Question

Show how depth-first search works on the graph of Figure 22.6. Assume that the for loop of lines 5–7 of the DFS procedure considers the vertices in reverse alphabetical order, and assume that each adjacency list is ordered alphabetically. Show the discovery and finishing times for each vertex, and show the classification of each edge.

directed graph for use in Exercises 22.3-2 and 22.52 Figure 22.6 A directed graph for use in Exercises 22.3-2 and 22.5-2.

DIJKSTRA(G,w,s)

1INITIALIZE-SINGLE-SOURCE(G,s)

2 S ??

3 Q ? V[G]

4 while Q =?

5 do u ? EXTRACT-MIN(Q)

6 S ? S?{u}

7 for each vertex v ?Adj[u]

8 do RELAX(u,v,w)

Answer 1

solution: The discovery and finishing times for an each vertex are shown below as 1,16 17,20 2,7 8,15 18,19 3,6 9,12 13,1 Vy 10,11 Tree edges: (q, s), (s, v), (v, w), (q, t), (t, x), (x, z). (t, y), (r, u) Back edges: (w, s), (z, x), (y, q) Forward edges: (q, w) Cross edges: (r, y), (u,y)