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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.
compare and contrast the bubble sort,quick sort,merge sort and radix sort
Program: Creation of Doubly Linked List OUTPUT Input the values of the element -1111 to come out : 1 Input the values of the element -1111 to come out : 2 Inpu
You have to sort a list L having of a sorted list followed by a few "random" elements. Which sorting methods would be especially suitable for this type of task? Insertion sort
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Q. Make the 11 item hash table resulting from hashing the given keys: 12, 44, 13, 88, 23, 94, 11, 39, 20, 16 and 5 by making use of the hash function h(i) = (2i+5) mod 11.
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