c. Consider the following complete graph G on five nodes, labelled A, B, C, D, and E, B 1 | | 2 4 4 5 A 4 D 3 3 E The weight of each edge is given in the box attached to the edge. i. Use Prim's Algorithm to compute the minimum spanning tree for G, from the starting node A. [4 marks] ii. What is the total weight obtained by the pre-order traversal of the minimum spanning tree computed for part (i), starting from and returning to node A? [2 marks] iii. Apply two iterations of the 2-opt Algorithm, stating the total weight of the new traversal after each iteration. [6 marks] iv. Does the 2-opt algorithm always provide the optimal solution to the travelling salesman problem? Expain your answer. [2 marks]