Hello Roger,
I understand - taking your last question into account where you wanted
to generate the sequences - that you want the XSLT rules to verify, if
some set of sequences is a solution for the combinatorical problem:
For the set S with m elements list the n-tuples for n := [0, m]
(https://en.wikipedia.org/wiki/Permutation#Permutations_with_repetition)
The total number of "permutations with repetition" according to this
requirement will be
sum(m^k) for k := 0 to m and m := count(element)
Hopefully the mathematical background helps you tackling the problem...
One straight solution based on this mathematical fact would be to check
whether the are
"sum(m^k) for k := 0 to m and m := count(element)" different sequences.
Best regards
Christoph Naber
Am 19.11.2017 um 19:38 schrieb Costello, Roger L. costello(_at_)mitre(_dot_)org:
Hi Folks,
I have a set:
<set>
<element>A</element>
<element>B</element>
</set>
Here are some sequences derived from the set:
<sequences>
<sequence/>
<sequence>
<item>A</item>
</sequence>
<sequence>
<item>B</item>
</sequence>
<sequence>
<item>A</item>
<item>A</item>
</sequence>
<sequence>
<item>A</item>
<item>B</item>
</sequence>
<sequence>
<item>B</item>
<item>A</item>
</sequence>
<sequence>
<item>B</item>
<item>B</item>
</sequence>
</sequences>
Notice that:
- there is an empty sequence
- there is a sequence corresponding to each element of the set
- and there are other sequences (that I'm not concerned with for now)
I want to create XPath expressions which express the rules that sequences must
satisfy to be valid.
First rule: There must be an empty sequence. I expressed that rule with this
XPath expression:
sequence[not(item)]
Assume that the root element, <sequences>, is the context node.
Is that the right way to express the rule? Is there a better XPath expression? By
"better" I mean simpler, plainer, more transparent. I seek simplicity and
clarity over efficiency and cleverness.
Second rule: There must be a singleton sequence corresponding to every element in the set. A
"singleton sequence" is a <sequence> containing one <item>.
I expressed that rule with this XPath expression:
every $element in $set//element satisfies exists(sequence[(item = $element) and
not(item[2])])
Assume that $set is a variable whose value is the set.
Is that the right way to express the rule? Is there a better XPath expression?
/Roger
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