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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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a painting is 20 cm wider than its height. its area is 2400 centimeter squared. find its lenght and width
3 3/7 + 2 8/9 * 4=
a=halfbh a=17 b=5
Determine or find out if the following series converges or diverges. If it converges find out its value. Solution We first require the partial sums for this series.
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Averigua que nùmero de cinco cifras se esconde detras de las pistas dadas La cifra de las unidades es par, mayor que 6 y coincide con las decenas de mil. La cifra de las decenas se
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