Question

3. Consider the following directed, weighted graph (6 marks): 3 2 7 1 8 1 2 -4 5 4 4 3 -5 (a) Calculate the shortest paths (Dijkstra's algorithm) from A to every other vertex. Show your steps in the table below. (2 points) Vertex Distance Path 1 0 2 3 4 5 (b) Can Dijkstra's algorithm calculate the shortest path in part a) if no where exactly it fails? (2 points) (c) What single edge could be removed from the graph in such that Dijkstra's algorithm would work correctly? (2 points) (d) Calculate the shortest path for the above graph using Bellman-Ford Algorithm. (2 points)

          3. Consider the following directed, weighted graph (6 marks):
3
2
7
1
8
1
2
-4
5
4
4
3
-5
(a) Calculate the shortest paths (Dijkstra's algorithm) from A to every other vertex. Show your
steps in the table below. (2 points)
Vertex	Distance	Path
1	0
2
3
4
5
(b) Can Dijkstra's algorithm calculate the shortest path in part a) if no where exactly it fails? (2
points)
(c) What single edge could be removed from the graph in such that Dijkstra's algorithm would
work correctly? (2 points)
(d) Calculate the shortest path for the above graph using Bellman-Ford Algorithm. (2 points)

3. Consider the following directed, weighted graph (6 marks):
3
2
7
1
8
1
2
-4
5
4
4
3
-5
(a) Calculate the shortest paths (Dijkstra's algorithm) from A to every other vertex. Show your
steps in the table below. (2 points)
Vertex Distance Path
1 0
2
3
4
5
(b) Can Dijkstra's algorithm calculate the shortest path in part a) if no where exactly it fails? (2
points)
(c) What single edge could be removed from the graph in such that Dijkstra's algorithm would
work correctly? (2 points)
(d) Calculate the shortest path for the above graph using Bellman-Ford Algorithm. (2 points)

Added by Kiara G.

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