a reply to gist 438980

gistfile1.txt

Inspired by 
http://gist.github.com/438980
and, in turn
http://www.reddit.com/r/programming/comments/cehbe/awesome_lego_robot_monster_chessand_shit_gets/c0s0afu


jholman $ python symm.py 3 | wc -l
18
jholman $ python symm.py 4 | wc -l
60
jholman $ python symm.py 5 | wc -l
150

Now, to ensure that I'm not counting any ineligible candidates, 
I print out all rotations, remove duplicates, and then manually 
verify that it's four times as many as with simple output above.

jholman $ python symm.py 4 True | sort | uniq | wc -l
240
jholman $ python symm.py 5 True | sort | uniq | wc -l
600

And now for some raw output:

jholman $ python symm.py 2
AAAB
AABB
ABBB
jholman $ python symm.py 3
AAAB
AAAC
AABB
AABC
AACB
AACC
ABAC
ABBB
ABBC
ABCB
ABCC
ACBB
ACBC
ACCB
ACCC
BBBC
BBCC
BCCC

symm.py

rot = lambda a,n: a[n%len(a):] + a[:n%len(a)]
rotset = lambda a: set([rot(a,i) for i in range(len(a))])

def all_patterns(num,show_all = False): # I need a Design Pattern for exponential iteration
    already_saw = set([])
    for i in range(num):
        for j in range(num):
            for k in range(num):
                for m in range(num):
                    pattern = [i,j,k,m]
                    word = ''.join(map(lambda x:chr(x+65), pattern))
                    rots = rotset(word)
                    if len(rots) == 4 and len(rots.intersection(already_saw)) == 0:
                        already_saw.update(rots)
                        if show_all:
                            for w in rots:
                                print w
                        else:
                            print word

if __name__ == '__main__':
    from sys import argv
    show_all = False
    n = 3
    if len(argv) > 2 and argv[2] == 'True':
        show_all = True
    if len(argv) > 1:
        try:
            n = int(argv[1])
        except ValueError:
            pass
    all_patterns(n,show_all)