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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.
Should video game companies continue to alter their products to include other functions, such as e-mail
i have a question about discret math
any tutorials?
y=f(a^x) and f(sinx)=lnx find dy/dx? Solution) dy/dx exist only when 0 1 as the function y = f(a^x) itself does not exist.
State clearly that the current in an RLC circuit with an AC source with and without the use of complex variables
Linear Equations - Resolving and identifying linear first order differential equations. Separable Equations - Resolving and identifying separable first order differential
tan45 degrees=tan(90degrees-45degrees)
find the points on y axis whose distances from the points A(6,7) and B(4,-3) are in the ratio 1:2
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