# Recursive generator for combinations of a multiset?

John O'Hagan research at johnohagan.com
Sat Nov 23 02:07:32 CET 2013

```On Thu, 21 Nov 2013 18:14:41 -0800 (PST)
James <hslee911 at yahoo.com> wrote:

> On Thursday, November 21, 2013 5:01:15 AM UTC-8, John O'Hagan wrote:

[...]

> > > On 21 November 2013 06:46, John O'Hagan
> >
> > > wrote:
> >

[...]

> >
> > > > def multicombs(it, r):
> >
> > > >     result = it[:r]
> >
> > > >     yield result
> >
> > > >     while 1:
> >
> > > >         for i in range(-1, -r - 1, -1):
> >
> > > >             rep = result[i]
> >
> > > >             if rep < it[i]:
> >
> > > >                 break
> >
> > > >         else:
> >
> > > >             break
> >
> > > >         for j, n in enumerate(it):
> >
> > > >             if n > rep:
> >
> > > >                 break
> >
> > > >         result = result[:i] + it[j:j - i]
> >
> > > >         yield result
> >
> > >

[...]

> >
> > I neglected to mention that multicombs takes a sorted iterable;
> >
> > it doesn't work right otherwise. I'd forgotten that because my
> >
> > wordlists are guaranteed sorted by the way they're built. Sorry
> >
> > that.
> >
> >
> >
> > In my use-case the first argument to multicombs is a tuple of words
> >
> > which may contain duplicates, and it produces all unique
> > combinations
> >
> > of a certain length of those words, eg:
> >
> >
> >
> > list(multicombs(('cat', 'hat', 'in', 'the', 'the'), 3))
> >
> >
> >
> > [('cat', 'hat', 'in'), ('cat', 'hat', 'the'), ('cat', 'in', 'the'),
> >
> > ('cat', 'the', 'the'), ('hat', 'in', 'the'), ('hat', 'the', 'the'),
> >
> > ('in', 'the', 'the')]
> >
> >

[...]

> > What I'm looking for is a recursive algorithm which does what
> >
> > multicombs does (order unimportant) so that I can apply a pruning
> >
> > shortcut like the one I used in the recursive cartesian product
> >
> > algorithm in my original post.
> >
> >
> >
> > Multiset combination algorithms seem pretty thin on the ground out
> >
> > there - as I said, I could only find a description of the procedure
> >
> > above, no actual code. The ones I did find are non-recursive. I'm
> >
> > hoping some combinatorics and/or recursion experts can offer
> >
> >

[...]

> >
> > John
>
> Could convert the following perl script to python?
>
> use Data::Dump qw(dump);
> dump combo([@ARGV], 3);
>
> sub combo {
> my (\$t, \$k) = @_;
> my @T = @\$t;
> my @R = ();
> my %g = ();
> if (\$k == 1) {
>         for (@T) {
>                 push @R, \$_ unless \$g{\$_}++;
>         }
> } else {
>         while (my \$x = shift @T) {
>         \$p = combo([@T], \$k-1);
>         for (@{\$p}) {
>                 my \$q = \$x.",".\$_;
>                 push @R, \$q unless \$g{\$q}++;
>         }
>         }
> }
> [@R];
> }
>
> \$ prog.pl cat hat in the the
> [
>   "cat,hat,in",
>   "cat,hat,the",
>   "cat,in,the",
>   "cat,the,the",
>   "hat,in,the",
>   "hat,the,the",
>   "in,the,the",
> ]
>
> James

Thanks. Now I just have to learn Perl to understand what that
does! :)

Regards,

--

John

```