can you clarify what you mean by "permutation" here? You don't seem to
be using the normal mathematical or English meaning you would not
normally consider AAA to be a permutation of ABC?
I think you want all non empty sequences of length n using items from
a set of size n?
On 18 November 2017 at 19:10, Costello, Roger L. costello(_at_)mitre(_dot_)org
<xsl-list-service(_at_)lists(_dot_)mulberrytech(_dot_)com> wrote:
Hi Folks,
I want an XSLT program that generates sequences of the permutations of a set.
For example, here is a set containing 2 elements:
<set>
<element>A</element>
<element>B</element>
</set>
I want the XSLT to generate these sequences:
<sequences>
<sequence/>
<sequence>A</sequence>
<sequence>B</sequence>
<sequence>AA</sequence>
<sequence>AB</sequence>
<sequence>BA</sequence>
<sequence>BB</sequence>
</sequences>
Let's take another example. Here is a set containing 3 elements:
<set>
<element>A</element>
<element>B</element>
<element>C</element>
</set>
I want the XSLT to generate these sequences:
<sequences>
<sequence/>
<sequence>A</sequence>
<sequence>B</sequence>
<sequence>C</sequence>
<sequence>AA</sequence>
<sequence>AB</sequence>
<sequence>AC</sequence>
<sequence>BA</sequence>
<sequence>BB</sequence>
<sequence>BC</sequence>
<sequence>CA</sequence>
<sequence>CB</sequence>
<sequence>CC</sequence>
<sequence>AAA</sequence>
<sequence>AAB</sequence>
<sequence>AAC</sequence>
<sequence>ABA</sequence>
<sequence>ABB</sequence>
<sequence>ABC</sequence>
<sequence>ACA</sequence>
<sequence>ACB</sequence>
<sequence>ACC</sequence>
<sequence>BAA</sequence>
<sequence>BAB</sequence>
<sequence>BAC</sequence>
<sequence>BBA</sequence>
<sequence>BBB</sequence>
<sequence>BBC</sequence>
<sequence>BCA</sequence>
<sequence>BCB</sequence>
<sequence>BCC</sequence>
<sequence>CAA</sequence>
<sequence>CAB</sequence>
<sequence>CAC</sequence>
<sequence>CBA</sequence>
<sequence>CBB</sequence>
<sequence>CBC</sequence>
<sequence>CCA</sequence>
<sequence>CCB</sequence>
<sequence>CCC</sequence>
</sequences>
I desire all the sequences -- including the empty sequence -- of all the
permutations, up to the length of the set.
I have written (below) an XSLT program to do this. But, I have two questions:
1. Is it correct? Do you see any errors in my XSLT implementation?
2. I seek plainness and transparency over efficiency and cleverness. I want
the XSLT to be super-super-easy to understand. It must use meaningful names.
Can you suggest ways to make the XSLT more plain, more transparent, more
easily understandable? /Roger
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform";
xmlns:xs="http://www.w3.org/2001/XMLSchema";
exclude-result-prefixes="xs generate"
xmlns:generate="function"
version="2.0">
<xsl:output method="xml" />
<xsl:variable name="empty" select="''" as="xs:string"/>
<xsl:variable name="one" select="1" as="xs:integer"/>
<xsl:variable name="set_elements" select="/set/element" as="xs:string+"/>
<xsl:template match="/">
<sequences>
<sequence/>
<xsl:sequence select="generate:sequences_of_length_n($empty,
$one)" />
</sequences>
</xsl:template>
<xsl:function name="generate:sequences_of_length_n"
as="element(sequence)*">
<xsl:param name="sequences_of_length_n_minus_1" as="xs:string*" />
<xsl:param name="n" as="xs:integer" />
<xsl:if test="$n le count($set_elements)">
<xsl:variable name="sequences_of_length_n" as="xs:string+">
<xsl:for-each select="$sequences_of_length_n_minus_1">
<xsl:variable name="a_sequence_of_length_n_minus_1"
select="." as="xs:string"/>
<xsl:for-each select="$set_elements">
<xsl:variable name="a_set_element" select="."
as="xs:string"/>
<xsl:sequence
select="concat($a_sequence_of_length_n_minus_1, $a_set_element)" />
</xsl:for-each>
</xsl:for-each>
</xsl:variable>
<xsl:for-each select="$sequences_of_length_n">
<sequence><xsl:value-of select="."/></sequence>
</xsl:for-each>
<xsl:sequence
select="generate:sequences_of_length_n($sequences_of_length_n, $n+1)" />
</xsl:if>
</xsl:function>
</xsl:stylesheet>
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