3. Consider the following network of computers: E 3 The numbers labelling each edge indicate the number of Macquariecoin it costs to send a message along that network connection. We wish

to minimise the costs of sending messages by finding paths of minimal length in this weighted graph. Use Dijkstra's algorithm to construct a shortest-path spanning tree rooted at computer C. In your an- swer, you should: (a) [3 marks]. Draw the graph and illustrate the spanning tree you construct within it. (b) [5 marks]. Show your working by displaying, at each step of execution, the contents of the fringe list, clearly identifying the edge which will be added to the tree next. (c) [3 marks]. List the length of each shortest path starting from the chosen root computer C to each of the other computers in the network.