1. Run DFS on the graph in Fig. 22.8 (p. 615), under the assumption that the adjacency list is ordered DFS procedure considers the vertices in alphabetical order, and assume that each adjacency list is ordered alphabetically. Show the discovery and finish times for each vertex, and show the classification of each edge. Show the topological order of vertices obtained by this run of DFS.

2. Scheduling to minimize average completion time.

3. Find the underlying simple graph of a multigraph. Solve this problem without using hashing.

4. Run the Huffman coding algorithm on the following input: Alphabet C = {p, r, a, i, s, e, d}, with frequencies f as percentages= {12, 16, 16, 12, 16, 16, 12}. Draw the optimal coding tree and the (weighted) average code length. Show the steps. Write the codes for "paradise" and "airspeed".

Figure 22.8 A dag for topological sorting