floyd' algorithm is to weighted graphs what is to unweighted graphs floyd' algorithm uses the representation of graph what is an approximate big time for an attempt to solve the knight' tour in figure is the route abceda the minimum solution for the traveling salesman problemexperiments carrying out these experiments will help to provide insights into the topics covered in the no programming is involved use the graphw workshop applet to find the minimum spanning tree of the graph shown in figure "train fares in magnaguena consider the graph to be undirectedthat isignore the arrows use the graphdw workshop applet to solve the shortest-path problem for the graph in figure "train fares in magnaguena,but derive new weights for all the edges by subtracting those shown in the figure from draw graph with five vertices and five edges then use pencil and paper to implement djikstra' algorithm for this graph show the tree and the shortestpath array at each step programming projects writing programs to solve the programming projects helps to solidify your understanding of the material and demonstrates how the concepts are applied (as noted in the introductionqualified instructors may obtain completed solutions to the programming projects on the publisher' web site modify the path java program (listing to print table of the minimum costs to get from any vertex to any other vertex this exercise will require some fiddling with routines that assume the starting vertex is always so far we've implemented graphs as adjacency matrices or adjacency lists another approach is to use java references to represent edgesso that vertex object contains list of references to other vertices that it' connected to in directed graph reference used this way is especially intuitive because it "pointsfrom one vertex to another write program that implements this scheme the main(method should be similar to main(in the path java program (listing so that it creates the graph shown in figure using the same addvertex(and addedge(calls it should then display connectivity