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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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(1 0 3 21 -1 1 -1 1) find A-1
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a bathroom measure 250 cm by 175 cm calculate the side of the largest square tile that can tile the floor
275/41
Four-year-old Mariamma was reciting number names - some of them in order, and others randomly. The child's aunt, sitting nearby, asked her, "Can you write 'two'?" She said she coul
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