Brute Force Algorithm to solve the TSP in Delphi [closed] - algorithm

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I'm writing a program for an extended project to simulate the travelling salesman problem. So far I have written it to allow the user to enter a route, as well as 'solving' a route using a nearest neighbour algorithm. I am now trying to write a brute force algorithm to solve for a selection of cities, from 3 cities up to about 13/14. The program is for the purpose of showing how the increase in number of cities leads to an exponential/factorial increase in the time taken to calculate the shortest route. I have tried to write a recursive function but cannot get my head around how it would work. I am in desperate need of some guidance as to how to do this. Any help would be appreciated.

Answer 1

Since there is no tag with Delphi version, then any version suits the TopicStarter just fine. I would base thus draft on XE2 version then. I also would assume that each town is only visited once. I would assume that there is a road network rather than a private airplane, that is between any chosen cities A and B there may be direct path or may not (connection only through other cities).
type TCity = class
public
Name : string;
Routes : TList<TCity>; // available roads to/from this place
LeftFor : integer; // where did the merchant went next; -1 if did not arrived or left, used to iterate all the paths
CameFrom: TCity; // nil initially
.....
End; // writing this draft from phone ( testing official StackOverflow Android app) would not write boilerplate with creating/free in internal objects - do it yourself
Type TPath = TArray<TCity>; // for your app you would add segments and total cost and whatever
Var World: TArray<TCity >; // fill cities and links yourself
AllPaths: TList<TPath>; // create yourself
Current: TList<TCity >; // create yourself
Procedure SaveResult;
Begin AllPaths.Add( Current.ToArray) end;
Function TryNextCity: boolean;
Var c1,c2: TCity; I : integer;
Begin
c1 := Current.Last; // where we are
While true do begin
Inc( c1.LeftFor) ;
If c1.LeftFor >= c1.Routes.Count // tried all ways?
Then Exit( false );
c2 := c1.Routes (. c1.LeftFor .);
if c2 = c1.CameFrom then continue;
if c2.LeftFor >= 0 then continue; // already were there
AddCity(c2);
Exit( True) ;
End;
End;
Procedure AddCity( const City: TCity) ;
Begin
Assert ( not Current.Contains( City) ) ;
If Current.Count = 0
then City.CameFrom := nil //starting point
else City.CameFrom := Current.Last;
City.LeftFor := -1;
Current.Add(City) ;
End;
Procedure Withdraw;
Begin
Assert ( Current.Count > 0);
With Current.Last do begin
CameFrom := nil;
LeftFor := -1;
End;
Current.Delete( Current.Count - 1) ;
End;
Procedure Recurs;
Var DeadEnd : boolean;
Begin
DeadEnd := true;
while TryNextCity() do begin
DeadEnd := false;
Recurs();
end;
if DeadEnd then SaveResult();
Withdraw ();
End;
Procedure RunBruteForce;
Var c: TCity ;
Begin
AllPaths.Clear;
For c in world do begin
Current.Clear;
AddCity( c );
Recurs();
End;
End;
PS. #MartynA looks like I cannot comment my answer now in Android. So my reply is: this questions as is now falls into a triangle between "do my homework", "write a textbook or at least an essay" and "throw a bunch of vague nice ideas, correct per se, but none of which would be detailed and complete enough to be called an answer".
I only started the answer to try new SO app, and only go on for it does not have options to delete the answer.