Combinations of lists

[88888 Dihedral]

On Thursday, October 4, 2012 11:12:41 PM UTC+8, Steen Lysgaard wrote:
> 2012/10/4 Joshua Landau <joshua.landau.ws at gmail.com>:
> 
> > On 3 October 2012 21:15, Steen Lysgaard <boxeakasteen at gmail.com> wrote:
> 
> >>
> 
> >> Hi,
> 
> >>
> 
> >> thanks for your interest. Sorry for not being completely clear, yes
> 
> >> the length of m will always be half of the length of h.
> 
> >
> 
> >
> 
> > (Please don't top post)
> 
> >
> 
> > I have a solution to this, then.
> 
> > It's not short or fast, but it's a lot faster than yours.
> 
> >
> 
> > But first let me explain the most obvious optimization to your version of
> 
> > the code:
> 
> >
> 
> >> combs = set()
> 
> >>
> 
> >>
> 
> >> for a in permutations(range(len(h)),len(h)):
> 
> >>     comb = []
> 
> >>     for i in range(len(h)):
> 
> >>         comb.append(c[i][a[i]])
> 
> >>     comb.sort()
> 
> >>
> 
> >>     frzn = tuple(comb)
> 
> >>     if frzn not in combs:
> 
> >>         combs.add(frzn)
> 
> >
> 
> >
> 
> >  What I have done here is make your "combs" a set. This helps because you
> 
> > are searching inside it and that is an O(N) operation... for lists.
> 
> > A set can do the same in O(1). Simplez.
> 
> >
> 
> > first  = list("AABBCCDDEE")
> 
> > second = list("abcde")
> 
> > import itertools
> 
> > #
> 
> > # Generator, so ignoring case convention
> 
> > class force_unique_combinations:
> 
> > def __init__(self, lst, n):
> 
> > self.cache = set()
> 
> > self.internal_iter = itertools.combinations(lst, n)
> 
> > def __iter__(self):
> 
> > return self
> 
> > def __next__(self):
> 
> > while True:
> 
> > nxt = next(self.internal_iter)
> 
> > if not nxt in self.cache:
> 
> > self.cache.add(nxt)
> 
> > return nxt
> 
> > def combine(first, second):
> 
> > sletter = second[0]
> 
> > first_combinations = force_unique_combinations(first, 2)
> 
> > if len(second) == 1:
> 
> > for combination in first_combinations:
> 
> > yield [sletter+combination[0], sletter+combination[1]]
> 
> > else:
> 
> > for combination in first_combinations:
> 
> > first_ = first[:]
> 
> > first_.remove(combination[0])
> 
> > first_.remove(combination[1])
> 
> > prefix = [sletter+combination[0], sletter+combination[1]]
> 
> > for inner in combine(first_, second[1:]):
> 
> > yield prefix + inner
> 
> >
> 
> >
> 
> > This is quite naive, because I don't know how to properly implement
> 
> > force_unique_combinations, but it runs. I hope this is right. If you need
> 
> > significantly more speed your best chance is probably Cython or C, although
> 
> > I don't doubt 10x more speed may well be possible from within Python.
> 
> >
> 
> >
> 
> > Also, 88888 Dihedral is a bot, or at least pretending like crazy to be one.
> 
> 
> 
> Great, I've now got a solution much faster than what I could come up with.
> 
> Thanks to the both of you.
> 
> And a good spot on 88... I could not for my life understand what he
> 
> (it) had written.
> 
> 
> 
> /Steen

If an unique order is defined, then it is trivial to solve this problem
without any recursions.