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1. a) Given a digraph G = (V,E), prove that if we add a constant k to the length of every arc coming out from the root node r, the shortest path tree remains the same. Do this by using potentials:
i) Show there is a potential y* for the new costs for which the paths in the tree to each node v have cost y*v, and
ii) explain why this proves it. What is the relationship between the shortest path distances of the modified problem and those of the original problem?
b) Can adding a constant k to the length of every arc coming out from a non-root node produce a change in the shortest path tree? Justify your answer.
the first question should be done using the website given (www.desmos.com/calculator )and another good example to explain using the graph ( https://www.desmos.com/calculator/ydimzr
i need some information on this topic for my holidays project..plz guide me what to do
mr ouma bought two sets of spanners for sh 300per set two machanic vice at sh 1000each three set of screw driver at sh 115 per set and tool box for sh 300
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