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Question 5 (20 pts) Given the undirected graph G in Figure 3, answer the questions ul 12 Figure 3: Graph G in Q5 a. Find the shortest path from s to t using Dijkstras algorithm. Clearly show each step (7 pts) b. Find a minimum spanning tree with root as vertex x using Prims algorithm in Section 11.5 of the textbook. (5 pts) Explicitly show every step of computation c. Following edges are added to G one-by-one in order: Without ever calling Prims algorithm (or any other algorithm computing minimum spanning trees for graphs from scratch), modify the minimum spanning tree you generated in b so that it maintains to be a minimum spanning tree after the first weighted edge is added to G. Repeat this for the remaining edges, each time modifying the previously constructed minimum spanning tree. Separately draw minimum spanning trees of (5 pts) G for each new edge in given order. d. Do you think you can iteratively update the shortest path from s to t without calling Dijkstras algorithm upon the arrival of listed edges in c? Justify your answer (3 pts)

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