The Voyager spacecraft has been transported by an alien being to the Delta Quadrant of space, millions of light-years from Earth. Captain Janeway and her crew are attempting to plot the shortest course home. Below is a network of the possible routes through the Delta Quadrant, where the nodes are different worlds/planetary systems and the values on the branches are the actual times, in years, between the nodes. 

a. Determine the shortest route from their present location (at node 1) to Earth (node 22). Do NOT find the permanent set; only the shortest route to Earth.

b. When you are finished, give the total number of years it takes Voyager to reach Earth.

 
 

 
 

17 11 24 20 18 19 19 23 12 10 35 30 15 21 17 16 22 42 Voyager 26 16 18 28 26 34 1 18 14 7 Earth 4 22 22 41 19 37 20 14 16 16 29 17 31 12 16 27 12 14 18 23 17 29 13 24 19