Use Dijkstra's algorithm to construct a shortest path tree starting from vertex____ that includes all vertices in the original graph. Use the forma shown in the given table. After filling in the table, draw the resulting shortest path tree in the empty box. 2 b fringe list 2 a STEP vertices in tree next edge to add 1 d с 4 12 2 2 2 f 6 6 9 h 3 4 5 6 7 8

A B. D H Suppose you run the topological sort algorithm on the graph above starting at vertex C. Use the rule that when there is a choice of vertices for the algorithm to visit, it visits them in alphabetic order. Which vertex would end up first in the eventual topologically sorted order? Which would end up being second? Which would end up being third? Which would end up being fourth? Which would end up being fifth? Which would end up being sixth?

Write algorithm ShortestPath (G, s) pre-cond: G is a (directed or undirected) graph, and s is one of its nodes. post-cond: π specifies a shortest path from s to each node of G, and d specifiestheir lengths.

Please provide all the spanning trees possible from the graph below:

a) Which edges would you keep for the minimum-weight spanning tree? (Indicate as vertex-vertex — eg. “K-P”... if there were vertices K and P.) b) Describe the algorithm you used to determine the minimum-weight spanning tree above. Did you face any challenges in applying this algorithm?

1. Use the graph below to answer the following questions. A B H 10 G 10 25 20 5 50 5 5 30 5 15 C 20 D F 15 E (a) Use Kruskal's Algorithm to produce a minimum spanning tree. Write down the edges that you choose in order of the algorithm. (b) Use Prim's Algorithm to produce a minimum spanning tree (assume A is the root/source). Write down the edges that you choose in order of the algorithm.

Show what the final distance and previous array values will be after running the shortest path algorithm from class on the following graph, starting at vertex 2: 1 6 5 4 4 4 2 7 0 5 5 6 2 2 3 13 6

11. For the given graph below, use the depth-first search algorithm to visit the vertices and write the sequence of the visit. Start from the vertex "A". At any given vertex, you will visit first the unexplored vertex that has least alphabetical order. с G E F Answer the sequence of visiting the vertices: -_