Topological sort

From Rosetta Code
Task
Topological sort
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.


Task;

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 dependents, (sic), have no dependents 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.


C.f.


There are two popular algorithms for topological sorting: Kahn's 1962 topological sort, and depth-first search. [1][2]

Ada[edit]

Digraphs: A package for directed graphs, representing nodes as positive numbers

The specification:

with Ada.Containers.Vectors; use Ada.Containers;
 
package Digraphs is
 
type Node_Idx_With_Null is new Natural;
subtype Node_Index is Node_Idx_With_Null range 1 .. Node_Idx_With_Null'Last;
-- a Node_Index is a number from 1, 2, 3, ... and the representative of a node
 
type Graph_Type is tagged private;
 
-- make sure Node is in Graph (possibly without connections)
procedure Add_Node
(Graph: in out Graph_Type'Class; Node: Node_Index);
 
-- insert an edge From->To into Graph; do nothing if already there
procedure Add_Connection
(Graph: in out Graph_Type'Class; From, To: Node_Index);
 
-- get the largest Node_Index used in any Add_Node or Add_Connection op.
-- iterate over all nodes of Graph: "for I in 1 .. Graph.Node_Count loop ..."
function Node_Count(Graph: Graph_Type) return Node_Idx_With_Null;
 
-- remove an edge From->To from Fraph; do nothing if not there
-- Graph.Node_Count is not changed
procedure Del_Connection
(Graph: in out Graph_Type'Class; From, To: Node_Index);
 
-- check if an edge From->to exists in Graph
function Connected
(Graph: Graph_Type; From, To: Node_Index) return Boolean;
 
-- data structure to store a list of nodes
package Node_Vec is new Vectors(Positive, Node_Index);
 
-- get a list of all nodes From->Somewhere in Graph
function All_Connections
(Graph: Graph_Type; From: Node_Index) return Node_Vec.Vector;
 
Graph_Is_Cyclic: exception;
 
-- a depth-first search to find a topological sorting of the nodes
-- raises Graph_Is_Cyclic if no topological sorting is possible
function Top_Sort
(Graph: Graph_Type) return Node_Vec.Vector;
 
private
 
package Conn_Vec is new Vectors(Node_Index, Node_Vec.Vector, Node_Vec."=");
 
type Graph_Type is new Conn_Vec.Vector with null record;
 
end Digraphs;

The implementation:

package body Digraphs is
 
function Node_Count(Graph: Graph_Type) return Node_Idx_With_Null is
begin
return Node_Idx_With_Null(Graph.Length);
end Node_Count;
 
procedure Add_Node(Graph: in out Graph_Type'Class; Node: Node_Index) is
begin
for I in Node_Index range Graph.Node_Count+1 .. Node loop
Graph.Append(Node_Vec.Empty_Vector);
end loop;
end Add_Node;
 
procedure Add_Connection
(Graph: in out Graph_Type'Class; From, To: Node_Index) is
begin
Graph.Add_Node(Node_Index'Max(From, To));
declare
Connection_List: Node_Vec.Vector := Graph.Element(From);
begin
for I in Connection_List.First_Index .. Connection_List.Last_Index loop
if Connection_List.Element(I) >= To then
if Connection_List.Element(I) = To then
return; -- if To is already there, don't add it a second time
else -- I is the first index with Element(I)>To, insert To here
Connection_List.Insert(Before => I, New_Item => To);
Graph.Replace_Element(From, Connection_List);
return;
end if;
end if;
end loop;
-- there was no I with no Element(I) > To, so insert To at the end
Connection_List.Append(To);
Graph.Replace_Element(From, Connection_List);
return;
end;
end Add_Connection;
 
procedure Del_Connection
(Graph: in out Graph_Type'Class; From, To: Node_Index) is
Connection_List: Node_Vec.Vector := Graph.Element(From);
begin
for I in Connection_List.First_Index .. Connection_List.Last_Index loop
if Connection_List.Element(I) = To then
Connection_List.Delete(I);
Graph.Replace_Element(From, Connection_List);
return; -- we are done
end if;
end loop;
end Del_Connection;
 
function Connected
(Graph: Graph_Type; From, To: Node_Index) return Boolean is
Connection_List: Node_Vec.Vector renames Graph.Element(From);
begin
for I in Connection_List.First_Index .. Connection_List.Last_Index loop
if Connection_List.Element(I) = To then
return True;
end if;
end loop;
return False;
end Connected;
 
function All_Connections
(Graph: Graph_Type; From: Node_Index) return Node_Vec.Vector is
begin
return Graph.Element(From);
end All_Connections;
 
function Top_Sort
(Graph: Graph_Type) return Node_Vec.Vector is
 
Result: Node_Vec.Vector;
Visited: array(1 .. Graph.Node_Count) of Boolean := (others => False);
Active: array(1 .. Graph.Node_Count) of Boolean := (others => False);
 
procedure Visit(Node: Node_Index) is
begin
if not Visited(Node) then
Visited(Node) := True;
Active(Node)  := True;
declare
Cons: Node_Vec.Vector := All_Connections(Graph, Node);
begin
for Idx in Cons.First_Index .. Cons.Last_Index loop
Visit(Cons.Element(Idx));
end loop;
end;
Active(Node) := False;
Result.Append(Node);
else
if Active(Node) then
raise Constraint_Error with "Graph is Cyclic";
end if;
end if;
end Visit;
 
begin
for Some_Node in Visited'Range loop
Visit(Some_Node);
end loop;
return Result;
end Top_Sort;
 
end Digraphs;

Set_of_Names: Translating strings into numbers and vice versa

The specification:

private with Ada.Containers.Indefinite_Vectors;
 
generic
type Index_Type_With_Null is new Natural;
package Set_Of_Names is
subtype Index_Type is Index_Type_With_Null
range 1 .. Index_Type_With_Null'Last;
-- manage a set of strings;
-- each string in the set is assigned a unique index of type Index_Type
 
type Set is tagged private;
 
-- inserts Name into Names; do nothing if already there;
procedure Add(Names: in out Set; Name: String);
 
-- Same operation, additionally emiting Index=Names.Idx(Name)
procedure Add(Names: in out Set; Name: String; Index: out Index_Type);
 
-- remove Name from Names; do nothing if not found
-- the removal may change the index of other strings in Names
procedure Sub(Names: in out Set; Name: String);
 
-- returns the unique index of Name in Set; or 0 if Name is not there
function Idx(Names: Set; Name: String) return Index_Type_With_Null;
 
-- returns the unique name of Index;
function Name(Names: Set; Index: Index_Type) return String;
 
-- first index, last index and total number of names in set
-- to iterate over Names, use "for I in Names.Start .. Names.Stop loop ...
function Start(Names: Set) return Index_Type;
function Stop(Names: Set) return Index_Type_With_Null;
function Size(Names: Set) return Index_Type_With_Null;
 
private
 
package Vecs is new Ada.Containers.Indefinite_Vectors
(Index_Type => Index_Type, Element_Type => String);
 
type Set is new Vecs.Vector with null record;
 
end Set_Of_Names;

The implementation

package body Set_Of_Names is
 
use type Ada.Containers.Count_Type, Vecs.Cursor;
 
function Start(Names: Set) return Index_Type is
begin
if Names.Length = 0 then
return 1;
else
return Names.First_Index;
end if;
end Start;
 
function Stop(Names: Set) return Index_Type_With_Null is
begin
if Names.Length=0 then
return 0;
else
return Names.Last_Index;
end if;
end Stop;
 
function Size(Names: Set) return Index_Type_With_Null is
begin
return Index_Type_With_Null(Names.Length);
end Size;
 
procedure Add(Names: in out Set; Name: String; Index: out Index_Type) is
I: Index_Type_With_Null := Names.Idx(Name);
begin
if I = 0 then -- Name is not yet in Set
Names.Append(Name);
Index := Names.Stop;
else
Index := I;
end if;
end Add;
 
procedure Add(Names: in out Set; Name: String) is
I: Index_Type;
begin
Names.Add(Name, I);
end Add;
 
procedure Sub(Names: in out Set; Name: String) is
I: Index_Type_With_Null := Names.Idx(Name);
begin
if I /= 0 then -- Name is in set
Names.Delete(I);
end if;
end Sub;
 
function Idx(Names: Set; Name: String) return Index_Type_With_Null is
begin
for I in Names.First_Index .. Names.Last_Index loop
if Names.Element(I) = Name then
return I;
end if;
end loop;
return 0;
end Idx;
 
function Name(Names: Set; Index: Index_Type) return String is
begin
return Names.Element(Index);
end Name;
 
end Set_Of_Names;

Toposort: Putting things together for the main program

with Ada.Text_IO, Digraphs, Set_Of_Names, Ada.Command_Line;
 
procedure Toposort is
 
-- shortcuts for package names, intantiation of generic package
package TIO renames Ada.Text_IO;
package DG renames Digraphs;
package SN is new Set_Of_Names(DG.Node_Idx_With_Null);
 
-- reat the graph from the file with the given Filename
procedure Read(Filename: String; G: out DG.Graph_Type; N: out SN.Set) is
 
-- finds the first word in S(Start .. S'Last), delimited by spaces
procedure Find_Token(S: String; Start: Positive;
First: out Positive; Last: out Natural) is
 
begin
First := Start;
while First <= S'Last and then S(First)= ' ' loop
First := First + 1;
end loop;
Last := First-1;
while Last < S'Last and then S(Last+1) /= ' ' loop
Last := Last + 1;
end loop;
end Find_Token;
 
File: TIO.File_Type;
begin
TIO.Open(File, TIO.In_File, Filename);
TIO.Skip_Line(File, 2);
-- the first two lines contain header and "===...==="
while not TIO.End_Of_File(File) loop
declare
Line: String := TIO.Get_Line(File);
First: Positive;
Last: Natural;
To, From: DG.Node_Index;
begin
Find_Token(Line, Line'First, First, Last);
if Last >= First then
N.Add(Line(First .. Last), From);
G.Add_Node(From);
loop
Find_Token(Line, Last+1, First, Last);
exit when Last < First;
N.Add(Line(First .. Last), To);
G.Add_Connection(From, To);
end loop;
end if;
end;
end loop;
TIO.Close(File);
end Read;
 
Graph: DG.Graph_Type;
Names: SN.Set;
 
begin
Read(Ada.Command_Line.Argument(1), Graph, Names);
 
-- eliminat self-cycles
for Start in 1 .. Graph.Node_Count loop
Graph.Del_Connection(Start, Start);
end loop;
 
-- perform the topological sort and output the result
declare
Result: DG.Node_Vec.Vector;
begin
Result := Graph.Top_Sort;
for Index in Result.First_Index .. Result.Last_Index loop
TIO.Put(Names.Name(Result.Element(Index)));
if Index < Result.Last_Index then
TIO.Put(" -> ");
end if;
end loop;
TIO.New_Line;
exception
when DG.Graph_Is_Cyclic =>
TIO.Put_Line("There is no topological sorting -- the Graph is cyclic!");
end;
end Toposort;
Output:

Given the name of the file with the dependencies as the parameter, Toposort generates the following output:

std -> synopsys -> ieee -> std_cell_lib -> dware -> dw02 -> gtech -> dw01 -> ramlib ->  des_system_lib -> dw03 -> dw04 -> dw05 -> dw06 -> dw07

If the dependencies is circular, the the Toposort tells that:

There is no topological sorting -- the Graph is cyclic!

Bracmat[edit]

(     ("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.)
(cycle-11.cycle-12)
(cycle-12.cycle-11)
(cycle-21.dw01 cycle-22 dw02 dw03)
(cycle-22.cycle-21 dw01 dw04)
 : ?libdeps
& :?indeps
& ( toposort
= A Z res module dependants todo done
.  !arg:(?todo.?done)
& ( areDone
=
.  !arg:
|  !arg
 : ( %@
 : [%( !module+!done+!indeps:?+(? !sjt ?)+?
| ~(!libdeps:? (!sjt.?) ?)
& !sjt !indeps:?indeps
)
)
 ?arg
& areDone$!arg
)
& (  !todo
 :  ?A
(?module.?dependants&areDone$!dependants)
( ?Z
& toposort$(!A !Z.!done !module):?res
)
& !res
| (!todo.!done)
)
)
& toposort$(!libdeps.):(?cycles.?res)
& out$("
compile order:" !indeps !res "\ncycles:" !cycles)
);
Output:
compile order:
  ieee
  std
  dware
  dw02
  dw05
  dw06
  dw07
  gtech
  dw01
  dw04
  ramlib
  std_cell_lib
  synopsys
  des_system_lib
  dw03

cycles:
  (cycle-11.cycle-12)
  (cycle-12.cycle-11)
  (cycle-21.dw01 cycle-22 dw02 dw03)
  (cycle-22.cycle-21 dw01 dw04)

C[edit]

Parses a multiline string and show the compile order. Note that four lines were added to the example input to form two separate cycles. Code is a little ugly.

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
 
char input[] =
"des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee\n"
"dw01 ieee dw01 dware gtech\n"
"dw02 ieee dw02 dware\n"
"dw03 std synopsys dware dw03 dw02 dw01 ieee gtech\n"
"dw04 dw04 ieee dw01 dware gtech\n"
"dw05 dw05 ieee dware\n"
"dw06 dw06 ieee dware\n"
"dw07 ieee dware\n"
"dware ieee dware\n"
"gtech ieee gtech\n"
"ramlib std ieee\n"
"std_cell_lib ieee std_cell_lib\n"
"synopsys\n"
"cycle_11 cycle_12\n"
"cycle_12 cycle_11\n"
"cycle_21 dw01 cycle_22 dw02 dw03\n"
"cycle_22 cycle_21 dw01 dw04";
 
typedef struct item_t item_t, *item;
struct item_t { const char *name; int *deps, n_deps, idx, depth; };
 
int get_item(item *list, int *len, const char *name)
{
int i;
item lst = *list;
 
for (i = 0; i < *len; i++)
if (!strcmp(lst[i].name, name)) return i;
 
lst = *list = realloc(lst, ++*len * sizeof(item_t));
i = *len - 1;
memset(lst + i, 0, sizeof(item_t));
lst[i].idx = i;
lst[i].name = name;
return i;
}
 
void add_dep(item it, int i)
{
if (it->idx == i) return;
it->deps = realloc(it->deps, (it->n_deps + 1) * sizeof(int));
it->deps[it->n_deps++] = i;
}
 
int parse_input(item *ret)
{
int n_items = 0;
int i, parent, idx;
item list = 0;
 
char *s, *e, *word, *we;
for (s = input; ; s = 0) {
if (!(s = strtok_r(s, "\n", &e))) break;
 
for (i = 0, word = s; ; i++, word = 0) {
if (!(word = strtok_r(word, " \t", &we))) break;
idx = get_item(&list, &n_items, word);
 
if (!i) parent = idx;
else add_dep(list + parent, idx);
}
}
 
*ret = list;
return n_items;
}
 
/* recursively resolve compile order; negative means loop */
int get_depth(item list, int idx, int bad)
{
int max, i, t;
 
if (!list[idx].deps)
return list[idx].depth = 1;
 
if ((t = list[idx].depth) < 0) return t;
 
list[idx].depth = bad;
for (max = i = 0; i < list[idx].n_deps; i++) {
if ((t = get_depth(list, list[idx].deps[i], bad)) < 0) {
max = t;
break;
}
if (max < t + 1) max = t + 1;
}
return list[idx].depth = max;
}
 
int main()
{
int i, j, n, bad = -1, max, min;
item items;
n = parse_input(&items);
 
for (i = 0; i < n; i++)
if (!items[i].depth && get_depth(items, i, bad) < 0) bad--;
 
for (i = 0, max = min = 0; i < n; i++) {
if (items[i].depth > max) max = items[i].depth;
if (items[i].depth < min) min = items[i].depth;
}
 
printf("Compile order:\n");
for (i = min; i <= max; i++) {
if (!i) continue;
 
if (i < 0) printf(" [unorderable]");
else printf("%d:", i);
 
for (j = 0; j < n || !putchar('\n'); j++)
if (items[j].depth == i)
printf(" %s", items[j].name);
}
 
return 0;
}
Output:
(items on the same row can be compiled together)
Compile order:
[unorderable] cycle_21 cycle_22
[unorderable] cycle_11 cycle_12
1: std synopsys ieee
2: std_cell_lib ramlib dware gtech
3: dw02 dw01 dw05 dw06 dw07
4: des_system_lib dw03 dw04

C++[edit]

Using the same input string as the C solution. C++11 neccessary.

#include <unordered_map>
#include <string>
#include <sstream>
#include <vector>
#include <iostream>
 
using namespace std;
 
string input = {
"des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee\n"
"dw01 ieee dw01 dware gtech\n"
"dw02 ieee dw02 dware\n"
"dw03 std synopsys dware dw03 dw02 dw01 ieee gtech\n"
"dw04 dw04 ieee dw01 dware gtech\n"
"dw05 dw05 ieee dware\n"
"dw06 dw06 ieee dware\n"
"dw07 ieee dware\n"
"dware ieee dware\n"
"gtech ieee gtech\n"
"ramlib std ieee\n"
"std_cell_lib ieee std_cell_lib\n"
"synopsys\n"
"cycle_11 cycle_12\n"
"cycle_12 cycle_11\n"
"cycle_21 dw01 cycle_22 dw02 dw03\n"
"cycle_22 cycle_21 dw01 dw04" };
 
class TopSort {
 
public:
TopSort(const string& input){
stringstream ss(input);
string buf;
 
while(getline(ss, buf)){
stringstream ls(buf);
string target, subtarget;
ls >> target;
 
while(ls >> subtarget){
if(target.compare(subtarget) == 0)
continue;
 
dependencies.emplace(subtarget, 0);
parents[subtarget].push_back(target);
++dependencies[target];
}
}
}
 
void solve(){
for(const auto& pair : dependencies)
if(pair.second == 0)
sorted.push_back(pair.first);
 
for(unsigned int i = 0; i < sorted.size(); ++i){
string target = sorted[i];
 
for(string& parent : parents[target])
if(--dependencies[parent] == 0)
sorted.push_back(parent);
}
 
for(const auto& pair : dependencies)
if(pair.second != 0)
unorderable.push_back(pair.first);
}
 
friend ostream& operator<<(ostream& os, const TopSort& ts) {
for(const string& s : ts.sorted)
os << s << endl;
if(ts.unorderable.size() > 0){
cout << "Unorderable:" << endl;
for(const string& s : ts.unorderable)
os << s << endl;
}
return os;
}
 
private:
 
vector<string> sorted;
vector<string> unorderable;
 
unordered_map<string, int> dependencies;
unordered_map<string, vector<string>> parents;
};
 
int main () {
TopSort ts(input);
ts.solve();
cout << ts;
}

Clojure[edit]

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.

Implementation[edit]
(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))
=====
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)"

CoffeeScript[edit]

 
toposort = (targets) ->
# targets is hash of sets, where keys are parent nodes and
# where values are sets that contain nodes that must precede the parent
 
# Start by identifying obviously independent nodes
independents = []
do ->
for k of targets
if targets[k].cnt == 0
delete targets[k]
independents.push k
 
# Note reverse dependencies for theoretical O(M+N) efficiency.
reverse_deps = []
do ->
for k of targets
for child of targets[k].v
reverse_deps[child] ?= []
reverse_deps[child].push k
 
# Now be greedy--start with independent nodes, then start
# breaking dependencies, and keep going as long as we still
# have independent nodes left.
result = []
while independents.length > 0
k = independents.pop()
result.push k
for parent in reverse_deps[k] or []
set_remove targets[parent], k
if targets[parent].cnt == 0
independents.push parent
delete targets[parent]
 
# Show unresolvable dependencies
for k of targets
console.log "WARNING: node #{k} is part of cyclical dependency"
result
 
parse_deps = ->
# parse string data, remove self-deps, and fill in gaps
#
# e.g. this would transform {a: "a b c", d: "e"} to this:
# a: set(b, c)
# b: set()
# c: set()
# d: set(e)
# e: set()
targets = {}
deps = set()
for k, v of data
targets[k] = set()
children = v.split(' ')
for child in children
continue if child == ''
set_add targets[k], child unless child == k
set_add deps, child
 
# make sure even leaf nodes are in targets
for dep of deps.v
if dep not of targets
targets[dep] = set()
targets
 
set = ->
cnt: 0
v: {}
 
set_add = (s, e) ->
return if s.v[e]
s.cnt += 1
s.v[e] = true
 
set_remove = (s, e) ->
return if !s.v[e]
s.cnt -= 1
delete s.v[e]
 
data =
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: ""
 
 
targets = parse_deps()
console.log toposort targets
 
 

Common Lisp[edit]

(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)

D[edit]

Translation of: Python
import std.stdio, std.string, std.algorithm, std.range;
 
final class ArgumentException : Exception {
this(string text) pure nothrow @safe [email protected]*/ {
super(text);
}
}
 
alias TDependencies = string[][string];
 
string[][] topoSort(TDependencies d) pure /*nothrow @safe*/ {
foreach (immutable k, v; d)
d[k] = v.sort().uniq.filter!(s => s != k).array;
foreach (immutable s; d.byValue.join.sort().uniq)
if (s !in d)
d[s] = [];
 
string[][] sorted;
while (true) {
string[] ordered;
 
foreach (immutable item, const dep; d)
if (dep.empty)
ordered ~= item;
if (!ordered.empty)
sorted ~= ordered.sort().release;
else
break;
 
TDependencies dd;
foreach (immutable item, const dep; d)
if (!ordered.canFind(item))
dd[item] = dep.filter!(s => !ordered.canFind(s)).array;
d = dd;
}
 
//if (!d.empty)
if (d.length > 0)
throw new ArgumentException(format(
"A cyclic dependency exists amongst:\n%s", d));
 
return sorted;
}
 
void main() {
immutable data =
"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"
;
 
TDependencies deps;
foreach (immutable line; data.splitLines)
deps[line.split[0]] = line.split[1 .. $];
 
auto depw = deps.dup;
foreach (immutable idx, const subOrder; depw.topoSort)
writefln("#%d : %s", idx + 1, subOrder);
 
writeln;
depw = deps.dup;
depw["dw01"] ~= "dw04";
foreach (const subOrder; depw.topoSort) // Should throw.
subOrder.writeln;
}
Output:
#1 : ["ieee", "std", "synopsys"]
#2 : ["dware", "gtech", "ramlib", "std_cell_lib"]
#3 : ["dw01", "dw02", "dw05", "dw06", "dw07"]
#4 : ["des_system_lib", "dw03", "dw04"]
[email protected](7): A cyclic dependency exists amongst:
[dw01:[dw04],des_system_lib:[dw01],dw03:[dw01],dw04:[dw01]]
----------------
...\topo.d(71): _Dmain
----------------

E[edit]

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"]

EchoLisp[edit]

We use the low-level primitives of the 'graph' library to build the directed graph and implement the topological sort.

Data

 
(define dependencies
'((des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee)
(dw01 ieee dw01 dware gtech) ;; bad graph add dw04
(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 )))
 
 
;; build dependency graph
;; a depends on b
;; add arc (arrow) a --> b
(lib 'graph.lib)
(define (a->b g a b)
(unless (equal? a b)
(graph-make-arc g (graph-make-vertex g a) (graph-make-vertex g b))))
 
(define (add-dependencies g dep-list)
(for* ((dep dep-list) (b (rest dep))) (a->b g b (first dep))))
 

Implementation

Remove all vertices with in-degree = 0, until to one left. (in-degree = number of arrows to a vertex)

 
;; topological sort
;;
;; Complexity O (# of vertices + # of edges)
 
(define (t-sort g)
(stack 'Z) ; vertices of d°(0)
(stack 'S) ; ordered result
 
;; mark all vertices with their in-degree = # of incoming arcs
;; push all vertices u such as d°(u) = 0
(for ((u g)) (mark u (graph-vertex-indegree g u))
(when (zero? (mark? u)) (push 'Z u)))
 
;pop a d°(0) vertex u - add it to result
;decrement in-degree of all v vertices u->v
; if d°(v) = 0, push it
 
(while (not (stack-empty? 'Z))
(let (( u (pop 'Z)))
(push 'S u)
(for ((v (graph-vertex-out g u)))
(mark v (1- (mark? v)))
(when (zero? (mark? v)) (push 'Z v)))))
 
;; finish
(writeln 't-sort (map vertex-label (stack->list 'S)))
 
;; check no one remaining
(for ((u g))
(unless (zero? (mark? u))
(error " ♻️ t-sort:cyclic" (map vertex-label (graph-cycle g))))))
 
 
Output:
 
(define g (make-graph "VHDL"))
(add-dependencies g dependencies)
(graph-print g)
 
(t-sort g)
→ t-sort (std synopsys ieee dware dw02 dw05 dw06 dw07 gtech dw01 dw03 dw04 ramlib
std_cell_lib des_system_lib)
 
;; Error case
;; add dw01 -> dw04
(t-sort g)
t-sort (std synopsys ieee dware dw02 dw05 dw06 dw07 gtech ramlib std_cell_lib)
⛔️ error: ♻️ t-sort:cyclic (dw04 dw01)
 

Elixir[edit]

Translation of: Erlang
defmodule Topological do
def sort(library) do
g = :digraph.new
Enum.each(library, fn {l,deps} ->
 :digraph.add_vertex(g,l) # noop if library already added
Enum.each(deps, fn d -> add_dependency(g,l,d) end)
end)
if t = :digraph_utils.topsort(g) do
print_path(t)
else
IO.puts "Unsortable contains circular dependencies:"
Enum.each(:digraph.vertices(g), fn v ->
if vs = :digraph.get_short_cycle(g,v), do: print_path(vs)
end)
end
end
 
defp print_path(l), do: IO.puts Enum.join(l, " -> ")
 
defp add_dependency(_g,l,l), do: :ok
defp add_dependency(g,l,d) do
 :digraph.add_vertex(g,d) # noop if dependency already added
 :digraph.add_edge(g,d,l) # Dependencies represented as an edge d -> l
end
end
 
libraries = [
des_system_lib: ~w[std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee]a,
dw01: ~w[ieee dw01 dware gtech]a,
dw02: ~w[ieee dw02 dware]a,
dw03: ~w[std synopsys dware dw03 dw02 dw01 ieee gtech]a,
dw04: ~w[dw04 ieee dw01 dware gtech]a,
dw05: ~w[dw05 ieee dware]a,
dw06: ~w[dw06 ieee dware]a,
dw07: ~w[ieee dware]a,
dware: ~w[ieee dware]a,
gtech: ~w[ieee gtech]a,
ramlib: ~w[std ieee]a,
std_cell_lib: ~w[ieee std_cell_lib]a,
synopsys: []
]
Topological.sort(libraries)
 
IO.puts ""
bad_libraries = Keyword.update!(libraries, :dw01, &[:dw04 | &1])
Topological.sort(bad_libraries)
Output:
std -> synopsys -> ieee -> dware -> dw02 -> dw05 -> gtech -> dw01 -> dw03 -> dw04 -> ramlib -> std_cell_lib -> des_system_lib -> dw06 -> dw07

Unsortable contains circular dependencies:
dw04 -> dw01 -> dw04
dw01 -> dw04 -> dw01

Erlang[edit]

 
-module(topological_sort).
-compile(export_all).
 
-define(LIBRARIES,
[{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, []}]).
 
-define(BAD_LIBRARIES,
[{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, []}]).
 
main() ->
top_sort(?LIBRARIES),
top_sort(?BAD_LIBRARIES).
 
top_sort(Library) ->
G = digraph:new(),
lists:foreach(fun ({L,Deps}) ->
digraph:add_vertex(G,L), % noop if library already added
lists:foreach(fun (D) ->
add_dependency(G,L,D)
end, Deps)
end, Library),
T = digraph_utils:topsort(G),
case T of
false ->
io:format("Unsortable contains circular dependencies:~n",[]),
lists:foreach(fun (V) ->
case digraph:get_short_cycle(G,V) of
false ->
ok;
Vs ->
print_path(Vs)
end
end, digraph:vertices(G));
_ ->
print_path(T)
end.
 
print_path(L) ->
lists:foreach(fun (V) -> io:format("~s -> ",[V]) end,
lists:sublist(L,length(L)-1)),
io:format("~s~n",[lists:last(L)]).
 
add_dependency(_G,_L,_L) ->
ok;
add_dependency(G,L,D) ->
digraph:add_vertex(G,D), % noop if dependency already added
digraph:add_edge(G,D,L). % Dependencies represented as an edge D -> L
 
Output:
 
62> topological_sort:main().
synopsys -> std -> ieee -> dware -> dw02 -> dw05 -> ramlib -> std_cell_lib -> dw06 -> dw07 -> gtech -> dw01 -> des_system_lib -> dw03 -> dw04
Unsortable contains circular dependencies:
dw04 -> dw01 -> dw04
dw01 -> dw04 -> dw01
ok

Erlang has a built in digraph library and datastructure. digraph_utils contains the top_sort function which provides a topological sort of the vertices or returns false if it's not possible (due to circular references). The digraph module contains get_short_cycle which returns the shortest cycle involving a vertex.

Forth[edit]

Provides syntactical sugar for inputting the data in a way similar to the way given in the task description.

Implementation: Each node (with dependencies) goes through three states: At the start, it contains an execution token (xt, similar to a function pointer) that calls all before-nodes. At the start of that, the xt called by the node changes to PROCESSING; if that is ever called, there is a cycle (or self-reference), and if it is not a self-reference, the cycle is printed. When the processing of the before-nodes is complete, the present node is printed, and the xt changes to DROP, so any further processing of the node does nothing.

This implements depth-first search with PROCESSING being the temporary mark, and DROP being the permanent mark.

The cool thing about this implementation is that we don't need a single conditional branch for topologically sorting the dependencies of a single node; there are a few for deciding what to output on a cycle, but if we are happy with more primitive output, we can get rid of that; we do have EXECUTE instead, so we don't get rid of branch mispredictions, but given our representation of the dependencies, we need the indirect branch anyway.

A Forth-specific (although unidiomatic) feature is that we can recognize self-references and print cycles without building an extra data structure, because the chain of nodes we are looking at is on the data stack.

Another Forth feature is that we use the dictionary as symbol table for input processing: Each node is turned into a Forth word. Also, the list of dependencies is turned into an anonymous colon definition rather than some list or array.

This code uses a number of Gforth extensions, some just as minor conveniences, some more substantial (although nothing that could not be replaced with a few lines of standard code).

Works with: Gforth
variable nodes 0 nodes ! \ linked list of nodes
 
: node. ( body -- )
body> >name name>string type ;
 
: nodeps ( body -- )
\ the word referenced by body has no (more) dependencies to resolve
['] drop over ! node. space ;
 
: processing ( body1 ... bodyn body -- body1 ... bodyn )
\ the word referenced by body is in the middle of resolving dependencies
2dup <> if \ unless it is a self-reference (see task description)
['] drop over !
." (cycle: " dup node. >r 1 begin \ print the cycle
dup pick dup r@ <> while
space node. 1+ repeat
." ) " 2drop r>
then drop ;
 
: >processing ( body -- body )
['] processing over ! ;
 
: node ( "name" -- )
\ define node "name" and initialize it to having no dependences
create
['] nodeps , \ on definition, a node has no dependencies
nodes @ , lastxt nodes ! \ linked list of nodes
does> ( -- )
dup @ execute ; \ perform xt associated with node
 
: define-nodes ( "names" <newline> -- )
\ define all the names that don't exist yet as nodes
begin
parse-name dup while
2dup find-name 0= if
2dup nextname node then
2drop repeat
2drop ;
 
: deps ( "name" "deps" <newline> -- )
\ name is after deps. Implementation: Define missing nodes, then
\ define a colon definition for
>in @ define-nodes >in !
' :noname ]] >processing [[ source >in @ /string evaluate ]] nodeps ; [[
swap >body ! 0 parse 2drop ;
 
: all-nodes ( -- )
\ call all nodes, and they then print their dependences and themselves
nodes begin
@ dup while
dup execute
>body cell+ repeat
drop ;
 
deps des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee
deps dw01 ieee dw01 dware gtech
deps dw02 ieee dw02 dware
deps dw03 std synopsys dware dw03 dw02 dw01 ieee gtech
deps dw04 dw04 ieee dw01 dware gtech
deps dw05 dw05 ieee dware
deps dw06 dw06 ieee dware
deps dw07 ieee dware
deps dware ieee dware
deps gtech ieee gtech
deps ramlib std ieee
deps std_cell_lib ieee std_cell_lib
deps synopsys
\ to test the cycle recognition (overwrites dependences for dw1 above)
deps dw01 ieee dw01 dware gtech dw04
 
all-nodes
Output:
ieee dware dw07 dw06 dw05 gtech (cycle: dw04 dw01) dw01 dw04 std synopsys dw02 dw03 ramlib std_cell_lib des_system_lib

Fortran[edit]

FORTRAN 77[edit]

Main routine for topological sort. Input : IDEP is an array ND x 2 of dependencies, with IDEP(I,1) depending on IDEP(I,2). NL is the number of libraries to sort, ND the number of dependencies, one for each pair of ordered libraries. Array IPOS is used internally by the routine, to maintain a list of positions of libraries in IORD. Output : IORD(1:NO) is the compile order, and IORD(NO+1:NL) contains unordered libraries.

This implementation is not optimal: for each level of dependency (for example A -> B -> C counts as three levels), there is a loop through all dependencies in IDEP. It would be possible to optimize a bit, without changing the main idea, by first sorting IDEP according to first column, and using more temporary space, keeping track of where is located data in IDEP for each library (all dependencies of a same library being grouped).

      SUBROUTINE TSORT(NL,ND,IDEP,IORD,IPOS,NO)
IMPLICIT NONE
INTEGER NL,ND,NO,IDEP(ND,2),IORD(NL),IPOS(NL),I,J,K,IL,IR,IPL,IPR
DO 10 I=1,NL
IORD(I)=I
10 IPOS(I)=I
K=1
20 J=K
K=NL+1
DO 30 I=1,ND
IL=IDEP(I,1)
IR=IDEP(I,2)
IPL=IPOS(IL)
IPR=IPOS(IR)
IF(IL.EQ.IR .OR. IPL.GE.K .OR. IPL.LT.J .OR. IPR.LT.J) GO TO 30
K=K-1
IPOS(IORD(K))=IPL
IPOS(IL)=K
IORD(IPL)=IORD(K)
IORD(K)=IL
30 CONTINUE
IF(K.GT.J) GO TO 20
NO=J-1
END

An example. Dependencies are encoded to make program shorter (in array ICODE).

      PROGRAM EX_TSORT
IMPLICIT NONE
INTEGER NL,ND,NC,NO,IDEP,IORD,IPOS,ICODE,I,J,IL,IR
PARAMETER(NL=15,ND=44,NC=69)
CHARACTER*(20) LABEL
DIMENSION IDEP(ND,2),LABEL(NL),IORD(NL),IPOS(NL),ICODE(NC)
DATA LABEL/'DES_SYSTEM_LIB','DW01','DW02','DW03','DW04','DW05',
1 'DW06','DW07','DWARE','GTECH','RAMLIB','STD_CELL_LIB','SYNOPSYS',
2 'STD','IEEE'/
DATA ICODE/1,14,13,12,1,3,2,11,15,0,2,15,2,9,10,0,3,15,3,9,0,4,14,
213,9,4,3,2,15,10,0,5,5,15,2,9,10,0,6,6,15,9,0,7,7,15,9,0,8,15,9,0,
39,15,9,0,10,15,10,0,11,14,15,0,12,15,12,0,0/
 
C DECODE DEPENDENCIES AND BUILD IDEP ARRAY
I=0
J=0
10 I=I+1
IL=ICODE(I)
IF(IL.EQ.0) GO TO 30
20 I=I+1
IR=ICODE(I)
IF(IR.EQ.0) GO TO 10
J=J+1
IDEP(J,1)=IL
IDEP(J,2)=IR
GO TO 20
30 CONTINUE
 
C SORT LIBRARIES ACCORDING TO DEPENDENCIES (TOPOLOGICAL SORT)
CALL TSORT(NL,ND,IDEP,IORD,IPOS,NO)
 
PRINT*,'COMPILE ORDER'
DO 40 I=1,NO
40 PRINT*,LABEL(IORD(I))
PRINT*,'UNORDERED LIBRARIES'
DO 50 I=NO+1,NL
50 PRINT*,LABEL(IORD(I))
END
Output:
 COMPILE ORDER
 IEEE
 STD
 SYNOPSYS
 STD_CELL_LIB
 RAMLIB
 GTECH
 DWARE
 DW07
 DW06
 DW05
 DW02
 DW01
 DW04
 DW03
 DES_SYSTEM_LIB
 UNORDERED LIBRARIES
Output:
with alternate input (DW01 depends also on DW04):
 COMPILE ORDER
 IEEE                
 STD                 
 SYNOPSYS            
 STD_CELL_LIB        
 RAMLIB              
 GTECH               
 DWARE               
 DW07                
 DW06                
 DW05                
 DW02                
 UNORDERED LIBRARIES
 DW04                
 DW03                
 DW01                
 DES_SYSTEM_LIB      

Modern Fortran[edit]

A modern Fortran (95-2008) version of the TSORT subroutine is shown here (note that the IPOS array is not an input).

subroutine tsort(nl,nd,idep,iord,no)
 
implicit none
 
integer,intent(in) :: nl
integer,intent(in) :: nd
integer,dimension(nd,2),intent(in) :: idep
integer,dimension(nl),intent(out) :: iord
integer,intent(out) :: no
 
integer :: i,j,k,il,ir,ipl,ipr,ipos(nl)
 
do i=1,nl
iord(i)=i
ipos(i)=i
end do
k=1
do
j=k
k=nl+1
do i=1,nd
il=idep(i,1)
ir=idep(i,2)
ipl=ipos(il)
ipr=ipos(ir)
if (il==ir .or. ipl>=k .or. ipl<j .or. ipr<j) cycle
k=k-1
ipos(iord(k))=ipl
ipos(il)=k
iord(ipl)=iord(k)
iord(k)=il
end do
if (k<=j) exit
end do
no=j-1
 
end subroutine tsort
 

FunL[edit]

def topsort( graph ) =    
val L = seq()
val S = seq()
val g = dict( graph )
 
for (v, es) <- g
g(v) = seq( es )
 
for (v, es) <- g if es.isEmpty()
S.append( v )
 
while not S.isEmpty()
val n = S.remove( 0 )
L.append( n )
 
for (m, es) <- g if n in es
if (es -= n).isEmpty()
S.append( m )
 
for (v, es) <- g
if not es.isEmpty()
return None
 
Some( L.toList() )
 
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
'''
 
// convert dependencies data into a directed graph
graph = dict()
deps = set()
 
for l <- WrappedString( dependencies ).lines() if l.trim() != ''
case list(l.trim().split('\\s+')) of
[a] -> graph(a) = []
h:t ->
d = set( t )
d -= h // remove self dependencies
graph(h) = d
deps ++= t
 
// add graph vertices for dependencies not appearing in left column
for e <- deps if e not in graph
graph(e) = []
 
case topsort( graph ) of
None -> println( 'un-orderable' )
Some( ordering ) -> println( ordering )
Output:
[synopsys, ieee, std, dware, std_cell_lib, gtech, ramlib, dw06, dw05, dw02, dw07, dw01, dw03, dw04, des_system_lib]

Go[edit]

Kahn[edit]

package main
 
import (
"fmt"
"strings"
)
 
var data = `
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 `

 
func main() {
g, in, err := parseLibComp(data)
if err != nil {
fmt.Println(err)
return
}
order, cyclic := topSortKahn(g, in)
if cyclic != nil {
fmt.Println("Cyclic:", cyclic)
return
}
fmt.Println("Order:", order)
}
 
type graph map[string][]string
type inDegree map[string]int
 
// parseLibComp parses the text format of the task and returns a graph
// representation and a list of the in-degrees of each node. The returned graph
// represents compile order rather than dependency order. That is, for each map
// map key n, the map elements are libraries that depend on n being compiled
// first.
func parseLibComp(data string) (g graph, in inDegree, err error) {
// small sanity check on input
lines := strings.Split(data, "\n")
if len(lines) < 3 || !strings.HasPrefix(lines[2], "=") {
return nil, nil, fmt.Errorf("data format")
}
// toss header lines
lines = lines[3:]
// scan and interpret input, build graph
g = graph{}
in = inDegree{}
for _, line := range lines {
libs := strings.Fields(line)
if len(libs) == 0 {
continue // allow blank lines
}
lib := libs[0]
g[lib] = g[lib]
for _, dep := range libs[1:] {
in[dep] = in[dep]
if dep == lib {
continue // ignore self dependencies
}
successors := g[dep]
for i := 0; ; i++ {
if i == len(successors) {
g[dep] = append(successors, lib)
in[lib]++
break
}
if dep == successors[i] {
break // ignore duplicate dependencies
}
}
}
}
return g, in, nil
}
 
// General purpose topological sort, not specific to the application of
// library dependencies. Adapted from Wikipedia pseudo code, one main
// difference here is that this function does not consume the input graph.
// WP refers to incoming edges, but does not really need them fully represented.
// A count of incoming edges, or the in-degree of each node is enough. Also,
// WP stops at cycle detection and doesn't output information about the cycle.
// A little extra code at the end of this function recovers the cyclic nodes.
func topSortKahn(g graph, in inDegree) (order, cyclic []string) {
var L, S []string
// rem for "remaining edges," this function makes a local copy of the
// in-degrees and consumes that instead of consuming an input.
rem := inDegree{}
for n, d := range in {
if d == 0 {
// accumulate "set of all nodes with no incoming edges"
S = append(S, n)
} else {
// initialize rem from in-degree
rem[n] = d
}
}
for len(S) > 0 {
last := len(S) - 1 // "remove a node n from S"
n := S[last]
S = S[:last]
L = append(L, n) // "add n to tail of L"
for _, m := range g[n] {
// WP pseudo code reads "for each node m..." but it means for each
// node m *remaining in the graph.* We consume rem rather than
// the graph, so "remaining in the graph" for us means rem[m] > 0.
if rem[m] > 0 {
rem[m]-- // "remove edge from the graph"
if rem[m] == 0 { // if "m has no other incoming edges"
S = append(S, m) // "insert m into S"
}
}
}
}
// "If graph has edges," for us means a value in rem is > 0.
for c, in := range rem {
if in > 0 {
// recover cyclic nodes
for _, nb := range g[c] {
if rem[nb] > 0 {
cyclic = append(cyclic, c)
break
}
}
}
}
if len(cyclic) > 0 {
return nil, cyclic
}
return L, nil
}
Output:
Order: [std ieee std_cell_lib ramlib gtech dware dw07 dw06 dw05 dw02 dw01 dw04 synopsys dw03 des_system_lib]

Cycle detection demonstrated with the example in the task description:

Cyclic: [dw01 dw04]

Depth First[edit]

Topological sort only, this function can replace topSortKahn in above program. The in-degree list is not needed.

// General purpose topological sort, not specific to the application of
// library dependencies. Also adapted from Wikipedia pseudo code.
func topSortDFS(g graph) (order, cyclic []string) {
L := make([]string, len(g))
i := len(L)
temp := map[string]bool{}
perm := map[string]bool{}
var cycleFound bool
var cycleStart string
var visit func(string)
visit = func(n string) {
switch {
case temp[n]:
cycleFound = true
cycleStart = n
return
case perm[n]:
return
}
temp[n] = true
for _, m := range g[n] {
visit(m)
if cycleFound {
if cycleStart > "" {
cyclic = append(cyclic, n)
if n == cycleStart {
cycleStart = ""
}
}
return
}
}
delete(temp, n)
perm[n] = true
i--
L[i] = n
}
for n := range g {
if perm[n] {
continue
}
visit(n)
if cycleFound {
return nil, cyclic
}
}
return L, nil
}
Output:

(when used in program of Kahn example.)

Order: [ieee gtech synopsys dware dw07 dw06 dw02 dw01 dw04 std_cell_lib dw05 std ramlib dw03 des_system_lib]

And with the cycle added,

Cyclic: [dw04 dw01]

Haskell[edit]

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"]]

Icon and Unicon[edit]

Icon[edit]

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
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
->

Unicon[edit]

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

J[edit]

dependencySort=: monad define
parsed=. <@;:;._2 y
names=. {.&>parsed
depends=. (> [email protected]@#) 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

If we tried to also make dw01 depend on dw04, the sort would fail because of the circular dependency:

   dependencySort dependencies,'dw01 dw04',LF
|assertion failure: dependencySort
| -.1 e.(<0 1)|:depends

Here is an alternate implementation which uses a slightly different representation for the dependencies (instead of a boolean connection matrix to represent connections, we use a list of lists of indices to represent connections):

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.

Java[edit]

Works with: Java version 7
import java.util.*;
 
public class TopologicalSort {
 
public static void main(String[] args) {
String s = "std, ieee, des_system_lib, dw01, dw02, dw03, dw04, dw05,"
+ "dw06, dw07, dware, gtech, ramlib, std_cell_lib, synopsys";
 
Graph g = new Graph(s, new int[][]{
{2, 0}, {2, 14}, {2, 13}, {2, 4}, {2, 3}, {2, 12}, {2, 1},
{3, 1}, {3, 10}, {3, 11},
{4, 1}, {4, 10},
{5, 0}, {5, 14}, {5, 10}, {5, 4}, {5, 3}, {5, 1}, {5, 11},
{6, 1}, {6, 3}, {6, 10}, {6, 11},
{7, 1}, {7, 10},
{8, 1}, {8, 10},
{9, 1}, {9, 10},
{10, 1},
{11, 1}, {11, 10},
{12, 0}, {12, 1},
{13, 1}
});
 
System.out.println("Topologically sorted order: ");
System.out.println(g.topoSort());
}
}
 
class Graph {
String[] vertices;
boolean[][] adjacency;
int numVertices;
 
public Graph(String s, int[][] edges) {
vertices = s.split(",");
numVertices = vertices.length;
adjacency = new boolean[numVertices][numVertices];
 
for (int[] edge : edges)
adjacency[edge[0]][edge[1]] = true;
}
 
List<String> topoSort() {
List<String> result = new ArrayList<>();
List<Integer> todo = new LinkedList<>();
 
for (int i = 0; i < numVertices; i++)
todo.add(i);
 
try {
outer:
while (!todo.isEmpty()) {
for (Integer r : todo) {
if (!hasDependency(r, todo)) {
todo.remove(r);
result.add(vertices[r]);
// no need to worry about concurrent modification
continue outer;
}
}
throw new Exception("Graph has cycles");
}
} catch (Exception e) {
System.out.println(e);
return null;
}
return result;
}
 
boolean hasDependency(Integer r, List<Integer> todo) {
for (Integer c : todo) {
if (adjacency[r][c])
return true;
}
return false;
}
}
[std,  ieee,  dware,  dw02,  dw05, dw06,  dw07,  gtech,  dw01,  dw04,  ramlib,  std_cell_lib,  synopsys,  des_system_lib,  dw03]

jq[edit]

In the following, the graph of dependencies is represented as a JSON object with keys being the dependent entities, and each corresponding value being a list of its dependencies. For example: {"x": ["y", "z"] } means: x depends on y and z.

The tsort filter will accept a dependency graph with self-dependencies.

Implementation Notes: Notice that the main function, tsort, has an inner function which itself has an inner function.

The normalize filter eliminates self-dependencies from a dependency graph.

Efficiency: The implementation of tsort uses a tail-recursive helper function, _tsort/0, which incurs no overhead due to recursion as jq optimizes arity-0 tail-recursive functions.

Since the dependency graph is represented as a jq object, which acts like a hash, access to the dependencies of a particular dependent is fast.

To solve and print the solution to the given problem on a 1GHz machine takes about 5ms.

# independent/0 emits an array of the dependencies that have no dependencies
# Input: an object representing a normalized dependency graph
def independent:
. as $G
| reduce keys[] as $key
([];
. + ((reduce $G[$key][] as $node
([];
if ($G[$node] == null or ($G[$node]|length)==0) then . + [$node]
else .
end ))))
| unique;
 
# normalize/0 eliminates self-dependencies in the input dependency graph.
# Input: an object representing a dependency graph.
def normalize:
. as $G
| reduce keys[] as $key
($G;
.[$key] as $nodes
| if $nodes and ($nodes|index($key)) then .[$key] = $nodes - [$key] else . end);
 
 
# minus/1 removes all the items in ary from each of the values in the input object
# Input: an object representing a dependency graph
def minus(ary):
. as $G | reduce keys[] as $key ($G; $G[$key] -= ary);
 
# tsort/0 emits the topologically sorted nodes of the input,
# in ">" order.
# Input is assumed to be an object representing a dependency
# graph and need not be normalized.
def tsort:
# _sort: input: [L, Graph], where L is the tsort so far
def _tsort:
 
def done: [.[]] | all( length==0 );
 
.[0] as $L | .[1] as $G
| if ($G|done) then $L + (($G|keys) - $L)
else
($G|independent) as $I
| if (($I|length) == 0)
then error("the dependency graph is cyclic: \($G)")
else [ ($L + $I), ($G|minus($I))] | _tsort
end
end;
 
normalize | [[], .] | _tsort ;
 
tsort

Data:

{"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": []
}
 
Output:
 
$ jq -c -f tsort.jq tsort.json
["ieee","std","synopsys","dware","gtech","ramlib","std_cell_lib","dw01","dw02","des_system_lib","dw03","dw04","dw05","dw06","dw07"]
 

Mathematica[edit]

Work in Mathematica 8 or higher versions.

TopologicalSort[
Graph[Flatten[# /. {l_, ld_} :>
Map[# -> l &,
DeleteCases[ld, l]]]]] /. {_TopologicalSort -> $Failed} &@
{{"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", {}}}
Output:
{"ieee", "std_cell_lib", "gtech", "dware", "dw07", "dw06", "dw05", \
"dw02", "dw01", "dw04", "std", "ramlib", "synopsys", "dw03", \
"des_system_lib"}

If the data is un-orderable, it will return $Failed.

Object Pascal[edit]

Written for Free Pascal, but will probably work in Delphi if you change the required units.

 
program topologicalsortrosetta;
 
{*
Topological sorter to parse e.g. dependencies.
Written for FreePascal 2.4.x/2.5.1. Probably works in Delphi, but you'd have to
change some units.
*}
{$IFDEF FPC}
// FreePascal-specific setup
{$mode objfpc}
uses {$IFDEF UNIX}
cwstring, {* widestring support for unix *} {$IFDEF UseCThreads}
cthreads, {$ENDIF UseCThreads} {$ENDIF UNIX}
Classes,
SysUtils;
{$ENDIF}
 
type
RNodeIndex = record
NodeName: WideString; //Name of the node
//Index: integer; //Index number used in DepGraph. For now, we can distill the index from the array index. If we want to use a TList or similar, we'd need an index property
Order: integer; //Order when sorted
end;
 
RDepGraph = record
Node: integer; //Refers to Index in NodeIndex
DependsOn: integer; //The Node depends on this other Node.
end;
 
{ TTopologicalSort }
 
TTopologicalSort = class(TObject)
private
Nodes: array of RNodeIndex;
DependencyGraph: array of RDepGraph;
FCanBeSorted: boolean;
function SearchNode(NodeName: WideString): integer;
function SearchIndex(NodeID: integer): WideString;
function DepFromNodeID(NodeID: integer): integer;
function DepFromDepID(DepID: integer): integer;
function DepFromNodeIDDepID(NodeID, DepID: integer): integer;
procedure DelDependency(const Index: integer);
public
constructor Create;
destructor Destroy; override;
procedure SortOrder(var Output: TStringList);
procedure AddNode(NodeName: WideString);
procedure AddDependency(NodeName, DependsOn: WideString);
procedure AddNodeDependencies(NodeAndDependencies: TStringList);
//Each string has node, and the nodes it depends on. This allows insertion of an entire dependency graph at once
//procedure DelNode(NodeName: Widestring);
procedure DelDependency(NodeName, DependsOn: WideString);
 
property CanBeSorted: boolean read FCanBeSorted;
 
end;
 
const
INVALID = -1;
// index not found for index search functions, no sort order defined, or record invalid/deleted
 
function TTopologicalSort.SearchNode(NodeName: WideString): integer;
var
Counter: integer;
begin
// Return -1 if node not found. If node found, return index in array
Result := INVALID;
for Counter := 0 to High(Nodes) do
begin
if Nodes[Counter].NodeName = NodeName then
begin
Result := Counter;
break;
end;
end;
end;
 
function TTopologicalSort.SearchIndex(NodeID: integer): WideString;
//Look up name for the index
begin
if (NodeID > 0) and (NodeID <= High(Nodes)) then
begin
Result := Nodes[NodeID].NodeName;
end
else
begin
Result := 'ERROR'; //something's fishy, this shouldn't happen
end;
end;
 
function TTopologicalSort.DepFromNodeID(NodeID: integer): integer;
// Look for Node index number in the dependency graph
// and return the first node found. If nothing found, return -1
var
Counter: integer;
begin
Result := INVALID;
for Counter := 0 to High(DependencyGraph) do
begin
if DependencyGraph[Counter].Node = NodeID then
begin
Result := Counter;
break;
end;
end;
end;
 
function TTopologicalSort.DepFromDepID(DepID: integer): integer;
// Look for dependency index number in the dependency graph
// and return the index for the first one found. If nothing found, return -1
var
Counter: integer;
begin
Result := INVALID;
for Counter := 0 to High(DependencyGraph) do
begin
if DependencyGraph[Counter].DependsOn = DepID then
begin
Result := Counter;
break;
end;
end;
end;
 
function TTopologicalSort.DepFromNodeIDDepID(NodeID, DepID: integer): integer;
// Shows index for the dependency from NodeID on DepID, or INVALID if not found
var
Counter: integer;
begin
Result := INVALID;
for Counter := 0 to High(DependencyGraph) do
begin
if DependencyGraph[Counter].Node = NodeID then
if DependencyGraph[Counter].DependsOn = DepID then
begin
Result := Counter;
break;
end;
end;
end;
 
procedure TTopologicalSort.DelDependency(const Index: integer);
// Removes dependency from array.
// Is fastest when the dependency is near the top of the array
// as we're copying the remaining elements.
var
Counter: integer;
OriginalLength: integer;
begin
OriginalLength := Length(DependencyGraph);
if Index = OriginalLength - 1 then
begin
SetLength(DependencyGraph, OriginalLength - 1);
end;
if Index < OriginalLength - 1 then
begin
for Counter := Index to OriginalLength - 2 do
begin
DependencyGraph[Counter] := DependencyGraph[Counter + 1];
end;
SetLength(DependencyGraph, OriginalLength - 1);
end;
if Index > OriginalLength - 1 then
begin
// This could happen when deleting on an empty array:
raise Exception.Create('Tried to delete index ' + IntToStr(Index) +
' while the maximum index was ' + IntToStr(OriginalLength - 1));
end;
end;
 
constructor TTopologicalSort.Create;
begin
inherited Create;
end;
 
destructor TTopologicalSort.Destroy;
begin
// Clear up data just to make sure:
Finalize(DependencyGraph);
Finalize(Nodes);
inherited;
end;
 
procedure TTopologicalSort.SortOrder(var Output: TStringList);
var
Counter: integer;
NodeCounter: integer;
OutputSortOrder: integer;
DidSomething: boolean; //used to detect cycles (circular references)
Node: integer;
begin
OutputSortOrder := 0;
DidSomething := True; // prime the loop below
FCanBeSorted := True; //hope for the best.
while (DidSomething = True) do
begin
// 1. Find all nodes (now) without dependencies, output them first and remove the dependencies:
// 1.1 Nodes that are not present in the dependency graph at all:
for Counter := 0 to High(Nodes) do
begin
if DepFromNodeID(Counter) = INVALID then
begin
if DepFromDepID(Counter) = INVALID then
begin
// Node doesn't occur in either side of the dependency graph, so it has sort order 0:
DidSomething := True;
if (Nodes[Counter].Order = INVALID) or
(Nodes[Counter].Order > OutputSortOrder) then
begin
// Enter sort order if the node doesn't have a lower valid order already.
Nodes[Counter].Order := OutputSortOrder;
end;
end; //Invalid Dep
end; //Invalid Node
end; //Count
// Done with the first batch, so we can increase the sort order:
OutputSortOrder := OutputSortOrder + 1;
// 1.2 Nodes that are only present on the right hand side of the dep graph:
DidSomething := False;
// reverse order so we can delete dependencies without passing upper array
for Counter := High(DependencyGraph) downto 0 do
begin
Node := DependencyGraph[Counter].DependsOn; //the depended node
if (DepFromNodeID(Node) = INVALID) then
begin
DidSomething := True;
//Delete dependency so we don't hit it again:
DelDependency(Counter);
if (Nodes[Node].Order = INVALID) or (Nodes[Node].Order > OutputSortOrder) then
begin
// Enter sort order if the node doesn't have a lower valid order already.
Nodes[Node].Order := OutputSortOrder;
end;
end;
OutputSortOrder := OutputSortOrder + 1; //next iteration
end;
// 2. Go back to 1 until we can't do more work, and do some bookkeeping:
OutputSortOrder := OutputSortOrder + 1;
end; //outer loop for 1 to 2
OutputSortOrder := OutputSortOrder - 1; //fix unused last loop.
 
// 2. If we have dependencies left, we have a cycle; exit.
if (High(DependencyGraph) > 0) then
begin
FCanBeSorted := False; //indicate we have a cycle
Output.Add('Cycle (circular dependency) detected, cannot sort further. Dependencies left:');
for Counter := 0 to High(DependencyGraph) do
begin
Output.Add(SearchIndex(DependencyGraph[Counter].Node) +
' depends on: ' + SearchIndex(DependencyGraph[Counter].DependsOn));
end;
end
else
begin
// No cycle:
// Now parse results, if we have them
for Counter := 0 to OutputSortOrder do
begin
for NodeCounter := 0 to High(Nodes) do
begin
if Nodes[NodeCounter].Order = Counter then
begin
Output.Add(Nodes[NodeCounter].NodeName);
end;
end; //output each result
end; //order iteration
end; //cycle detection
end;
 
procedure TTopologicalSort.AddNode(NodeName: WideString);
var
NodesNewLength: integer;
begin
// Adds node; make sure we don't add duplicate entries
if SearchNode(NodeName) = INVALID then
begin
NodesNewLength := Length(Nodes) + 1;
SetLength(Nodes, NodesNewLength);
Nodes[NodesNewLength - 1].NodeName := NodeName; //Arrays are 0 based
//Nodes[NodesNewLength -1].Index := //If we change the object to a tlist or something, we already have an index property
Nodes[NodesNewLength - 1].Order := INVALID; //default value
end;
end;
 
procedure TTopologicalSort.AddDependency(NodeName, DependsOn: WideString);
begin
// Make sure both nodes in the dependency exist as a node
if SearchNode(NodeName) = INVALID then
begin
Self.AddNode(NodeName);
end;
if SearchNode(DependsOn) = INVALID then
begin
Self.AddNode(DependsOn);
end;
// Add the dependency, only if we don't depend on ourselves:
if NodeName <> DependsOn then
begin
SetLength(DependencyGraph, Length(DependencyGraph) + 1);
DependencyGraph[High(DependencyGraph)].Node := SearchNode(NodeName);
DependencyGraph[High(DependencyGraph)].DependsOn := SearchNode(DependsOn);
end;
end;
 
procedure TTopologicalSort.AddNodeDependencies(NodeAndDependencies: TStringList);
// Takes a stringlist containing a list of strings. Each string contains node names
// separated by spaces. The first node depends on the others. It is permissible to have
// only one node name, which doesn't depend on anything.
// This procedure will add the dependencies and the nodes in one go.
var
Deplist: TStringList;
StringCounter: integer;
NodeCounter: integer;
begin
if Assigned(NodeAndDependencies) then
begin
DepList := TStringList.Create;
try
for StringCounter := 0 to NodeAndDependencies.Count - 1 do
begin
// For each string in the argument: split into names, and process:
DepList.Delimiter := ' '; //use space to separate the entries
DepList.StrictDelimiter := False; //allows us to ignore double spaces in input.
DepList.DelimitedText := NodeAndDependencies[StringCounter];
for NodeCounter := 0 to DepList.Count - 1 do
begin
if NodeCounter = 0 then
begin
// Add the first node, which might be the only one.
Self.AddNode(Deplist[0]);
end;
 
if NodeCounter > 0 then
begin
// Only add dependency from the second item onwards
// The AddDependency code will automatically add Deplist[0] to the Nodes, if required
Self.AddDependency(DepList[0], DepList[NodeCounter]);
end;
end;
end;
finally
DepList.Free;
end;
end;
end;
 
procedure TTopologicalSort.DelDependency(NodeName, DependsOn: WideString);
// Delete the record.
var
NodeID: integer;
DependsID: integer;
Dependency: integer;
begin
NodeID := Self.SearchNode(NodeName);
DependsID := Self.SearchNode(DependsOn);
if (NodeID <> INVALID) and (DependsID <> INVALID) then
begin
// Look up dependency and delete it.
Dependency := Self.DepFromNodeIDDepID(NodeID, DependsID);
if (Dependency <> INVALID) then
begin
Self.DelDependency(Dependency);
end;
end;
end;
 
// Main program:
var
InputList: TStringList; //Lines of dependencies
TopSort: TTopologicalSort; //Topological sort object
OutputList: TStringList; //Sorted dependencies
Counter: integer;
begin
 
//Actual sort
InputList := TStringList.Create;
// Add rosetta code sample input separated by at least one space in the lines
InputList.Add(
'des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee');
InputList.Add('dw01 ieee dw01 dware gtech');
InputList.Add('dw02 ieee dw02 dware');
InputList.Add('dw03 std synopsys dware dw03 dw02 dw01 ieee gtech');
InputList.Add('dw04 dw04 ieee dw01 dware gtech');
InputList.Add('dw05 dw05 ieee dware');
InputList.Add('dw06 dw06 ieee dware');
InputList.Add('dw07 ieee dware');
InputList.Add('dware ieee dware');
InputList.Add('gtech ieee gtech');
InputList.Add('ramlib std ieee');
InputList.Add('std_cell_lib ieee std_cell_lib');
InputList.Add('synopsys');
TopSort := TTopologicalSort.Create;
OutputList := TStringList.Create;
try
TopSort.AddNodeDependencies(InputList); //read in nodes
TopSort.SortOrder(OutputList); //perform the sort
for Counter := 0 to OutputList.Count - 1 do
begin
writeln(OutputList[Counter]);
end;
except
on E: Exception do
begin
Writeln(stderr, 'Error: ', DateTimeToStr(Now),
': Error sorting. Technical details: ',
E.ClassName, '/', E.Message);
end;
end; //try
OutputList.Free;
TopSort.Free;
InputList.Free;
end.
 

OCaml[edit]

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 rev_unique =
List.fold_left (fun acc x -> if List.mem x acc then acc else x::acc) []
 
let libs = (* list items, each being unique *)
rev_unique (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".

Oz[edit]

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 

Pascal[edit]

See Object Pascal

Perl[edit]

In July 2002, Topological Sort was the monthly Perl Golf course. The post-mortem contains many solutions. This code was adapted from the solution that scored 144.39.

The algorithm used allows the output to be clustered; libraries on the same line are all independent (given the building of any previous lines of libraries), and so could be built in parallel.

sub print_topo_sort {
my %deps = @_;
 
my %ba;
while ( my ( $before, $afters_aref ) = each %deps ) {
for my $after ( @{ $afters_aref } ) {
$ba{$before}{$after} = 1 if $before ne $after;
$ba{$after} ||= {};
}
}
 
while ( my @afters = sort grep { ! %{ $ba{$_} } } keys %ba ) {
print "@afters\n";
delete @ba{@afters};
delete @{$_}{@afters} for values %ba;
}
 
print !!%ba ? "Cycle found! ". join( ' ', sort keys %ba ). "\n" : "---\n";
}
 
my %deps = (
des_system_lib => [qw( std synopsys std_cell_lib des_system_lib dw02
dw01 ramlib ieee )],
dw01 => [qw( ieee dw01 dware gtech )],
dw02 => [qw( ieee dw02 dware )],
dw03 => [qw( std synopsys dware dw03 dw02 dw01 ieee gtech )],
dw04 => [qw( dw04 ieee dw01 dware gtech )],
dw05 => [qw( dw05 ieee dware )],
dw06 => [qw( dw06 ieee dware )],
dw07 => [qw( ieee dware )],
dware => [qw( ieee dware )],
gtech => [qw( ieee gtech )],
ramlib => [qw( std ieee )],
std_cell_lib => [qw( ieee std_cell_lib )],
synopsys => [qw( )],
);
print_topo_sort(%deps);
push @{ $deps{'dw01'} }, 'dw04'; # Add unresolvable dependency
print_topo_sort(%deps);
Output:
ieee std synopsys
dware gtech ramlib std_cell_lib
dw01 dw02 dw05 dw06 dw07
des_system_lib dw03 dw04
---
ieee std synopsys
dware gtech ramlib std_cell_lib
dw02 dw05 dw06 dw07
Cycle found! des_system_lib dw01 dw03 dw04

Perl 6[edit]

Translation of: Perl
Works with: rakudo version 2016.01
sub print_topo_sort ( %deps ) {
my %ba;
for %deps.kv -> $before, @afters {
for @afters -> $after {
%ba{$before}{$after} = 1 if $before ne $after;
%ba{$after} //= {};
}
}
 
while %ba.grep( not *.value )».key -> @afters {
say ~@afters.sort;
%ba{@afters}:delete;
for %ba.values { .{@afters}:delete }
}
 
say %ba ?? "Cycle found! {%ba.keys.sort}" !! '---';
}
 
my %deps =
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 => < >;
 
print_topo_sort(%deps);
%deps<dw01> = <ieee dw01 dware gtech dw04>; # Add unresolvable dependency
print_topo_sort(%deps);
Output:
ieee std synopsys
dware gtech ramlib std_cell_lib
dw01 dw02 dw05 dw06 dw07
des_system_lib dw03 dw04
---
ieee std synopsys
dware gtech ramlib std_cell_lib
dw02 dw05 dw06 dw07
Cycle found! des_system_lib dw01 dw03 dw04

Some differences from the Perl 5 version include use of formal parameters; use of » as a "hyper" operator, that is, a parallelizable implicit loop; and use of normal lambda-like notation to bind loop parameters, so we can have multiple loop parameters bound on each iteration. Also, since => is now a real pair composer rather than a synonym for comma, the data can be represented with real pair notation that points to quoted word lists delimited by angle brackets rather than [qw(...)].

PicoLisp[edit]

(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)

PowerShell[edit]

#Input Data
$a=@"
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
"
@
#Convert to Object[]
$c = switch ( $a.split([char] 10) ) {
$_ {
$b=$_.split(' ')
New-Object PSObject -Property @{
Library = $b[0]
"Library Dependencies" = @( $( $b[1..($b.length-1)] | Where-Object { $_ -match '\w' } ) )
}
}
}
#Add pure dependencies
$c | ForEach-Object {
$_."Library Dependencies" | Where-Object {
$d=$_
$(:andl foreach($i in $c) {
if($d -match $i.Library) {
$false
break andl
}
}) -eq $null
} | ForEach-Object {
$c+=New-Object PSObject -Property @{
Library=$_
"Library Dependencies"=@()
}
}
}
#Associate with a dependency value
##Initial Dependency Value
$d = $c | Sort Library | Select-Object Library,"Library Dependencies",@{
Name="Dep Value"
Expression={
1
}
}
##Modify Dependency Value, perform check for incorrect dependency
##Dep Value is determined by a parent child relationship, if a library is a parent, all libraries dependant on it are children
for( $i=0; $i -lt $d.count; $i++ ) {
$errmsg=""
foreach( $j in ( 0..( $d.count - 1 ) | Where-Object { $_ -ne $i } ) ) {
#Foreach other Child Library where this is a dependency, increase the Dep Value of the Child
if( $( :orl foreach( $k in $d[$j]."Library Dependencies" ) {
if( $k -match $d[$i].Library ) {
foreach( $n in $d[$i]."Library Dependencies" ) {
if( $n -match $d[$j].Library ) {
$errmsg="Error Cyclic Dependency {0}<->{1}" -f $d[$i].Library, $d[$j].Library
break
}
}
$true
break orl
}
} ) ) {
#If the child has already been processed, increase the Dep Value of its children
if( $j -lt $i ) {
foreach( $l in ( 0..( $d.count - 1 ) | Where-Object { $_ -ne $j } ) ) {
if( $( :orl2 foreach( $m in $d[$l]."Library Dependencies" ) {
if( $m -match $d[$j].Library ) {
$true
break orl2
}
} ) ) {
$d[$l]."Dep Value"+=$d[$i]."Dep Value"
}
}
}
$d[$j]."Dep Value"+=$d[$i]."Dep Value"
}
if( $errmsg -ne "" ) {
$errmsg
$d=$null
break
}
}
}
#Sort and Display
if( $d ) {
$d | Sort "Dep Value",Library | ForEach-Object {
"{0,-14} LIBRARY DEPENDENCIES`n{1,-14} ====================" -f "LIBRARY", "======="
} {
"{0,-14} $($_."Library Dependencies")" -f $_.Library
}
}

PureBasic[edit]

#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

Python[edit]

try:
from functools import reduce
except:
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 toposort2(data):
for k, v in data.items():
v.discard(k) # Ignore self dependencies
extra_items_in_deps = reduce(set.union, data.values()) - set(data.keys())
data.update({item:set() for item in extra_items_in_deps})
while True:
ordered = set(item for item,dep in data.items() if not dep)
if not ordered:
break
yield ' '.join(sorted(ordered))
data = {item: (dep - ordered) for item,dep in data.items()
if item not in ordered}
assert not data, "A cyclic dependency exists amongst %r" % data
 
print ('\n'.join( toposort2(data) ))

Ordered output
items on a line could be processed in any sub-order or, indeed, in parallel:

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 115, in <module>
    print ('\n'.join( toposort2(data) ))
  File "C:\Documents and Settings\All Users\Documents\Paddys\topological_sort.py", line 113, in toposort2
    assert not data, "A cyclic dependency exists amongst %r" % data
AssertionError: A cyclic dependency exists amongst {'dw04': {'dw01'}, 'dw03': {'dw01'}, 'dw01': {'dw04'}, 'des_system_lib': {'dw01'}}

R[edit]

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
 

Racket[edit]

 
#lang racket
 
(define G
(make-hash
'((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 . ()))))
 
(define (clean G)
(define G* (hash-copy G))
(for ([(from tos) G])
 ; remove self dependencies
(hash-set! G* from (remove from tos))
 ; make sure all nodes are present in the ht
(for ([to tos]) (hash-update! G* to (λ(_)_) '())))
G*)
 
(define (incoming G)
(define in (make-hash))
(for* ([(from tos) G] [to tos])
(hash-update! in to (λ(fs) (cons from fs)) '()))
in)
 
(define (nodes G) (hash-keys G))
(define (out G n) (hash-ref G n '()))
(define (remove! G n m) (hash-set! G n (remove m (out G n))))
 
(define (topo-sort G)
(define n (length (nodes G)))
(define in (incoming G))
(define (no-incoming? n) (empty? (hash-ref in n '())))
(let loop ([L '()] [S (list->set (filter no-incoming? (nodes G)))])
(cond [(set-empty? S)
(if (= (length L) n)
L
(error 'topo-sort (~a "cycle detected" G)))]
[else
(define n (set-first S))
(define S\n (set-rest S))
(for ([m (out G n)])
(remove! G n m)
(remove! in m n)
(when (no-incoming? m)
(set! S\n (set-add S\n m))))
(loop (cons n L) S\n)])))
 
(topo-sort (clean G))
 

Output:

 
'(synopsys ieee dware gtech std_cell_lib std ramlib dw07 dw06 dw05 dw01 dw04 dw02 dw03 des_system_lib)
 

REXX[edit]

Translation of: FORTRAN 77
/*REXX pgm does a topological sort (orders such that no item precedes a dependent item).*/
idep.=0; ipos.=0; iord.=0 /*initialize some stemmed arrays to 0.*/
label= 'DES_SYSTEM_LIB DW01 DW02 DW03 DW04 DW05 DW06 DW07 DWARE GTECH RAMLIB',
'STD_CELL_LIB SYNOPSYS STD IEEE'
 
icode=1 14 13 12 1 3 2 11 15 0 2 15 2 9 10 0 3 15 3 9 0 4 14 213 9 4 3 2 15 10 0 5 5 15 2,
9 10 0 6 6 15 9 0 7 7 15 9 0 8 15 9 0 39 15 9 0 10 15 10 0 11 14 15 0 12 15 12 0 0
 
idep.=0; ipos.=0; iord.=0 /*initialize some stemmed arrays to 0.*/
nl=15; nd=44; nc=69; j=0; i=0 /* " " "parms" and indices.*/
 
10: i=i+1
il=word(icode, i)
if il==0 then signal 30
20: i=i+1
ir=word(icode, i)
if ir==0 then signal 10
j=j+1
idep.j.1=il
idep.j.2=ir
signal 20
30: call tsort
say '═══compile order═══'
q=0; do o=no by -1 for no; q=q+1
say word(label, iord.o)
end /*o*/
if q==0 then q='no'
say ' ('q "libraries found.)"
say
say '═══unordered libraries═══'
q=0; do u=no+1 to nl; q=q+1
say word(label, iord.u)
end /*u*/
if q==0 then q='no'
say ' ('q "unordered libraries found.)"
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
tSort: procedure expose nl nd idep. iord. ipos. no
do i=1 for nl
iord.i=i
ipos.i=i
end /*i*/
k=1
do forever
j=k
k=nl+1
do i=1 for nd
il=idep.i.1
ir=ipos.il
ipl=ipos.il
ipr=ipos.ir
if il==ir | ipl>.k | ipl<j | ipr<j then iterate
k=k-1
_=iord.k; ipos._=ipl
ipos.il=k
iord.ipl=iord.k
iord.k=il
end /*i*/
if k<=j then leave
end /*forever*/
no=j-1
return

output

═══compile order═══
IEEE
STD
SYNOPSYS
STD_CELL_LIB
RAMLIB
GTECH
DWARE
DW07
DW06
DW05
DW04
DW03
DW02
DW01
DES_SYSTEM_LIB
   (15 libraries found.)

═══unordered libraries═══
   (no unordered libraries found.)

Ruby[edit]

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|
key, *libs = line.split
depends[key] = libs
libs.each {|lib| depends[lib] ||= []}
end
 
begin
p depends.tsort
depends["dw01"] << "dw04"
p depends.tsort
rescue TSort::Cyclic => e
puts "\ncycle 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
Output:
["std", "synopsys", "ieee", "std_cell_lib", "dware", "dw02", "gtech", "dw01", "ramlib", "des_system_lib", "dw03", "dw04", "dw05", "dw06", "dw07"]

cycle detected: topological sort failed: ["dw01", "dw04"]

Sidef[edit]

Translation of: Perl
func print_topo_sort (deps) {
var ba = Hash.new;
deps.each { |before, afters|
afters.each { |after|
if (before != after) {
ba{before}{after} = 1;
};
ba{after} \\= Hash.new;
}
};
 
loop {
var afters = ba.keys.grep {|k| ba{k}.values.len == 0 }.sort;
afters.len || break;
say afters.join(" ");
ba.delete(afters...);
ba.values.each { |v| v.delete(afters...) };
};
 
say (ba.len ? "Cicle found! #{ba.keys.sort}" : "---");
}
 
var deps = Hash.new(
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 => < >
);
 
print_topo_sort(deps);
deps{:dw01}.append('dw04'); # Add unresolvable dependency
print_topo_sort(deps);
Output:
ieee std synopsys
dware gtech ramlib std_cell_lib
dw01 dw02 dw05 dw06 dw07
des_system_lib dw03 dw04
---
ieee std synopsys
dware gtech ramlib std_cell_lib
dw02 dw05 dw06 dw07
Cicle found! des_system_lib dw01 dw03 dw04

Tcl[edit]

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"

UNIX Shell[edit]

The Unix tsort(1) utility does a topological sort. Each line of input must have two items in order, like 'std des_system_lib'.[3]

Works with: Bourne Shell
$ awk '{ for (i = 1; i <= NF; i++) print $i, $1 }' <<! | tsort
> 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
> !
ieee
dware
dw02
dw05
dw06
dw07
gtech
dw01
dw04
std_cell_lib
synopsys
std
dw03
ramlib
des_system_lib

If the graph of dependencies contains a cycle, BSD's tsort(1) will print messages to standard error, break the cycle (by deleting one of the dependencies), continue the sort, and exit 0. So if dw04 becomes a dependency of dw01, then tsort(1) finds the cycle between dw01 and dw04.

ieee
dware
dw02
dw05
dw06
dw07
gtech
std_cell_lib
synopsys
std
ramlib
tsort: cycle in data
tsort: dw01
tsort: dw04
dw01
des_system_lib
dw03
dw04

Ursala[edit]

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,~&[email protected])^|/~& ~&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

VBScript[edit]

Implementation[edit]
 
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
 
Invocation[edit]
 
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
 
Output[edit]
----- 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
-----

Visual Basic .NET[edit]

Adapted from http://tawani.blogspot.com/2009/02/topological-sorting-and-cyclic.html which was itself an adaptation of Java code. I added the Rosetta code specific format of dependencies, as well as checks for references to self.

' Adapted from:
' http://tawani.blogspot.com/2009/02/topological-sorting-and-cyclic.html
' added/changed:
' - conversion to VB.Net (.Net 2 framework)
' - added Rosetta Code dependency format parsing
' - check & removal of self-dependencies before sorting
Module Program
Sub Main()
Dim Fields As New List(Of Field)()
' You can also add Dependson using code like:
' .DependsOn = New String() {"ieee", "dw01", "dware"} _
 
fields.Add(New Field() With { _
.Name = "des_system_lib", _
.DependsOn = Split("std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee", " ") _
})
fields.Add(New Field() With { _
.Name = "dw01", _
.DependsOn = Split("ieee dw01 dware gtech", " ") _
})
fields.Add(New Field() With { _
.Name = "dw02", _
.DependsOn = Split("ieee dw02 dware", " ") _
})
fields.Add(New Field() With { _
.Name = "dw03", _
.DependsOn = Split("std synopsys dware dw03 dw02 dw01 ieee gtech", " ") _
})
fields.Add(New Field() With { _
.Name = "dw04", _
.DependsOn = Split("dw04 ieee dw01 dware gtech", " ") _
})
fields.Add(New Field() With { _
.Name = "dw05", _
.DependsOn = Split("dw05 ieee dware", " ") _
})
fields.Add(New Field() With { _
.Name = "dw06", _
.DependsOn = Split("dw06 ieee dware", " ") _
})
fields.Add(New Field() With { _
.Name = "dw07", _
.DependsOn = Split("ieee dware", " ") _
})
fields.Add(New Field() With { _
.Name = "dware", _
.DependsOn = Split("ieee dware", " ") _
})
fields.Add(New Field() With { _
.Name = "gtech", _
.DependsOn = Split("ieee gtech", " ") _
})
fields.Add(New Field() With { _
.Name = "ramlib", _
.DependsOn = Split("std ieee", " ") _
})
fields.Add(New Field() With { _
.Name = "std_cell_lib", _
.DependsOn = Split("ieee std_cell_lib", " ") _
})
fields.Add(New Field() With { _
.Name = "synopsys" _
})
Console.WriteLine("Input:")
For Each ThisField As field In fields
Console.WriteLine(ThisField.Name)
If ThisField.DependsOn IsNot Nothing Then
For Each item As String In ThisField.DependsOn
Console.WriteLine(" -{0}", item)
Next
End If
Next
 
Console.WriteLine(vbLf & "...Sorting..." & vbLf)
 
Dim sortOrder As Integer() = getTopologicalSortOrder(fields)
 
For i As Integer = 0 To sortOrder.Length - 1
Dim field = fields(sortOrder(i))
Console.WriteLine(field.Name)
' Write up dependencies, too:
'If field.DependsOn IsNot Nothing Then
' For Each item As String In field.DependsOn
' Console.WriteLine(" -{0}", item)
' Next
'End If
Next
Console.Write("Press any key to continue . . . ")
Console.ReadKey(True)
End Sub
 
Private Sub CheckDependencies (ByRef Fields As List(Of Field))
' Make sure all objects we depend on are part of the field list
' themselves, as there may be dependencies that are not specified as fields themselves.
' Remove dependencies on fields themselves.Y
Dim AField As Field, ADependency As String
 
For i As Integer = Fields.Count - 1 To 0 Step -1
AField=fields(i)
If AField.DependsOn IsNot Nothing then
For j As Integer = 0 To Ubound(AField.DependsOn)
ADependency = Afield.DependsOn(j)
' We ignore fields that depends on themselves:
If AField.Name <> ADependency then
If ListContainsVertex(fields, ADependency) = False Then
' Add the dependent object to the field list, as it
' needs to be there, without any dependencies
Fields.Add(New Field() With { _
.Name = ADependency _
})
End If
End If
Next j
End If
Next i
End Sub
 
Private Sub RemoveSelfDependencies (ByRef Fields As List(Of Field))
' Make sure our fields don't depend on themselves.
' If they do, remove the dependency.
Dim InitialUbound as Integer
For Each AField As Field In Fields
If AField.DependsOn IsNot Nothing Then
InitialUbound = Ubound(AField.DependsOn)
For i As Integer = InitialUbound to 0 Step - 1
If Afield.DependsOn(i) = Afield.Name Then
' This field depends on itself, so remove
For j as Integer = i To UBound(AField.DependsOn)-1
Afield.DependsOn(j)=Afield.DependsOn(j+1)
Next
ReDim Preserve Afield.DependsOn(UBound(Afield.DependsOn)-1)
End If
Next
End If
Next
End Sub
 
Private Function ListContainsVertex(Fields As List(Of Field), VertexName As String) As Boolean
' Check to see if the list of Fields already contains a vertext called VertexName
Dim Found As Boolean = False
For i As Integer = 0 To fields.Count - 1
If Fields(i).Name = VertexName Then
Found = True
Exit For
End If
Next
Return Found
End Function
 
Private Function getTopologicalSortOrder(ByRef Fields As List(Of Field)) As Integer()
' Gets sort order. Will also add required dependencies to
' Fields.
 
' Make sure we don't have dependencies on ourselves.
' We'll just get rid of them.
RemoveSelfDependencies(Fields)
 
'First check depencies, add them to Fields if required:
CheckDependencies(Fields)
' Now we have the correct Fields list, so we can proceed:
Dim g As New TopologicalSorter(fields.Count)
Dim _indexes As New Dictionary(Of String, Integer)(fields.count)
 
'add vertex names to our lookup dictionaey
For i As Integer = 0 To fields.Count - 1
_indexes(fields(i).Name.ToLower()) = g.AddVertex(i)
Next
 
'add edges
For i As Integer = 0 To fields.Count - 1
If fields(i).DependsOn IsNot Nothing Then
For j As Integer = 0 To fields(i).DependsOn.Length - 1
g.AddEdge(i, _indexes(fields(i).DependsOn(j).ToLower()))
Next
End If
Next
 
Dim result As Integer() = g.Sort()
Return result
End Function
 
Private Class Field
Public Property Name() As String
Get
Return m_Name
End Get
Set
m_Name = Value
End Set
End Property
Private m_Name As String
Public Property DependsOn() As String()
Get
Return m_DependsOn
End Get
Set
m_DependsOn = Value
End Set
End Property
Private m_DependsOn As String()
End Class
End Module
Class TopologicalSorter
''source adapted from:
''http://tawani.blogspot.com/2009/02/topological-sorting-and-cyclic.html
''which was adapted from:
''http://www.java2s.com/Code/Java/Collections-Data-Structure/Topologicalsorting.htm
#Region "- Private Members -"
 
Private ReadOnly _vertices As Integer()
' list of vertices
Private ReadOnly _matrix As Integer(,)
' adjacency matrix
Private _numVerts As Integer
' current number of vertices
Private ReadOnly _sortedArray As Integer()
' Sorted vertex labels
 
#End Region
 
#Region "- CTors -"
 
Public Sub New(size As Integer)
_vertices = New Integer(size - 1) {}
_matrix = New Integer(size - 1, size - 1) {}
_numVerts = 0
For i As Integer = 0 To size - 1
For j As Integer = 0 To size - 1
_matrix(i, j) = 0
Next
Next
' sorted vert labels
_sortedArray = New Integer(size - 1) {}
End Sub
 
#End Region
 
#Region "- Public Methods -"
 
Public Function AddVertex(vertex As Integer) As Integer
_vertices(System.Threading.Interlocked.Increment(_numVerts)-1) = vertex
Return _numVerts - 1
End Function
 
Public Sub AddEdge(start As Integer, [end] As Integer)
_matrix(start, [end]) = 1
End Sub
 
Public Function Sort() As Integer()
' Topological sort
While _numVerts > 0
' while vertices remain,
' get a vertex with no successors, or -1
Dim currentVertex As Integer = noSuccessors()
If currentVertex = -1 Then
' must be a cycle
Throw New Exception("Graph has cycles")
End If
 
' insert vertex label in sorted array (start at end)
_sortedArray(_numVerts - 1) = _vertices(currentVertex)
 
' delete vertex
deleteVertex(currentVertex)
End While
 
' vertices all gone; return sortedArray
Return _sortedArray
End Function
 
#End Region
 
#Region "- Private Helper Methods -"
 
' returns vert with no successors (or -1 if no such verts)
Private Function noSuccessors() As Integer
For row As Integer = 0 To _numVerts - 1
Dim isEdge As Boolean = False
' edge from row to column in adjMat
For col As Integer = 0 To _numVerts - 1
If _matrix(row, col) > 0 Then
' if edge to another,
isEdge = True
' this vertex has a successor try another
Exit For
End If
Next
If Not isEdge Then
' if no edges, has no successors
Return row
End If
Next
Return -1
' no
End Function
 
Private Sub deleteVertex(delVert As Integer)
' if not last vertex, delete from vertexList
If delVert <> _numVerts - 1 Then
For j As Integer = delVert To _numVerts - 2
_vertices(j) = _vertices(j + 1)
Next
 
For row As Integer = delVert To _numVerts - 2
moveRowUp(row, _numVerts)
Next
 
For col As Integer = delVert To _numVerts - 2
moveColLeft(col, _numVerts - 1)
Next
End If
_numVerts -= 1
' one less vertex
End Sub
 
Private Sub moveRowUp(row As Integer, length As Integer)
For col As Integer = 0 To length - 1
_matrix(row, col) = _matrix(row + 1, col)
Next
End Sub
 
Private Sub moveColLeft(col As Integer, length As Integer)
For row As Integer = 0 To length - 1
_matrix(row, col) = _matrix(row, col + 1)
Next
End Sub
 
#End Region
End Class
 
Output[edit]
Input:
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

...Sorting...

des_system_lib
ramlib
dw03
std
std_cell_lib
dw04
dw01
gtech
dw07
dw06
dw05
dw02
dware
ieee
synopsys
Press any key to continue . . .

zkl[edit]

Translation of: Wikipedia

Input data is munged

fcn topoSort(data){ // data is L( L(root,L(leaves)),...)
allDs:=data.pump(List,fcn(rds){ T(Void.Write,Void.Write,rds[1]) }).copy();
roots:=D(data); // dictionary of root:leaves
L:=List();
S:=data.pump(List,'wrap([(r,_)]){ if(allDs.holds(r)) Void.Skip else r }).copy();
while(S){ //while S is non-empty do
(n:=S.pop()) : L.append(_); //remove a node n from S, add n to tail of L
foreach m in (ds:=roots.find(n,List)){ //node m with an edge e from n to m
allDs.del(allDs.index(m));
if (Void==allDs.find(m)) S.append(m); //m has no other incoming edges
} roots.del(n); // remove edge e from the graph
}
if(roots) throw(Exception.ValueError("Cycle: "+roots.keys));
L
}
data:=T(
"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", "",
);
data=data.pump(List,Void.Read,fcn(r,ds){
T( r, ds.replace(r,"").strip().split().copy() ) // leaves writable 'cause they will be
});
topoSort(data).println();
Output:
L("dw07","dw06","dw05","dw04","dw03","des_system_lib","ramlib",
  "std","dw01","gtech","dw02","dware","std_cell_lib","ieee","synopsys")

Adding dw04 to dw01 ("dw01", "ieee dw01 dware gtech dw04") and running:

Output:
ValueError : Cycle: L("dw01","dw04","dware","gtech")
  1. wp: topological sorting
  2. Jason Sachs "Ten little algorithms, part 4: topological sort".
  3. wp: tsort