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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.
Q. Write an algorithm INSERT which takes a pointer to a sorted list and a pointer to a node and inserts the node into its correct position or place in the list. Ans: /* s
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There are four data type groups: Integer kepts whole numbers and signed numbers Floating-point Stores real numbers (fractional values). Perfect for storing bank deposit
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