This program generates Sierpinski graphs associated to the Tower of Hanoi game. You can customize the amount of disks (and the number of tower) by calling the function generer with the two numbers as arguments respectively. For example, you obtain a graph for 3 disks and 4 towers by calling generer(3, 4).
Tower of Hanoi is a game mostly known as three disks, placed by ascendant sizes on a column, that you have to move to a third column by swapping them from column to column (three total columns available) while always keeping heavier disks under lighter ones.
The main file is written recursively which makes it usable for any parameter. To use it, run the generer command (generer(n: int = 3, colonnes: int = 3), n is the number of disks), it outputs a dictionary explained below.
The second file has a more understandable approach but much harder to generalize with more disks or columns. It outputs the same kind of object as the main function.
The output is a dictionary where each key is an object and each value is a list of every object it is linked to.
An object of the graph is a set of n letters, n being the number of disks. By ranking the disks by weight, the #k letter corresponds to the column where the #k disk is. A branch represents one (legal) move. The fastest solve is the shortest path from 'AA..A' to '&&..&' where '&' is the last column.
The classic graph, generated on 3 disks and 3 columns, is a triangle, named 'Sierpinski's Triangle'. However, if you extend to four columns, it becomes a square, and so on.