b. (8 marks) i (6 marks) Consider a weighted version of the directed graph in (a.), given below. Carry out the steps of Dijkstra's shortest path algorithm starting at vertex S, and consequently give the shortest path from S to vertex T and its length. 6 3 3 ii (2 marks) For a graph G-(V,E), what is the worst-case time complexity of the version of Dijkstra's shortest path algorithm examined in lectures? (Your answer should be in terms of |V] and/or |E|.) c. (6 marks) Consider an arbitrary weighted directed graph G- (V, E) with weights w: E-R (that is, the weights are real numbers). Assume that when you run Dijkstra's shortest path algorithm on G from some vertex s EV to another vertex t e V, you get shortest path Now, consider the same graph G (V, E) with weights that are double the original weights (i.e. with weights u: E -R such that u'(e2(e) for any e E E). Will running Dijkstra's shortest path algorithm on graph G with weights w from s to t also produce the same shortest path X If so, explain why (in no more than 5 lines). If not, give a counter-example