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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.
The sum of three consecutive even integers is 102. What is the value of the largest consecutive integer? Three consecutive even integers are numbers in order such as 4, 6, and
A rectangular container is 15 cm wide and 5 cm long, and contains water to a depth of 8 cm. An object is placed in the water and the water rises 2.3 cm. Determine the volume of the
1
What is the subset of {a,b,c}
briefly explain what is meant by LPP
1 1 1 1 1 2 1 2 ? and 40/2=? 2/40=?
56+3
Round 468.235 to the nearest hundredth ? The hundredths place is the second digit to the right of the decimal point (3). To decide how to round, you must like as at the digit t
find the polar coordinates of each point with the given rectangular coordinates. (-(squareroot(3)),3
how to work out consumer arithmetic?
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