785 miles from Chicago, and is nearer than the other options.
Once in Dallas he has notched up 706 + 785 miles. He then has to choose
between Albuquerque and El Paso. He chooses Albuquerque because it is closer.
From Albuquerque he has to go to El Paso whereupon he has visited all the cities
and, job done, he returns to Bismarck. His total mileage is 706 + 785 + 580 +
236 + 1100 = 3407 miles. This route BCDAEB is much shorter than his previous
route and he has made a saving on carbon emissions too.
This way of thinking is often called the greedy method of finding a short
route. This is because James Cook’s decision is always a local one – he is in a
certain city and looks for the best route out of that city. With this method he
never attempts to look forward by more than one step at a time. It is not
strategic because it takes no overall account of the best route. The fact that he
finished in El Paso meant he was forced to take a long route back to Bismarck. So
a shorter route has been found, but is it the shortest route? James is intrigued.
James sees how he can take advantage of there being only five cities involved.
With so few it is possible to list all the possible routes and to then select the
shortest one. With five cities there are only 24 routes to examine or just 12 if we
count a route and its reverse as equivalent. This is permissible because both have
the same total mileage. The method serves James Cook well and he learns that
the route BAEDCB (or its reverse BCDEAB) is actually optimum, being only 3199
miles long.
Back in Bismarck James realizes his travel is taking too long. It is not the