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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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DEVELOPING PRE-NUMBER CONCEPTS : Previously you have read how children acquire concepts. You know that, for children to grasp a concept, they must be given several opportunities
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Q. Suppose the probability of David coming to a party is 75% and the probability of Jason coming to a party is 85%. What is the probability that they will both come to a party, a
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