Question

An autonomous military drone is required to fly over 14 locations as part of surveillance operation. It must plan a route to minimise the distance travelled. Treating this as a TSP(travelers salesman problem) in which the drone starts from one of the locations, how many possible routes might the drone take?

Answer 1

To better understand the problem let us consider a small number so that we can simulate all the possible routes.

Let's say we have four locations A, B, C and D: .

Now, I want to get all possibilities between those cities, which are: [A, B, C, D, A], [A, B, D, C, A], [A, C, B, D, A]

Since you always start and end at location A and the direction doesn't matter, there are (4-1)!/2 = 3 possibilities.

So, the general formula can be derived as (n-1)!/2 when we start and end at from a particular location as seen in the above example as location A.

In the above formula, n represents the TOTAL number of locations.

Here, in our question we consider 14 locations.

Hence, the drone has to take (14-1)!/2 = 3113510400 if it starts from one of the locations.

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