Topological sort
From Rosetta Code
You are encouraged to solve this task according to the task description, using any language you may know.
Given a mapping between items, and items they depend on, a topological sort orders items so that no item precedes an item it depends upon.
The compiling of a library in the VHDL language has the constraint that a library must be compiled after any library it depends on. A tool exists that extracts library dependencies. The task is to write a function that will return a valid compile order of VHDL libraries from their dependencies.
- Assume library names are single words.
- Items mentioned as only dependants, (sic), have no dependants of their own, but their order of compiling must be given.
- Any self dependencies should be ignored.
- Any un-orderable dependencies should be flagged.
Use the following data as an example:
LIBRARY LIBRARY DEPENDENCIES ======= ==================== des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee dw01 ieee dw01 dware gtech dw02 ieee dw02 dware dw03 std synopsys dware dw03 dw02 dw01 ieee gtech dw04 dw04 ieee dw01 dware gtech dw05 dw05 ieee dware dw06 dw06 ieee dware dw07 ieee dware dware ieee dware gtech ieee gtech ramlib std ieee std_cell_lib ieee std_cell_lib synopsys
Note: the above data would be un-orderable if, for example, dw04 is added to the list of dependencies of dw01.
Contents |
[edit] Clojure
Here is a quick implementation in Clojure, developed at Java Posse Roundup 2010 in collaboration with Fred Simon, with a bit of subsequent simplification by Joel Neely.
Dependencies are represented by a map from each item to the set of items on which it depends. The first function (dep), builds a dependency map for a single item.
The next few functions (empty-dep, pair-dep, default-deps, declared-deps, and deps) are used to construct the map from a list that alternates items with lists of their dependencies.
The next three functions (no-dep-items, remove-items, and topo-sort-deps) are the core of the topological sort algorithm, which iteratively removes items with no remaining dependencies from the map and "stacks" them onto the result. When the map becomes empty the reversed result is returned. If no dependency-free items can be found, then any non-empty remainder of the map contains cycles.
The last function (topo-sort) is simply a helper which applies topo-sort-deps to a dependency map constructed from the item-and-list-of-dependencies input list.
[edit] Implementation
(use 'clojure.set)
(use 'clojure.contrib.seq-utils)
(defn dep
"Constructs a single-key dependence, represented as a map from
item to a set of items, ensuring that item is not in the set."
[item items]
{item (difference (set items) (list item))})
(defn empty-dep
"Constructs a single-key dependence from item to an empty set."
[item]
(dep item '()))
(defn pair-dep
"Invokes dep after destructuring item and items from the argument."
[[item items]]
(dep item items))
(defn default-deps
"Constructs a default dependence map taking every item
in the argument to an empty set"
[items]
(apply merge-with union (map empty-dep (flatten items))))
(defn declared-deps
"Constructs a dependence map from a list containaining
alternating items and list of their predecessor items."
[items]
(apply merge-with union (map pair-dep (partition 2 items))))
(defn deps
"Constructs a full dependence map containing both explicitly
represented dependences and default empty dependences for
items without explicit predecessors."
[items]
(merge (default-deps items) (declared-deps items)))
(defn no-dep-items
"Returns all keys from the argument which have no (i.e. empty) dependences."
[deps]
(filter #(empty? (deps %)) (keys deps)))
(defn remove-items
"Returns a dependence map with the specified items removed from keys
and from all dependence sets of remaining keys."
[deps items]
(let [items-to-remove (set items)
remaining-keys (difference (set (keys deps)) items-to-remove)
remaining-deps (fn [x] (dep x (difference (deps x) items-to-remove)))]
(apply merge (map remaining-deps remaining-keys))))
(defn topo-sort-deps
"Given a dependence map, returns either a list of items in which each item
follows all of its predecessors, or a string showing the items among which
there is a cyclic dependence preventing a linear order."
[deps]
(loop [remaining-deps deps
result '()]
(if (empty? remaining-deps)
(reverse result)
(let [ready-items (no-dep-items remaining-deps)]
(if (empty? ready-items)
(str "ERROR: cycles remain among " (keys remaining-deps))
(recur (remove-items remaining-deps ready-items)
(concat ready-items result)))))))
(defn topo-sort
"Given a list of alternating items and predecessor lists, constructs a
full dependence map and then applies topo-sort-deps to that map."
[items]
(topo-sort-deps (deps items)))
Examples of sortable and non-sortable data:
(def good-sample
'(:des_system_lib (:std :synopsys :std_cell_lib :des_system_lib :dw02 :dw01 :ramlib :ieee)
:dw01 (:ieee :dw01 :dware :gtech)
:dw02 (:ieee :dw02 :dware)
:dw03 (:std :synopsys :dware :dw03 :dw02 :dw01 :ieee :gtech)
:dw04 (:dw04 :ieee :dw01 :dware :gtech)
:dw05 (:dw05 :ieee :dware)
:dw06 (:dw06 :ieee :dware)
:dw07 (:ieee :dware)
:dware (:ieee :dware)
:gtech (:ieee :gtech)
:ramlib (:std :ieee)
:std_cell_lib (:ieee :std_cell_lib)
:synopsys ()))
(def cyclic-dependence
'(:dw01 (:dw04)))
(def bad-sample
(concat cyclic-dependence good-sample))
[edit] Output
Clojure 1.1.0
1:1 user=> #<Namespace topo>
1:2 topo=> (topo-sort good-sample)
(:std :synopsys :ieee :gtech :ramlib :dware :std_cell_lib :dw07 :dw06 :dw05 :dw01 :dw02 :des_system_lib :dw03 :dw04)
1:3 topo=> (topo-sort bad-sample)
"ERROR: cycles remain among (:dw01 :dw04 :dw03 :des_system_lib)"
[edit] Common Lisp
(defun topological-sort (graph &key (test 'eql))
"Graph is an association list whose keys are objects and whose
values are lists of objects on which the corresponding key depends.
Test is used to compare elements, and should be a suitable test for
hash-tables. Topological-sort returns two values. The first is a
list of objects sorted toplogically. The second is a boolean
indicating whether all of the objects in the input graph are present
in the topological ordering (i.e., the first value)."
(let ((entries (make-hash-table :test test)))
(flet ((entry (vertex)
"Return the entry for vertex. Each entry is a cons whose
car is the number of outstanding dependencies of vertex
and whose cdr is a list of dependants of vertex."
(multiple-value-bind (entry presentp) (gethash vertex entries)
(if presentp entry
(setf (gethash vertex entries) (cons 0 '()))))))
;; populate entries initially
(dolist (vertex graph)
(destructuring-bind (vertex &rest dependencies) vertex
(let ((ventry (entry vertex)))
(dolist (dependency dependencies)
(let ((dentry (entry dependency)))
(unless (funcall test dependency vertex)
(incf (car ventry))
(push vertex (cdr dentry))))))))
;; L is the list of sorted elements, and S the set of vertices
;; with no outstanding dependencies.
(let ((L '())
(S (loop for entry being each hash-value of entries
using (hash-key vertex)
when (zerop (car entry)) collect vertex)))
;; Until there are no vertices with no outstanding dependencies,
;; process vertices from S, adding them to L.
(do* () ((endp S))
(let* ((v (pop S)) (ventry (entry v)))
(remhash v entries)
(dolist (dependant (cdr ventry) (push v L))
(when (zerop (decf (car (entry dependant))))
(push dependant S)))))
;; return (1) the list of sorted items, (2) whether all items
;; were sorted, and (3) if there were unsorted vertices, the
;; hash table mapping these vertices to their dependants
(let ((all-sorted-p (zerop (hash-table-count entries))))
(values (nreverse L)
all-sorted-p
(unless all-sorted-p
entries)))))))
Provided example in which all items can be sorted:
> (defparameter *dependency-graph*
'((des-system-lib std synopsys std-cell-lib des-system-lib dw02 dw01 ramlib ieee)
(dw01 ieee dw01 dware gtech)
(dw02 ieee dw02 dware)
(dw03 std synopsys dware dw03 dw02 dw01 ieee gtech)
(dw04 dw04 ieee dw01 dware gtech)
(dw05 dw05 ieee dware)
(dw06 dw06 ieee dware)
(dw07 ieee dware)
(dware ieee dware)
(gtech ieee gtech)
(ramlib std ieee)
(std-cell-lib ieee std-cell-lib)
(synopsys)))
*DEPENDENCY-GRAPH*
> (topological-sort *dependency-graph*)
(IEEE DWARE DW02 DW05 DW06 DW07 GTECH DW01 DW04 STD-CELL-LIB SYNOPSYS STD DW03 RAMLIB DES-SYSTEM-LIB)
T
NIL
Provided example with dw04 added to the dependencies of dw01. Some vertices are ordered, but the second return is nil, indicating that not all vertices could be sorted. The third return value is the hash table containing entries for the four vertices that couldn't be sorted. (The variable / stores the list of values produced by the last form, and describe prints information about an object.)
> (defparameter *dependency-graph*
'((des-system-lib std synopsys std-cell-lib des-system-lib dw02 dw01 ramlib ieee)
(dw01 ieee dw01 dw04 dware gtech)
(dw02 ieee dw02 dware)
(dw03 std synopsys dware dw03 dw02 dw01 ieee gtech)
(dw04 dw04 ieee dw01 dware gtech)
(dw05 dw05 ieee dware)
(dw06 dw06 ieee dware)
(dw07 ieee dware)
(dware ieee dware)
(gtech ieee gtech)
(ramlib std ieee)
(std-cell-lib ieee std-cell-lib)
(synopsys)))
*DEPENDENCY-GRAPH*
> (topological-sort *dependency-graph*)
(IEEE DWARE DW02 DW05 DW06 DW07 GTECH STD-CELL-LIB SYNOPSYS STD RAMLIB)
NIL
#<EQL Hash Table{4} 200C9023>
> (describe (third /))
#<EQL Hash Table{4} 200C9023> is a HASH-TABLE
DW01 (1 DW04 DW03 DES-SYSTEM-LIB)
DW04 (1 DW01)
DW03 (1)
DES-SYSTEM-LIB (1)
[edit] E
def makeQueue := <elib:vat.makeQueue>
def topoSort(data :Map[any, Set[any]]) {
# Tables of nodes and edges
def forwardEdges := [].asMap().diverge()
def reverseCount := [].asMap().diverge()
def init(node) {
reverseCount[node] := 0
forwardEdges[node] := [].asSet().diverge()
}
for node => deps in data {
init(node)
for dep in deps { init(dep) }
}
# 'data' holds the dependencies. Compute the other direction.
for node => deps in data {
for dep ? (dep != node) in deps {
forwardEdges[dep].addElement(node)
reverseCount[node] += 1
}
}
# Queue containing all elements that have no (initial or remaining) incoming edges
def ready := makeQueue()
for node => ==0 in reverseCount {
ready.enqueue(node)
}
var result := []
while (ready.optDequeue() =~ node :notNull) {
result with= node
for next in forwardEdges[node] {
# Decrease count of incoming edges and enqueue if none
if ((reverseCount[next] -= 1).isZero()) {
ready.enqueue(next)
}
}
forwardEdges.removeKey(node)
}
if (forwardEdges.size().aboveZero()) {
throw(`Topological sort failed: $forwardEdges remains`)
}
return result
}
pragma.enable("accumulator")
def dataText := "\
des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee
dw01 ieee dw01 dware gtech
dw02 ieee dw02 dware
dw03 std synopsys dware dw03 dw02 dw01 ieee gtech
dw04 dw04 ieee dw01 dware gtech
dw05 dw05 ieee dware
dw06 dw06 ieee dware
dw07 ieee dware
dware ieee dware
gtech ieee gtech
ramlib std ieee
std_cell_lib ieee std_cell_lib
synopsys\
"
def data := accum [].asMap() for rx`(@item.{17})(@deps.*)` in dataText.split("\n") { _.with(item.trim(), deps.split(" ").asSet()) }
println(topoSort(data))
Output: ["std", "synopsys", "ieee", "dware", "gtech", "ramlib", "std_cell_lib", "dw02", "dw05", "dw06", "dw07", "dw01", "des_system_lib", "dw03", "dw04"]
[edit] Haskell
import Data.List
import Data.Maybe
import Control.Arrow
import System.Random
import Control.Monad
combs 0 _ = [[]]
combs _ [] = []
combs k (x:xs) = map (x:) (combs (k-1) xs) ++ combs k xs
depLibs :: [(String, String)]
depLibs = [("des_system_lib","std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee"),
("dw01","ieee dw01 dware gtech"),
("dw02","ieee dw02 dware"),
("dw03","std synopsys dware dw03 dw02 dw01 ieee gtech"),
("dw04","dw04 ieee dw01 dware gtech"),
("dw05","dw05 ieee dware"),
("dw06","dw06 ieee dware"),
("dw07","ieee dware"),
("dware","ieee dware"),
("gtech","ieee gtech"),
("ramlib","std ieee"),
("std_cell_lib","ieee std_cell_lib"),
("synopsys",[])]
toposort xs
| (not.null) cycleDetect = error $ "Dependency cycle detected for libs " ++ show cycleDetect
| otherwise = foldl makePrecede [] dB
where dB = map ((\(x,y) -> (x,y \\ x)). (return *** words)) xs
makePrecede ts ([x],xs) = nub $ case elemIndex x ts of
Just i -> uncurry(++) $ first(++xs) $ splitAt i ts
_ -> ts ++ xs ++ [x]
cycleDetect = filter ((>1).length)
$ map (\[(a,as), (b,bs)] -> (a `intersect` bs) ++ (b `intersect`as))
$ combs 2 dB
output:
*Main> toposort depLibs
["std","synopsys","ieee","std_cell_lib","dware","dw02","gtech","dw01","ramlib","des_system_lib","dw03","dw04","dw05","dw06","dw07"]
*Main> toposort $ (\(xs,(k,ks):ys) -> xs++ (k,ks++" dw04"):ys) $ splitAt 1 depLibs
*** Exception: Dependency cycle detected for libs [["dw01","dw04"]]
[edit] Icon and Unicon
[edit] Icon
This solution uses an efficient internal representation for a graph that limits the number of nodes to no more than 256.
The resulting topological ordering is displayed so elements on each line are independent and so can be built in parallel once the preceding lines of elements have been built.
record graph(nodes,arcs)
global ex_name, in_name
procedure main()
show(tsort(getgraph()))
end
procedure tsort(g)
t := ""
while (n := g.nodes -- pnodes(g)) ~== "" do {
t ||:= "("||n||")"
g := delete(g,n)
}
if g.nodes == '' then return t
write("graph contains the cycle:")
write("\t",genpath(fn := !g.nodes,fn,g))
end
## pnodes(g) -- return the predecessor nodes of g
# (those that have an arc from them)
procedure pnodes(g)
static labels, fromnodes
initial {
labels := &ucase
fromnodes := 'ACEGIKMOQSUWY'
}
return cset(select(g.arcs,labels, fromnodes))
end
## select(s,image,object) - efficient node selection
procedure select(s,image,object)
slen := *s
ilen := *image
return if slen <= ilen then map(object[1+:slen/2],image[1+:slen],s)
else map(object,image,s[1+:ilen]) || select(s[1+ilen:0],image,object)
end
## delete(g,x) -- deletes all nodes in x from graph g
# note that arcs must be deleted as well
procedure delete(g,x)
t := ""
g.arcs ? while arc := move(2) do if not upto(x,arc) then t ||:= arc
return graph(g.nodes--x,t)
end
## getgraph() -- read and construct a graph
# graph is described via sets of arcs, as in:
#
# from to1 to2 to3
#
# external names are converted to single character names for efficiency
# self-referential arcs are ignored
procedure getgraph()
static labels
initial labels := &cset
ex_name := table()
in_name := table()
count := 0
arcstr := ""
nodes := ''
every line := !&input do {
nextWord := create genWords(line)
if nfrom := @nextWord then {
/in_name[nfrom] := &cset[count +:= 1]
/ex_name[in_name[nfrom]] := nfrom
nodes ++:= in_name[nfrom]
while nto := @nextWord do {
if nfrom ~== nto then {
/in_name[nto] := &cset[count +:= 1]
/ex_name[in_name[nto]] := nto
nodes ++:= in_name[nto]
arcstr ||:= in_name[nfrom] || in_name[nto]
}
}
}
}
return graph(nodes,arcstr)
end
# generate all 'words' in string
procedure genWords(s)
static wchars
initial wchars := &cset -- ' \t'
s ? while tab(upto(wchars))\1 do suspend tab(many(wchars))\1
end
## show(t) - return the external names (in order) for the nodes in t
# Each output line contains names that are independent of each other
procedure show(t)
line := ""
every n := !t do
case n of {
"(" : line ||:= "\n\t("
")" : line[-1] := ")"
default : line ||:= ex_name[n] || " "
}
write(line)
end
## genpath(f,t,g) -- generate paths from f to t in g
procedure genpath(f,t,g, seen)
/seen := ''
seen ++:= f
sn := nnodes(f,g)
if t ** sn == t then return ex_name[f] || " -> " || ex_name[t]
suspend ex_name[f] || " -> " || genpath(!(sn --seen),t,g,seen)
end
## nnodes(f,g) -- compute all nodes that could follow f in g
procedure nnodes(f,g)
t := ''
g.arcs ? while arc := move(2) do if arc[1] == f then t ++:= arc[2]
return t
end
Sample output:
->tsort <tsort.data (std synopsys ieee) (std_cell_lib ramlib dware gtech) (dw02 dw01 dw05 dw06 dw07) (des_system_lib dw03 dw04) ->
When run with the cycle suggested in the problem statement:
->tsort <tsort.data
graph contains the cycle:
dw01 -> dw04 -> dw01
->
[edit] Unicon
The Icon solution also works in Unicon, but the following variant removes the 256-node limit by using sets instead of csets with the same algorithm that produces output so each line gives the elements that can be built in parallel once the elements in the preceding lines have been built.
record graph(nodes,arcs)
procedure main()
show(tsort(getgraph()))
end
procedure tsort(g)
t := []
while *(n := g.nodes -- pnodes(g)) > 0 do {
every put(p := [], !n)
put(t, p)
g := delete(g,n)
}
if *g.nodes = 0 then return t
write("graph contains the cycle:")
write("\t",genpath(fn := !g.nodes,fn,g))
end
procedure pnodes(g)
cp := create !g.arcs
every insert(p := set(), |1(@cp,@cp))
return p
end
procedure delete(g,x)
arcs := []
cp := create !g.arcs
while (f := @cp, t := @cp) do {
if !x == (f|t) then next
every put(arcs,f|t)
}
return graph(g.nodes--x, arcs)
end
procedure getgraph()
arcs := []
nodes := set()
every line := !&input do {
nextWord := create genWords(line)
if nfrom := @nextWord then {
insert(nodes, nfrom)
while nto := @nextWord do {
if nfrom ~== nto then {
insert(nodes, nto)
every put(arcs, nfrom | nto)
}
}
}
}
return graph(nodes,arcs)
end
procedure genWords(s)
static wchars
initial wchars := &cset -- ' \t'
s ? while tab(upto(wchars))\1 do suspend tab(many(wchars))\1
end
procedure show(t)
line := ""
every n := !t do
case type(n) of {
"list" : line ||:= "\n\t("||toString(n)||")"
default : line ||:= " "||n
}
write(line)
end
procedure toString(n)
every (s := "") ||:= !n || " "
return s[1:-1] | s
end
procedure genpath(f,t,g, seen)
/seen := set()
insert(seen, f)
sn := nnodes(f,g)
if member(sn, t) then return f || " -> " || t
suspend f || " -> " || genpath(!(sn--seen),t,g,seen)
end
procedure nnodes(f,g)
t := set()
cp := create !g.arcs
while (af := @cp, at := @cp) do if af == f then insert(t, at)
return t
end
[edit] J
dependencySort=: monad define
parsed=. <@;:;._2 y
names=. {.&>parsed
depends=. (> =@i.@#) names e.S:1 parsed
depends=. (+. +./ .*.~)^:_ depends
assert.-.1 e. (<0 1)|:depends
(-.&names ~.;parsed),names /: +/"1 depends
)
With the sample data set:
dependencies=: noun define des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee dw01 ieee dw01 dware gtech dw02 ieee dw02 dware dw03 std synopsys dware dw03 dw02 dw01 ieee gtech dw04 dw04 ieee dw01 dware gtech dw05 dw05 ieee dware dw06 dw06 ieee dware dw07 ieee dware dware ieee dware gtech ieee gtech ramlib std ieee std_cell_lib ieee std_cell_lib synopsys )
We would get:
>dependencySort dependencies std ieee dware gtech ramlib std_cell_lib synopsys dw02 dw05 dw06 dw07 dw01 dw04 dw03 des_system_lib
Here is an alternate implementation which uses a slightly different representation for the dependencies:
depSort=: monad define
parsed=. <@;:;._2 y
names=. {.&>parsed
depends=. (-.L:0"_1 #,.i.@#) names i.L:1 parsed
depends=. (~.@,&.> ;@:{L:0 1~)^:_ depends
assert.-.1 e. (i.@# e.S:0"0 ])depends
(-.&names ~.;parsed),names /: #@> depends
)
It's results are identical to the first implementation, but this might be more efficient in typical cases.
[edit] OCaml
let dep_libs = [
("des_system_lib", ["std"; "synopsys"; "std_cell_lib"; "des_system_lib"; "dw02"; "dw01"; "ramlib"; "ieee"]);
("dw01", (*"dw04"::*)["ieee"; "dw01"; "dware"; "gtech"]);
("dw02", ["ieee"; "dw02"; "dware"]);
("dw03", ["std"; "synopsys"; "dware"; "dw03"; "dw02"; "dw01"; "ieee"; "gtech"]);
("dw04", ["dw04"; "ieee"; "dw01"; "dware"; "gtech"]);
("dw05", ["dw05"; "ieee"; "dware"]);
("dw06", ["dw06"; "ieee"; "dware"]);
("dw07", ["ieee"; "dware"]);
("dware", ["ieee"; "dware"]);
("gtech", ["ieee"; "gtech"]);
("ramlib", ["std"; "ieee"]);
("std_cell_lib", ["ieee"; "std_cell_lib"]);
("synopsys", []);
]
let dep_libs =
let f (lib, deps) = (* remove self dependency *)
(lib,
List.filter (fun d -> d <> lib) deps) in
List.map f dep_libs
let libs = (* list items, each being unique *)
let rec aux acc = function
| [] -> (acc)
| x::xs -> aux (if List.mem x acc then acc else x::acc) xs
in
aux [] (List.flatten(List.map (fun (lib, deps) -> lib::deps) dep_libs))
let get_deps lib =
try (List.assoc lib dep_libs)
with Not_found -> []
let res =
let rec aux acc later todo progress =
match todo, later with
| [], [] -> (List.rev acc)
| [], _ ->
if progress
then aux acc [] later false
else invalid_arg "un-orderable data"
| x::xs, _ ->
let deps = get_deps x in
let ok = List.for_all (fun dep -> List.mem dep acc) deps in
if ok
then aux (x::acc) later xs true
else aux acc (x::later) xs progress
in
let starts, todo = List.partition (fun lib -> get_deps lib = []) libs in
aux starts [] todo false
let () =
print_string "result: \n ";
print_endline (String.concat ", " res);
;;
If dw04 is added to the set of dependencies of dw01 to make the data un-orderable (uncomment it), an exception is raised:
Exception: Invalid_argument "un-orderable data".
[edit] Oz
Using constraint propagation and search:
declare
Deps = unit(
des_system_lib: [std synopsys std_cell_lib des_system_lib
dw02 dw01 ramlib ieee]
dw01: [ieee dw01 dware gtech]
dw02: [ieee dw02 dware]
dw03: [std synopsys dware dw03 dw02 dw01 ieee gtech]
dw04: [dw04 ieee dw01 dware gtech]
dw05: [dw05 ieee dware]
dw06: [dw06 ieee dware]
dw07: [ieee dware]
dware: [ieee dware]
gtech: [ieee gtech]
ramlib: [std ieee]
std_cell_lib: [ieee std_cell_lib]
synopsys:nil
)
%% Describe possible solutions
proc {TopologicalOrder Solution}
FullDeps = {Complete Deps}
in
%% The solution is a record that maps library names
%% to finite domain variables.
%% The smaller the value, the earlier it must be compiled
Solution = {FD.record sol {Arity FullDeps} 1#{Width FullDeps}}
%% for every lib on the left side
{Record.forAllInd FullDeps
proc {$ LibName Dependants}
%% ... and every dependant on the right side
for Dependant in Dependants do
%% propagate compilation order
if Dependant \= LibName then
Solution.LibName >: Solution.Dependant
end
end
end
}
%% enumerate solutions
{FD.distribute naive Solution}
end
%% adds empty list of dependencies for libs that only occur on the right side
fun {Complete Dep}
AllLibs = {Nub {Record.foldL Dep Append nil}}
in
{Adjoin
{List.toRecord unit {Map AllLibs fun {$ L} L#nil end}}
Dep}
end
%% removes duplicates
fun {Nub Xs}
D = {Dictionary.new}
in
for X in Xs do D.X := unit end
{Dictionary.keys D}
end
%% print grouped by parallelizable jobs
proc {PrintSolution Sol}
for I in 1..{Record.foldL Sol Value.max 1} do
for Lib in {Arity {Record.filter Sol fun {$ X} X == I end}} do
{System.printInfo Lib#" "}
end
{System.printInfo "\n"}
end
end
fun {GetOrderedLibs Sol}
{Map
{Sort {Record.toListInd Sol} CompareSecond}
SelectFirst}
end
fun {CompareSecond A B} A.2 < B.2 end
fun {SelectFirst X} X.1 end
in
case {SearchOne TopologicalOrder}
of nil then {System.showInfo "Un-orderable."}
[] [Sol] then
{System.showInfo "A possible topological ordering: "}
{ForAll {GetOrderedLibs Sol} System.showInfo}
{System.showInfo "\nBONUS - grouped by parallelizable compile jobs:"}
{PrintSolution Sol}
end
Output:
A possible topological ordering: synopsys std ieee std_cell_lib ramlib gtech dware dw07 dw06 dw05 dw02 dw01 dw04 dw03 des_system_lib BONUS - grouped by parallelizable compile jobs: ieee std synopsys dware gtech ramlib std_cell_lib dw01 dw02 dw05 dw06 dw07 des_system_lib dw03 dw04
[edit] PicoLisp
(de sortDependencies (Lst)
(setq Lst # Build a flat list
(uniq
(mapcan
'((L)
(put (car L) 'dep (cdr L)) # Store dependencies in 'dep' properties
(copy L) )
(mapcar uniq Lst) ) ) ) # without self-dependencies
(make
(while Lst
(ifn (find '((This) (not (: dep))) Lst) # Found non-depending lib?
(quit "Can't resolve dependencies" Lst)
(del (link @) 'Lst) # Yes: Store in result
(for This Lst # and remove from 'dep's
(=: dep (delete @ (: dep))) ) ) ) ) )
Output:
: (sortDependencies
(quote
(des-system-lib std synopsys std-cell-lib des-system-lib dw02 dw01 ramlib ieee)
(dw01 ieee dw01 dware gtech)
(dw02 ieee dw02 dware)
(dw03 std synopsys dware dw03 dw02 dw01 ieee gtech)
(dw04 dw04 ieee dw01 dware gtech)
(dw05 dw05 ieee dware)
(dw06 dw06 ieee dware)
(dw07 ieee dware)
(dware ieee dware)
(gtech ieee gtech)
(ramlib std ieee)
(std-cell-lib ieee std-cell-lib)
(synopsys) ) )
-> (std synopsys ieee std-cell-lib ramlib dware dw02 gtech dw01 des-system-lib dw03 dw04 dw05 dw06 dw07)
[edit] PureBasic
#EndOfDataMarker$ = "::EndOfData::"
DataSection
;"LIBRARY: [LIBRARY_DEPENDENCY_1 LIBRARY_DEPENDENCY_2 ... LIBRARY_DEPENDENCY_N]
Data.s "des_system_lib: [std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee]"
Data.s "dw01: [ieee dw01 dware gtech]"
;Data.s "dw01: [ieee dw01 dware gtech dw04]" ;comment the previous line and uncomment this one for cyclic dependency
Data.s "dw02: [ieee dw02 dware]"
Data.s "dw03: [std synopsys dware dw03 dw02 dw01 ieee gtech]"
Data.s "dw04: [dw04 ieee dw01 dware gtech]"
Data.s "dw05: [dw05 ieee dware]"
Data.s "dw06: [dw06 ieee dware]"
Data.s "dw07: [ieee dware]"
Data.s "dware: [ieee dware]"
Data.s "gtech: [ieee gtech]"
Data.s "ramlib: [std ieee]"
Data.s "std_cell_lib: [ieee std_cell_lib]"
Data.s "synopsys: nil"
Data.s #EndOfDataMarker$
EndDataSection
Structure DAG_node
Value.s
forRemoval.i ;flag marks elements that should be removed the next time they are accessed
List dependencies.s()
EndStructure
If Not OpenConsole()
MessageRequester("Error","Unable to open console")
End
EndIf
;// initialize Directed Acyclic Graph //
Define i, itemData.s, firstBracketPos
NewList DAG.DAG_node()
Repeat
Read.s itemData
itemData = Trim(itemData)
If itemData <> #EndOfDataMarker$
AddElement(DAG())
;add library
DAG()\Value = Trim(Left(itemData, FindString(itemData, ":", 1) - 1))
;parse library dependencies
firstBracketPos = FindString(itemData, "[", 1)
If firstBracketPos
itemData = Trim(Mid(itemData, firstBracketPos + 1, FindString(itemData, "]", 1) - firstBracketPos - 1))
For i = (CountString(itemData, " ") + 1) To 1 Step -1
AddElement(DAG()\dependencies())
DAG()\dependencies() = StringField(itemData, i, " ")
Next
EndIf
EndIf
Until itemData = #EndOfDataMarker$
;// process DAG //
;create DAG entry for nodes listed in dependencies but without their own entry
NewMap libraries()
ForEach DAG()
ForEach DAG()\dependencies()
libraries(DAG()\dependencies()) = #True
If DAG()\dependencies() = DAG()\Value
DeleteElement(DAG()\dependencies()) ;remove self-dependencies
EndIf
Next
Next
ForEach DAG()
If FindMapElement(libraries(),DAG()\Value)
DeleteMapElement(libraries(),DAG()\Value)
EndIf
Next
ResetList(DAG())
ForEach libraries()
AddElement(DAG())
DAG()\Value = MapKey(libraries())
Next
ClearMap(libraries())
;process DAG() repeatedly until no changes occur
NewList compileOrder.s()
Repeat
noChangesMade = #True
ForEach DAG()
If DAG()\forRemoval
DeleteElement(DAG())
Else
;remove dependencies that have been placed in the compileOrder
ForEach DAG()\dependencies()
If FindMapElement(libraries(),DAG()\dependencies())
DeleteElement(DAG()\dependencies())
EndIf
Next
;add DAG() entry to compileOrder if it has no more dependencies
If ListSize(DAG()\dependencies()) = 0
AddElement(compileOrder())
compileOrder() = DAG()\Value
libraries(DAG()\Value) = #True ;mark the library for removal as a dependency
DAG()\forRemoval = #True
noChangesMade = #False
EndIf
EndIf
Next
Until noChangesMade
If ListSize(DAG())
PrintN("Cyclic dependencies detected in:" + #CRLF$)
ForEach DAG()
PrintN(" " + DAG()\Value)
Next
Else
PrintN("Compile order:" + #CRLF$)
ForEach compileOrder()
PrintN(" " + compileOrder())
Next
EndIf
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
Input()
CloseConsole()
Sample output for no dependencies:
Compile order: ieee std dware gtech ramlib std_cell_lib synopsys dw01 dw02 dw03 dw04 dw05 dw06 dw07 des_system_lib
Sample output when cyclic dependencies are present:
Cyclic dependencies detected in: des_system_lib dw01 dw03 dw04
[edit] Python
try:
from functools import reduce
except:
pass
from pprint import pprint as pp
from copy import deepcopy
class CyclicDependencyError(Exception): pass
data = {
'des_system_lib': set('std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee'.split()),
'dw01': set('ieee dw01 dware gtech'.split()),
'dw02': set('ieee dw02 dware'.split()),
'dw03': set('std synopsys dware dw03 dw02 dw01 ieee gtech'.split()),
'dw04': set('dw04 ieee dw01 dware gtech'.split()),
'dw05': set('dw05 ieee dware'.split()),
'dw06': set('dw06 ieee dware'.split()),
'dw07': set('ieee dware'.split()),
'dware': set('ieee dware'.split()),
'gtech': set('ieee gtech'.split()),
'ramlib': set('std ieee'.split()),
'std_cell_lib': set('ieee std_cell_lib'.split()),
'synopsys': set(),
}
def toposort(dependencies):
givenchildren = set(dependencies.keys())
givenparents = reduce(set.union,
( set(parents)
for parents in dependencies.values() )
)
data = deepcopy(dependencies)
# Every parent is also a child, sometimes of nothing.
originalchildren = givenparents - givenchildren
for child in originalchildren:
data[child] = set() # No parents
# Self dependencies are no dependencies
for child, parents in data.items():
parents.discard(child)
order = []
while data:
nocurrentdependencies = [child
for child, parents in data.items()
if not parents]
if not nocurrentdependencies and data:
#raise CyclicDependencyError("Does not involve items: %s" % order)
raise CyclicDependencyError("Involving items from: %s" % data.keys())
order += sorted(nocurrentdependencies)
nocurrentdependencies = set(nocurrentdependencies)
for parents in data.values():
parents -= nocurrentdependencies
for child in nocurrentdependencies:
del data[child]
return order
print (', '.join( toposort(data) ))
Ordered output:
ieee, std, synopsys, dware, gtech, ramlib, std_cell_lib, dw01, dw02, dw05, dw06, dw07, des_system_lib, dw03, dw04
If dw04 is added to the set of dependencies of dw01 to make the data un-orderable, an exception is raised:
Traceback (most recent call last):
File "C:\Documents and Settings\All Users\Documents\Paddys\topological_sort.py", line 77, in <module>
print (', '.join( toposort(data) ))
File "C:\Documents and Settings\All Users\Documents\Paddys\topological_sort.py", line 67, in toposort
raise CyclicDependencyError("Involving items from: %s" % data.keys())
CyclicDependencyError: Involving items from: ['des_system_lib', 'dw04', 'dw03', 'dw01']
[edit] R
First make the list
deps <- list(
"des_system_lib" = c("std", "synopsys", "std_cell_lib", "des_system_lib", "dw02", "dw01", "ramlib", "ieee"),
"dw01" = c("ieee", "dw01", "dware", "gtech", "dw04"),
"dw02" = c("ieee", "dw02", "dware"),
"dw03" = c("std", "synopsys", "dware", "dw03", "dw02", "dw01", "ieee", "gtech"),
"dw04" = c("dw04", "ieee", "dw01", "dware", "gtech"),
"dw05" = c("dw05", "ieee", "dware"),
"dw06" = c("dw06", "ieee", "dware"),
"dw07" = c("ieee", "dware"),
"dware" = c("ieee", "dware"),
"gtech" = c("ieee", "gtech"),
"ramlib" = c("std", "ieee"),
"std_cell_lib" = c("ieee", "std_cell_lib"),
"synopsys" = c())
Topological sort function. It will throw an error if it cannot complete, printing the list of items which cannot be ordered. If it succeeds, returns the list of items in topological order.
tsort <- function(deps) {
nm <- names(deps)
libs <- union(as.vector(unlist(deps)), nm)
s <- c()
# first libs that depend on nothing
for(x in libs) {
if(!(x %in% nm)) {
s <- c(s, x)
}
}
k <- 1
while(k > 0) {
k <- 0
for(x in setdiff(nm, s)) {
r <- c(s, x)
if(length(setdiff(deps[[x]], r)) == 0) {
s <- r
k <- 1
}
}
}
if(length(s) < length(libs)) {
v <- setdiff(libs, s)
stop(sprintf("Unorderable items :\n%s", paste("", v, sep="", collapse="\n")))
}
s
}
On the given example :
tsort(deps)
# [1] "std" "ieee" "dware" "gtech" "ramlib"
# [6] "std_cell_lib" "synopsys" "dw01" "dw02" "dw03"
#[11] "dw04" "dw05" "dw06" "dw07" "des_system_lib"
If dw01 depends on dw04 as well :
Unorderable items :
des_system_lib
dw01
dw04
dw03
[edit] Ruby
Uses the TSort module from the Ruby stdlib.
require 'tsort'
class Hash
include TSort
alias tsort_each_node each_key
def tsort_each_child(node, &block)
fetch(node).each(&block)
end
end
depends = {}
DATA.each do |line|
libs = line.split(' ')
key = libs.shift
depends[key] = libs
libs.each {|lib| depends[lib] ||= []}
end
begin
p depends.tsort
depends["dw01"] << "dw04"
p depends.tsort
rescue TSort::Cyclic => e
puts "cycle detected: #{e}"
end
__END__
des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee
dw01 ieee dw01 dware gtech
dw02 ieee dw02 dware
dw03 std synopsys dware dw03 dw02 dw01 ieee gtech
dw04 dw04 ieee dw01 dware gtech
dw05 dw05 ieee dware
dw06 dw06 ieee dware
dw07 ieee dware
dware ieee dware
gtech ieee gtech
ramlib std ieee
std_cell_lib ieee std_cell_lib
synopsys
Produces:
["ieee", "dware", "gtech", "dw01", "dw02", "std", "synopsys", "dw03", "dw04", "dw05", "std_cell_lib", "ramlib", "des_system_lib", "dw06", "dw07"] cycle detected: topological sort failed: ["dw01", "dw04"]
[edit] Tcl
Works with: Tcl version 8.5
package require Tcl 8.5
proc topsort {data} {
# Clean the data
dict for {node depends} $data {
if {[set i [lsearch -exact $depends $node]] >= 0} {
set depends [lreplace $depends $i $i]
dict set data $node $depends
}
foreach node $depends {dict lappend data $node}
}
# Do the sort
set sorted {}
while 1 {
# Find available nodes
set avail [dict keys [dict filter $data value {}]]
if {![llength $avail]} {
if {[dict size $data]} {
error "graph is cyclic, possibly involving nodes \"[dict keys $data]\""
}
return $sorted
}
# Note that the lsort is only necessary for making the results more like other langs
lappend sorted {*}[lsort $avail]
# Remove from working copy of graph
dict for {node depends} $data {
foreach n $avail {
if {[set i [lsearch -exact $depends $n]] >= 0} {
set depends [lreplace $depends $i $i]
dict set data $node $depends
}
}
}
foreach node $avail {
dict unset data $node
}
}
}
Demonstration code (which parses it from the format that the puzzle was posed in):
set inputData {
des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee
dw01 ieee dw01 dware gtech
dw02 ieee dw02 dware
dw03 std synopsys dware dw03 dw02 dw01 ieee gtech
dw04 dw04 ieee dw01 dware gtech
dw05 dw05 ieee dware
dw06 dw06 ieee dware
dw07 ieee dware
dware ieee dware
gtech ieee gtech
ramlib std ieee
std_cell_lib ieee std_cell_lib
synopsys
}
foreach line [split $inputData \n] {
if {[string trim $line] eq ""} continue
dict set parsedData [lindex $line 0] [lrange $line 1 end]
}
puts [topsort $parsedData]
Sample output:
ieee std synopsys dware gtech ramlib std_cell_lib dw01 dw02 dw05 dw06 dw07 des_system_lib dw03 dw04
If the suggested extra arc is added, this is the error output:
graph is cyclic, possibly involving nodes "des_system_lib dw01 dw03 dw04"
[edit] UNIX Shell
The unix tsort utility does a topological sort where dependencies on multiple items must be reformatted as multiple lines of dependencies of an item and only one dependant.
bash$ tsort <<!
> des_system_lib des_system_lib
> des_system_lib dw01
> des_system_lib dw02
> des_system_lib ieee
> des_system_lib ramlib
> des_system_lib std
> des_system_lib std_cell_lib
> des_system_lib synopsys
> dw01 dw01
> dw01 dware
> dw01 gtech
> dw01 ieee
> dw02 dw02
> dw02 dware
> dw02 ieee
> dw03 dw01
> dw03 dw02
> dw03 dw03
> dw03 dware
> dw03 gtech
> dw03 ieee
> dw03 std
> dw03 synopsys
> dw04 dw01
> dw04 dw04
> dw04 dware
> dw04 gtech
> dw04 ieee
> dw05 dw05
> dw05 dware
> dw05 ieee
> dw06 dw06
> dw06 dware
> dw06 ieee
> dw07 dware
> dw07 ieee
> dware dware
> dware ieee
> gtech gtech
> gtech ieee
> ramlib ieee
> ramlib std
> std_cell_lib ieee
> std_cell_lib std_cell_lib
!
des_system_lib
dw03
dw04
dw05
dw06
dw07
std_cell_lib
ramlib
synopsys
dw02
dw01
std
gtech
dware
ieee
bash$
[edit] Ursala
The tsort function takes a list of pairs <(lib: <dep...>)...> and returns a pair of lists (<lib...>,<lib...>) with the topologically sorted libraries on the left and the unorderable libraries, if any, on the right. Self-dependences are ignored and unlisted libraries are presumed independent.
tsort = ~&nmnNCjA*imSLs2nSjiNCSPT; @NiX ^=lxPrnSPX ^(~&rlPlT,~&rnPrmPljA*D@r)^|/~& ~&m!=rnSPlX
test program:
#import std
dependence_table = -[
LIBRARY LIBRARY DEPENDENCIES
======= ====================
des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee
dw01 ieee dw01 dware gtech
dw02 ieee dw02 dware
dw03 std synopsys dware dw03 dw02 dw01 ieee gtech
dw04 dw04 ieee dw01 dware gtech
dw05 dw05 ieee dware
dw06 dw06 ieee dware
dw07 ieee dware
dware ieee dware
gtech ieee gtech
ramlib std ieee
std_cell_lib ieee std_cell_lib
synopsys ]-
parse = ~&htA*FS+ sep` *tttt
#show+
main = <.~&l,@r ~&i&& 'unorderable: '--> mat` ~~ tsort parse dependence_table
With the given table, the output is
std ieee synopsys std_cell_lib ramlib gtech dware dw07 dw06 dw05 dw02 dw01 dw04 dw03 des_system_lib
When the suggested dependence is added, the output becomes
std ieee synopsys std_cell_lib ramlib gtech dware dw07 dw06 dw05 dw02 unorderable: des_system_lib dw01 dw03 dw04
[edit] VBScript
[edit] Implementation
class topological
dim dictDependencies
dim dictReported
dim depth
sub class_initialize
set dictDependencies = createobject("Scripting.Dictionary")
set dictReported = createobject("Scripting.Dictionary")
depth = 0
end sub
sub reset
dictReported.removeall
end sub
property let dependencies( s )
'assuming token tab token-list newline
dim i, j ,k
dim aList
dim dep
dim a1
aList = Split( s, vbNewLine )
'~ remove empty lines at end
do while aList( UBound( aList ) ) = vbnullstring
redim preserve aList( UBound( aList ) - 1 )
loop
for i = lbound( aList ) to ubound( aList )
aList( i ) = Split( aList( i ), vbTab, 2 )
a1 = Split( aList( i )( 1 ), " " )
k = 0
for j = lbound( a1) to ubound(a1)
if a1(j) <> aList(i)(0) then
a1(k) = a1(j)
k = k + 1
end if
next
redim preserve a1(k-1)
aList(i)(1) = a1
next
for i = lbound( aList ) to ubound( aList )
dep = aList(i)(0)
if not dictDependencies.Exists( dep ) then
dictDependencies.add dep, aList(i)(1)
end if
next
end property
sub resolve( s )
dim i
dim deps
'~ wscript.echo string(depth,"!"),s
depth = depth + 1
if dictDependencies.Exists(s) then
deps = dictDependencies(s)
for i = lbound(deps) to ubound(deps)
resolve deps(i)
next
end if
if not seen(s) then
wscript.echo s
see s
end if
depth = depth - 1
end sub
function seen( key )
seen = dictReported.Exists( key )
end function
sub see( key )
dictReported.add key, ""
end sub
property get keys
keys = dictDependencies.keys
end property
end class
[edit] Invocation
dim toposort
set toposort = new topological
toposort.dependencies = "des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee" & vbNewLine & _
"dw01 ieee dw01 dware gtech" & vbNewLine & _
"dw02 ieee dw02 dware" & vbNewLine & _
"dw03 std synopsys dware dw03 dw02 dw01 ieee gtech" & vbNewLine & _
"dw04 dw04 ieee dw01 dware gtech" & vbNewLine & _
"dw05 dw05 ieee dware" & vbNewLine & _
"dw06 dw06 ieee dware" & vbNewLine & _
"dw07 ieee dware" & vbNewLine & _
"dware ieee dware" & vbNewLine & _
"gtech ieee gtech" & vbNewLine & _
"ramlib std ieee" & vbNewLine & _
"std_cell_lib ieee std_cell_lib" & vbNewLine & _
"synopsys "
dim k
for each k in toposort.keys
wscript.echo "----- " & k
toposort.resolve k
wscript.echo "-----"
toposort.reset
next
[edit] Output
----- des_system_lib std synopsys ieee std_cell_lib dware dw02 gtech dw01 ramlib des_system_lib ----- ----- dw01 ieee dware gtech dw01 ----- ----- dw02 ieee dware dw02 ----- ----- dw03 std synopsys ieee dware dw02 gtech dw01 dw03 ----- ----- dw04 ieee dware gtech dw01 dw04 ----- ----- dw05 ieee dware dw05 ----- ----- dw06 ieee dware dw06 ----- ----- dw07 ieee dware dw07 ----- ----- dware ieee dware ----- ----- gtech ieee gtech ----- ----- ramlib std ieee ramlib ----- ----- std_cell_lib ieee std_cell_lib ----- ----- synopsys synopsys -----
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