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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.
how many zeros comes in crore, lac,billion etc.
-3+4 #Minimum 100 words accepted#
How do I solve logx/log2x=2
1) A local factory makes sheets of plywood. Records are kept on the number of mild defects that occur on each sheet. Letting the random variable x represent the number of mild de
Fundamental Theorem of Calculus, Part II Assume f ( x ) is a continuous function on [a,b] and also assume that F ( x ) is any anti- derivative for f ( x ) . Then,
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tan9x = (tan7x + tan2x)/(1 - tan7x*tan2x) here its given 1 - tan2x*tan7x= 0 implies tan9x = infinity since tan9x = (3tan3x - tan^3(3x))/(1 - 3tan^2 (3x)) = infinity implies
Charlie needs to know the area of his property, that measures 120 ft through 150 ft. Which formula will he use? The area of a rectangle is length × width.
a) Specify that a tree has at least 2 vertices of degree 1. b) What is the largest number of vertices in a graph with 35 edges if all vertices are
what is x(5x4)=26?
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