lib: introduce listDfs and toposort, add example to hasPrefix

This commit is contained in:
Jan Malakhovski 2015-11-25 19:07:19 +00:00
parent c49f2a0854
commit 363b0fd040

View file

@ -256,6 +256,86 @@ rec {
reverseList = xs: reverseList = xs:
let l = length xs; in genList (n: elemAt xs (l - n - 1)) l; let l = length xs; in genList (n: elemAt xs (l - n - 1)) l;
/* Depth-First Search (DFS) for lists `list != []`.
`before a b == true` means that `b` depends on `a` (there's an
edge from `b` to `a`).
Examples:
listDfs true hasPrefix [ "/home/user" "other" "/" "/home" ]
== { minimal = "/"; # minimal element
visited = [ "/home/user" ]; # seen elements (in reverse order)
rest = [ "/home" "other" ]; # everything else
}
listDfs true hasPrefix [ "/home/user" "other" "/" "/home" "/" ]
== { cycle = "/"; # cycle encountered at this element
loops = [ "/" ]; # and continues to these elements
visited = [ "/" "/home/user" ]; # elements leading to the cycle (in reverse order)
rest = [ "/home" "other" ]; # everything else
*/
listDfs = stopOnCycles: before: list:
let
dfs' = us: visited: rest:
let
c = filter (x: before x us) visited;
b = partition (x: before x us) rest;
in if stopOnCycles && (length c > 0)
then { cycle = us; loops = c; inherit visited rest; }
else if length b.right == 0
then # nothing is before us
{ minimal = us; inherit visited rest; }
else # grab the first one before us and continue
dfs' (head b.right)
([ us ] ++ visited)
(tail b.right ++ b.wrong);
in dfs' (head list) [] (tail list);
/* Sort a list based on a partial ordering using DFS. This
implementation is O(N^2), if your ordering is linear, use `sort`
instead.
`before a b == true` means that `b` should be after `a`
in the result.
Examples:
toposort hasPrefix [ "/home/user" "other" "/" "/home" ]
== { result = [ "/" "/home" "/home/user" "other" ]; }
toposort hasPrefix [ "/home/user" "other" "/" "/home" "/" ]
== { cycle = [ "/home/user" "/" "/" ]; # path leading to a cycle
loops = [ "/" ]; } # loops back to these elements
toposort hasPrefix [ "other" "/home/user" "/home" "/" ]
== { result = [ "other" "/" "/home" "/home/user" ]; }
toposort (a: b: a < b) [ 3 2 1 ] == { result = [ 1 2 3 ]; }
*/
toposort = before: list:
let
dfsthis = listDfs true before list;
toporest = toposort before (dfsthis.visited ++ dfsthis.rest);
in
if length list < 2
then # finish
{ result = list; }
else if dfsthis ? "cycle"
then # there's a cycle, starting from the current vertex, return it
{ cycle = reverseList ([ dfsthis.cycle ] ++ dfsthis.visited);
inherit (dfsthis) loops; }
else if toporest ? "cycle"
then # there's a cycle somewhere else in the graph, return it
toporest
# Slow, but short. Can be made a bit faster with an explicit stack.
else # there are no cycles
{ result = [ dfsthis.minimal ] ++ toporest.result; };
/* Sort a list based on a comparator function which compares two /* Sort a list based on a comparator function which compares two
elements and returns true if the first argument is strictly below elements and returns true if the first argument is strictly below
the second argument. The returned list is sorted in an increasing the second argument. The returned list is sorted in an increasing