2 m 1 3 2 2 Figure 1: A directed weighted graph. Question 2015 points) Starting from S, trace the operations of the Prim's minimum spanning tree algorithm on the graph given in Figure 1. Question 3 (15 points) Trace the operations of Kruskal's minimum spanning tree algorithm on the graph given in Figure 1. Question 4.45 points) Starting from S, trace the operations of breadth-first traversal on the graph given in Figure 1. Question 5 (20 points) Given Figure 1 and starting from S. a) Trace the operations of depth-first traversal. b) Give the post-order numbers for all the nodes. c) Give the pre-order numbers for all the nodes. d) List the tree ares, cross aros, forward arcs, and backward ares