all possible combinations

[John Machin]

rbt wrote:
> Thanks to all who were helpful... some of you guys are too harsh and
> cynical.

Reality check: wander down to your nearest military establishment, ask a 
drill sergeant to demonstrate "harsh and cynical".

> Here's what I came up with. I believe it's a proper
> combination, but I'm sure someone will point out that I'm wrong ;)
> 
> groups = [list('abc'),list('abc'),list('abc'),list('abc')]
> 
> already = []

In general, a set would be better than a list (1) conceptually (2) when 
the number of elements is large.

> 
> while 1:
> 
>     LIST = []

Read the style guide -- http://www.python.org/peps/pep-0008.html

> 
>     for g in groups:
>         sample = random.sample(g, 1)
>         LIST.append(sample[0])
> 
>     STRING = ''.join(LIST)
>     if STRING not in already:
>         print STRING
>         already.append(STRING)
>     if len(already) == 81:
>         break
> 

You don't need to use random sampling. Paul Rubin has shown how it can 
be done deterministically. The following is a generalisation of his 
code; it generates all possible assemblies of size n from a list of 
parts. Is this helpful?

def all_size_n_knickers(rqd_size, pieces):
     npieces = len(pieces)
     knicker_count = npieces ** rqd_size
     austen = [npieces ** (rqd_size-k-1) for k in xrange(rqd_size)]
     for i in xrange(knicker_count):
         knicker = [pieces[j] for j in [(i // d) % npieces for d in austen]]
         yield knicker

for alist in all_size_n_knickers(4, 'abc'):
     print ''.join(alist)

print
print list(all_size_n_knickers(2, [1, 42, 666]))