Re: [xsl] All combinations from a sequence

Thanks a lot, Michael Kay, just what I needed!

After a bit of thinking and just for handling a sequence of strings I came up 
with this:

  <xsl:function name="my:powerset" as="xs:string*">
    <xsl:param name="seq" as="xs:string+"/>
    <xsl:variable name="N" select="count($seq)" as="xs:integer"/>
    <xsl:sequence select="
    for $i in 0 to xs:integer(math:pow(2, $N)) - 1
    return string-join( 
      for $j in 1 to $N 
      return (
        if ($i idiv math:pow(2, $j -1) mod 2 eq 1) 
          then $seq[$j] 
          else ()
          )
      , '')
    "/>
  </xsl:function>

No recursion necessary, and not too difficult to follow.

my:powerset(('A','B','C','D')) creates: '', 'A', 'B', 'AB', 'C', 'AC', 'BC', 
'ABC', 'D', 'AD', 'BD', 'ABD', 'CD', 'ACD', 'BCD', 'ABCD'

Best regards,

- Michael Müller-Hillebrand


> Am 30.09.2021 um 16:37 schrieb Michael Kay mike(_at_)saxonica(_dot_)com 
> <xsl-list-service(_at_)lists(_dot_)mulberrytech(_dot_)com>:
>
> There's a nice algorithm here
>
> https://www.geeksforgeeks.org/power-set/
>
> which abstracts to
>
> for $i in 1 to math:pow(2, count($input))
> return combination($i)
>
> where combination($i) includes or excludes each $input[$N] depending on 
> whether bit $N is set in $i, which you can determine using bin:shift() from 
> the EXPath binary module.
>
> Michael Kay
>
> > On 30 Sep 2021, at 15:20, Michael Müller-Hillebrand mmh(_at_)docufy(_dot_)de 
> > <xsl-list-service(_at_)lists(_dot_)mulberrytech(_dot_)com> wrote:
> >
> > Good afternoon,
> >
> > I have a sequence of items and I need all combinations (not permutations) in 
> > all possible lengths.
> >
> > I saw what I want described as "powerset" in the Python docs: 
> > powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)
> >
> > In XPath notation and based on strings:
> >
> > my:powerset(('A','B','C','D'))
> >
> > This sequence of 4 items should result in a sequence of 16 strings (order 
> > not important) representing all possible combinations: 'ABCD', 'ABC', 'ABD', 
> > 'ACD', 'AB', 'AC', 'AD', 'A', 'BCD', 'BC', 'BD', 'B', 'CD', 'C', 'D', ''
> >
> > Or more general, the result could be an array of sequences.
> >
> > To get this as a solution in XSLT/XPath I am currently fiddling around with 
> > a recursive function including head() and tail() and count() but I have the 
> > impression I am overcomplicating things.
> >
> > I am wondering, if this is a use case for fold-left() or if I should rather 
> > think of a filter that drops 0, 1, 2 or 3 items from the sequence. Or is 
> > there a well-known algorithm with a cool name?
> >
> > Any hints are, as always, very welcome, thanks a lot,
> >
> > - Michael
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