4. (a) Use Dijkstra's algorithm to find the shortest path from node A to node F in the following network and give its length. A C 2 7 5 B 24 13 6 3 F 14 1 E

A B C D E F A D -- B 51 51 36 45 -- с 36 45 D E F 8 14 58 35 16 23 47 52 20 55 53 12 8 35 47 14 16 52 55 58 23 20 53 12 - The weights of edges in a graph are shown in the table above. Apply the nearest neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDEFA

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Use Djkstra's algorithm to find the shortest path from a to z. in order to get credit for this question you must SHOW ALL WORK. 3.

Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination. (a) For the forward recursion formulation of this problem, how many stages are there, and what arethe states for each stage? Stage 1: n = 1 Stage 2: n = 2 origin) ( Stage 3: n = 3 S A B C (b) Use forward recursion to solve this problem. However, instead of using the usual tables, show your work graphically. In particular, start with the given network, where the answers already are given for f (Sn) for four of the nodes; then solve for and fill in f2 (B) and fi* (0). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T. (c) Use forward recursion to solve this problem by manually constructing the usual tables for n = 3, n = 2, and n = 1.…