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Dynamic programming illustration (see Anderson, Sweeney & Williams, An Intro to Mgt Science, 6th Ed.), or Hillier & Lieberman, various editions. We have a network on a number of states/cities. We want to find the length of the shortest route from every state to the final/last state. As special case, this allows us to find the cheapest/shortest path from state 1 to the final state.;