I think you're looking for Heap's algorithm, although a quick search on CPAN and a look on Rosettacode doesn't yet show me an existing Perl implementation. Update: Sorry, that was permutations, you're looking for combinations.

Update 2019-10-05: I've just released this as Algorithm::Odometer::Gray!

Update 2: Knuth's "The Art of Computer Programming", "Generating all n-tuples", Algorithm H, "Loopless reflected mixed-radix Gray generation". Best I can do at the moment is an implementation in Python from the Sage project, here. Update 3: The exact same algorithm appears to be described in this freely available paper: Loopless Functional Algorithms as "Algorithm C" in the section "9.5. Non-binary Gray codes".

Final Update: I think I've implemented the algorithm as described:

sub mixedgray_it {
    my @w = @_;
    my @m = map { 0+@$_ } @w;
    die "all items must have at least two positions"
        if grep {$_<2} @m;
    my @a = (0) x @m;
    my @f =  0 .. @m;
    my @o = (1) x @m;
    my $done;
    return sub {
        return undef if $done;
        my $rv = [map {$w[$_][$a[$_]]} 0..$#w];
        if ($f[0]==@w) { $done=1; return $rv }
        my $j = $f[0]; $f[0] = 0;
        $a[$j] += $o[$j];
        if ($a[$j]==0 || $a[$j]==$m[$j]-1) {
            $o[$j] = -$o[$j];
            $f[$j] = $f[$j+1];
            $f[$j+1] = $j+1;
        }
        return $rv;
    }
}

use Data::Dump;
my $it = mixedgray_it(['a','b','c'],[1,2]);
while (defined( my $c = $it->() ))
    { dd $c }

__END__

["a", 1]
["b", 1]
["c", 1]
["c", 2]
["b", 2]
["a", 2]

[download]

In reply to Re: Minimally changing combinations (updated!) by haukex
in thread Minimally changing combinations by Yary

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.