Best route finding (path finding) software

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Details

I need a software which will calculate best route on map build by hex tiles.

Map may look like on pic01.jpg.

Map may have different shapes and tiles.

White circles symbolize cities. On the hex with cities there is value.

Lines symbolize tracks (paths)

Round tokens symbolize company station in the city.

Each company have some trains which may be different type (explained later in example).

Task:

Based on photo of the map software should recognize logic situation from photo and calculate best route for all available trains for specific company, with restrictions:

- each train may go by the same route (path) only once

- there must be at least one company station on each route

- one train cannot visit the same city more than one time

- red regions counts as a city and it value depends of selected stage

- cities with other companies stations and with no empty white circle or company station are blocked. Route is broken. Route may start or finished on this station but cannot pass by this city.

- the route value is the sum of the values of each visited city

- best route is route which highest value

- they may be special rules for map example based on pic01.jpg: making route by one train from red region marked by "W" with red region marked by "E" this route get extra bonus

Example based on pic02.jpg

Orange company has trains:

1x Type "2"

1x Type "3"

Type "3" means that this train may visit 3 cities maximum (but may visit also 2 cities)

Type "4" means that this train may visit 4 cities maximum (but may visit also 2 or 3 cities)

There "Brown" stage so all red areas are count with brown values.

Best routes are:

1st route made by type "4" train (BLUE): 40 (brown) + 90 + 70 + 60 (brown) + 50 (W bonus) + 30 (E bonus) = 340

2nd route made by type "3" train (RED): 90 + 30 +70 = 190

So best route value is: 340 + 190 = 530

.... more description attached

Required functions:

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