Data Structures and Algorithm Analysis - Computer Science at ...

386 Chap. 11 Graphs/** Breadth first (queue-based) search */static void BFS(Graph G, int start) {Queue Q = new AQueue(G.n());Q.enqueue(start);G.setMark(start, VISITED);while (Q.length() > 0) { // Process each vertex on Qint v = Q.dequeue();}}PreVisit(G, v);// Take appropriate actionfor (int w = G.first(v); w < G.n(); w = G.next(v, w))if (G.getMark(w) == UNVISITED) { // Put neighbors on QG.setMark(w, VISITED);Q.enqueue(w);}PostVisit(G, v);// Take appropriate actionFigure 11.10 Implementation for the breadth-first graph traversal algorithmABABCCDDFFEE(a)(b)Figure 11.11 (a) A graph. (b) The breadth-first search tree for the graph whenstarting at Vertex A.illustrates the problem. An acceptable topological sort for this example is J1, J2,J3, J4, J5, J6, J7.A topological sort may be found by performing a DFS on the graph. When avertex is visited, no action is taken (i.e., function PreVisit does nothing). Whenthe recursion pops back to that vertex, function PostVisit prints the vertex. Thisyields a topological sort in reverse order. It does not matter where the sort starts, aslong as all vertices are visited in the end. Figure 11.13 shows an implementationfor the DFS-based algorithm.Using this algorithm starting at J1 and visiting adjacent neighbors in alphabeticorder, vertices of the graph in Figure 11.14 are printed out in the order J7, J5, J4,J6, J2, J3, J1. Reversing this yields the topological sort J1, J3, J2, J6, J4, J5, J7.