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1. a) Find the shortest paths from r to all other nodes in the digraph G=(V,E) shown below using the Bellman-Ford algorithm (as taught in class). Please show your work, and draw the final shortest dipath tree on a copy of a diagram of the digraph.
b) Using the potential y found in a), find a new set of costs c* for G which are non-negative, and preserve shortest dipaths.
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If the vertices of a triangle are (1, k), (4, -3), (-9, 7) and its area is 15 sq units, find the value(s) of k..
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