By Robert Sedgewick

Graph algorithms are serious for more than a few functions, akin to community connectivity, circuit layout, scheduling, transaction processing, and source allocation. This paintings offers many algorithms and their motives. it's also specific figures, with accompanying remark.

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

**Example text**

To handle various specialized graph-processing problems, we often need to add specialized auxiliary data structures to the graph ADT. The most common such data structure is a vertex-indexed array, as we saw already in Chapter 1, where we used vertex-indexed arrays to answer connectivity queries. We use vertex-indexed arrays 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.

14 Write a representation-independent graph ADT function that uses GRAPHedges to print out all the edges in the graph, in the format used in this text (vertex numbers separated by a hyphen). 1 that uses an array of edges to represent the graph. Modify GRAPHinit to take the maximum number of edges allowed as its second argument, for use in allocating the edge array. Use a brute-force implementation of GRAPHremoveE that removes an edge v-w by scanning the array to find v-w or w-v, and then exchanges the edge found with the final one in the array.

This assumption comes into play only when the number of edges is tiny in comparison to the number of vertices—a rare situation. Typically, the number of edges far exceeds the number of vertices (V/E is much less than 1). A bipartite graph is a graph whose vertices we can divide into two sets such that all edges connect a vertex in one set with a vertex in the other set. 5 gives an example of a bipartite graph. Bipartite graphs arise in a natural way in many situations, such as the matching problems described at the beginning of this chapter.