Example of how to use the module:
import graph_unique_paths as g
solver = g.Graph()
solver.solve('data/1_start_1_end.json')
It accepts a path to a .json file (the file defines the directed graph as a JSON object) and returns a list of all the unique paths, given the requirement that one begin on a start node and finish on an end node.
To run the tests: python -m unittest discover (while in the graph-unique-paths directory)
This program calculates the maximum unique paths for directed graphs which have start and end nodes (you must start on a start node, and end on an end node). I was originally inspired by wanting to know how many permutations the "wheel" puzzles from the game The Witness had (the ones in the desert area). But this module is sufficiently flexible that you can use it on other types of graphs too.
The Witness puzzles have 7 normal nodes (which all act as starting points), and 6 of those nodes have "end" nodes attached to the outside of them (where your path finishes and you're unable to draw anymore).
You can't revisit or pass through a node if you've been on it in the past. There are 12 normal vertices in the puzzle. If you count the edge normal nodes connecting to the end nodes, there are 18 vertices.
End nodes are special: you can't start on an end node, and you must finish on one.
Here's my attempt to draw an ASCII version of the puzzle (end nodes not shown):
+------+
| |
| |X
XXX+------+XXXXX
XXXX X XXXXX
XXXXXX X XXXX
+------+XXXX X XXXXX+-------+
| | X | |
| | X | |
+------+XX X XXXXX| |
X XXXXX +--------+ XXXXXXX +-------+
X XXXXX | |XXXXX X
X XXXXXX| | X
X XXX | |X X
X XXXX +--------+XXXXX X
X XXXX X XXXX X
X XXX X XXX X
X XXX X XXXXX X
+-------+ X XXXX X
| | X +-------+
| | XX | |
| | X | |
+-------+XXX X | |
XXXXXX X XXXX+-------+
XXX +-------+ XXXXXX
XXXXX | | XXXXX
X | |
| |
+-------+
If that diagram doesn't make sense, try this URL, which has screenshots from the game: http://www.ign.com/wikis/the-witness/Desert_Ruins