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#!/usr/bin/env python
# Author: Jared Brothers 
# Find the orderings of a set of dominoes such that
# adjacent dominoes share a number and the other two
# numbers differ by one.

def search(start):
    """ Depth first search, generating all solutions. """
    fringe = [start]
    while fringe:
        s = fringe.pop()
        if s.check():
            yield s
        fringe.extend(s.successors())

class state():
    """ A state in the search space.  """
    def __init__(self, d, r):
        """ The ordered dominoes are in done (list),
        and the unordered dominoes are in rest (set). """
        self.done = d
        self.rest = r

    def __str__(self):
        return str(self.done)

    def check(self):
        """ Is this a solution? """
        return not self.rest

    def successors(self):
        """ The states you can get to by moving a domino from rest to done. """
        if self.done:
            # Try only dominoes adjacent to the previous one,
            a,b = self.done[-1]
            a1 = (a + 1) % n
            a2 = (a - 1) % n
            b1 = (b + 1) % n
            b2 = (b - 1) % n
            adjs = set([(a,b1), (b1,a), (a,b2), (b2,a), (b,a1), (a1,b), (b,a2), (a2,b)])
            for x in self.rest.intersection(adjs):
                d = self.done[:]
                d.append(x)
                r = self.rest.copy()
                r.discard(x)
                yield state(d, r)
        else:
            # or all the rest if nothing has been done yet.
            for x in sorted(self.rest):
                d = [x]
                r = self.rest.copy()
                r.discard(x)
                yield state(d, r)

if __name__ == '__main__':
    n = 7 # The number of numbers. The number of dominoes is sum(range(n + 1)).
    start = state([], set((a, b) for a in range(n) for b in range(a + 1)))
    for s in search(start):
        print(s)