Topological sort
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.
You are encouraged to solve this task according to the task description, using any language you may know.
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
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.
There are two popular algorithms for topological sorting:
11l
<lang 11l>V 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[String]()
]
F toposort2(&data)
L(k, v) data
v.discard(k)
Set[String] extra_items_in_deps
L(v) data.values()
extra_items_in_deps.update(v)
extra_items_in_deps = extra_items_in_deps - Set(data.keys())
L(item) extra_items_in_deps
data[item] = Set[String]()
[String] r
L
Set[String] ordered
L(item, dep) data
I dep.empty
ordered.add(item)
I ordered.empty
L.break
r.append(sorted(Array(ordered)).join(‘ ’))
[String = Set[String]] new_data
L(item, dep) data
I item !C ordered
new_data[item] = dep - ordered
data = move(new_data)
assert(data.empty, ‘A cyclic dependency exists’) R r
print(toposort2(&data).join("\n"))</lang>
- Output:
ieee std synopsys dware gtech ramlib std_cell_lib dw01 dw02 dw05 dw06 dw07 des_system_lib dw03 dw04
Ada
Digraphs: A package for directed graphs, representing nodes as positive numbers
The specification:
<lang Ada>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;</lang>
The implementation:
<lang Ada>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;</lang>
Set_of_Names: Translating strings into numbers and vice versa
The specification:
<lang Ada>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;</lang>
The implementation
<lang Ada>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;</lang>
Toposort: Putting things together for the main program
<lang Ada>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;</lang>
- 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
<lang bracmat>( ("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) );</lang>
- 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
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. <lang c>#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; }</lang>
- Output:
(items on the same row can be compiled together)<lang>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</lang>
C#
<lang csharp> namespace Algorithms {
using System; using System.Collections.Generic; using System.Linq;
public class TopologicalSorter<ValueType>
{
private class Relations
{
public int Dependencies = 0;
public HashSet<ValueType> Dependents = new HashSet<ValueType>();
}
private Dictionary<ValueType, Relations> _map = new Dictionary<ValueType, Relations>();
public void Add(ValueType obj)
{
if (!_map.ContainsKey(obj)) _map.Add(obj, new Relations());
}
public void Add(ValueType obj, ValueType dependency)
{
if (dependency.Equals(obj)) return;
if (!_map.ContainsKey(dependency)) _map.Add(dependency, new Relations());
var dependents = _map[dependency].Dependents;
if (!dependents.Contains(obj))
{
dependents.Add(obj);
if (!_map.ContainsKey(obj)) _map.Add(obj, new Relations());
++_map[obj].Dependencies;
}
}
public void Add(ValueType obj, IEnumerable<ValueType> dependencies)
{
foreach (var dependency in dependencies) Add(obj, dependency);
}
public void Add(ValueType obj, params ValueType[] dependencies)
{
Add(obj, dependencies as IEnumerable<ValueType>);
}
public Tuple<IEnumerable<ValueType>, IEnumerable<ValueType>> Sort()
{
List<ValueType> sorted = new List<ValueType>(), cycled = new List<ValueType>();
var map = _map.ToDictionary(kvp => kvp.Key, kvp => kvp.Value);
sorted.AddRange(map.Where(kvp => kvp.Value.Dependencies == 0).Select(kvp => kvp.Key));
for (int idx = 0; idx < sorted.Count; ++idx) sorted.AddRange(map[sorted[idx]].Dependents.Where(k => --map[k].Dependencies == 0));
cycled.AddRange(map.Where(kvp => kvp.Value.Dependencies != 0).Select(kvp => kvp.Key));
return new Tuple<IEnumerable<ValueType>, IEnumerable<ValueType>>(sorted, cycled);
}
public void Clear()
{
_map.Clear();
}
}
}
/* Example usage with Task object
- /
namespace ExampleApplication {
using Algorithms; using System; using System.Collections.Generic; using System.Linq;
public class Task
{
public string Message;
}
class Program
{
static void Main(string[] args)
{
List<Task> tasks = new List<Task>
{
new Task{ Message = "A - depends on B and C" }, //0
new Task{ Message = "B - depends on none" }, //1
new Task{ Message = "C - depends on D and E" }, //2
new Task{ Message = "D - depends on none" }, //3
new Task{ Message = "E - depends on F, G and H" }, //4
new Task{ Message = "F - depends on I" }, //5
new Task{ Message = "G - depends on none" }, //6
new Task{ Message = "H - depends on none" }, //7
new Task{ Message = "I - depends on none" }, //8
};
TopologicalSorter<Task> resolver = new TopologicalSorter<Task>();
// now setting relations between them as described above
resolver.Add(tasks[0], new[] { tasks[1], tasks[2] });
//resolver.Add(tasks[1]); // no need for this since the task was already mentioned as a dependency
resolver.Add(tasks[2], new[] { tasks[3], tasks[4] });
//resolver.Add(tasks[3]); // no need for this since the task was already mentioned as a dependency
resolver.Add(tasks[4], tasks[5], tasks[6], tasks[7]);
resolver.Add(tasks[5], tasks[8]);
//resolver.Add(tasks[6]); // no need for this since the task was already mentioned as a dependency
//resolver.Add(tasks[7]); // no need for this since the task was already mentioned as a dependency
//resolver.Add(tasks[3], tasks[0]); // uncomment this line to test cycled dependency
var result = resolver.Sort();
var sorted = result.Item1;
var cycled = result.Item2;
if (!cycled.Any())
{
foreach (var d in sorted) Console.WriteLine(d.Message);
}
else
{
Console.Write("Cycled dependencies detected: ");
foreach (var d in cycled) Console.Write($"{d.Message[0]} ");
Console.WriteLine();
}
Console.WriteLine("exiting...");
}
}
}
</lang>
- Output:
<lang>B - depends on none
D - depends on none G - depends on none H - depends on none I - depends on none F - depends on I E - depends on F, G and H C - depends on D and E A - depends on B and C exiting...</lang>
- Output:
(with cycled dependency)<lang>Cycled dependencies detected
exiting...</lang>
C++
C++11
<lang cpp>#include <map>
- include <set>
template<typename Goal> class topological_sorter { protected:
struct relations {
std::size_t dependencies;
std::set<Goal> dependents;
};
std::map<Goal, relations> map;
public:
void add_goal(Goal const &goal) {
map[goal];
}
void add_dependency(Goal const &goal, Goal const &dependency) {
if (dependency == goal)
return;
auto &dependents = map[dependency].dependents;
if (dependents.find(goal) == dependents.end()) {
dependents.insert(goal);
++map[goal].dependencies;
}
}
template<typename Container>
void add_dependencies(Goal const &goal, Container const &dependencies) {
for (auto const &dependency : dependencies)
add_dependency(goal, dependency);
}
template<typename ResultContainer, typename CyclicContainer>
void destructive_sort(ResultContainer &sorted, CyclicContainer &unsortable) {
sorted.clear();
unsortable.clear();
for (auto const &lookup : map) {
auto const &goal = lookup.first;
auto const &relations = lookup.second;
if (relations.dependencies == 0)
sorted.push_back(goal);
}
for (std::size_t index = 0; index < sorted.size(); ++index)
for (auto const &goal : map[sorted[index]].dependents)
if (--map[goal].dependencies == 0)
sorted.push_back(goal);
for (auto const &lookup : map) {
auto const &goal = lookup.first;
auto const &relations = lookup.second;
if (relations.dependencies != 0)
unsortable.push_back(goal);
}
}
template<typename ResultContainer, typename CyclicContainer>
void sort(ResultContainer &sorted, CyclicContainer &unsortable) {
topological_sorter<Goal> temporary = *this;
temporary.destructive_sort(sorted, unsortable);
}
void clear() {
map.clear();
}
};
/*
Example usage with text strings */
- include <fstream>
- include <sstream>
- include <iostream>
- include <string>
- include <vector>
using namespace std;
void display_heading(string const &message) {
cout << endl << "~ " << message << " ~" << endl;
} void display_results(string const &input) {
topological_sorter<string> sorter;
vector<string> sorted, unsortable;
stringstream lines(input);
string line;
while (getline(lines, line)) {
stringstream buffer(line);
string goal, dependency;
buffer >> goal;
sorter.add_goal(goal);
while (buffer >> dependency)
sorter.add_dependency(goal, dependency);
}
sorter.destructive_sort(sorted, unsortable);
if (sorted.size() == 0)
display_heading("Error: no independent variables found!");
else {
display_heading("Result");
for (auto const &goal : sorted)
cout << goal << endl;
}
if (unsortable.size() != 0) {
display_heading("Error: cyclic dependencies detected!");
for (auto const &goal : unsortable)
cout << goal << endl;
}
} int main(int argc, char **argv) {
if (argc == 1) {
string example = "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";
display_heading("Example: each line starts with a goal followed by it's dependencies");
cout << example << endl;
display_results(example);
display_heading("Enter lines of data (press enter when finished)");
string line, data;
while (getline(cin, line) && !line.empty())
data += line + '\n';
if (!data.empty())
display_results(data);
} else
while (*(++argv)) {
ifstream file(*argv);
typedef istreambuf_iterator<char> iterator;
display_results(string(iterator(file), iterator()));
}
}</lang>
C++17
<lang cpp>#include <unordered_map>
- include <unordered_set>
- include <vector>
template <typename ValueType> class topological_sorter { public:
using value_type = ValueType;
protected:
struct relations
{
std::size_t dependencies { 0 };
std::unordered_set<value_type> dependents {};
};
std::unordered_map<value_type, relations> _map {};
public:
void add(const value_type &object)
{
_map.try_emplace(object, relations {});
}
void add(const value_type &object, const value_type &dependency)
{
if (dependency == object) return;
auto &dependents = _map[dependency].dependents;
if (dependents.find(object) == std::end(dependents))
{
dependents.insert(object);
++_map[object].dependencies;
}
}
template <typename Container>
void add(const value_type &object, const Container &dependencies)
{
for (auto const &dependency : dependencies) add(object, dependency);
}
void add(const value_type &object, const std::initializer_list<value_type> &dependencies)
{
add<std::initializer_list<value_type>>(object, dependencies);
}
template<typename... Args>
void add(const value_type &object, const Args&... dependencies)
{
(add(object, dependencies), ...);
}
auto sort()
{
std::vector<value_type> sorted, cycled;
auto map { _map };
for (const auto &[object, relations] : map) if (!relations.dependencies) sorted.emplace_back(object);
for (decltype(std::size(sorted)) idx = 0; idx < std::size(sorted); ++idx)
for (auto const& object : map[sorted[idx]].dependents)
if (!--map[object].dependencies) sorted.emplace_back(object);
for (const auto &[object, relations] : map) if (relations.dependencies) cycled.emplace_back(std::move(object));
return std::pair(std::move(sorted), std::move(cycled)); }
void clear()
{
_map.clear();
}
};
/* Example usage with shared_ptr to class
- /
- include <iostream>
- include <memory>
int main() {
using namespace std::string_literals;
struct task
{
std::string message;
task(const std::string &v) : message { v } {}
~task() { std::cout << message[0] << " - destroyed" << std::endl; }
};
using task_ptr = std::shared_ptr<task>;
std::vector<task_ptr> tasks
{
// defining simple tasks
std::make_shared<task>("A - depends on B and C"s), //0
std::make_shared<task>("B - depends on none"s), //1
std::make_shared<task>("C - depends on D and E"s), //2
std::make_shared<task>("D - depends on none"s), //3
std::make_shared<task>("E - depends on F, G and H"s), //4
std::make_shared<task>("F - depends on I"s), //5
std::make_shared<task>("G - depends on none"s), //6
std::make_shared<task>("H - depends on none"s), //7
std::make_shared<task>("I - depends on none"s), //8
};
topological_sorter<task_ptr> resolver;
// now setting relations between them as described above
resolver.add(tasks[0], { tasks[1], tasks[2] });
//resolver.add(tasks[1]); // no need for this since the task was already mentioned as a dependency
resolver.add(tasks[2], { tasks[3], tasks[4] });
//resolver.add(tasks[3]); // no need for this since the task was already mentioned as a dependency
resolver.add(tasks[4], tasks[5], tasks[6], tasks[7]); // using templated add with fold expression
resolver.add(tasks[5], tasks[8]);
//resolver.add(tasks[6]); // no need for this since the task was already mentioned as a dependency
//resolver.add(tasks[7]); // no need for this since the task was already mentioned as a dependency
//resolver.add(tasks[3], tasks[0]); // uncomment this line to test cycled dependency
const auto &[sorted, cycled] = resolver.sort();
if (std::empty(cycled))
{
for (auto const& d: sorted)
std::cout << d->message << std::endl;
}
else
{
std::cout << "Cycled dependencies detected: ";
for (auto const& d: cycled)
std::cout << d->message[0] << " ";
std::cout << std::endl; }
//tasks.clear(); // uncomment this line to destroy all tasks in sorted order.
std::cout << "exiting..." << std::endl;
return 0;
}</lang>
- Output:
<lang>I - depends on none
H - depends on none G - depends on none D - depends on none B - depends on none F - depends on I E - depends on F, G and H C - depends on D and E A - depends on B and C exiting... A - destroyed B - destroyed C - destroyed D - destroyed E - destroyed F - destroyed G - destroyed H - destroyed I - destroyed</lang>
- Output:
(with cycled dependency)<lang>Cycled dependencies detected
exiting... A - destroyed B - destroyed C - destroyed D - destroyed E - destroyed F - destroyed G - destroyed H - destroyed I - destroyed</lang>
Clojure
Here is a quick implementation in Clojure, developed at Java Posse Roundup 2010 in collaboration with Fred Simon, with a bit of subsequent simplification by Joel Neely.
Dependencies are represented by a map from each item to the set of items on which it depends. The first function (dep), builds a dependency map for a single item.
The next few functions (empty-dep, pair-dep, default-deps, declared-deps, and deps) are used to construct the map from a list that alternates items with lists of their dependencies.
The next three functions (no-dep-items, remove-items, and topo-sort-deps) are the core of the topological sort algorithm, which iteratively removes items with no remaining dependencies from the map and "stacks" them onto the result. When the map becomes empty the reversed result is returned. If no dependency-free items can be found, then any non-empty remainder of the map contains cycles.
The last function (topo-sort) is simply a helper which applies topo-sort-deps to a dependency map constructed from the item-and-list-of-dependencies input list.
Implementation
<lang clojure>(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)))
</lang>
Examples of sortable and non-sortable data:
<lang clojure>(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))</lang>
=====
- Output:
=====
<lang clojure>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)"</lang>
CoffeeScript
<lang coffeescript> 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
</lang>
Common Lisp
<lang lisp>(defun topological-sort (graph &key (test 'eql))
"Graph is an association list whose keys are objects and whose
values are lists of objects on which the corresponding key depends. Test is used to compare elements, and should be a suitable test for hash-tables. Topological-sort returns two values. The first is a list of objects sorted toplogically. The second is a boolean indicating whether all of the objects in the input graph are present in the topological ordering (i.e., the first value)."
(let ((entries (make-hash-table :test test)))
(flet ((entry (vertex)
"Return the entry for vertex. Each entry is a cons whose
car is the number of outstanding dependencies of vertex
and whose cdr is a list of dependants of vertex."
(multiple-value-bind (entry presentp) (gethash vertex entries)
(if presentp entry
(setf (gethash vertex entries) (cons 0 '()))))))
;; populate entries initially
(dolist (vertex graph)
(destructuring-bind (vertex &rest dependencies) vertex
(let ((ventry (entry vertex)))
(dolist (dependency dependencies)
(let ((dentry (entry dependency)))
(unless (funcall test dependency vertex)
(incf (car ventry))
(push vertex (cdr dentry))))))))
;; L is the list of sorted elements, and S the set of vertices
;; with no outstanding dependencies.
(let ((L '())
(S (loop for entry being each hash-value of entries
using (hash-key vertex)
when (zerop (car entry)) collect vertex)))
;; Until there are no vertices with no outstanding dependencies,
;; process vertices from S, adding them to L.
(do* () ((endp S))
(let* ((v (pop S)) (ventry (entry v)))
(remhash v entries)
(dolist (dependant (cdr ventry) (push v L))
(when (zerop (decf (car (entry dependant))))
(push dependant S)))))
;; return (1) the list of sorted items, (2) whether all items
;; were sorted, and (3) if there were unsorted vertices, the
;; hash table mapping these vertices to their dependants
(let ((all-sorted-p (zerop (hash-table-count entries))))
(values (nreverse L)
all-sorted-p
(unless all-sorted-p
entries)))))))</lang>
Provided example in which all items can be sorted:
<lang lisp>> (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</lang>
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.)
<lang lisp>> (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)</lang>
Crystal
<lang crystal>def dfs_topo_visit(n, g, tmp, permanent, l)
if permanent.includes?(n)
return
elsif tmp.includes?(n)
raise "unorderable: circular dependency detected involving '#{n}'"
end
tmp.add(n)
g[n].each { |m|
dfs_topo_visit(m, g, tmp, permanent, l)
}
tmp.delete(n) permanent.add(n) l.insert(0, n)
end
def dfs_topo_sort(g)
tmp = Set(String).new permanent = Set(String).new l = Array(String).new
while true
keys = g.keys.to_set - permanent
if keys.empty?
break
end
n = keys.first
dfs_topo_visit(n, g, tmp, permanent, l)
end
return l
end
def build_graph(deps)
g = {} of String => Set(String)
deps.split("\n").each { |line|
line_split = line.strip.split
line_split.each { |dep|
unless g.has_key?(dep)
g[dep] = Set(String).new
end
unless line_split[0] == dep
g[dep].add(line_split[0])
end
}
}
return g
end
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"
circular_deps = "\ncyc01 cyc02
cyc02 cyc01"
puts dfs_topo_sort(build_graph(data)).join(" -> ") puts "" puts dfs_topo_sort(build_graph(data + circular_deps)).join(" -> ") </lang>
- Output:
ieee -> gtech -> dware -> dw07 -> dw06 -> dw05 -> dw01 -> dw04 -> dw02 -> std_cell_lib -> synopsys -> std -> ramlib -> dw03 -> des_system_lib Unhandled exception: unorderable: circular dependency detected involving 'cyc01' (Exception)
D
<lang d>import std.stdio, std.string, std.algorithm, std.range;
final class ArgumentException : Exception {
this(string text) pure nothrow @safe /*@nogc*/ {
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.dup.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;
}</lang>
- Output:
#1 : ["ieee", "std", "synopsys"] #2 : ["dware", "gtech", "ramlib", "std_cell_lib"] #3 : ["dw01", "dw02", "dw05", "dw06", "dw07"] #4 : ["des_system_lib", "dw03", "dw04"] topo.ArgumentException@topo.d(7): A cyclic dependency exists amongst: [dw01:[dw04],des_system_lib:[dw01],dw03:[dw01],dw04:[dw01]] ---------------- ...\topo.d(71): _Dmain ----------------
E
<lang e>def makeQueue := <elib:vat.makeQueue>
def topoSort(data :Map[any, Set[any]]) {
# Tables of nodes and edges
def forwardEdges := [].asMap().diverge()
def reverseCount := [].asMap().diverge()
def init(node) {
reverseCount[node] := 0
forwardEdges[node] := [].asSet().diverge()
}
for node => deps in data {
init(node)
for dep in deps { init(dep) }
}
# 'data' holds the dependencies. Compute the other direction.
for node => deps in data {
for dep ? (dep != node) in deps {
forwardEdges[dep].addElement(node)
reverseCount[node] += 1
}
}
# Queue containing all elements that have no (initial or remaining) incoming edges
def ready := makeQueue()
for node => ==0 in reverseCount {
ready.enqueue(node)
}
var result := []
while (ready.optDequeue() =~ node :notNull) {
result with= node
for next in forwardEdges[node] {
# Decrease count of incoming edges and enqueue if none
if ((reverseCount[next] -= 1).isZero()) {
ready.enqueue(next)
}
}
forwardEdges.removeKey(node)
}
if (forwardEdges.size().aboveZero()) {
throw(`Topological sort failed: $forwardEdges remains`)
}
return result
}</lang>
<lang e>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))</lang>
- Output:
["std", "synopsys", "ieee", "dware", "gtech", "ramlib", "std_cell_lib", "dw02", "dw05", "dw06", "dw07", "dw01", "des_system_lib", "dw03", "dw04"]
EchoLisp
We use the low-level primitives of the 'graph' library to build the directed graph and implement the topological sort.
Data
<lang lisp> (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)))) </lang> Implementation
Remove all vertices with in-degree = 0, until to one left. (in-degree = number of arrows to a vertex) <lang lisp>
- 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))))))
</lang>
- Output:
<lang lisp> (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) </lang>
Elixir
<lang elixir>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)</lang>
- 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
<lang erlang> -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
</lang>
- Output:
<lang erlang> 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</lang>
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
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).
<lang forth>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</lang>
- Output:
ieee dware dw07 dw06 dw05 gtech (cycle: dw04 dw01) dw01 dw04 std synopsys dw02 dw03 ramlib std_cell_lib des_system_lib
Fortran
FORTRAN 77
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). <lang fortran> 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</lang>
An example. Dependencies are encoded to make program shorter (in array ICODE).
<lang fortran> 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</lang>
- 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
A modern Fortran (95-2008) version of the TSORT subroutine is shown here (note that the IPOS array is not an input). <lang fortran>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 </lang>
FunL
<lang funl>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 )</lang>
- Output:
[synopsys, ieee, std, dware, std_cell_lib, gtech, ramlib, dw06, dw05, dw02, dw07, dw01, dw03, dw04, des_system_lib]
Go
Kahn
<lang go>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
}</lang>
- 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
Topological sort only, this function can replace topSortKahn in above program. The in-degree list is not needed. <lang go>// 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
}</lang>
- 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
<lang haskell>import Data.List ((\\), elemIndex, intersect, nub) import Data.Bifunctor (bimap, first)
combs 0 _ = [[]] combs _ [] = [] combs k (x:xs) = ((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 :: [(String, String)] -> [String] toposort xs
| (not . null) cycleDetect =
error $ "Dependency cycle detected for libs " ++ show cycleDetect
| otherwise = foldl makePrecede [] dB
where
dB = (\(x, y) -> (x, y \\ x)) . bimap 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) $
(\[(a, as), (b, bs)] -> (a `intersect` bs) ++ (b `intersect` as)) <$>
combs 2 dB
main :: IO () main = print $ toposort depLibs</lang>
- Output:
<lang haskell>*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"</lang>
Huginn
<lang huginn>import Algorithms as algo; import Text as text;
class DirectedGraph { _adjecentVertices = {}; add_vertex( vertex_ ) { _adjecentVertices[vertex_] = []; } add_edge( from_, to_ ) { _adjecentVertices[from_].push( to_ ); } adjecent_vertices( vertex_ ) { return ( vertex_ ∈ _adjecentVertices ? _adjecentVertices.get( vertex_ ) : [] ); } }
class DepthFirstSearch { _visited = set(); _postOrder = []; _cycleDetector = set(); run( graph_, start_ ) { _cycleDetector.insert( start_ ); _visited.insert( start_ ); for ( vertex : graph_.adjecent_vertices( start_ ) ) { if ( vertex == start_ ) { continue; } if ( vertex ∈ _cycleDetector ) { throw Exception( "A cycle involving vertices {} found!".format( _cycleDetector ) ); } if ( vertex ∉ _visited ) { run( graph_, vertex ); } } _postOrder.push( start_ ); _cycleDetector.erase( start_ ); } topological_sort( graph_ ) { for ( vertex : graph_._adjecentVertices ) { if ( vertex ∉ _visited ) { run( graph_, vertex ); } } return ( _postOrder ); } }
main() { rawdata = "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"; dg = DirectedGraph(); for ( l : algo.filter( text.split( rawdata, "\n" ), @( x ) { size( x ) > 0; } ) ) { def = algo.materialize( algo.map( text.split( l, "|" ), string.strip ), list ); dg.add_vertex( def[0] ); for ( n : algo.filter( algo.map( text.split( def[1], " " ), string.strip ), @( x ) { size( x ) > 0; } ) ) { dg.add_edge( def[0], n ); } } dfs = DepthFirstSearch(); print( "{}\n".format( dfs.topological_sort( dg ) ) ); }</lang>
Icon and Unicon
Icon
This solution uses an efficient internal representation for a graph that limits the number of nodes to no more than 256.
The resulting topological ordering is displayed so elements on each line are independent and so can be built in parallel once the preceding lines of elements have been built.
<lang icon>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</lang>
- 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
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.
<lang icon>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</lang>
J
<lang J>dependencySort=: monad define
parsed=. <@;:;._2 y
names=. {.&>parsed
depends=. (> =@i.@#) names e.S:1 parsed
depends=. (+. +./ .*.~)^:_ depends
assert.-.1 e. (<0 1)|:depends
(-.&names ~.;parsed),names /: +/"1 depends
)</lang>
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:
<lang J> >dependencySort dependencies
std ieee dware gtech ramlib std_cell_lib synopsys dw02 dw05 dw06 dw07 dw01 dw04 dw03 des_system_lib</lang>
If we tried to also make dw01 depend on dw04, the sort would fail because of the circular dependency:
<lang J> dependencySort dependencies,'dw01 dw04',LF |assertion failure: dependencySort | -.1 e.(<0 1)|:depends</lang>
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):
<lang J>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
)</lang>
It's results are identical to the first implementation, but this might be more efficient in typical cases.
Java
<lang java>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},
{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;
}
}</lang>
[std, ieee, dware, dw02, dw05, dw06, dw07, gtech, dw01, dw04, ramlib, std_cell_lib, synopsys, des_system_lib, dw03]
JavaScript
ES6
<lang JavaScript>const libs =
`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`;
// A map of the input data, with the keys as the packages, and the values as // and array of packages on which it depends. const D = libs
.split('\n')
.map(e => e.split(' ').filter(e => e != ))
.reduce((p, c) =>
p.set(c[0], c.filter((e, i) => i > 0 && e !== c[0] ? e : null)), new Map());
[].concat(...D.values()).forEach(e => {
D.set(e, D.get(e) || [])
});
// The above map rotated so that it represents a DAG of the form // Map { // A => [ A, B, C], // B => [C], // C => [] // } // where each key represents a node, and the array contains the edges. const G = [...D.keys()].reduce((p, c) =>
p.set( c, [...D.keys()].filter(e => D.get(e).includes(c))), new Map()
);
// An array of leaf nodes; nodes with 0 in degrees. const Q = [...D.keys()].filter(e => D.get(e).length == 0);
// The result array. const S = []; while (Q.length) {
const u = Q.pop();
S.push(u);
G.get(u).forEach(v => {
D.set(v, D.get(v).filter(e => e !== u));
if (D.get(v).length == 0) {
Q.push(v);
}
});
}
console.log('Solution:', S); </lang>
Output: <lang JavaScript> Solution: [
'ieee', 'std_cell_lib', 'gtech', 'dware', 'dw07', 'dw06', 'dw05', 'dw02', 'dw01', 'dw04', 'std', 'ramlib', 'synopsys', 'dw03', 'des_system_lib' ]
</lang>
jq
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. <lang jq># 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 | with_entries(.value -= 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</lang> Data: <lang json>{"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": []
} </lang>
- Output:
<lang jq> $ 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"] </lang>
Julia
<lang julia>function toposort(data::Dict{T,Set{T}}) where T
data = copy(data)
for (k, v) in data
delete!(v, k)
end
extraitems = setdiff(reduce(∪, values(data)), keys(data))
for item in extraitems
data[item] = Set{T}()
end
rst = Vector{T}()
while true
ordered = Set(item for (item, dep) in data if isempty(dep))
if isempty(ordered) break end
append!(rst, ordered)
data = Dict{T,Set{T}}(item => setdiff(dep, ordered) for (item, dep) in data if item ∉ ordered)
end
@assert isempty(data) "a cyclic dependency exists amongst $(keys(data))"
return rst
end
data = Dict{String,Set{String}}(
"des_system_lib" => Set(split("std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee")),
"dw01" => Set(split("ieee dw01 dware gtech")),
"dw02" => Set(split("ieee dw02 dware")),
"dw03" => Set(split("std synopsys dware dw03 dw02 dw01 ieee gtech")),
"dw04" => Set(split("dw04 ieee dw01 dware gtech")),
"dw05" => Set(split("dw05 ieee dware")),
"dw06" => Set(split("dw06 ieee dware")),
"dw07" => Set(split("ieee dware")),
"dware" => Set(split("ieee dware")),
"gtech" => Set(split("ieee gtech")),
"ramlib" => Set(split("std ieee")),
"std_cell_lib" => Set(split("ieee std_cell_lib")),
"synopsys" => Set(),
)
println("# Topologically sorted:\n - ", join(toposort(data), "\n - "))</lang>
- Output:
# Topologically sorted: - synopsys - ieee - std - ramlib - dware - gtech - std_cell_lib - dw07 - dw05 - dw02 - dw01 - dw06 - des_system_lib - dw03 - dw04
Kotlin
<lang scala>// version 1.1.51
val s = "std, ieee, des_system_lib, dw01, dw02, dw03, dw04, dw05, " +
"dw06, dw07, dware, gtech, ramlib, std_cell_lib, synopsys"
val deps = mutableListOf(
2 to 0, 2 to 14, 2 to 13, 2 to 4, 2 to 3, 2 to 12, 2 to 1,
3 to 1, 3 to 10, 3 to 11,
4 to 1, 4 to 10,
5 to 0, 5 to 14, 5 to 10, 5 to 4, 5 to 3, 5 to 1, 5 to 11,
6 to 1, 6 to 3, 6 to 10, 6 to 11,
7 to 1, 7 to 10,
8 to 1, 8 to 10,
9 to 1, 9 to 10,
10 to 1,
11 to 1,
12 to 0, 12 to 1,
13 to 1
)
class Graph(s: String, edges: List<Pair<Int,Int>>) {
val vertices = s.split(", ")
val numVertices = vertices.size
val adjacency = List(numVertices) { BooleanArray(numVertices) }
init {
for (edge in edges) adjacency[edge.first][edge.second] = true
}
fun hasDependency(r: Int, todo: List<Int>): Boolean {
return todo.any { adjacency[r][it] }
}
fun topoSort(): List<String>? {
val result = mutableListOf<String>()
val todo = MutableList<Int>(numVertices) { it }
try {
outer@ while(!todo.isEmpty()) {
for ((i, r) in todo.withIndex()) {
if (!hasDependency(r, todo)) {
todo.removeAt(i)
result.add(vertices[r])
continue@outer
}
}
throw Exception("Graph has cycles")
}
}
catch (e: Exception) {
println(e)
return null
}
return result
}
}
fun main(args: Array<String>) {
val g = Graph(s, deps)
println("Topologically sorted order:")
println(g.topoSort())
println()
// now insert 3 to 6 at index 10 of deps
deps.add(10, 3 to 6)
val g2 = Graph(s, deps)
println("Following the addition of dw04 to the dependencies of dw01:")
println(g2.topoSort())
}</lang>
- Output:
Topologically sorted order: [std, ieee, dware, dw02, dw05, dw06, dw07, gtech, dw01, dw04, ramlib, std_cell_lib, synopsys, des_system_lib, dw03] Following the addition of dw04 to the dependencies of dw01: java.lang.Exception: Graph has cycles null
This version follows python implementation and returns List of Lists which is useful for parallel execution for example
<lang scala> val graph = mapOf(
"des_system_lib" to "std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee".split(" ").toSet(),
"dw01" to "ieee dw01 dware gtech".split(" ").toSet(),
"dw02" to "ieee dw02 dware".split(" ").toSet(),
"dw03" to "std synopsys dware dw03 dw02 dw01 ieee gtech".split(" ").toSet(),
"dw04" to "dw04 ieee dw01 dware gtech".split(" ").toSet(),
"dw05" to "dw05 ieee dware".split(" ").toSet(),
"dw06" to "dw06 ieee dware".split(" ").toSet(),
"dw07" to "ieee dware".split(" ").toSet(),
"dware" to "ieee dware".split(" ").toSet(),
"gtech" to "ieee gtech".split(" ").toSet(),
"ramlib" to "std ieee".split(" ").toSet(),
"std_cell_lib" to "ieee std_cell_lib".split(" ").toSet(),
"synopsys" to setOf()
)
fun toposort( graph: Map<String,Set<String>> ): List<List<String>> {
var data = graph.map { (k,v) -> k to v.toMutableSet() }.toMap().toMutableMap()
// ignore self dependancies
data = data.map { (k,v) -> v.remove(k); k to v }.toMap().toMutableMap()
val extraItemsInDeps = data.values.reduce { a,b -> a.union( b ).toMutableSet() } - data.keys.toSet()
data.putAll( extraItemsInDeps.map { it to mutableSetOf<String>() }.toMap() )
val res = mutableListOf<List<String>>()
mainloop@ while( true ) {
innerloop@ while( true ) {
val ordered = data.filter{ (_,v) -> v.isEmpty() }.map { (k,_) -> k }
if( ordered.isEmpty() )
break@innerloop
res.add( ordered )
data = data.filter { (k,_) -> !ordered.contains(k) }.map { (k,v) -> v.removeAll(ordered); k to v }.toMap().toMutableMap()
}
if( data.isNotEmpty() )
throw Exception( "A cyclic dependency exists amongst: ${data.toList().joinToString { "," }}" )
else
break@mainloop
}
return res
}
fun main( args: Array<String> ) {
val result = toposort( graph )
println( "sorted dependencies:[\n${result.joinToString( ",\n")}\n]" )
}
</lang>
- Output:
sorted dependencies:[ [synopsys, std, ieee], [dware, gtech, ramlib, std_cell_lib], [dw01, dw02, dw05, dw06, dw07], [des_system_lib, dw03, dw04] ]
M2000 Interpreter
<lang M2000 Interpreter>Module testthis { \\ empty stack Flush inventory LL append LL, "des_system_lib":=(List:="std", "synopsys", "std_cell_lib", "des_system_lib", "dw02", "dw01", "ramlib", "ieee") REM append LL, "dw01":=(List:="dw04","ieee", "dw01", "dware", "gtech") append LL, "dw01":=(List:="ieee", "dw01", "dware", "gtech") append LL, "dw02":=(List:="ieee", "dw02", "dware") append LL, "dw03":=(List:="std", "synopsys", "dware", "dw03", "dw02", "dw01", "ieee", "gtech") append LL, "dw04":=(List:= "ieee", "dw01", "dware", "gtech") append LL, "dw05":=(List:="dw05", "ieee", "dware") append LL, "dw06":=(List:="dw06", "ieee", "dware") append LL, "dw07":=(List:="ieee", "dware") append LL, "dware":=(List:="ieee", "dware") append LL, "gtech":=(List:="ieee", "gtech") append LL, "ramlib":=(List:="std", "ieee") append LL, "std_cell_lib":=(List:="ieee", "std_cell_lib") append LL, "synopsys":=List \\ inventory itmes may have keys/items or keys. \\ here we have keys so keys return as item also \\ when we place an item in a key (an empty string) ... \\ we mark the item to not return the key but an empty string inventory final mm=each(LL) while mm k$=eval$(mm!) m=eval(mm) mmm=each(m) While mmm k1$=eval$(mmm!) if not exist(LL, k1$) then if not exist(final, k1$) then append final, k1$ return m, k1$:="" \\ mark that item else mmmm=Eval(LL) if len(mmmm)=0 then if not exist(final, k1$) then append final, k1$ return m, k1$:="" \\ mark that item end if end if end while end while mm=each(LL) while mm \\ using eval$(mm!) we read the key as string k$=eval$(mm!) if exist(final, k$) then continue m=eval(mm) mmm=each(m) While mmm \\ we read the item, if no item exist we get the key k1$=eval$(mmm) if k1$="" then continue if exist(final, k1$) then continue data k1$ \\ push to end to stack end while while not empty read k1$ if exist(final, k1$) then continue m=LL(k1$) mmm=each(m) delthis=0 While mmm k2$=eval$(mmm) if k2$="" then continue if k1$=k2$ then continue if exist(final, k2$) then continue push k2$ \\ push to top of stack return m, k2$:="" delthis++ end while if delthis=0 then if not exist(final, k1$) then mmm=each(m) While mmm k2$=eval$(mmm!) if k2$=k1$ then continue if exist(final, k2$) Else Print "unsorted:";k1$, k2$ end if end while append final, k1$ : Return LL, k1$:=List end if end if end while if not exist(final, k$) then append final, k$ end while document doc$ ret=each(final,1, -2) while ret doc$=eval$(ret)+" -> " end while doc$=final$(len(final)-1!) Report doc$ clipboard doc$ } testthis </lang>
- Output:
std -> synopsys -> ieee -> std_cell_lib -> ramlib -> gtech -> dware -> dw02 -> dw01 -> des_system_lib -> dw03 -> dw04 -> dw05 -> dw06 -> dw07 if we place REM at next line we get unsorted:dw01 dw04 std -> synopsys -> ieee -> std_cell_lib -> ramlib -> gtech -> dware -> dw01 -> dw02 -> des_system_lib -> dw03 -> dw04 -> dw05 -> dw06 -> dw07
Mathematica/Wolfram Language
Work in Mathematica 8 or higher versions. <lang mathematica>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", {}}}</lang>
- 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.
Mercury
<lang Mercury>
- - module topological_sort.
- - interface.
- - import_module io.
- - pred main(io::di,io::uo) is det.
- - implementation.
- - import_module string, solutions, list, set, require.
- - pred min_element(set(T),pred(T,T),T).
- - mode min_element(in,pred(in,in) is semidet,out) is nondet.
min_element(_,_,_):-fail. min_element(S,P,X):-
member(X,S), filter((pred(Y::in) is semidet :- P(Y,X)),S,LowerThanX), is_empty(LowerThanX).
- - pred topological_sort(set(T),pred(T,T),list(T),list(T)).
- - mode topological_sort(in,(pred((ground >> ground), (ground >> ground)) is semidet),in,out) is nondet.
- - pred topological_sort(set(T),pred(T,T),list(T)).
- - mode topological_sort(in,(pred((ground >> ground), (ground >> ground)) is semidet),out) is nondet.
topological_sort(S,P,Ac,L) :-
(
is_empty(S) -> L is Ac
; solutions(
pred(X::out) is nondet:- min_element(S,P,X) , Solutions ), ( is_empty(Solutions) -> error("No solution detected.\n") ; delete_list(Solutions,S,Sprime), append(Solutions,Ac,AcPrime), topological_sort(Sprime,P,AcPrime,L) )
).
topological_sort(S,P,L) :- topological_sort(S,P,[],L).
- - pred distribute(list(T)::in,{T,list(T)}::out) is det.
distribute([],_):-error("Error in distribute"). distribute([H|T],Z) :- Z = {H,T}.
- - pred db_compare({string,list(string)}::in,{string,list(string)}::in) is semidet.
db_compare({X1,L1},{X2,_}) :- not(X1=X2),list.member(X2,L1).
main(!IO) :-
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"],
Words=list.map(string.words,Input), list.map(distribute,Words,Db), solutions(pred(X::out) is nondet :- topological_sort(set.from_list(Db),db_compare,X),SortedWordLists), list.map(
pred({X,Y}::in,Z::out) is det:- X=Z, list.det_head(SortedWordLists), CompileOrder),
print(CompileOrder,!IO).
</lang>
Nim
<lang Nim>import sequtils, strutils, sets, tables, sugar
type StringSet = HashSet[string]
proc topSort(data: var OrderedTable[string, StringSet]) =
## Topologically sort the data in place.
var ranks: Table[string, Natural] # Maps the keys to a rank.
# Remove self dependencies. for key, values in data.mpairs: values.excl key
# Add extra items (i.e items present in values but not in keys).
for values in toSeq(data.values):
for value in values:
if value notin data:
data[value] = initHashSet[string]()
# Find ranks. var deps = data # Working copy of the table. var rank = 0 while deps.len > 0:
# Find a key with an empty dependency set.
var keyToRemove: string
for key, values in deps.pairs:
if values.card == 0:
keyToRemove = key
break
if keyToRemove.len == 0:
# Not found: there is a cycle.
raise newException(ValueError, "Unorderable items found: " & toSeq(deps.keys).join(", "))
# Assign a rank to the key and remove it from keys and values.
ranks[keyToRemove] = rank
inc rank
deps.del keyToRemove
for k, v in deps.mpairs:
v.excl keyToRemove
# Sort the original data according to the ranks. data.sort((x, y) => cmp(ranks[x[0]], ranks[y[0]]))
when isMainModule:
const Data = {"des_system_lib": ["std", "synopsys", "std_cell_lib",
"des_system_lib", "dw02", "dw01",
"ramlib", "ieee"].toHashSet,
"dw01": ["ieee", "dw01", "dware", "gtech"].toHashSet,
"dw02": ["ieee", "dw02", "dware"].toHashSet,
"dw03": ["std", "synopsys", "dware", "dw03",
"dw02", "dw01", "ieee", "gtech"].toHashSet,
"dw04": ["dw04", "ieee", "dw01", "dware", "gtech"].toHashSet,
"dw05": ["dw05", "ieee", "dware"].toHashSet,
"dw06": ["dw06", "ieee", "dware"].toHashSet,
"dw07": ["ieee", "dware"].toHashSet,
"dware": ["ieee", "dware"].toHashSet,
"gtech": ["ieee", "gtech"].toHashSet,
"ramlib": ["std", "ieee"].toHashSet,
"std_cell_lib": ["ieee", "std_cell_lib"].toHashSet,
"synopsys": initHashSet[string]()}.toOrderedTable
# Process the original data (without cycle). echo "Data without cycle. Order after sorting:" var data = Data try: data.topSort() for key in data.keys: echo key except ValueError: echo getCurrentExceptionMsg()
# Process the modified data (with a cycle). echo "\nData with a cycle:" data = Data data["dw01"].incl "dw04" try: data.topSort() for key in data.keys: echo key except ValueError: echo getCurrentExceptionMsg()</lang>
Object Pascal
Written for Free Pascal, but will probably work in Delphi if you change the required units. <lang Object Pascal> 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. </lang>
OCaml
<lang ocaml>let dep_libs = [
("des_system_lib", ["std"; "synopsys"; "std_cell_lib"; "des_system_lib"; "dw02"; "dw01"; "ramlib"; "ieee"]);
("dw01", (*"dw04"::*)["ieee"; "dw01"; "dware"; "gtech"]);
("dw02", ["ieee"; "dw02"; "dware"]);
("dw03", ["std"; "synopsys"; "dware"; "dw03"; "dw02"; "dw01"; "ieee"; "gtech"]);
("dw04", ["dw04"; "ieee"; "dw01"; "dware"; "gtech"]);
("dw05", ["dw05"; "ieee"; "dware"]);
("dw06", ["dw06"; "ieee"; "dware"]);
("dw07", ["ieee"; "dware"]);
("dware", ["ieee"; "dware"]);
("gtech", ["ieee"; "gtech"]);
("ramlib", ["std"; "ieee"]);
("std_cell_lib", ["ieee"; "std_cell_lib"]);
("synopsys", []);
]
let dep_libs =
let f (lib, deps) = (* remove self dependency *)
(lib,
List.filter (fun d -> d <> lib) deps) in
List.map f dep_libs
let 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);
- </lang>
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".
OxygenBasic
<lang> 'TOPOLOGICAL SORT
uses parseutil 'getword() lenw uses console
string dat=" 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 " gosub Dims gosub CaptureData gosub GetSystemLibs gosub RemoveSelfReference gosub OrderByDependency gosub DisplayResults end
/*RESULTS:
libraries in dependency order ----------------------------- std ieee dware gtech ramlib std_cell_lib synopsys dw01 dw02 des_system_lib dw03 dw04 dw05 dw06 dw07
<<
remainder: ---------- <<
- /
Dims:
=
'VARIABLES int p 'width of first column int h 'length of each line int i 'iterator / counter int j 'main iterator int b 'table char offset int e 'end of each line int bd 'each offset of dependencises line int le 'length of each lib name int lend 'size of table int k 'character indexer int m 'iterator int n 'iterator int cw 'presence flag int lw 'length of keyword int a 'iinstr result int dc 'new lib list indexer / counter string wr 'keyword string wn 'keyword '--arrays-- string datl[64] 'list of lib names string datd[64] 'lists of lib dependencies string datn[64] 'new list in dependency ordert ret
CaptureData:
==
dat=lcase dat 'GET HEADING POSITION p=instr dat,"library depend" p-=3 'crlf -1 'REMOVE HEADING h=instr 3,dat,cr h+=2 h=instr h,dat,cr 'to remove underlines 'print h cr h+=2 dat=mid dat,h 'print dat "<" cr b=1 'PREPARE DATA lend=len dat do
i++ datl[i]=rtrim(mid(dat,b,p)) le=len datl[i] e=instr b+le,dat,cr bd=b+p datd[i]=" "+mid(dat,bd,e-bd)+" " 'print datl[i] "," datd[i] cr b=e+2 if b>lend-2 exit do endif
loop ret
GetSystemLibs:
==
'SCAN DEPENDENCIES 'GET SYSTEM LIBS NOT LISTED for j=1 to i
k=1
do
wr=getword datd[j],k
if not wr
exit do
endif
cw=0
for m=1 to i
if wr=datl[m] 'on lib list
cw=m
endif
next
if cw=0 'lib not on library list
'add wr to new lib list
dc++ : datn[dc]=wr
'remove lib names from dependency lists
gosub BlankOutNames
endif
loop
next 'j group of dependencies ret
RemoveSelfReference:
========
'REMOVE SELF REFERENCE + NO DEPENDENCIES for j=1 to i
wr=" "+datl[j]+" " lw=len(wr) a=instr(datd[j],wr) if a mid(datd[j],a,space(lw)) 'blank out self endif gosub RemoveLibFromLists
next ret ' OrderByDependency:
======
' for j=1 to i
if datl[j] gosub RemoveLibFromLists if cw then j=0 'repeat cycle endif
next ret ' DisplayResults:
===
print cr cr print "libraries in dependency order" cr print "-----------------------------" cr for j=1 to dc
print datn[j] cr
next print "<<" cr cr print "remainder:" cr print "----------" cr for j=1 to i
if datl[j] print datl[j] " , " datd[j] cr endif
next print "<<" cr
pause end
RemoveLibFromLists:
=======
cw=0 k=1 : wr=getword datd[j],k if lenw=0
dc++ : datn[dc]=datl[j] 'add to new lib list datl[j]="" : datd[j]="" 'eliminate frecord rom further checks gosub BlankOutNames 'eliminate all lib references from table cw=1 'flag alteration
endif ret
BlankOutNames:
==
wn=" "+datn[dc]+" " 'add word boundaries lw=len wn for n=1 to i
if datd[n]
a=instr(datd[n],wn)
if a
mid datd[n],a,space(lw) 'blank out
endif
endif
next ret </lang>
Oz
Using constraint propagation and search: <lang oz>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</lang>
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
See Object Pascal
Perl
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.
<lang perl>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);</lang>
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
Phix
Implemented as a trivial normal sort.
sequence names enum RANK, NAME, DEP -- content of names -- rank is 1 for items to compile first, then 2, etc, -- or 0 if cyclic dependencies prevent compilation. -- name is handy, and makes the result order alphabetic! -- dep is a list of dependencies (indexes to other names) function add_dependency(string name) integer k = find(name,vslice(names,NAME)) if k=0 then names = append(names,{0,name,{}}) k = length(names) end if return k end function procedure topsort(string input) names = {} sequence lines = split(input,'\n') for i=1 to length(lines) do sequence line = split(lines[i]), dependencies = {} integer k = add_dependency(line[1]) for j=2 to length(line) do integer l = add_dependency(line[j]) if l!=k then -- ignore self-references dependencies &= l end if end for names[k][DEP] = dependencies end for -- Now populate names[RANK] iteratively: bool more = true integer rank = 0 while more do more = false rank += 1 for i=1 to length(names) do if names[i][RANK]=0 then bool ok = true for j=1 to length(names[i][DEP]) do integer ji = names[i][DEP][j], nr = names[ji][RANK] if nr=0 or nr=rank then -- not yet compiled, or same pass ok = false exit end if end for if ok then names[i][RANK] = rank more = true end if end if end for end while names = sort(names) -- (ie by [RANK=1] then [NAME=2]) integer prank = names[1][RANK] if prank=0 then puts(1,"** CYCLIC **:") end if for i=1 to length(names) do rank = names[i][RANK] if i>1 then puts(1,iff(rank=prank?" ":"\n")) end if puts(1,names[i][NAME]) prank = rank end for puts(1,"\n") end procedure constant 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""" topsort(input) puts(1,"\nbad input:\n") topsort(input&"\ndw01 dw04")
- Output:
Items on the same line can be compiled at the same time, and each line is alphabetic.
ieee std synopsys dware gtech ramlib std_cell_lib dw01 dw02 dw05 dw06 dw07 des_system_lib dw03 dw04 bad input: ** CYCLIC **:des_system_lib dw01 dw03 dw04 ieee std synopsys dware gtech ramlib std_cell_lib dw02 dw05 dw06 dw07
PicoLisp
<lang PicoLisp>(de sortDependencies (Lst)
(setq Lst # Build a flat list
(uniq
(mapcan
'((L)
(put (car L) 'dep (cdr L)) # Store dependencies in 'dep' properties
(copy L) )
(mapcar uniq Lst) ) ) ) # without self-dependencies
(make
(while Lst
(ifn (find '((This) (not (: dep))) Lst) # Found non-depending lib?
(quit "Can't resolve dependencies" Lst)
(del (link @) 'Lst) # Yes: Store in result
(for This Lst # and remove from 'dep's
(=: dep (delete @ (: dep))) ) ) ) ) )</lang>
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
<lang PowerShell>#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 $_.Library
}
}</lang>
PureBasic
<lang PureBasic>#EndOfDataMarker$ = "::EndOfData::" DataSection
;"LIBRARY: [LIBRARY_DEPENDENCY_1 LIBRARY_DEPENDENCY_2 ... LIBRARY_DEPENDENCY_N] Data.s "des_system_lib: [std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee]" Data.s "dw01: [ieee dw01 dware gtech]" ;Data.s "dw01: [ieee dw01 dware gtech dw04]" ;comment the previous line and uncomment this one for cyclic dependency Data.s "dw02: [ieee dw02 dware]" Data.s "dw03: [std synopsys dware dw03 dw02 dw01 ieee gtech]" Data.s "dw04: [dw04 ieee dw01 dware gtech]" Data.s "dw05: [dw05 ieee dware]" Data.s "dw06: [dw06 ieee dware]" Data.s "dw07: [ieee dware]" Data.s "dware: [ieee dware]" Data.s "gtech: [ieee gtech]" Data.s "ramlib: [std ieee]" Data.s "std_cell_lib: [ieee std_cell_lib]" Data.s "synopsys: nil" Data.s #EndOfDataMarker$
EndDataSection
Structure DAG_node
Value.s forRemoval.i ;flag marks elements that should be removed the next time they are accessed List dependencies.s()
EndStructure
If Not OpenConsole()
MessageRequester("Error","Unable to open console")
End
EndIf
- // initialize Directed Acyclic Graph //
Define i, itemData.s, firstBracketPos NewList DAG.DAG_node() Repeat
Read.s itemData
itemData = Trim(itemData)
If itemData <> #EndOfDataMarker$
AddElement(DAG())
;add library
DAG()\Value = Trim(Left(itemData, FindString(itemData, ":", 1) - 1))
;parse library dependencies
firstBracketPos = FindString(itemData, "[", 1)
If firstBracketPos
itemData = Trim(Mid(itemData, firstBracketPos + 1, FindString(itemData, "]", 1) - firstBracketPos - 1))
For i = (CountString(itemData, " ") + 1) To 1 Step -1
AddElement(DAG()\dependencies())
DAG()\dependencies() = StringField(itemData, i, " ")
Next
EndIf
EndIf
Until itemData = #EndOfDataMarker$
- // process DAG //
- create DAG entry for nodes listed in dependencies but without their own entry
NewMap libraries() ForEach DAG()
ForEach DAG()\dependencies()
libraries(DAG()\dependencies()) = #True
If DAG()\dependencies() = DAG()\Value
DeleteElement(DAG()\dependencies()) ;remove self-dependencies
EndIf
Next
Next
ForEach DAG()
If FindMapElement(libraries(),DAG()\Value) DeleteMapElement(libraries(),DAG()\Value) EndIf
Next
ResetList(DAG()) ForEach libraries()
AddElement(DAG()) DAG()\Value = MapKey(libraries())
Next ClearMap(libraries())
- process DAG() repeatedly until no changes occur
NewList compileOrder.s() Repeat
noChangesMade = #True
ForEach DAG()
If DAG()\forRemoval
DeleteElement(DAG())
Else
;remove dependencies that have been placed in the compileOrder
ForEach DAG()\dependencies()
If FindMapElement(libraries(),DAG()\dependencies())
DeleteElement(DAG()\dependencies())
EndIf
Next
;add DAG() entry to compileOrder if it has no more dependencies
If ListSize(DAG()\dependencies()) = 0
AddElement(compileOrder())
compileOrder() = DAG()\Value
libraries(DAG()\Value) = #True ;mark the library for removal as a dependency
DAG()\forRemoval = #True
noChangesMade = #False
EndIf
EndIf
Next
Until noChangesMade
If ListSize(DAG())
PrintN("Cyclic dependencies detected in:" + #CRLF$)
ForEach DAG()
PrintN(" " + DAG()\Value)
Next
Else
PrintN("Compile order:" + #CRLF$)
ForEach compileOrder()
PrintN(" " + compileOrder())
Next
EndIf
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit") Input() CloseConsole()</lang> 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
Python 3
<lang python>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) ))</lang>
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'}}
Python 3.9 graphlib
<lang python>from graphlib import TopologicalSorter
- LIBRARY mapped_to LIBRARY DEPENDENCIES
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(),
}
- Ignore self dependencies
for k, v in data.items():
v.discard(k)
ts = TopologicalSorter(data) print(tuple(ts.static_order()))</lang>
- Output:
('synopsys', 'std', 'ieee', 'dware', 'gtech', 'ramlib', 'std_cell_lib', 'dw02', 'dw05', 'dw06', 'dw07', 'dw01', 'des_system_lib', 'dw03', 'dw04')
R
First make the list <lang R> 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()) </lang>
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. <lang R> 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(depsx, 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 } </lang>
On the given example : <lang R> tsort(deps)
- [1] "std" "ieee" "dware" "gtech" "ramlib"
- [6] "std_cell_lib" "synopsys" "dw01" "dw02" "dw03"
- [11] "dw04" "dw05" "dw06" "dw07" "des_system_lib"
</lang>
If dw01 depends on dw04 as well :
<lang R> Unorderable items : des_system_lib dw01 dw04 dw03 </lang>
Racket
<lang racket>
- 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)) </lang> Output: <lang racket> '(synopsys ieee dware gtech std_cell_lib std ramlib dw07 dw06 dw05 dw01 dw04 dw02 dw03 des_system_lib) </lang>
Raku
(formerly Perl 6)
<lang perl6>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);</lang>
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(...)].
REXX
Some of the FORTRAN 77 statements were converted to do loops (or do structures), and
some variables were camel capitalized.
<lang rexx>/*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.*/
nL= 15; nd= 44; nc= 69 /* " " "parms" and indices.*/
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
j= 0
do i=1
iL= word(iCode, i); if iL==0 then leave
do forever; i= i+1
iR= word(iCode, i); if iR==0 then leave
j= j+1; iDep.j.1= iL
iDep.j.2= iR
end /*forever*/
end /*i*/
call tSort say '═══compile order═══' @= 'libraries found.)'
- =0; do o=nO by -1 for nO; #= #+1; say word(label, iOrd.o)
end /*o*/; if #==0 then #= 'no'
say ' ('# @; say say '═══unordered libraries═══'
- =0; do u=nO+1 to nL; #= #+1; say word(label, iOrd.u)
end /*u*/; if #==0 then #= 'no'
say ' ('# "unordered" @ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ tSort: procedure expose iDep. iOrd. iPos. nd nL nO
do i=1 for nL; iOrd.i= i; iPos.i= i
end /*i*/
k= 1
do until k<=j; 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*/
end /*until*/
nO= j-1; return</lang>
- 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
Uses the TSort module from the Ruby stdlib. <lang ruby>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</lang>
- 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"]
Rust
<lang rust>use std::boxed::Box; use std::collections::{HashMap, HashSet};
- [derive(Debug, PartialEq, Eq, Hash)]
struct Library<'a> {
name: &'a str, children: Vec<&'a str>, num_parents: usize,
}
fn build_libraries(input: Vec<&str>) -> HashMap<&str, Box<Library>> {
let mut libraries: HashMap<&str, Box<Library>> = HashMap::new();
for input_line in input {
let line_split = input_line.split_whitespace().collect::<Vec<&str>>();
let name = line_split.get(0).unwrap();
let mut num_parents: usize = 0;
for parent in line_split.iter().skip(1) {
if parent == name {
continue;
}
if !libraries.contains_key(parent) {
libraries.insert(
parent,
Box::new(Library {
name: parent,
children: vec![name],
num_parents: 0,
}),
);
} else {
libraries.get_mut(parent).unwrap().children.push(name);
}
num_parents += 1;
}
if !libraries.contains_key(name) {
libraries.insert(
name,
Box::new(Library {
name,
children: Vec::new(),
num_parents,
}),
);
} else {
libraries.get_mut(name).unwrap().num_parents = num_parents;
}
}
libraries
}
fn topological_sort<'a>(
mut libraries: HashMap<&'a str, Box<Library<'a>>>,
) -> Result<Vec<&'a str>, String> {
let mut needs_processing = libraries
.iter()
.map(|(k, _v)| k.clone())
.collect::<HashSet<&str>>();
let mut options: Vec<&str> = libraries
.iter()
.filter(|(_k, v)| v.num_parents == 0)
.map(|(k, _v)| *k)
.collect();
let mut sorted: Vec<&str> = Vec::new();
while !options.is_empty() {
let cur = options.pop().unwrap();
for children in libraries
.get_mut(cur)
.unwrap()
.children
.drain(0..)
.collect::<Vec<&str>>()
{
let child = libraries.get_mut(children).unwrap();
child.num_parents -= 1;
if child.num_parents == 0 {
options.push(child.name)
}
}
sorted.push(cur);
needs_processing.remove(cur);
}
match needs_processing.is_empty() {
true => Ok(sorted),
false => Err(format!("Cycle detected among {:?}", needs_processing)),
}
}
fn main() {
let input: Vec<&str> = vec![
"des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee\n",
"dw01 ieee dw01 dware gtech dw04\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",
];
let libraries = build_libraries(input);
match topological_sort(libraries) {
Ok(sorted) => println!("{:?}", sorted),
Err(msg) => println!("{:?}", msg),
}
} </lang> Output:
["std", "synopsys", "ieee", "std_cell_lib", "ramlib", "gtech", "dware", "dw07", "dw06", "dw05", "dw02", "dw01", "dw04", "dw03", "des_system_lib"]
Output if we make dw01 depend on dw04 by changing input to
"des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee\n",
"dw01 ieee dw01 dware gtech dw04\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 detected among {\"dw03\", \"des_system_lib\", \"dw04\", \"dw01\"}"
Scheme
<lang scheme> (import (chezscheme)) (import (srfi srfi-1))
(define (remove-self-dependency pair)
(let ((key (car pair))
(value (cdr pair)))
(cons key (remq key value))))w
(define (remove-self-dependencies alist)
(map remove-self-dependency alist))
(define (add-missing-items dependencies)
(let loop ((items (delete-duplicates (append-map cdr dependencies) eq?))
(out dependencies))
(if (null? items)
out
(let ((item (car items)))
(if (assq item out)
(loop (cdr items) out)
(loop (cdr items) (cons (cons item '()) out)))))))
(define (lift dependencies batch)
(let loop ((dependencies dependencies)
(out '()))
(if (null? dependencies)
out
(let ((key (caar dependencies))
(value (cdar dependencies)))
(if (null? value)
(loop (cdr dependencies) out)
(loop (cdr dependencies)
(cons (cons key (lset-difference eq? value batch))
out)))))))
(define (topological-sort dependencies)
(let* ((dependencies (remove-self-dependencies dependencies))
(dependencies (add-missing-items dependencies)))
(let loop ((out '())
(dependencies dependencies))
(if (null? dependencies)
(reverse out)
(let ((batch (map car (filter (lambda (pair) (null? (cdr pair))) dependencies))))
(if (null? batch)
#f
(loop (cons batch out) (lift dependencies batch))))))))
(define example
'((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 . ())))
(write (topological-sort example))
(define unsortable
'((des_system_lib . (std synopsys std_cell_lib des_system_lib dw02
dw01 ramlib ieee))
(dw01 . (ieee dw01 dware gtech 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 . ())))
(newline) (write (topological-sort unsortable)) </lang>
Sidef
<lang ruby>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);</lang>
- 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
Swift
<lang swift>let libs = [
("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", [])
]
struct Library {
var name: String var children: [String] var numParents: Int
}
func buildLibraries(_ input: [(String, [String])]) -> [String: Library] {
var libraries = [String: Library]()
for (name, parents) in input {
var numParents = 0
for parent in parents where parent != name {
numParents += 1
libraries[parent, default: Library(name: parent, children: [], numParents: 0)].children.append(name) }
libraries[name, default: Library(name: name, children: [], numParents: numParents)].numParents = numParents }
return libraries
}
func topologicalSort(libs: [String: Library]) -> [String]? {
var libs = libs
var needsProcessing = Set(libs.keys)
var options = libs.compactMap({ $0.value.numParents == 0 ? $0.key : nil })
var sorted = [String]()
while let cur = options.popLast() {
for children in libs[cur]?.children ?? [] {
libs[children]?.numParents -= 1
if libs[children]?.numParents == 0 {
options.append(libs[children]!.name)
}
}
libs[cur]?.children.removeAll()
sorted.append(cur) needsProcessing.remove(cur) }
guard needsProcessing.isEmpty else {
return nil
}
return sorted
}
print(topologicalSort(libs: buildLibraries(libs))!)</lang>
- Output:
["ieee", "std_cell_lib", "gtech", "dware", "dw07", "dw06", "dw05", "dw02", "dw01", "dw04", "std", "ramlib", "synopsys", "dw03", "des_system_lib"]
Tcl
<lang tcl>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 }
}
}</lang> Demonstration code (which parses it from the format that the puzzle was posed in): <lang tcl>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 $parsedData]</lang> Sample output:
ieee std synopsys dware gtech ramlib std_cell_lib dw01 dw02 dw05 dw06 dw07 des_system_lib dw03 dw04
If the suggested extra arc is added, this is the error output:
graph is cyclic, possibly involving nodes "des_system_lib dw01 dw03 dw04"
UNIX Shell
The Unix tsort(1) utility does a topological sort. Each line of input must have two items in order, like 'std des_system_lib'.[4]
<lang bash>$ 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</lang>
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
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. <lang Ursala>tsort = ~&nmnNCjA*imSLs2nSjiNCSPT; @NiX ^=lxPrnSPX ^(~&rlPlT,~&rnPrmPljA*D@r)^|/~& ~&m!=rnSPlX</lang> test program: <lang Ursala>#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</lang> 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
Implementation
<lang vb> 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 </lang>
Invocation
<lang vb> 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 </lang>
Output
----- des_system_lib std synopsys ieee std_cell_lib dware dw02 gtech dw01 ramlib des_system_lib ----- ----- dw01 ieee dware gtech dw01 ----- ----- dw02 ieee dware dw02 ----- ----- dw03 std synopsys ieee dware dw02 gtech dw01 dw03 ----- ----- dw04 ieee dware gtech dw01 dw04 ----- ----- dw05 ieee dware dw05 ----- ----- dw06 ieee dware dw06 ----- ----- dw07 ieee dware dw07 ----- ----- dware ieee dware ----- ----- gtech ieee gtech ----- ----- ramlib std ieee ramlib ----- ----- std_cell_lib ieee std_cell_lib ----- ----- synopsys synopsys -----
Visual Basic .NET
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. <lang vbnet>' 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 </lang>
Output
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 . . .
Wren
<lang ecmascript>class Graph {
construct new(s, edges) {
_vertices = s.split(", ")
var n = _vertices.count
_adjacency = List.filled(n, null)
for (i in 0...n) _adjacency[i] = List.filled(n, false)
for (edge in edges) _adjacency[edge[0]][edge[1]] = true
}
hasDependency(r, todo) {
for (c in todo) if (_adjacency[r][c]) return true
return false
}
topoSort() {
var res = []
var todo = List.filled(_vertices.count, 0)
for (i in 0...todo.count) todo[i] = i
while (!todo.isEmpty) {
var outer = false
var i = 0
for (r in todo) {
if (!hasDependency(r, todo)) {
todo.removeAt(i)
res.add(_vertices[r])
outer = true
break
}
i = i + 1
}
if (!outer) {
System.print("Graph has cycles")
return ""
}
}
return res
}
}
var s = "std, ieee, des_system_lib, dw01, dw02, dw03, dw04, dw05, " +
"dw06, dw07, dware, gtech, ramlib, std_cell_lib, synopsys"
var deps = [
[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], [12, 0], [12, 1], [13, 1]
]
var g = Graph.new(s, deps) System.print("Topologically sorted order:") System.print(g.topoSort()) System.print() // now insert [3, 6] at index 10 of deps deps.insert(10, [3, 6]) var g2 = Graph.new(s, deps) System.print("Following the addition of dw04 to the dependencies of dw01:") System.print(g2.topoSort())</lang>
- Output:
Topologically sorted order: [std, ieee, dware, dw02, dw05, dw06, dw07, gtech, dw01, dw04, ramlib, std_cell_lib, synopsys, des_system_lib, dw03] Following the addition of dw04 to the dependencies of dw01: Graph has cycles
zkl
Input data is munged <lang zkl>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:=Dictionary(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
}</lang> <lang zkl>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();</lang>
- 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")