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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.
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consumer behaviour in my feild of studies accounting ..
A train covered a certain distance at a uniform speed. If the train would have been 6km/hr faster, it would have taken 4hours less than the scheduled time. And if the train were
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01010011 01100101 01101101 01110000 01100101 01110010 00100000 01000110 01101001 00100001
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joey asked 30 randomly selected students if they drank milk, juice, or bottled water with their lunch. He found that 9 drank milk, 16 drank juice, and 5 drank bottled water. If the
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