adjacent to each graph vertex. 7). 7. 1: We associate each vertex with its set of adjacent vertices (those connected to it by a single edge). Each edge affects two sets: For every edge u-v in the graph, u appears in v's set and v appears in u's set. 2 is a method that illustrates the use of the iterator class in the graph ADT. This method extracts a graph's set of edges and returns it in a client-supplied array. A graph is nothing more nor less than its set of edges, and we often need a way to retrieve a graph in this form, regardless of its internal representation.

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