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:
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
elements and returns true if the first argument is strictly below
the second argument. The returned list is sorted in an increasing