Р349РBostonР191РNew YorkР1090РMiamiР595РAtlantaР606Р760Р722РChicagoР2451Р834РDenverР957Р860Р908Р1855Р Several types of problems involving weighted graphs arise frequently. Determining a path of least length between two vertices in work is one such problem. To be more specific, let the length of a path in a weighted graph be the sum of the weights of the edges of this path.(The reader should note that this use of the term length is different from the use of length to denote the number of edges in a path in a graph without weights.) РThe question is: What is a shortest path, that is, a path of least length, between two given vertices? For instance, in the airline system represented by the weighted graph shown in Figure 1, what is a shortest path in air distance between Boston and Los Angles?
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