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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.
Solve by factorization X 2 +(a/a+b + a+b/a)x+1 = 0 X 2 +(a/a+b + a+b/a)x+1 => X 2 +(a/a+b x a+b/ax + a/a+b .a+b/a) => X[x+a/a+b] +a+b/a[a+a*a+b]= 0 => X= -a
if a&b are aconsra
the mass of a container is 5.81kg when full with sugar .the mass of container is 3.8kg when 3/8 of the sugar is removed.what is the mass of empty container
i need some information on this topic for my holidays project..plz guide me what to do
As1212uestion #Minimum 100 words accepted#
SA= Ph+2B L=36 ft W=10 ft H=20 ft P=92 ft B=360 ft
A 'woman was trying to teach her three-year-old child the numbers from 1to 5 from a children's book on numbers. Each number was illustrated by the same number of trees drawn next t
What is the objective of lipids metabolism ? After studying this unit, you will be able to: 1. explain how fatty acids are oxidized for the production of energy, 2. describe
max z=3x1+2x2 s.t x1+2x2 3x1+2x2>=6 x1+4x2 x1,x2,x3>=0
MATHEMATICS - IN OUR LIVES : What is the most obvious example of mathematics in your life? To many of us it is the maths that we studied in school. But is that all the mathemat
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