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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.
Determine the Disjoint of division method A polygon is disjoint from the viewport if the x- and y-extents of the polygon do not overlap the viewport anywhere. In this case; reg
Task If quicksort is so quick, why bother with anything else? If bubble sort is so bad, why even mention it? For that matter, why are there so many sorting algorithms? Your
Q. Explain that how do we implement two stacks in one array A[1..n] in such a way that neither the stack overflows unless the total number of elements in both stacks together is n.
prove that n/100=omega(n)
State the range of operation of ADT Operations of the Range of T ADT includes following, where a, b ∈ T and r and s are values of Range of T: a...b-returns a range value (an
I need help writing a pseudocode for my assignment can anyone help?
You are given two jugs, a 4-gallon one and a 3-gallon one. Neither has any measuring marker on it. There is a tap that can be used to fill the jugs with water. How can you get exac
An AVL tree is a binary search tree that has the given properties: The sub-tree of each of the node differs in height through at most one. Each sub tree will be an AVL tre
Since memory is becoming more & cheaper, the prominence of runtime complexity is enhancing. However, it is very much significant to analyses the amount of memory utilized by a prog
(1) (i) Add the special form let to the metacircular interpreter Hint: remember let is just syntactic sugar for a lambda expression and so a rewrite to the lambda form is all t
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