Re: Generic De Bruijn Sequence

[LanX]

Did you consult wikipedia or search for other algorithms?

Many sources recommend an algorithm from Frank Ruskey , easily found implemented in various languages, here one in Python De_Bruijn_sequence#Algorithm which is not too hard to be ported.

Besides: The minimal length k^n is proven to be always achievable.

Which consequently means at least your first result and hence your algorithm is wrong.

update

De Bruijn is supposed to be cyclic!

AAACCCBCCACBBCBACABCAABBBABAA

[QM]

De Bruijn is supposed to be cyclic AAACCCBCCACBBCBACABCAABBBABAA

Yes. The last $n-1 chars overlap with the beginning. The debug prints show each permutation lined up with the output string, so you can see how the graph is traversed and the output constructed. I could have just used the last char of each permutation, and had a true De Bruijn output, but that didn't suit my needs.

I found the Python code, but didn't like it because of the lack of explanation. To understand it, I have to trace code that does a lot of index math, instead of reading comments hinting at an algorithm that makes sense on a higher level. It's not far removed from pointer math and assembler code, so it doesn't seem very Pythonic, as they like to say.

If nothing else, my code at least tries to say what it's doing. So the next guy can try to understand it, and not blindly accept it, nor need to walk through on paper to believe that it's correct.

[LanX]

> . The last $n-1 chars overlap with the beginning

> debruijn.pl 5 2 
AAEEDECEBEADDCDBDACCBCABBA 
123456789012345678901234567890

I don't understand how $n=5 (Alphabet size according to your code) results in length 26 instead of 25.

please explain°

edit

>  walk through on paper to believe that it's correct.

Your user image shows Richard P. Feynman and you are questioning scientific reviews in mathematics? Ironic :)

UPDATE

") did you mean $t-1 ?

[QM]

") did you mean $t-1 ?

Yes. In my original code, I used $n for both. But later realized I could split that into 2 parameters. I probably used $n here through that mistake.

[LanX]

> so it doesn't seem very Pythonic, as they like to say.

seems to be a port of the ruby version which is pretty straight forward ported for a Perl hacker

http://gist.github.com/jonelf/3423148

update

Basically it's a inductive solution building complex sequences from more primitive ones starting with (1,1).

I'm sure porting to Perl, using longer var names and dumping part solutions would explain the idea.

update

Though finding the original article would be better.

[BrowserUk]

De Bruijn is supposed to be cyclic! AAACCCBCCACBBCBACABCAABBBABAA

Maybe, but practicality means it is far simpler and more efficient to repeat the end sequence than to wrap around.

[LanX]

Maybe in this case, but check the length of his results, either way they are inconsistent and hence wrong.

[BrowserUk]

but check the length of his results, either way they are inconsistent and hence wrong.

I've only had need to explore DeBruijn with a binary alphabet, so I'll defer to your judgement.