A Practical Introduction to Data Structures and Algorithm Analysis

402 Chap. 11 GraphsABABCCDDFFEE(a)(b)Figure 11.8 (a) A graph. (b) The depth-first search tree for the graph whenstarting at Vertex A.the edges that were followed to any new (unvisited) vertex during the traversal andleaves out the edges that lead to already visited vertices. DFS can be applied todirected or undirected graphs. Here is an implementation for the DFS algorithm:static void DFS(Graph G, int v) { // Depth first searchPreVisit(G, v);// Take appropriate actionG.setMark(v, VISITED);for (int w = G.first(v); w < G.n() ; w = G.next(v, w))if (G.getMark(w) == UNVISITED)DFS(G, w);PostVisit(G, v);// Take appropriate action}This implementation contains calls to functions PreVisit and PostVisit.These functions specify what activity should take place during the search. Justas a preorder tree traversal requires action before the subtrees are visited, somegraph traversals require that a vertex be processed before ones further along in theDFS. Alternatively, some applications require activity after the remaining verticesare processed; hence the call to function PostVisit. This would be a naturalopportunity to make use of the visitor design pattern described in Section 1.3.2.Figure 11.8 shows a graph and its corresponding depth-first search tree. Figure11.9 illustrates the DFS process for the graph of Figure 11.8(a).DFS processes each edge once in a directed graph. In an undirected graph,DFS processes each edge from both directions. Each vertex must be visited, butonly once, so the total cost is Θ(|V| + |E|).