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I'm trying to find all countries which are reachable by land by traversing from one country to another via land borders using the mondial.sql database. It must be done recursively and I found some functions online which I thought would be useful for joining sequences and to be able to exclude countries which have already been found.
The problem is I end up in a loop even though the countries that are to be excluded seems to be handled properly. So my thinking is that I might have to define a base case in some way to make the recursion stop once all possible countries have been found. How to achieve this with XQuery?
(:functx.value-union and is-value-in-sequence were found at http://www.xqueryfunctions.com/xq/:)
declare namespace functx = "http://www.functx.com";
declare function functx:value-union
( $arg1 as xs:anyAtomicType* ,
$arg2 as xs:anyAtomicType* ) as xs:anyAtomicType* {
distinct-values(($arg1, $arg2))
};
declare function functx:is-value-in-sequence
( $value as xs:anyAtomicType? ,
$seq as xs:anyAtomicType* ) as xs:boolean {
$value = $seq
} ;
(:Recursive function for finding reachable countries:)
declare function local:findReachable($countries, $country, $reachedCountries) {
let $reachableCountries := $countries[#car_code = $country/border/#country]
for $c in $reachableCountries
where not(functx:is-value-in-sequence($c, $reachedCountries))
return functx:value-union($c, local:findReachable($countries, $c, functx:value-union($reachableCountries,
$reachedCountries)))
};
let $countries := //country
let $startingCountry := //country[#car_code = 'S']
return local:findReachable($countries, $startingCountry, $startingCountry)

Your checks with $reachedCountries only guarantee that countries do not appear twice on the same path, but you still visit every country along every possible path, which takes a long time. There is no loop, just lots of redundancy.
Here is a simple depth-first search that does what you want:
declare function local:dfs($stack, $seen) {
if(empty($stack)) then $seen
else (
let $country := $stack[1]
let $neighbors :=
for $code in $country/border/#country[not(. = $seen/#car_code)]
return $country/../country[#car_code = $code]
return local:dfs(($neighbors, $stack[position() > 1]), ($seen, $neighbors))
)
};
local:dfs(doc('mondial.xml')//country[#car_code = 'S'], ())/name