Power set: Difference between revisions
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→{{header|Fōrmulæ}}
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'''Extra credit: ''' Demonstrate that your language supports these last two powersets.
<br><br>
=={{header|11l}}==
{{trans|Python}}
<syntaxhighlight lang="11l">F list_powerset(lst)
V result = [[Int]()]
L(x) lst
result.extend(result.map(subset -> subset [+] [@x]))
R result
print(list_powerset([1, 2, 3]))</syntaxhighlight>
{{out}}
<pre>
[[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
</pre>
=={{header|ABAP}}==
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This works for ABAP Version 7.40 and above
<syntaxhighlight lang="abap">
report z_powerset.
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)->add_element( `4` )->add_element( `4` ).
write: |𝑷( { set3->set~stringify( ) } ) -> { set3->build_powerset( )->set~stringify( ) }|, /.
</syntaxhighlight>
{{out}}
Line 233 ⟶ 249:
A solution (without recursion) that prints the power set of the n arguments passed by the command line. The idea is that the i'th bit of a natural between 0 and <math>2^n-1</math> indicates whether or not we should put the i'th element of the command line inside the set.
<syntaxhighlight lang="ada">
with Ada.Text_IO, Ada.Command_Line;
use Ada.Text_IO, Ada.Command_Line;
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end loop;
end powerset;
</syntaxhighlight>
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Requires: ALGOL 68g mk14.1+
<
PROC power set = ([]MEMBER s)[][]MEMBER:(
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printf(($"set["d"] = "$,member, repr set, set[member],$l$))
OD
)</
{{out}}
<pre>
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set[8] = (1, 2, 4);
</pre>
=={{header|APL}}==
{{works with|Dyalog APL}}
<syntaxhighlight lang="apl">ps←(↓∘⍉(2/⍨≢)⊤(⍳2*≢))(/¨)⊂</syntaxhighlight>
{{out}}
<!-- note: "line-height: 100%" makes Dyalog's boxed output look better.
Don't know why it wasn't already 100% though. -->
<pre style='line-height: 100%;'> ps 1 2 3 4
┌─┬─┬───┬─┬───┬───┬─────┬─┬───┬───┬─────┬───┬─────┬─────┬───────┬┐
│4│3│3 4│2│2 4│2 3│2 3 4│1│1 4│1 3│1 3 4│1 2│1 2 4│1 2 3│1 2 3 4││
└─┴─┴───┴─┴───┴───┴─────┴─┴───┴───┴─────┴───┴─────┴─────┴───────┴┘</pre>
<pre style='line-height: 100%;'> ps ⍬
┌┐
││
└┘</pre>
<pre style='line-height: 100%;'> ps ,⊂⍬
┌──┬┐
│┌┐││
│││││
│└┘││
└──┴┘</pre>
=={{header|AppleScript}}==
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(functional composition examples)
{{Trans|Haskell}}
<
-- powerset :: [a] -> [[a]]
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end script
end if
end mReturn</
{{Out}}
<
{"Empty set", {{}}},
{"Set containing only empty set", {{}, {{}}}}}</
=={{header|Arturo}}==
<syntaxhighlight lang="rebol">print powerset [1 2 3 4]</syntaxhighlight>
{{out}}
<pre>[2 3 4] [] [1 2 4] [1 2 3 4] [1 3 4] [1] [2] [1 3] [3 4] [4] [1 4] [3] [1 2] [2 3] [1 2 3] [2 4]</pre>
=={{header|ATS}}==
<syntaxhighlight lang="text">
(* ****** ****** *)
//
Line 495 ⟶ 548:
(* ****** ****** *)
</syntaxhighlight>
=={{header|AutoHotkey}}==
ahk [http://www.autohotkey.com/forum/viewtopic.php?t=44657&postdays=0&postorder=asc&start=147 discussion]
<
StringSplit a, a, `, ; a0 = #elements, a1,a2,... = elements of the set
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t .= "}`n{" ; new subsets in new lines
}
MsgBox % RegExReplace(SubStr(t,1,StrLen(t)-1),",}","}")</
=={{header|AWK}}==
<
#!/usr/local/bin/gawk -f
Line 522 ⟶ 575:
# For each input
{ for (i=0;i<=2^NF-1;i++) if (i == 0) printf("empty\n"); else printf("(%s)\n",tochar(i,NF)) }
</syntaxhighlight>
{{out}}
Line 546 ⟶ 599:
</pre>
=={{header|
==={{header|BBC BASIC}}===
The elements of a set are represented as the bits in an integer (hence the maximum size of set is 32).
<
PRINT FNpowerset(list$())
END
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s$ += "},"
NEXT i%
= LEFT$(s$) + "}"</
{{out}}
<pre>
{{},{1},{2},{1,2},{3},{1,3},{2,3},{1,2,3},{4},{1,4},{2,4},{1,2,4},{3,4},{1,3,4},{2,3,4},{1,2,3,4}}
</pre>
=={{header|BQN}}==
<syntaxhighlight lang="bqn">P ← (⥊·↕2⥊˜≠)/¨<</syntaxhighlight>
{{out}}
<pre>
P 1‿2‿3‿4‿5
⟨ ⟨⟩ ⟨ 5 ⟩ ⟨ 4 ⟩ ⟨ 4 5 ⟩ ⟨ 3 ⟩ ⟨ 3 5 ⟩ ⟨ 3 4 ⟩ ⟨ 3 4 5 ⟩ ⟨ 2 ⟩ ⟨ 2 5 ⟩ ⟨ 2 4 ⟩ ⟨ 2 4 5 ⟩ ⟨ 2 3 ⟩ ⟨ 2 3 5 ⟩ ⟨ 2 3 4 ⟩ ⟨ 2 3 4 5 ⟩ ⟨ 1 ⟩ ⟨ 1 5 ⟩ ⟨ 1 4 ⟩ ⟨ 1 4 5 ⟩ ⟨ 1 3 ⟩ ⟨ 1 3 5 ⟩ ⟨ 1 3 4 ⟩ ⟨ 1 3 4 5 ⟩ ⟨ 1 2 ⟩ ⟨ 1 2 5 ⟩ ⟨ 1 2 4 ⟩ ⟨ 1 2 4 5 ⟩ ⟨ 1 2 3 ⟩ ⟨ 1 2 3 5 ⟩ ⟨ 1 2 3 4 ⟩ ⟨ 1 2 3 4 5 ⟩ ⟩
</pre>
=={{header|Bracmat}}==
<
= done todo first
. !arg:(?done.?todo)
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)
& out$(powerset$(.1 2 3 4))
);</
{{out}}
<pre> 1 2 3 4
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=={{header|Burlesque}}==
<
blsq ) {1 2 3 4}R@
{{} {1} {2} {1 2} {3} {1 3} {2 3} {1 2 3} {4} {1 4} {2 4} {1 2 4} {3 4} {1 3 4} {2 3 4} {1 2 3 4}}
</syntaxhighlight>
=={{header|C}}==
<
struct node {
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powerset(argv + 1, argc - 1, 0);
return 0;
}</
{{out}}
<pre>
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[ 3 2 1 ]
</pre>
=={{header|C sharp|C#}}==
<syntaxhighlight lang="csharp">
public IEnumerable<IEnumerable<T>> GetPowerSet<T>(List<T> list)
{
return from m in Enumerable.Range(0, 1 << list.Count)
select
from i in Enumerable.Range(0, list.Count)
where (m & (1 << i)) != 0
select list[i];
}
public void PowerSetofColors()
{
var colors = new List<KnownColor> { KnownColor.Red, KnownColor.Green,
KnownColor.Blue, KnownColor.Yellow };
var result = GetPowerSet(colors);
Console.Write( string.Join( Environment.NewLine,
result.Select(subset =>
string.Join(",", subset.Select(clr => clr.ToString()).ToArray())).ToArray()));
}
</syntaxhighlight>
{{out}}
<pre>
Red
Green
Red,Green
Blue
Red,Blue
Green,Blue
Red,Green,Blue
Yellow
Red,Yellow
Green,Yellow
Red,Green,Yellow
Blue,Yellow
Red,Blue,Yellow
Green,Blue,Yellow
Red,Green,Blue,Yellow
</pre>
An alternative implementation for an arbitrary number of elements:
<syntaxhighlight lang="csharp">
public IEnumerable<IEnumerable<T>> GetPowerSet<T>(IEnumerable<T> input) {
var seed = new List<IEnumerable<T>>() { Enumerable.Empty<T>() }
as IEnumerable<IEnumerable<T>>;
return input.Aggregate(seed, (a, b) =>
a.Concat(a.Select(x => x.Concat(new List<T>() { b }))));
}
</syntaxhighlight>
Non-recursive version
<syntaxhighlight lang="csharp">
using System;
class Powerset
{
static int count = 0, n = 4;
static int [] buf = new int [n];
static void Main()
{
int ind = 0;
int n_1 = n - 1;
for (;;)
{
for (int i = 0; i <= ind; ++i) Console.Write("{0, 2}", buf [i]);
Console.WriteLine();
count++;
if (buf [ind] < n_1) { ind++; buf [ind] = buf [ind - 1] + 1; }
else if (ind > 0) { ind--; buf [ind]++; }
else break;
}
Console.WriteLine("n=" + n + " count=" + count);
}
}
</syntaxhighlight>
----------------
Recursive version
<syntaxhighlight lang="csharp">
using System;
class Powerset
{
static int n = 4;
static int [] buf = new int [n];
static void Main()
{
rec(0, 0);
}
static void rec(int ind, int begin)
{
for (int i = begin; i < n; i++)
{
buf [ind] = i;
for (int j = 0; j <= ind; j++) Console.Write("{0, 2}", buf [j]);
Console.WriteLine();
rec(ind + 1, buf [ind] + 1);
}
}
}</syntaxhighlight>
=={{header|C++}}==
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=== Non-recursive version ===
<
#include <set>
#include <vector>
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std::cout << " }\n";
}
}</
{{out}}
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This simplified version has identical output to the previous code.
<
#include <set>
#include <iostream>
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}
}
</syntaxhighlight>
=== Recursive version ===
<
#include <set>
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return powerset(s, s.size());
}
</syntaxhighlight>
=={{header|Clojure}}==
<
(def S #{1 2 3 4})
user> (subsets S)
(() (1) (2) (3) (4) (1 2) (1 3) (1 4) (2 3) (2 4) (3 4) (1 2 3) (1 2 4) (1 3 4) (2 3 4) (1 2 3 4))</
'''Alternate solution''', with no dependency on third-party library:
<
(reduce (fn [a x]
(into a (map #(conj % x)) a))
#{#{}} coll))
(powerset #{1 2 3})</
<
'''Using bit-test''':
see: https://clojuredocs.org/clojure.core/bit-test#example-5d401face4b0ca44402ef78b
<syntaxhighlight lang="clojure">(defn powerset [coll]
(let [cnt (count coll)
bits (Math/pow 2 cnt)]
(for [i (range bits)]
(for [j (range i)
:while (< j cnt)
:when (bit-test i j)]
(nth coll j)))))
(powerset [1 2 3])</syntaxhighlight>
<syntaxhighlight lang="clojure">(() (1) (2) (1 2) (3) (1 3) (2 3) (1 2 3))</syntaxhighlight>
=={{header|CoffeeScript}}==
<
print_power_set = (arr) ->
console.log "POWER SET of #{arr}"
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print_power_set [4, 2, 1]
print_power_set ['dog', 'c', 'b', 'a']
</syntaxhighlight>
{{out}}
<syntaxhighlight lang="text">
> coffee power_set.coffee
POWER SET of
Line 1,016 ⟶ 1,093:
[ 'dog', 'c', 'b' ]
[ 'dog', 'c', 'b', 'a' ]
</syntaxhighlight>
=={{header|ColdFusion}}==
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Port from the [[#JavaScript|JavaScript]] version,
compatible with ColdFusion 8+ or Railo 3+
<
{
var ps = [""];
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}
var res = powerset([1,2,3,4]);</
{{out}}
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=={{header|Common Lisp}}==
<
(if s (mapcan (lambda (x) (list (cons (car s) x) x))
(powerset (cdr s)))
'(())))</
{{out}}
Line 1,054 ⟶ 1,131:
((L I S P) (I S P) (L S P) (S P) (L I P) (I P) (L P) (P) (L I S) (I S) (L S) (S) (L I) (I) (L) NIL)
<
(reduce #'(lambda (item ps)
(append (mapcar #'(lambda (e) (cons item e))
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s
:from-end t
:initial-value '(())))</
{{out}}
>(power-set '(1 2 3))
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Alternate, more recursive (same output):
<
(if (null l)
(list nil)
(let ((prev (powerset (cdr l))))
(append (mapcar #'(lambda (elt) (cons (car l) elt)) prev)
prev))))</
Imperative-style using LOOP:
<
(loop for i below (expt 2 (length xs)) collect
(loop for j below i for x in xs if (logbitp j i) collect x)))</
{{out}}
>(powerset '(1 2 3)
Line 1,085 ⟶ 1,162:
Yet another imperative solution, this time with dolist.
<
(let ((pow-set (list nil)))
(dolist (element (reverse list) pow-set)
(dolist (set pow-set)
(push (cons element set) pow-set)))))</
{{out}}
>(power-set '(1 2 3))
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This implementation defines a range which *lazily* enumerates the power set.
<
import std.range;
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import std.stdio;
args[1..$].powerSet.each!writeln;
}</
An alternative version, which implements the range construct from scratch:
<
struct PowerSet(R)
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}
auto powerSet(R)(R r) { return PowerSet!R(r); }</
{{out}}
<pre>$ rdmd powerset a b c
Line 1,179 ⟶ 1,256:
["b", "c"]
["a", "b", "c"]</pre>
=== Alternative: using folds ===
An almost verbatim translation of the Haskell code in D.
Since D doesn't foldr, I've also copied Haskell's foldr implementation here.
Main difference from the Haskell:
#It isn't lazy (but it could be made so by implementing this as a generator)
Main differences from the version above:
#It isn't lazy
#It doesn't rely on integer bit fiddling, so it should work on arrays larger than size_t.
<syntaxhighlight lang="d">
// Haskell definition:
// foldr f z [] = z
// foldr f z (x:xs) = x `f` foldr f z xs
S foldr(T, S)(S function(T, S) f, S z, T[] rest) {
return (rest.length == 0) ? z : f(rest[0], foldr(f, z, rest[1..$]));
}
// Haskell definition:
//powerSet = foldr (\x acc -> acc ++ map (x:) acc) [[]]
T[][] powerset(T)(T[] set) {
import std.algorithm;
import std.array;
// Note: The types before x and acc aren't needed, so this could be made even more concise, but I think it helps
// to make the algorithm slightly clearer.
return foldr( (T x, T[][] acc) => acc ~ acc.map!(accx => x ~ accx).array , [[]], set );
}
</syntaxhighlight>
=={{header|Déjà Vu}}==
Line 1,184 ⟶ 1,294:
In Déjà Vu, sets are dictionaries with all values <code>true</code> and the default set to <code>false</code>.
<
local :out [ set{ } ]
for value in keys s:
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out
!. powerset set{ 1 2 3 4 }</
{{out}}
<pre>[ set{ } set{ 4 } set{ 3 4 } set{ 3 } set{ 2 3 } set{ 2 3 4 } set{ 2 4 } set{ 2 } set{ 1 2 } set{ 1 2 4 } set{ 1 2 3 4 } set{ 1 2 3 } set{ 1 3 } set{ 1 3 4 } set{ 1 4 } set{ 1 } ]</pre>
=={{header|Delphi}}==
{{libheader| System.SysUtils}}
{{Trans|C#}}
<syntaxhighlight lang="delphi">
program Power_set;
{$APPTYPE CONSOLE}
uses
System.SysUtils;
const
n = 4;
var
buf: TArray<Integer>;
procedure rec(ind, bg: Integer);
begin
for var i := bg to n - 1 do
begin
buf[ind] := i;
for var j := 0 to ind do
write(buf[j]: 2);
writeln;
rec(ind + 1, buf[ind] + 1);
end;
end;
begin
SetLength(buf, n);
rec(0,0);
{$IFNDEF UNIX}readln;{$ENDIF}
end.</syntaxhighlight>
=={{header|Dyalect}}==
{{trans|C#}}
<syntaxhighlight lang="dyalect">let n = 4
let buf = Array.Empty(n)
func rec(idx, begin) {
for i in begin..<n {
buf[idx] = i
for j in 0..idx {
print("{0, 2}".Format(buf[j]), terminator: "")
}
print("")
rec(idx + 1, buf[idx] + 1)
}
}
rec(0, 0)</syntaxhighlight>
=={{header|E}}==
<
def powerset(s) {
Line 1,208 ⟶ 1,373:
})
}
}</
It would also be possible to define an object which is the powerset of a provided set without actually instantiating all of its members immediately. [[Category:E examples needing attention]]
=={{header|EchoLisp}}==
<
(define (set-cons a A)
(make-set (cons a A)))
Line 1,245 ⟶ 1,410:
</syntaxhighlight>
=={{header|Elixir}}==
{{trans|Erlang}}
<
use Bitwise
def powerset1(list) do
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IO.inspect RC.powerset3([1,2,3])
IO.inspect RC.powerset1([])
IO.inspect RC.powerset1(["one"])</
{{out}}
Line 1,303 ⟶ 1,468:
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
</pre>
<
N = length(Lst),
Max = trunc(math:pow(2,N)),
[[lists:nth(Pos+1,Lst) || Pos <- lists:seq(0,N-1), I band (1 bsl Pos) =/= 0]
|| I <- lists:seq(0,Max-1)].</
{{out}}
Line 1,313 ⟶ 1,478:
Alternate shorter and more efficient version:
<
powerset([H|T]) -> PT = powerset(T),
[ [H|X] || X <- PT ] ++ PT.</
or even more efficient version:
<
powerset([H|T]) -> PT = powerset(T),
powerset(H, PT, PT).
powerset(_, [], Acc) -> Acc;
powerset(X, [H|T], Acc) -> powerset(X, T, [[X|H]|Acc]).</
=={{header|F Sharp|F#}}==
almost exact copy of OCaml version
<
let subsets xs = List.foldBack (fun x rest -> rest @ List.map (fun ys -> x::ys) rest) xs [[]]
</syntaxhighlight>
alternatively with list comprehension
<
let rec pow =
function
| [] -> [[]]
| x::xs -> [for i in pow xs do yield! [i;x::i]]
</syntaxhighlight>
=={{header|Factor}}==
We use hash sets, denoted by <code>HS{ }</code> brackets, for our sets. <code>members</code> converts from a set to a sequence, and <code><hash-set></code> converts back.
<
IN: powerset
: add ( set elt -- newset ) 1array <hash-set> union ;
: powerset ( set -- newset ) members { HS{ } } [ dupd [ add ] curry map append ] reduce <hash-set> ;</
Usage:
<
HS{
HS{ 1 2 3 4 }
Line 1,366 ⟶ 1,531:
HS{ 1 3 4 }
HS{ 2 3 4 }
}</
=={{header|Forth}}==
{{works with|4tH|3.61.0}}.
{{trans|C}}
<
: .set begin dup while ?print >r 1+ r> 1 rshift repeat drop drop ;
: .powerset 0 do ." ( " 1 i .set ." )" cr loop ;
Line 1,386 ⟶ 1,543:
: powerset 1 argn check-none check-size 1- lshift .powerset ;
powerset</
{{out}}
<pre>
Line 1,407 ⟶ 1,564:
( 1 2 3 4 )
</pre>
=={{header|FreeBASIC}}==
Los elementos de un conjunto se representan como bits en un número entero (por lo tanto, el tamaño máximo del conjunto es 32).
<syntaxhighlight lang="freebasic">Function ConjuntoPotencia(set() As String) As String
If Ubound(set,1) > 31 Then Print "Set demasiado grande para representarlo como un entero" : Exit Function
If Ubound(set,1) < 0 Then Print "{}": Exit Function ' Set vacío
Dim As Integer i, j
Dim As String s = "{"
For i = Lbound(set) To (2 Shl Ubound(set,1)) - 1
s += "{"
For j = Lbound(set) To Ubound(set,1)
If i And (1 Shl j) Then s += set(j) + ","
Next j
If Right(s,1) = "," Then s = Left(s,Len(s)-1)
s += "},"
Next i
Return Left(s,Len(s)-1) + "}"
End Function
Print "El power set de [1, 2, 3, 4] comprende:"
Dim As String set(3) = {"1", "2", "3", "4"}
Print ConjuntoPotencia(set())
Print !"\nEl power set de [] comprende:"
Dim As String set0()
Print ConjuntoPotencia(set0())
Print "El power set de [[]] comprende:"
Dim As String set1(0) = {""}
Print ConjuntoPotencia(set1())
Sleep</syntaxhighlight>
{{out}}
<pre>
El power set de [1, 2, 3, 4] comprende:
{{},{1},{2},{1,2},{3},{1,3},{2,3},{1,2,3},{4},{1,4},{2,4},{1,2,4},{3,4},{1,3,4},{2,3,4},{1,2,3,4}}
El power set de [] comprende:
{}
El power set de [[]] comprende:
{{},{}}
</pre>
=={{header|Frink}}==
Frink's set and array classes have built-in subsets[] methods that return all subsets. If called with an array, the results are arrays. If called with a set, the results are sets.
<
a = new set[1,2,3,4]
a.subsets[]
</syntaxhighlight>
=={{header|FunL}}==
FunL uses Scala type <code>scala.collection.immutable.Set</code> as it's set type, which has a built-in method <code>subsets</code> returning an (Scala) iterator over subsets.
<
The powerset function could be implemented in FunL directly as:
<
powerset( {} ) = {{}}
powerset( s ) =
acc = powerset( s.tail() )
acc + map( x -> {s.head()} + x, acc )</
or, alternatively as:
<
def powerset( s ) = foldr( \x, acc -> acc + map( a -> {x} + a, acc), {{}}, s )
println( powerset({1, 2, 3, 4}) )</
{{out}}
Line 1,440 ⟶ 1,639:
{{}, {4}, {1, 2}, {1, 3}, {2, 3, 4}, {3}, {1, 2, 3, 4}, {1, 4}, {1, 2, 3}, {2}, {1, 2, 4}, {1}, {3, 4}, {2, 3}, {2, 4}, {1, 3, 4}}
</pre>
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Power_set}}
'''Solution'''
No program needed. Power set is intrinsically supported in Fōrmulæ.
'''Case 1.''' Power set of the set {1, 2, 3, 4}
[[File:Fōrmulæ - Power set 01.png]]
[[File:Fōrmulæ - Power set 02.png]]
'''Case 2.''' The power set of the empty set is the set which contains itself.
[[File:Fōrmulæ - Power set 03.png]]
[[File:Fōrmulæ - Power set 04.png]]
'''Case 3.''' The power set of the set which contains only the empty set, has two subsets, the empty set and the set which contains the empty set
[[File:Fōrmulæ - Power set 05.png]]
[[File:Fōrmulæ - Power set 06.png]]
'''Case 4.''' Even when it is intrinsically supported, a program can be written:
[[File:Fōrmulæ - Power set 07.png]]
[[File:Fōrmulæ - Power set 08.png]]
[[File:Fōrmulæ - Power set 09.png]]
=={{header|GAP}}==
<
Combinations([1, 2, 3]);
# [ [ ], [ 1 ], [ 1, 2 ], [ 1, 2, 3 ], [ 1, 3 ], [ 2 ], [ 2, 3 ], [ 3 ] ]
Line 1,449 ⟶ 1,682:
Combinations([1, 2, 3, 1]);
# [ [ ], [ 1 ], [ 1, 1 ], [ 1, 1, 2 ], [ 1, 1, 2, 3 ], [ 1, 1, 3 ], [ 1, 2 ], [ 1, 2, 3 ], [ 1, 3 ],
# [ 2 ], [ 2, 3 ], [ 3 ] ]</
=={{header|Go}}==
Line 1,458 ⟶ 1,691:
While the "add" and "has" methods make a usable set type, the power set method implemented here computes a result directly without using the add method. The algorithm ensures that the result will be a valid set as long as the input is a valid set. This allows the more efficient append function to be used.
<
import (
Line 1,598 ⟶ 1,831:
}
}
}</
{{out}}
<pre>
Line 1,616 ⟶ 1,849:
=={{header|Groovy}}==
Builds on the [[Combinations#Groovy|Combinations]] solution. '''Sets''' are not a "natural" collection type in Groovy. '''Lists''' are much more richly supported. Thus, this solution is liberally sprinkled with coercion from '''Set''' to '''List''' and from '''List''' to '''Set'''.
<syntaxhighlight lang
def powerSetRec(head, tail) {
if (!tail) return [head]
powerSetRec(head, tail.tail()) + powerSetRec(head + [tail.head()], tail.tail())
}
def powerSet
</syntaxhighlight>
Test program:
<syntaxhighlight lang="groovy">
def vocalists = [ 'C', 'S', 'N', 'Y' ] as Set
println
println powerSet(vocalists)
</syntaxhighlight>
{{out}}
<pre>
[C, S, N, Y]
[[], [Y], [N], [N, Y], [S], [S, Y], [S, N], [S, N, Y], [C], [C, Y], [C, N], [C, N, Y], [C, S], [C, S, Y], [C, S, N], [C, S, N, Y]]
</pre>
=={{header|Haskell}}==
<
import Control.Monad
Line 1,650 ⟶ 1,879:
listPowerset :: [a] -> [[a]]
listPowerset = filterM (const [True, False])</
<tt>listPowerset</tt> describes the result as all possible (using the list monad) filterings (using <tt>filterM</tt>) of the input list, regardless (using <tt>const</tt>) of each item's value. <tt>powerset</tt> simply converts the input and output from lists to sets.
'''Alternate Solution'''
<
powerset (head:tail) = acc ++ map (head:) acc where acc = powerset tail</
or
<
powerSet = foldr (\x acc -> acc ++ map (x:) acc) [[]]</
which could also be understood, in point-free terms, as:
<
powerSet = foldr ((mappend <*>) . fmap . (:)) (pure [])</
Examples:
Line 1,679 ⟶ 1,908:
A method using only set operations and set mapping is also possible. Ideally, <code>Set</code> would be defined as a Monad, but that's impossible given the constraint that the type of inputs to Set.map (and a few other functions) be ordered.
<
type Set=Set.Set
unionAll :: (Ord a) => Set (Set a) -> Set a
Line 1,693 ⟶ 1,922:
powerSet :: (Ord a) => Set a -> Set (Set a)
powerSet = (Set.fold (slift Set.union) (Set.singleton Set.empty)) . Set.map makeSet</
Usage:
<syntaxhighlight lang="haskell">
Prelude Data.Set> powerSet fromList [1,2,3]
fromList [fromList [], fromList [1], fromList [1,2], fromList [1,2,3], fromList [1,3], fromList [2], fromList [2,3], fromList [3]]</
=={{header|Icon}} and {{header|Unicon}}==
Line 1,707 ⟶ 1,936:
The following version returns a set containing the powerset:
<syntaxhighlight lang="icon">
procedure power_set (s)
result := set ()
Line 1,722 ⟶ 1,951:
return result
end
</syntaxhighlight>
To test the above procedure:
<syntaxhighlight lang="icon">
procedure main ()
every s := !power_set (set(1,2,3,4)) do { # requires '!' to generate items in the result set
Line 1,734 ⟶ 1,963:
}
end
</syntaxhighlight>
{{out}}
Line 1,760 ⟶ 1,989:
An alternative version, which generates each item in the power set in turn:
<syntaxhighlight lang="icon">
procedure power_set (s)
if *s = 0
Line 1,780 ⟶ 2,009:
}
end
</syntaxhighlight>
=={{header|J}}==
There are a [http://www.jsoftware.com/jwiki/Essays/Power_Set number of ways] to generate a power set in J. Here's one:
<
For example:
<
E
Line 1,795 ⟶ 2,024:
AE
AC
ACE</
In the typical use, this operation makes sense on collections of unique elements.
<
1 2 3
#ps 1 2 3 2 1
32
#ps ~.1 2 3 2 1
8</
In other words, the power set of a 5 element set has 32 sets where the power set of a 3 element set has 8 sets. Thus if elements of the original "set" were not unique then sets of the power "set" will also not be unique sets.
Line 1,813 ⟶ 2,042:
[[Category:Recursion]]
This implementation sorts each subset, but not the whole list of subsets (which would require a custom comparator). It also destroys the original set.
<
{
if(n<0)
Line 1,837 ⟶ 2,066:
ps.addAll(tmp);
return ps;
}</
===Iterative===
The iterative implementation of the above idea. Each subset is in the order that the element appears in the input list. This implementation preserves the input.
<
public static <T> List<List<T>> powerset(Collection<T> list) {
List<List<T>> ps = new ArrayList<List<T>>();
Line 1,865 ⟶ 2,094:
return ps;
}
</syntaxhighlight>
===Binary String===
This implementation works on idea that each element in the original set can either be in the power set or not in it. With <tt>n</tt> elements in the original set, each combination can be represented by a binary string of length <tt>n</tt>. To get all possible combinations, all you need is a counter from 0 to 2<sup>n</sup> - 1. If the k<sup>th</sup> bit in the binary string is 1, the k<sup>th</sup> element of the original set is in this combination.
<
LinkedList<T> A){
LinkedList<LinkedList<T>> ans= new LinkedList<LinkedList<T>>();
Line 1,884 ⟶ 2,113:
}
return ans;
}</
=={{header|JavaScript}}==
Line 1,893 ⟶ 2,122:
{{works with|SpiderMonkey}}
<
var ps = [[]];
for (var i=0; i < ary.length; i++) {
Line 1,906 ⟶ 2,135:
load('json2.js');
print(JSON.stringify(res));</
{{out}}
Line 1,916 ⟶ 2,145:
{{trans|Haskell}}
<
// translating: powerset = foldr (\x acc -> acc ++ map (x:) acc) [[]]
Line 1,936 ⟶ 2,165:
}
})();</
{{Out}}
<syntaxhighlight lang="javascript">{
"[1,2,3] ->":[[], [3], [2], [2, 3], [1], [1, 3], [1, 2], [1, 2, 3]],
"empty set ->":[[]],
"set which contains only the empty set ->":[[], [[]]]
}</
===ES6===
<
'use strict';
// powerset :: [a] -> [[a]]
const powerset = xs =>
xs.reduceRight((a, x) => [...a, ...
[]
]);
Line 1,966 ⟶ 2,195:
])
};
})()</
{{Out}}
<
"empty set ->":[[]],
"set which contains only the empty set ->":[[], [[]]]}</
=={{header|jq}}==
<
reduce .[] as $i ([[]];
reduce .[] as $r (.; . + [$r + [$i]]));</
Example:
[range(0;10)]|powerset|length
Line 1,982 ⟶ 2,211:
Extra credit:
<syntaxhighlight lang="jq">
# The power set of the empty set:
[] | powerset
Line 1,989 ⟶ 2,218:
# The power set of the set which contains only the empty set:
[ [] ] | powerset
# => [[],[[]]]</
====Recursive version====
<
if length == 0 then [[]]
else .[0] as $first
| (.[1:] | powerset)
| map([$first] + . ) + .
end;</
Example:
[1,2,3]|powerset
Line 2,002 ⟶ 2,231:
=={{header|Julia}}==
<
function powerset
result = Vector{T}[[]]
for elem in x, j in eachindex(result)
Line 2,010 ⟶ 2,239:
result
end
</syntaxhighlight>
{{Out}}
<pre>
julia> show(powerset([1,2,3]))
[Int64[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]
</pre>
===Non-Mutating Solution===
<syntaxhighlight lang="julia">
using Base.Iterators
function bitmask(u, max_size)
res = BitArray(undef, max_size)
res.chunks[1] = u%UInt64
res
end
function powerset(input_collection::Vector{T})::Vector{Vector{T}} where T
num_elements = length(input_collection)
bitmask_map(x) = Iterators.map(y -> bitmask(y, num_elements), x)
getindex_map(x) = Iterators.map(y -> input_collection[y], x)
UnitRange(0, (2^num_elements)-1) |>
bitmask_map |>
getindex_map |>
collect
end
</syntaxhighlight>
{{Out}}
<pre>
julia> show(powerset([1,2,3]))
[Int64[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
</pre>
=={{header|K}}==
<syntaxhighlight lang="k">
ps:{x@&:'+2_vs!_2^#x}
</syntaxhighlight>
Usage:
<syntaxhighlight lang="k">
ps "ABC"
(""
Line 2,032 ⟶ 2,288:
"AB"
"ABC")
</syntaxhighlight>
=={{header|Kotlin}}==
<syntaxhighlight lang="scala">// purely functional & lazy version, leveraging recursion and Sequences (a.k.a. streams)
fun <T> Set<T>.subsets(): Sequence<Set<T>> =
when (size) {
0 -> sequenceOf(emptySet())
else -> {
val head = first()
}
// if recursion is an issue, you may change it this way:
fun <T> Set<T>.subsets(): Sequence<Set<T>> = sequence {
when (size)
else ->
val head =
val tail = this@subsets -
for (subset in tail.subsets())
yield(setOf(head) + subset)
}
}
}
}
</syntaxhighlight>
{{out}}
<pre>
Power set of
[]
[4]
[
[3, 4]
[
[
[
[2, 3, 4]
[1]
[1, 4]
[1, 3]
[1, 3, 4]
[1, 2]
[1, 2, 4]
[1, 2, 3]
[1, 2, 3, 4]
Power set of
[]
Power set of
[]
[[]]
</pre>
=={{header|Lambdatalk}}==
<syntaxhighlight lang="scheme">
{def powerset
{def powerset.r
{lambda {:ary :ps :i}
{if {= :i {A.length :ary}}
then :ps
else {powerset.r :ary
{powerset.rr :ary :ps {A.length :ps} :i 0}
{+ :i 1}} }}}
{def powerset.rr
{lambda {:ary :ps :len :i :j}
{if {= :j :len}
then :ps
else {powerset.rr :ary
{A.addlast! {A.concat {A.get :j :ps}
{A.new {A.get :i :ary}}}
:ps}
:len
:i
{+ :j 1}} }}}
{lambda {:ary}
{A.new {powerset.r :ary {A.new {A.new}} 0}}}}
-> powerset
{powerset {A.new 1 2 3 4}}
-> [[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3],[4],[1,4],[2,4],[1,2,4],[3,4],[1,3,4],[2,3,4],[1,2,3,4]]]
</syntaxhighlight>
=={{header|Logo}}==
<
if empty? :set [output [[]]]
localmake "rest powerset butfirst :set
Line 2,110 ⟶ 2,389:
show powerset [1 2 3]
[[1 2 3] [1 2] [1 3] [1] [2 3] [2] [3] []]</
=={{header|Logtalk}}==
<
:- public(powerset/2).
Line 2,137 ⟶ 2,416:
reverse(Tail, [Head| List], Reversed).
:- end_object.</
Usage example:
<
PowerSet = [[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3],[4],[1,4],[2,4],[1,2,4],[3,4],[1,3,4],[2,3,4],[1,2,3,4]]
yes</
=={{header|Lua}}==
<
--returns the powerset of s, out of order.
function powerset(s, start)
Line 2,179 ⟶ 2,458:
return ret
end
</syntaxhighlight>
=={{header|M4}}==
<
`ifelse($#, 0, ``$0'',
eval($2 <= $3), 1,
Line 2,203 ⟶ 2,482:
`{powerpart(0, substr(`$1', 1, eval(len(`$1') - 2)))}')dnl
dnl
powerset(`{a,b,c}')</
{{out}}
Line 2,209 ⟶ 2,488:
{{},{a},{a,b},{a,b,c},{a,c},{b},{b,c},{c}}
</pre>
=={{header|Maple}}==
<syntaxhighlight lang="maple">
combinat:-powerset({1,2,3,4});
</syntaxhighlight>
{{out}}
<pre>
Line 2,222 ⟶ 2,500:
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
Built-in function that either gives all possible subsets,
subsets with at most n elements, subsets with exactly n elements
or subsets containing between n and m elements.
Example of all subsets:
<
gives:
<
Subsets[list, {n, Infinity}] gives all the subsets that have n elements or more.
Line 2,242 ⟶ 2,520:
Sets are not an explicit data type in MATLAB, but cell arrays can be used for the same purpose. In fact, cell arrays have the benefit of containing any kind of data structure. So, this powerset function will work on a set of any type of data structure, without the need to overload any operators.
<
pset = cell(size(theSet)); %Preallocate memory
Line 2,259 ⟶ 2,537:
end
end</
Sample Usage:
Powerset of the set of the empty set.
<
ans =
{} {1x1 cell} %This is the same as { {},{{}} }</
Powerset of { {1,2},3 }.
<
ans =
{1x0 cell} {1x1 cell} {1x1 cell} {1x2 cell} %This is the same as { {},{{1,2}},{3},{{1,2},3} }</
=={{header|Maxima}}==
<
/* {{}, {1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 4}, {1, 3}, {1, 3, 4},
{1, 4}, {2}, {2, 3}, {2, 3, 4}, {2, 4}, {3}, {3, 4}, {4}} */</
=={{header|Nim}}==
<
proc hash(x: HashSet[int]): Hash =
var h = 0
for i in x: h = h !& hash(i)
result = !$h
proc powerset[T](inset: HashSet[T]): HashSet[HashSet[T]] =
result.incl(initHashSet[T]()) # Initialized with empty set.
for val in inset:
let previous = result
for aSet in previous:
var newSet = aSet
newSet.incl(val)
result.incl(newSet)
echo powerset([1,2,3,4].toHashSet())</syntaxhighlight>
{{out}}
<pre>{{4, 3, 1}, {3, 2, 1}, {3}, {3, 1}, {2}, {4, 3, 2, 1}, {}, {4, 2}, {4, 2, 1}, {4, 3, 2}, {1}, {3, 2}, {4, 3}, {4}, {4, 1}, {2, 1}}
</pre>
=={{header|Objective-C}}==
<
+ (NSArray *)powerSetForArray:(NSArray *)array {
Line 2,318 ⟶ 2,598:
}
return subsets;
}</
=={{header|OCaml}}==
Line 2,324 ⟶ 2,604:
The standard library already implements a proper ''Set'' datatype. As the base type is unspecified, the powerset must be parameterized as a module. Also, the library is lacking a ''map'' operation, which we have to implement first.
<
struct
Line 2,340 ⟶ 2,620:
;;
end;; (* PowerSet *)</
version for lists:
<
=={{header|OPL}}==
<syntaxhighlight lang="opl">
{string} s={"A","B","C","D"};
range r=1.. ftoi(pow(2,card(s)));
Line 2,357 ⟶ 2,636:
writeln(s2);
}
</syntaxhighlight>
which gives
<
[{} {"A"} {"B"} {"A" "B"} {"C"} {"A" "C"} {"B" "C"} {"A" "B" "C"} {"D"} {"A"
"D"} {"B" "D"} {"A" "B" "D"} {"C" "D"} {"A" "C" "D"} {"B" "C" "D"}
{"A" "B" "C" "D"}]
</syntaxhighlight>
=={{header|Oz}}==
Oz has a library for finite set constraints. Creating a power set is a trivial application of that:
<
%% Given a set as a list, returns its powerset (again as a list)
fun {Powerset Set}
Line 2,390 ⟶ 2,664:
end
in
{Inspect {Powerset [1 2 3 4]}}</
A more convential implementation without finite set constaints:
<
case Set of nil then [nil]
[] H|T thens
Line 2,400 ⟶ 2,674:
{Append Acc {Map Acc fun {$ A} H|A end}}
end
end</
=={{header|PARI/GP}}==
<
{{works with|PARI/GP|2.10.0+}}
The <code>forsubset</code> iterator was added in version 2.10.0 to efficiently iterate over combinations and power sets.
<
forsubset(#S,s,print1(vecextract(S,s)" "))</
{{out}}
<pre>[] ["a"] ["b"] ["c"] ["a", "b"] ["a", "c"] ["b", "c"] ["a", "b", "c"]</pre>
Line 2,419 ⟶ 2,693:
This module has an iterator over the power set. Note that it does not enforce that the input array is a set (no duplication). If each subset is processed immediately, this has an advantage of very low memory use.
<
my @S = ("a","b","c");
my @PS;
Line 2,426 ⟶ 2,700:
push @PS, "[@$p]"
}
say join(" ",@PS);</
{{out}}
<pre>[a b c] [b c] [a c] [c] [a b] [b] [a] []</pre>
Line 2,433 ⟶ 2,707:
{{libheader|ntheory}}
The simplest solution is to use the one argument version of the combination iterator, which iterates over the power set.
<
my @S = qw/a b c/;
forcomb { print "[@S[@_]] " } scalar(@S);
print "\n";</
{{out}}
<pre>[] [a] [b] [c] [a b] [a c] [b c] [a b c]</pre>
Using the two argument version of the iterator gives a solution similar to the
<
my @S = qw/a b c/;
for $k (0..@S) {
Line 2,447 ⟶ 2,721:
forcomb { print "[@S[@_]] " } @S,$k;
}
print "\n";</
{{out}}
<pre>[] [a] [b] [c] [a b] [a c] [b c] [a b c] </pre>
Similar to the Pari/GP solution, one can also use <tt>vecextract</tt> with an integer mask to select elements. Note that it does not enforce that the input array is a set (no duplication). This also has low memory if each subset is processed immediately and the range is applied with a loop rather than a map. A solution using <tt>vecreduce</tt> could be done identical to the array reduce solution shown later.
<
my @S = qw/a b c/;
my @PS = map { "[".join(" ",vecextract(\@S,$_))."]" } 0..2**scalar(@S)-1;
say join(" ",@PS);</
{{out}}
<pre>[] [a] [b] [a b] [c] [a c] [b c] [a b c]</pre>
Line 2,463 ⟶ 2,737:
The CPAN module [https://metacpan.org/pod/Set::Object Set::Object] provides a set implementation for sets of arbitrary objects, for which a powerset function could be defined and used like so:
<
sub powerset {
Line 2,476 ⟶ 2,750:
my $powerset = powerset($set);
print $powerset->as_string, "\n";</
{{out}}
Line 2,486 ⟶ 2,760:
using a hash as the underlying representation (like the task description suggests):
<
sub new { bless { map {$_ => undef} @_[1..$#_] }, shift; }
sub elements { sort keys %{shift()} }
sub as_string { 'Set(' . join(' ', sort keys %{shift()}) . ')' }
# ...more set methods could be defined here...
}</
''(Note: For a ready-to-use module that uses this approach, and comes with all the standard set methods that you would expect, see the CPAN module [https://metacpan.org/pod/Set::Tiny Set::Tiny])''
Line 2,499 ⟶ 2,773:
We could implement the function as an imperative foreach loop similar to the <code>Set::Object</code> based solution above, but using list folding (with the help of Perl's <code>List::Util</code> core module) seems a little more elegant in this case:
<
sub powerset {
Line 2,509 ⟶ 2,783:
my @subsets = powerset($set);
print $_->as_string, "\n" for @subsets;</
{{out}}
Line 2,528 ⟶ 2,802:
Recursive solution:
<
@_ ? map { $_, [$_[0], @$_] } powerset(@_[1..$#_]) : [];
}</
List folding solution:
<
sub powerset {
@{( reduce { [@$a, map([@$_, $b], @$a)] } [[]], @_ )}
}</
Usage & output:
<
my @powerset = powerset(@set);
Line 2,548 ⟶ 2,822:
}
print set_to_string(@powerset), "\n";</
{{out}}
<pre>
Line 2,561 ⟶ 2,835:
The following algorithm uses one bit of memory for every element of the original set (technically it uses several bytes per element with current versions of Perl). This is essentially doing a <tt>vecextract</tt> operation by hand.
<
use warnings;
sub powerset :prototype(&@) {
my $callback = shift;
my $bitmask = '';
Line 2,582 ⟶ 2,856:
powerset { ++$i } 1..9;
print "The powerset of a nine element set contains $i elements.\n";
</syntaxhighlight>
{{out}}
<pre>powerset of empty set:
Line 2,607 ⟶ 2,881:
</pre>
The technique shown above will work with arbitrarily large sets, and uses a trivial amount of memory.
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #004080;">sequence</span> <span style="color: #000000;">powerset</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">step</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">pst</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">key</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000080;font-style:italic;">/*data*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000080;font-style:italic;">/*user_data*/</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">k</span><span style="color: #0000FF;"><</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">powerset</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">step</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">step</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">powerset</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">powerset</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">key</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #000000;">step</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">power_set</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">powerset</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">({},</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">dict_size</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)))</span>
<span style="color: #000000;">step</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #7060A8;">traverse_dict</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">routine_id</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"pst"</span><span style="color: #0000FF;">),</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">powerset</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">d1234</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">new_dict</span><span style="color: #0000FF;">({{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}})</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">power_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d1234</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">d0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">new_dict</span><span style="color: #0000FF;">()</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">power_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d0</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">setd</span><span style="color: #0000FF;">({},</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d0</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">power_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d0</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
{{},{1},{2},{1,2},{3},{1,3},{2,3},{1,2,3},{4},{1,4},{2,4},{1,2,4},{3,4},{1,3,4},{2,3,4},{1,2,3,4}}
{{}}
{{},{{}}}
</pre>
===alternative===
Adapted from the one I used on [[Ascending_primes#powerset]].
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">power_set</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">powerset</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{}},</span> <span style="color: #000000;">subset</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{{},</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}}</span>
<span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">subset</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">next</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">subset</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">sub</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">subset</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ni</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sub</span><span style="color: #0000FF;">),</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">next</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">next</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">ni</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">powerset</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">powerset</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ni</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">subset</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">next</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">powerset</span><span style="color: #0000FF;">)=</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">powerset</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">power_set</span><span style="color: #0000FF;">({</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">})</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">power_set</span><span style="color: #0000FF;">({</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">power_set</span><span style="color: #0000FF;">({})</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">power_set</span><span style="color: #0000FF;">({{}})</span>
<!--</syntaxhighlight>-->
{{out}}
Guaranteed to be in length order, and index order within each length.
<pre>
{{},{1},{2},{3},{4},{1,2},{1,3},{1,4},{2,3},{2,4},{3,4},{1,2,3},{1,2,4},{1,3,4},{2,3,4},{1,2,3,4}}
{{},{4},{3},{2},{1},{4,3},{4,2},{4,1},{3,2},{3,1},{2,1},{4,3,2},{4,3,1},{4,2,1},{3,2,1},{4,3,2,1}}
{{}}
{{},{{}}}
Line 2,676 ⟶ 2,957:
=={{header|PHP}}==
<syntaxhighlight lang="php">
<?php
function get_subset($binary, $arr) {
Line 2,736 ⟶ 3,017:
print_power_sets(array('dog', 'c', 'b', 'a'));
?>
</syntaxhighlight>
{{out}}
<syntaxhighlight lang="text">
POWER SET of []
POWER SET of [singleton]
Line 2,760 ⟶ 3,041:
b c dog
a b c dog
</syntaxhighlight>
=={{header|PicoLisp}}==
<
(ifn Lst
(cons)
Line 2,769 ⟶ 3,050:
(conc
(mapcar '((X) (cons (car Lst) X)) L)
L ) ) ) )</
=={{header|PL/I}}==
{{trans|REXX}}
<
/*--------------------------------------------------------------------
* 06.01.2014 Walter Pachl translated from REXX
Line 2,838 ⟶ 3,119:
End;
End;</
{{out}}
<pre>{}
Line 2,858 ⟶ 3,139:
=={{header|PowerShell}}==
<syntaxhighlight lang="powershell">
function power-set ($array) {
if($array) {
Line 2,893 ⟶ 3,174:
$setC | foreach{"{"+"$_"+"}"}
$OFS = " "
</syntaxhighlight>
<b>Output:</b>
<pre>
Line 2,932 ⟶ 3,213:
The definitions here are elementary, logical (cut-free),
and efficient (within the class of comparably generic implementations).
<
subseq( [], []).
Line 2,938 ⟶ 3,219:
subseq( [X|Xs], [X|Ys] ) :- subseq(Xs, Ys).
subseq( [X|Xs], [_|Ys] ) :- append(_, [X|Zs], Ys), subseq(Xs, Zs).
</syntaxhighlight>
{{out}}
<pre>?- powerset([1,2,3], X).
Line 2,953 ⟶ 3,234:
===Single-Functor Definition===
<
power_set( [X|Xs], PS) :-
power_set(Xs, PS1),
maplist( append([X]), PS1, PS2 ), % i.e. prepend X to each PS1
append(PS1, PS2, PS).</
{{out}}
<pre>?- power_set([1,2,3,4,5,6,7,8], X), length(X,N), writeln(N).
Line 2,966 ⟶ 3,247:
CHR is a programming language created by '''Professor Thom Frühwirth'''.<br>
Works with SWI-Prolog and module chr written by '''Tom Schrijvers''' and '''Jan Wielemaker'''.
<
:- chr_constraint chr_power_set/2, chr_power_set/1, clean/0.
Line 2,984 ⟶ 3,265:
empty_element @ chr_power_set([], _) <=> chr_power_set([]).
</
{{out}}
<pre> ?- chr_power_set([1,2,3,4], []), findall(L, find_chr_constraint(chr_power_set(L)), LL), clean.
Line 2,992 ⟶ 3,273:
=={{header|PureBasic}}==
This code is for console mode.
<
Define argc=CountProgramParameters()
If argc>=(SizeOf(Integer)*8) Or argc<1
Line 3,016 ⟶ 3,297:
PrintN("}")
EndIf
EndIf</
<!-- Output modified with a line break to avoid being too long -->
{{out}}
Line 3,024 ⟶ 3,305:
=={{header|Python}}==
<
# the power set of the empty set has one element, the empty set
result = [[]]
Line 3,043 ⟶ 3,324:
def powerset(s):
return frozenset(map(frozenset, list_powerset(list(s))))</
<tt>list_powerset</tt> computes the power set of a list of distinct elements. <tt>powerset</tt> simply converts the input and output from lists to sets. We use the <tt>frozenset</tt> type here for immutable sets, because unlike mutable sets, it can be put into other sets.
Line 3,057 ⟶ 3,338:
==== Further Explanation ====
If you take out the requirement to produce sets and produce list versions of each powerset element, then add a print to trace the execution, you get this simplified version of the program above where it is easier to trace the inner workings
<
r = [[]]
for e in s:
Line 3,065 ⟶ 3,346:
s= [0,1,2,3]
print "\npowersetlist(%r) =\n %r" % (s, powersetlist(s))</
{{out}}
Line 3,080 ⟶ 3,361:
If you list the members of the set and include them according to if the corresponding bit position of a binary count is true then you generate the powerset.
(Note that only frozensets can be members of a set in the second function)
<
''' Generate a 'powerset' for sequence types that are indexable by integers.
Uses a binary count to enumerate the members and returns a list
Line 3,104 ⟶ 3,385:
set([frozenset([7]), frozenset([8, 6, 7]), frozenset([6]), frozenset([6, 7]), frozenset([]), frozenset([8]), frozenset([8, 7]), frozenset([8, 6])])
'''
return set( frozenset(x) for x in powersequence(list(s)) )</
=== Recursive Alternative ===
This is an (inefficient) recursive version that almost reflects the recursive definition of a power set as explained in http://en.wikipedia.org/wiki/Power_set#Algorithms. It does not create a sorted output.
<
def p(l):
if not l: return [[]]
return p(l[1:]) + [[l[0]] + x for x in p(l[1:])]
</syntaxhighlight>
===Python: Standard documentation===
Pythons [http://docs.python.org/3/library/itertools.html?highlight=powerset#itertools-recipes documentation] has a method that produces the groupings, but not as sets:
<
>>> from itertools import chain, combinations
>>>
Line 3,143 ⟶ 3,424:
(3, 4),
(4,)}
>>> </
=={{header|Qi}}==
{{trans|Scheme}}
<syntaxhighlight lang="qi">
(define powerset
[] -> [[]]
[A|As] -> (append (map (cons A) (powerset As))
(powerset As)))
</syntaxhighlight>
=={{header|Quackery}}==
Quackery is, when seen from a certain perspective, an assembly language that recognises
only three types, "operators", which correspond to op-codes, "numbers" i.e. bignums, and
"nests" which are ordered sequences of zero of more operator, bignums and nests. Everything
else is a matter of interpretation.
Integers can be used as a set of natural numbers, with (in binary) 0 corresponding to the
empty set, 1 corresponding to the set of the natural number 1, 10 corresponding to the set
of the natural number 2, 11 corresponding to the set of the natural numbers 1 and 2, and so
on. With this sort of set, enumerating the powerset of the numbers 0 to 4, for example
simply consists of enumerating the numbers 0 to 15 inclusive. Operations on this sort of
set, such as union and intersection, correspond to bitwise logic operators.
The other way of implementing sets is with nests, with each item in a nest corresponding
to an item in the set. This is computationally slower and more complex to code, but has the
advantage that it permits sets of sets, which are required for this task.
<syntaxhighlight lang="quackery"> [ stack ] is (ps).stack
[ stack ] is (ps).items
[ stack ] is (ps).result
[ 1 - (ps).items put
0 (ps).stack put
[] (ps).result put
[ (ps).result take
(ps).stack behead
drop nested join
(ps).result put
(ps).stack take
dup (ps).items share
= iff
[ drop
(ps).stack size 1 > iff
[ 1 (ps).stack tally ] ]
else
[ dup (ps).stack put
1+ (ps).stack put ]
(ps).stack size 1 = until ]
(ps).items release
(ps).result take ] is (ps) ( n --> )
[ dup size dip
[ witheach
[ over swap peek swap ] ]
nip pack ] is arrange ( [ [ --> [ )
[ dup [] = iff
nested done
dup size (ps)
' [ [ ] ] swap join
[] unrot witheach
[ dip dup arrange
nested
rot swap join swap ]
drop ] is powerset ( [ --> [ )
' [ [ 1 2 3 4 ] [ ] [ [ ] ] ]
witheach
[ say "The powerset of "
dup echo cr
powerset witheach [ echo cr ]
cr ]</syntaxhighlight>
{{out}}
<pre>The powerset of [ 1 2 3 4 ]
[ ]
[ 1 ]
[ 1 2 ]
[ 1 2 3 ]
[ 1 2 3 4 ]
[ 1 2 4 ]
[ 1 3 ]
[ 1 3 4 ]
[ 1 4 ]
[ 2 ]
[ 2 3 ]
[ 2 3 4 ]
[ 2 4 ]
[ 3 ]
[ 3 4 ]
[ 4 ]
The powerset of [ ]
[ ]
The powerset of [ [ ] ]
[ ]
[ [ ] ]
</pre>
=={{header|R}}==
===Non-recursive version===
The conceptual basis for this algorithm is the following:
<syntaxhighlight lang="text">for each element in the set:
for each subset constructed so far:
new subset = (subset + element)
</syntaxhighlight>
This method is much faster than a recursive method, though the speed is still O(2^n).
<
ps
ps[[1]]
for(element in set){ #For each element in the set, take all subsets
temp
for(subset in 1:length(ps)){ #by adding "element" to each of them.
temp[[subset]] = c(ps[[subset]],element)
}
ps
}
}
powerset(1:4)
</syntaxhighlight>
The list "temp" is a compromise between the speed costs of doing
Line 3,190 ⟶ 3,563:
The sets package includes a recursive method to calculate the power set.
However, this method takes ~100 times longer than the non-recursive method above.
<syntaxhighlight lang
An example with a vector.
<
sv <- as.set(v)
2^sv</
{{}, {1}, {4}, {9}, {1, 4}, {1, 9}, {4, 9}, {1, 4, 9}}
An example with a list.
<
sl <- as.set(l)
2^sl</
{{}, {1}, {"qwerty"}, {<<list(2)>>}, {1, <<list(2)>>}, {"qwerty",
1}, {"qwerty", <<list(2)>>}, {"qwerty", 1, <<list(2)>>}}
=={{header|Racket}}==
<
;;; Direct translation of 'functional' ruby method
(define (powerset s)
Line 3,211 ⟶ 3,584:
(list->set (set-map outer-set
(λ(inner-set) (set-add inner-set element)))))))
</syntaxhighlight>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|rakudo|2014-02-25}}
<syntaxhighlight lang="raku" line>sub powerset(Set $s) { $s.combinations.map(*.Set).Set }
say powerset set <a b c d>;</syntaxhighlight>
{{out}}
<pre>set(set(), set(a), set(b), set(c), set(d), set(a, b), set(a, c), set(a, d), set(b, c), set(b, d), set(c, d), set(a, b, c), set(a, b, d), set(a, c, d), set(b, c, d), set(a, b, c, d))</pre>
If you don't care about the actual <tt>Set</tt> type, the <tt>.combinations</tt> method by itself may be good enough for you:
<syntaxhighlight lang="raku" line>.say for <a b c d>.combinations</syntaxhighlight>
{{out}}
<pre>
a
b
c
d
a b
a c
a d
b c
b d
c d
a b c
a b d
a c d
b c d
a b c d</pre>
=={{header|Rascal}}==
<
import Set;
public set[set[&T]] PowerSet(set[&T] s) = power(s);
</syntaxhighlight>
{{out}}
<
rascal>PowerSet({1,2,3,4})
set[set[int]]: {
Line 3,240 ⟶ 3,640:
{}
}
</syntaxhighlight>
=={{header|REXX}}==
<
text='one two three four'
n=words(text)
psi=0
Do k=0 To n
Do while
Parse Var cc elist '/' cc /* get i from comb's result string */
psl=''
Do While elist<>'' /* loop through elements */
psl=psl','word(text,e) /* add corresponding test word to set */
End
psl=substr(psl,2) /* get rid of leading comma
Say right(psi,2) '{'psl'}' /* show this element of the power set */
End
End
Exit
comb: Procedure
/***********************************************************************
* Returns the combinations of size digits out of things digits
* e.g. comb(4,2) -> ' 1 2/1 3/1 4/2 3/2 4/3 4/'
1 2/ 1 3/ 1 4/ 2 3/ 2 4/ 3 4 /
***********************************************************************/
Parse Arg things,size
n=2**things-1
list=''
Do u=1 To n
co=combinations(u)
If co>'' Then
list=list '/' combinations(u)
End
Return substr(space(list),2) '/' /* remove leading / */
combinations: Procedure Expose things size
Parse Arg u
nc=0
bu=x2b(d2x(u))
bu1=space(translate(bu,' ',0),0)
If length(bu1)=size Then Do
res=''
Do i=1 To things
If substr(ub,i,1)=1 Then res=res i
Return res
End
Else
Return ''</syntaxhighlight>
{{out|output|text= when using the default input:}}
<pre>
Line 3,298 ⟶ 3,717:
=={{header|Ring}}==
<
# Project : Power set
Line 3,319 ⟶ 3,738:
next
return left(s,len(s)-1) + "}"
</syntaxhighlight>
Output:
<pre>
{{},{1},{2},{1,2},{3},{1,3},{2,3},{1,2,3},{4},{1,4},{2,4},{1,2,4},{3,4},{1,3,4},{2,3,4},{1,2,3,4}}
</pre>
=={{header|RPL}}==
{{works with|Halcyon Calc|4.2.8}}
{| class="wikitable"
! RPL code
! Comment
|-
|
≪
'''IF''' DUP SIZE
'''THEN''' LAST OVER SWAP GET → last
≪ LIST→ 1 - SWAP DROP →LIST '''POWST'''
1 OVER SIZE '''FOR''' j
DUP j GET last + 1 →LIST + '''NEXT'''
≫
'''ELSE''' 1 →LIST '''END'''
≫ ''''POWST'''' STO
|
'''POWST''' ''( { set } -- { power set } )''
if set is not empty
then store last item
get power set of ''{ set } - last item''
for all sets of ''{ set } - last item'' power set
add last item to set, then set to power set
else return { { } }
|}
{ 1 2 3 4 } '''POWST'''
{ } '''POWST'''
{{out}}
<pre>
2: { { } { 1 } { 2 } { 1 2 } { 3 } { 1 3 } { 2 3 } { 1 2 3 } { 4 } { 1 4 } { 2 4 } { 1 2 4 } { 3 4 } { 1 3 4 } { 2 3 4 } { 1 2 3 4 } }
1: { { } }
</pre>
=={{header|Ruby}}==
<
# See the link if you want a shorter version.
# This was intended to show the reader how the method works.
Line 3,369 ⟶ 3,824:
p %w(one two three).func_power_set
p Set[1,2,3].powerset</
{{out}}
<pre>
Line 3,375 ⟶ 3,830:
[[], ["one"], ["two"], ["one", "two"], ["three"], ["one", "three"], ["two", "three"], ["one", "two", "three"]]
#<Set: {#<Set: {}>, #<Set: {1}>, #<Set: {2}>, #<Set: {1, 2}>, #<Set: {3}>, #<Set: {1, 3}>, #<Set: {2, 3}>, #<Set: {1, 2, 3}>}>
</pre>
=={{header|Rust}}==
This implementation consumes the input set, requires that the type <b>T</b> has a full order a.k.a implements the <b>Ord</b> trait and that <b>T</b> is clonable.
<syntaxhighlight lang="rust">use std::collections::BTreeSet;
fn powerset<T: Ord + Clone>(mut set: BTreeSet<T>) -> BTreeSet<BTreeSet<T>> {
if set.is_empty() {
let mut powerset = BTreeSet::new();
powerset.insert(set);
return powerset;
}
// Access the first value. This could be replaced with `set.pop_first().unwrap()`
// But this is an unstable feature
let entry = set.iter().nth(0).unwrap().clone();
set.remove(&entry);
let mut powerset = powerset(set);
for mut set in powerset.clone().into_iter() {
set.insert(entry.clone());
powerset.insert(set);
}
powerset
}
fn main() {
let set = (1..5).collect();
let set = powerset(set);
println!("{:?}", set);
let set = ["a", "b", "c", "d"].iter().collect();
let set = powerset(set);
println!("{:?}", set);
}
</syntaxhighlight>
{{out}}
<pre>
{{}, {1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 4}, {1, 3}, {1, 3, 4}, {1, 4}, {2}, {2, 3}, {2, 3, 4}, {2, 4}, {3}, {3, 4}, {4}}
{{}, {"a"}, {"a", "b"}, {"a", "b", "c"}, {"a", "b", "c", "d"}, {"a", "b", "d"}, {"a", "c"}, {"a", "c", "d"}, {"a", "d"}, {"b"}, {"b", "c"}, {"b", "c", "d"}, {"b", "d"}, {"c"}, {"c", "d"}, {"d"}}
</pre>
=={{header|SAS}}==
<syntaxhighlight lang="sas">
options mprint mlogic symbolgen source source2;
Line 3,432 ⟶ 3,928:
%end;
%Mend SubSets;
</syntaxhighlight>
You can then call the macro as:
<syntaxhighlight lang="sas">
%SubSets(FieldCount = 5);
</syntaxhighlight>
The output will be the dataset SUBSETS
Line 3,481 ⟶ 3,977:
=={{header|Scala}}==
<
object Powerset extends App {
Line 3,489 ⟶ 3,985:
Set(2, 3), Set(2, 4), Set(3, 4), Set(1, 2, 3), Set(1, 3, 4), Set(1, 2, 4), Set(2, 3, 4), Set(1, 2, 3, 4)))
println(s"Successfully completed without errors. [total ${currentTime - executionStart} ms]")
}</
Another option that produces lazy sequence of the sets:
<
A tail-recursive version:
<
def powerset_rec(acc: List[Set[A]], remaining: List[A]): List[Set[A]] = remaining match {
case Nil => acc
Line 3,501 ⟶ 3,997:
}
powerset_rec(List(Set.empty[A]), s.toList)
}</
=={{header|Scheme}}==
{{trans|Common Lisp}}
<
(if (null? set)
'(())
Line 3,517 ⟶ 4,013:
(display (power-set (list "A" "C" "E")))
(newline)</
{{out}}
((1 2 3) (1 2) (1 3) (1) (2 3) (2) (3) ())
((A C E) (A C) (A E) (A) (C E) (C) (E) ())
Call/cc generation:<
(define (iter yield)
(let recur ((a '()) (b lst))
Line 3,544 ⟶ 4,040:
(display a)
(newline)
(loop (x)))))</
{{out}}
<pre>(1 2)
Line 3,554 ⟶ 4,050:
()</pre>
Iterative:<
(define (power_set_iter set)
(let loop ((res '(())) (s set))
Line 3,560 ⟶ 4,056:
res
(loop (append (map (lambda (i) (cons (car s) i)) res) res) (cdr s)))))
</syntaxhighlight>
{{out}}
Line 3,599 ⟶ 4,095:
=={{header|Seed7}}==
<
const func array bitset: powerSet (in bitset: baseSet) is func
Line 3,627 ⟶ 4,123:
writeln(aSet);
end for;
end func;</
{{out}}
Line 3,650 ⟶ 4,146:
=={{header|SETL}}==
<
Pempty := pow({});
PPempty := pow(Pempty);
Line 3,656 ⟶ 4,152:
print(Pfour);
print(Pempty);
print(PPempty);</
{{out}}
Line 3,664 ⟶ 4,160:
=={{header|Sidef}}==
<
for i in (0 .. arr.len) {
say arr.combinations(i)
}</
{{out}}
Line 3,676 ⟶ 4,172:
[["a", "b", "c"]]
</pre>
=={{header|Simula}}==
<
BEGIN
Line 3,800 ⟶ 4,297:
END;
END.
</syntaxhighlight>
{{out}}
<pre>
Line 3,819 ⟶ 4,316:
Code from [http://smalltalk.gnu.org/blog/bonzinip/fun-generators Bonzini's blog]
<
power [
^(0 to: (1 bitShift: self size) - 1) readStream collect: [ :each || i |
Line 3,825 ⟶ 4,322:
self select: [ :elem | (each bitAt: (i := i + 1)) = 1 ] ]
]
].</
<
each asArray printNl ].
#( 'A' 'C' 'E' ) power do: [ :each |
each asArray printNl ].</
=={{header|Standard ML}}==
version for lists:
<
=={{header|Swift}}==
{{works with|Swift|Revision 4 - tested with Xcode 9.2 playground}}
<
guard elements.count > 0 else {
return [[]]
Line 3,855 ⟶ 4,352:
// Example:
powersetFrom([1, 2, 4])</
{{out}}
<pre>{
Line 3,868 ⟶ 4,365:
}</pre>
<
powersetFrom(["a", "b", "d"])</
{{out}}
<pre>{
Line 3,883 ⟶ 4,380:
=={{header|Tcl}}==
<
set res [list [list]]
foreach e $l {
Line 3,890 ⟶ 4,387:
return $res
}
puts [subsets {a b c d}]</
{{out}}
<pre>{} a b {a b} c {a c} {b c} {a b c} d {a d} {b d} {a b d} {c d} {a c d} {b c d} {a b c d}</pre>
===Binary Count Method===
<
set res {}
for {set i 0} {$i < 2**[llength $set]} {incr i} {
Line 3,905 ⟶ 4,402:
}
return $res
}</
=={{header|TXR}}==
Line 3,911 ⟶ 4,408:
The power set function can be written concisely like this:
<
(mappend* (op comb s) (range 0 (length s))))</
This generates the lists of combinations of all possible lengths, from 0 to the length of <code>s</code> and catenates them. The <code>comb</code> function generates a lazy list, so it is appropriate to use <code>mappend*</code> (the lazy version of <code>mappend</code>) to keep the behavior lazy.
Line 3,918 ⟶ 4,415:
A complete program which takes command line arguments and prints the power set in comma-separated brace notation:
<
(mappend* (op comb s) (range 0 (length s)))))
@(bind pset @(power-set *args*))
Line 3,925 ⟶ 4,422:
{@(rep)@pset, @(last)@pset@(empty)@(end)}
@ (end)
@(end)</
{{out}}
<pre>$ txr rosetta/power-set.txr 1 2 3
Line 3,940 ⟶ 4,437:
generalizes to strings and vectors.
<
(mappend* (op comb s) (range 0 (length s))))
(prinl (power-set "abc"))
(prinl (power-set "b"))
(prinl (power-set ""))
(prinl (power-set #(1 2 3))))</
{{out}}
<pre>$ txr power-set-generic.txr
Line 3,952 ⟶ 4,449:
("")
(#() #(1) #(2) #(3) #(1 2) #(1 3) #(2 3) #(1 2 3))</pre>
=={{header|UNIX Shell}}==
From [http://www.catonmat.net/blog/set-operations-in-unix-shell/ here]
<syntaxhighlight lang="bash">p() { [ $# -eq 0 ] && echo || (shift; p "$@") | while read r ; do echo -e "$1 $r\n$r"; done }</syntaxhighlight>
Usage
<syntaxhighlight lang="bash">|p `cat` | sort | uniq
A
C
E
^D</syntaxhighlight>
=={{header|UnixPipes}}==
<
| cat A
a
Line 3,977 ⟶ 4,484:
b c
c
</syntaxhighlight>
=={{header|Ursala}}==
Line 3,995 ⟶ 4,492:
The powerset function is a standard library function,
but could be defined as shown below.
<
test program:
<
test = powerset {'a','b','c','d'}</
{{out}}
<pre>{
Line 4,021 ⟶ 4,518:
=={{header|V}}==
V has a built in called powerlist
<
=[[A C E] [A C] [A E] [A] [C E] [C] [E] []]</
its implementation in std.v is (like joy)
<
[null?]
[unitlist]
Line 4,031 ⟶ 4,528:
[dup swapd [cons] map popd swoncat]
linrec].
</syntaxhighlight>
=={{header|VBA}}==
<syntaxhighlight lang="vb">Option Base 1
Private Function power_set(ByRef st As Collection) As Collection
Dim subset As Collection, pwset As New Collection
For i = 0 To 2 ^ st.Count - 1
Set subset = New Collection
For j = 1 To st.Count
If i And 2 ^ (j - 1) Then subset.Add st(j)
Next j
pwset.Add subset
Next i
Set power_set = pwset
End Function
Private Function print_set(ByRef st As Collection) As String
'assume st is a collection of collections, holding integer variables
Dim s() As String, t() As String
ReDim s(st.Count)
'Debug.Print "{";
For i = 1 To st.Count
If st(i).Count > 0 Then
ReDim t(st(i).Count)
For j = 1 To st(i).Count
Select Case TypeName(st(i)(j))
Case "Integer": t(j) = CStr(st(i)(j))
Case "Collection": t(j) = "{}" 'assumes empty
End Select
Next j
s(i) = "{" & Join(t, ", ") & "}"
Else
s(i) = "{}"
End If
Next i
print_set = "{" & Join(s, ", ") & "}"
End Function
Public Sub rc()
Dim rcset As New Collection, result As Collection
For i = 1 To 4
rcset.Add i
Next i
Debug.Print print_set(power_set(rcset))
Set rcset = New Collection
Debug.Print print_set(power_set(rcset))
Dim emptyset As New Collection
rcset.Add emptyset
Debug.Print print_set(power_set(rcset))
Debug.Print
End Sub</syntaxhighlight>{{out}}
<pre>{{}, {1}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}, {4}, {1, 4}, {2, 4}, {1, 2, 4}, {3, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
{{}}
{{}, {{}}}</pre>
=={{header|VBScript}}==
<
q = n
Dec2Bin = ""
Line 4,066 ⟶ 4,614:
End Function
WScript.StdOut.Write PowerSet("1,2,3,4")</
{{out}}
<pre>{{},{1},{2},{1,2},{3},{1,3},{2,3},{1,2,3},{4},{1,4},{2,4},{1,2,4},{3,4},{1,3,4},{2,3,4},{1,2,3,4}}</pre>
=={{header|Wren}}==
{{libheader|Wren-perm}}
Although we have a module for sets, they are based on maps whose keys must be value types. This means that sets of sets are technically impossible because sets themselves are not value types.
We therefore use lists to represent sets which works fine here.
<syntaxhighlight lang="wren">import "./perm" for Powerset
var sets = [ [1, 2, 3, 4], [], [[]] ]
for (set in sets) {
System.print("The power set of %(set) is:")
System.print(Powerset.list(set))
System.print()
}</syntaxhighlight>
{{out}}
<pre>
The power set of [1, 2, 3, 4] is:
[[], [1], [2], [3], [4], [1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4], [1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4], [1, 2, 3, 4]]
The power set of [] is:
[[]]
The power set of [[]] is:
[[], [[]]]
</pre>
=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">func PowSet(Set, Size);
int Set, Size;
int N, M, Mask, DoComma;
[ChOut(0, ^{);
for N:= 0 to 1<<Size -1 do
[if N>0 then ChOut(0, ^,);
ChOut(0, ^{);
Mask:= 1; DoComma:= false;
for M:= 0 to Size-1 do
[if Mask & N then
[if DoComma then ChOut(0, ^,);
IntOut(0, Set(M));
DoComma:= true;
];
Mask:= Mask << 1;
];
ChOut(0, ^});
];
Text(0, "}^m^j");
];
[PowSet([2, 3, 5, 7], 4);
PowSet([1], 1);
PowSet(0, 0);
]</syntaxhighlight>
{{out}}
<pre>
{{},{2},{3},{2,3},{5},{2,5},{3,5},{2,3,5},{7},{2,7},{3,7},{2,3,7},{5,7},{2,5,7},{3,5,7},{2,3,5,7}}
{{},{1}}
{{}}
</pre>
=={{header|zkl}}==
Using a combinations function, build the power set from combinations of 1,2,... items.
<
(0).pump(list.len(),List, Utils.Helpers.pickNFrom.fp1(list),
T(Void.Write,Void.Write) ) .append(list)
}</
<syntaxhighlight lang="zkl">foreach n in (5){
ps:=pwerSet((1).pump(n,List)); ps.println(" Size = ",ps.len());
}</syntaxhighlight>
{{out}}
<pre>
|