Power set: Difference between revisions

{{trans|Python}}

 

V result = [[Int]()]

L(x) lst

R result

 

 

{{out}}

This works for ABAP Version 7.40 and above

 

report z_powerset.

 

)->add_element( `4` )->add_element( `4` ).

write: |𝑷( { set3->set~stringify( ) } ) -> { set3->build_powerset( )->set~stringify( ) }|, /.

 

{{out}}

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.

 

with Ada.Text_IO, Ada.Command_Line;

use Ada.Text_IO, Ada.Command_Line;

end loop;

end powerset;

 

 

 

Requires: ALGOL 68g mk14.1+

 

PROC power set = ([]MEMBER s)[][]MEMBER:(

printf(($"set["d"] = "$,member, repr set, set[member],$l$))

OD

{{out}}

<pre>

{{works with|Dyalog APL}}

 

 

{{out}}

(functional composition examples)

{{Trans|Haskell}}

 

-- powerset :: [a] -> [[a]]

end script

end if

{{Out}}

{"Empty set", {{}}},

 

=={{header|ATS}}==

(* ****** ****** *)

//

 

(* ****** ****** *)

 

=={{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

 

t .= "}`n{" ; new subsets in new lines

}

 

=={{header|AWK}}==

#!/usr/local/bin/gawk -f

 

# For each input

{ for (i=0;i<=2^NF-1;i++) if (i == 0) printf("empty\n"); else printf("(%s)\n",tochar(i,NF)) }

 

{{out}}

</pre>

 

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

s$ += "},"

NEXT i%

{{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|Bracmat}}==

= done todo first

. !arg:(?done.?todo)

)

& out$(powerset$(.1 2 3 4))

{{out}}

<pre> 1 2 3 4

=={{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}}

 

=={{header|C}}==

 

struct node {

powerset(argv + 1, argc - 1, 0);

return 0;

{{out}}

<pre>

 

=={{header|C sharp|C#}}==

public IEnumerable<IEnumerable<T>> GetPowerSet<T>(List<T> list)

{

}

 

 

{{out}}

An alternative implementation for an arbitrary number of elements:

 

public IEnumerable<IEnumerable<T>> GetPowerSet<T>(IEnumerable<T> input) {

var seed = new List<IEnumerable<T>>() { Enumerable.Empty<T>() }

a.Concat(a.Select(x => x.Concat(new List<T>() { b }))));

}

 

 

Non-recursive version

 

using System;

class Powerset

}

}

 

----------------

 

Recursive version

using System;

class Powerset

}

}

 

=={{header|C++}}==

=== Non-recursive version ===

 

#include <set>

#include <vector>

std::cout << " }\n";

}

 

{{out}}

This simplified version has identical output to the previous code.

 

#include <set>

#include <iostream>

}

}

 

=== Recursive version ===

 

#include <set>

 

return powerset(s, s.size());

}

 

=={{header|Clojure}}==

 

(def S #{1 2 3 4})

 

user> (subsets S)

 

'''Alternate solution''', with no dependency on third-party library:

(reduce (fn [a x]

(into a (map #(conj % x)) a))

#{#{}} coll))

 

 

'''Using bit-test''':

see: https://clojuredocs.org/clojure.core/bit-test#example-5d401face4b0ca44402ef78b

(let [cnt (count coll)

bits (Math/pow 2 cnt)]

(nth coll j)))))

 

 

=={{header|CoffeeScript}}==

print_power_set = (arr) ->

console.log "POWER SET of #{arr}"

print_power_set [4, 2, 1]

print_power_set ['dog', 'c', 'b', 'a']

{{out}}

> coffee power_set.coffee

POWER SET of

[ 'dog', 'c', 'b' ]

[ 'dog', 'c', 'b', 'a' ]

 

=={{header|ColdFusion}}==

Port from the [[#JavaScript|JavaScript]] version,

compatible with ColdFusion 8+ or Railo 3+

{

var ps = [""];

}

 

 

{{out}}

 

=={{header|Common Lisp}}==

(if s (mapcan (lambda (x) (list (cons (car s) x) x))

(powerset (cdr s)))

 

{{out}}

((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))

s

:from-end t

{{out}}

>(power-set '(1 2 3))

 

Alternate, more recursive (same output):

(if (null l)

(list nil)

(let ((prev (powerset (cdr l))))

(append (mapcar #'(lambda (elt) (cons (car l) elt)) prev)

 

 

Imperative-style using LOOP:

(loop for i below (expt 2 (length xs)) collect

{{out}}

>(powerset '(1 2 3)

 

Yet another imperative solution, this time with dolist.

(let ((pow-set (list nil)))

(dolist (element (reverse list) pow-set)

(dolist (set pow-set)

{{out}}

>(power-set '(1 2 3))

This implementation defines a range which *lazily* enumerates the power set.

 

import std.range;

 

import std.stdio;

args[1..$].powerSet.each!writeln;

 

An alternative version, which implements the range construct from scratch:

 

 

struct PowerSet(R)

}

 

{{out}}

<pre>$ rdmd powerset a b c

#It doesn't rely on integer bit fiddling, so it should work on arrays larger than size_t.

 

// Haskell definition:

// foldr f z [] = z

return foldr( (T x, T[][] acc) => acc ~ acc.map!(accx => x ~ accx).array , [[]], set );

}

 

=={{header|Déjà Vu}}==

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:

out

 

 

{{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|E}}==

 

 

def powerset(s) {

})

}

 

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)))

 

 

 

=={{header|Elixir}}==

{{trans|Erlang}}

use Bitwise

def powerset1(list) do

IO.inspect RC.powerset3([1,2,3])

IO.inspect RC.powerset1([])

 

{{out}}

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

</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]

 

{{out}}

 

Alternate shorter and more efficient version:

powerset([H|T]) -> PT = powerset(T),

 

or even more efficient version:

powerset([H|T]) -> PT = powerset(T),

powerset(H, PT, PT).

 

powerset(_, [], Acc) -> 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 [[]]

 

alternatively with list comprehension

 

let rec pow =

function

| [] -> [[]]

| x::xs -> [for i in pow xs do yield! [i;x::i]]

 

=={{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 ;

Usage:

HS{

HS{ 1 2 3 4 }

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 ;

: powerset 1 argn check-none check-size 1- lshift .powerset ;

 

{{out}}

<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).

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 String set1(0) = {""}

Print ConjuntoPotencia(set1())

{{out}}

<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[]

 

=={{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() )

 

or, alternatively as:

 

def powerset( s ) = foldr( \x, acc -> acc + map( a -> {x} + a, acc), {{}}, s )

 

 

{{out}}

=={{header|Fōrmulæ}}==

 

 

 

 

=={{header|GAP}}==

Combinations([1, 2, 3]);

# [ [ ], [ 1 ], [ 1, 2 ], [ 1, 2, 3 ], [ 1, 3 ], [ 2 ], [ 2, 3 ], [ 3 ] ]

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 ],

 

=={{header|Go}}==

 

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 (

}

}

{{out}}

<pre>

=={{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'''.

def powerSetRec(head, tail) {

if (!tail) return [head]

 

def powerSet(set) { powerSetRec([], set as List) as Set}

 

Test program:

def vocalists = [ 'C', 'S', 'N', 'Y' ] as Set

println vocalists

println powerSet(vocalists)

 

{{out}}

 

=={{header|Haskell}}==

import Control.Monad

 

 

listPowerset :: [a] -> [[a]]

<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'''

or

 

which could also be understood, in point-free terms, as:

 

Examples:

 

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

 

powerSet :: (Ord a) => Set a -> Set (Set a)

Usage:

Prelude Data.Set> powerSet fromList [1,2,3]

 

=={{header|Icon}} and {{header|Unicon}}==

The following version returns a set containing the powerset:

 

procedure power_set (s)

result := set ()

return result

end

 

To test the above procedure:

 

procedure main ()

every s := !power_set (set(1,2,3,4)) do { # requires '!' to generate items in the result set

}

end

 

{{out}}

An alternative version, which generates each item in the power set in turn:

 

procedure power_set (s)

if *s = 0

}

end

 

=={{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

AE

AC

 

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

 

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.

[[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)

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>>();

return ps;

}

 

===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 2ⁿ - 1. If the k^th bit in the binary string is 1, the k^th element of the original set is in this combination.

LinkedList<T> A){

LinkedList<LinkedList<T>> ans= new LinkedList<LinkedList<T>>();

}

return ans;

 

=={{header|JavaScript}}==

 

{{works with|SpiderMonkey}}

var ps = [[]];

for (var i=0; i < ary.length; i++) {

 

load('json2.js');

 

{{out}}

{{trans|Haskell}}

 

 

// translating: powerset = foldr (\x acc -> acc ++ map (x:) acc) [[]]

}

 

 

{{Out}}

 

"[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';

 

])

};

 

{{Out}}

"empty set ->":[[]],

 

=={{header|jq}}==

reduce .[] as $i ([[]];

Example:

[range(0;10)]|powerset|length

 

Extra credit:

# The power set of the empty set:

[] | powerset

# 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] + . ) + .

Example:

[1,2,3]|powerset

 

=={{header|Julia}}==

result = Vector{T}[[]]

for elem in x, j in eachindex(result)

result

end

{{Out}}

<pre>

julia> show(powerset([1,2,3]))

[Int64[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]

</pre>

 

=={{header|K}}==

ps:{x@&:'+2_vs!_2^#x}

Usage:

ps "ABC"

(""

"AB"

"ABC")

 

=={{header|Kotlin}}==

fun <T> Set<T>.subsets(): Sequence<Set<T>> =

when (size) {

}

}

 

{{out}}

[[]]

</pre>

 

=={{header|Logo}}==

if empty? :set [output [[]]]

localmake "rest powerset butfirst :set

 

show powerset [1 2 3]

 

=={{header|Logtalk}}==

 

:- public(powerset/2).

reverse(Tail, [Head| List], Reversed).

 

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]]

 

=={{header|Lua}}==

--returns the powerset of s, out of order.

function powerset(s, start)

return ret

end

 

=={{header|M4}}==

`ifelse($#, 0, ``$0'',

eval($2 <= $3), 1,

`{powerpart(0, substr(`$1', 1, eval(len(`$1') - 2)))}')dnl

dnl

 

{{out}}

 

=={{header|Maple}}==

combinat:-powerset({1,2,3,4});

{{out}}

<pre>

</pre>

 

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.

 

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

end

 

Sample Usage:

Powerset of the set of the empty set.

 

ans =

 

 

Powerset of { {1,2},3 }.

 

ans =

 

 

=={{header|Maxima}}==

/* {{}, {1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 4}, {1, 3}, {1, 3, 4},

 

=={{header|Nim}}==

proc hash(x: HashSet[int]): Hash =

result.incl(newSet)

 

=={{header|Objective-C}}==

 

+ (NSArray *)powerSetForArray:(NSArray *)array {

}

return subsets;

 

=={{header|OCaml}}==

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

 

;;

 

 

version for lists:

 

=={{header|OPL}}==

 

{string} s={"A","B","C","D"};

range r=1.. ftoi(pow(2,card(s)));

writeln(s2);

}

 

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"}]

 

=={{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}

end

in

 

A more convential implementation without finite set constaints:

case Set of nil then [nil]

[] H|T thens

{Append Acc {Map Acc fun {$ A} H|A 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.

{{out}}

<pre>[] ["a"] ["b"] ["c"] ["a", "b"] ["a", "c"] ["b", "c"] ["a", "b", "c"]</pre>

 

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;

push @PS, "[@$p]"

}

{{out}}

<pre>[a b c] [b c] [a c] [c] [a b] [b] [a] []</pre>

{{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);

{{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 Raku and Python array versions.

my @S = qw/a b c/;

for $k (0..@S) {

forcomb { print "[@S[@_]] " } @S,$k;

}

{{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;

{{out}}

<pre>[] [a] [b] [a b] [c] [a c] [b c] [a b c]</pre>

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 {

my $powerset = powerset($set);

 

 

{{out}}

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])''

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 {

my @subsets = powerset($set);

 

 

{{out}}

 

Recursive solution:

@_ ? map { $_, [$_[0], @$_] } powerset(@_[1..$#_]) : [];

 

List folding solution:

 

 

sub powerset {

@{( reduce { [@$a, map([@$_, $b], @$a)] } [[]], @_ )}

 

Usage & output:

my @powerset = powerset(@set);

 

}

 

{{out}}

<pre>

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;

my $callback = shift;

my $bitmask = '';

powerset { ++$i } 1..9;

print "The powerset of a nine element set contains $i elements.\n";

{{out}}

<pre>powerset of empty set:

 

=={{header|Phix}}==

{{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}}

{{}}

{{},{{}}}

 

=={{header|PHP}}==

<?php

function get_subset($binary, $arr) {

print_power_sets(array('dog', 'c', 'b', 'a'));

?>

{{out}}

POWER SET of []

POWER SET of [singleton]

b c dog

a b c dog

 

=={{header|PicoLisp}}==

(ifn Lst

(cons)

(conc

(mapcar '((X) (cons (car Lst) X)) L)

 

=={{header|PL/I}}==

{{trans|REXX}}

/*--------------------------------------------------------------------

* 06.01.2014 Walter Pachl translated from REXX

End;

 

{{out}}

<pre>{}

 

=={{header|PowerShell}}==

function power-set ($array) {

if($array) {

$setC | foreach{"{"+"$_"+"}"}

$OFS = " "

<b>Output:</b>

<pre>

The definitions here are elementary, logical (cut-free),

and efficient (within the class of comparably generic implementations).

 

subseq( [], []).

subseq( [X|Xs], [X|Ys] ) :- subseq(Xs, Ys).

subseq( [X|Xs], [_|Ys] ) :- append(_, [X|Zs], Ys), subseq(Xs, Zs).

{{out}}

<pre>?- powerset([1,2,3], X).

 

===Single-Functor Definition===

power_set( [X|Xs], PS) :-

power_set(Xs, PS1),

maplist( append([X]), PS1, PS2 ), % i.e. prepend X to each PS1

{{out}}

<pre>?- power_set([1,2,3,4,5,6,7,8], X), length(X,N), writeln(N).

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.

 

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.

=={{header|PureBasic}}==

This code is for console mode.

Define argc=CountProgramParameters()

If argc>=(SizeOf(Integer)*8) Or argc<1

PrintN("}")

EndIf

<!-- Output modified with a line break to avoid being too long -->

{{out}}

 

=={{header|Python}}==

# the power set of the empty set has one element, the empty set

result = [[]]

 

def powerset(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.

==== 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:

 

s= [0,1,2,3]

 

{{out}}

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

set([frozenset([7]), frozenset([8, 6, 7]), frozenset([6]), frozenset([6, 7]), frozenset([]), frozenset([8]), frozenset([8, 7]), frozenset([8, 6])])

'''

 

=== 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:])]

 

===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

>>>

(3, 4),

(4,)}

 

=={{header|Qi}}==

{{trans|Scheme}}

(define powerset

[] -> [[]]

[A|As] -> (append (map (cons A) (powerset As))

(powerset As)))

 

=={{header|R}}==

===Non-recursive version===

The conceptual basis for this algorithm is the following:

for each subset constructed so far:

new subset = (subset + element)

 

This method is much faster than a recursive method, though the speed is still O(2^n).

 

ps <- list()

ps[[1]] <- numeric() #Start with the empty set.

 

powerset(1:4)

 

The list "temp" is a compromise between the speed costs of doing

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.

An example with a vector.

sv <- as.set(v)

{{}, {1}, {4}, {9}, {1, 4}, {1, 9}, {4, 9}, {1, 4, 9}}

An example with a list.

sl <- as.set(l)

{{}, {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)

(list->set (set-map outer-set

(λ(inner-set) (set-add inner-set element)))))))

 

=={{header|Raku}}==

(formerly Perl 6)

{{works with|rakudo|2014-02-25}}

{{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:

{{out}}

<pre>&nbsp;

 

=={{header|Rascal}}==

import Set;

 

public set[set[&T]] PowerSet(set[&T] s) = power(s);

{{out}}

rascal>PowerSet({1,2,3,4})

set[set[int]]: {

{}

}

 

=={{header|REXX}}==

{{out|output|text=&nbsp; when using the default input:}}

<pre>

 

=={{header|Ring}}==

# Project : Power set

 

next

return left(s,len(s)-1) + "}"

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|Ruby}}==

# See the link if you want a shorter version.

# This was intended to show the reader how the method works.

p %w(one two three).func_power_set

 

{{out}}

<pre>

#<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.

 

 

fn powerset<T: Ord + Clone>(mut set: BTreeSet<T>) -> BTreeSet<BTreeSet<T>> {

println!("{:?}", set);

}

 

{{out}}

 

=={{header|SAS}}==

options mprint mlogic symbolgen source source2;

 

%end;

%Mend SubSets;

 

You can then call the macro as:

%SubSets(FieldCount = 5);

 

The output will be the dataset SUBSETS

 

=={{header|Scala}}==

 

object Powerset extends App {

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

}

powerset_rec(List(Set.empty[A]), s.toList)

 

=={{header|Scheme}}==

{{trans|Common Lisp}}

(if (null? set)

'(())

 

(display (power-set (list "A" "C" "E")))

{{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) ())

 

(define (iter yield)

(let recur ((a '()) (b lst))

(display a)

(newline)

{{out}}

<pre>(1 2)

()</pre>

 

(define (power_set_iter set)

(let loop ((res '(())) (s set))

res

(loop (append (map (lambda (i) (cons (car s) i)) res) res) (cdr s)))))

 

{{out}}

 

=={{header|Seed7}}==

const func array bitset: powerSet (in bitset: baseSet) is func

writeln(aSet);

end for;

 

{{out}}

 

=={{header|SETL}}==

Pempty := pow({});

PPempty := pow(Pempty);

print(Pfour);

print(Pempty);

 

{{out}}

 

=={{header|Sidef}}==

for i in (0 .. arr.len) {

say arr.combinations(i)

 

{{out}}

 

=={{header|Simula}}==

BEGIN

 

END;

END.

{{out}}

<pre>

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 |

self select: [ :elem | (each bitAt: (i := i + 1)) = 1 ] ]

]

 

each asArray printNl ].

 

#( 'A' 'C' 'E' ) power do: [ :each |

 

=={{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 [[]]

 

// Example:

{{out}}

<pre>{

}</pre>

 

{{out}}

<pre>{

 

=={{header|Tcl}}==

set res [list [list]]

foreach e $l {

return $res

}

{{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} {

}

return $res

 

=={{header|TXR}}==

The power set function can be written concisely like this:

 

 

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.

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*))

{@(rep)@pset, @(last)@pset@(empty)@(end)}

@ (end)

{{out}}

<pre>$ txr rosetta/power-set.txr 1 2 3

generalizes to strings and vectors.

 

(mappend* (op comb s) (range 0 (length s))))

(prinl (power-set "abc"))

(prinl (power-set "b"))

(prinl (power-set ""))

{{out}}

<pre>$ txr power-set-generic.txr

=={{header|UNIX Shell}}==

From [http://www.catonmat.net/blog/set-operations-in-unix-shell/ here]

Usage

A

C

E

 

=={{header|UnixPipes}}==

| cat A

a

b c

c

 

=={{header|Ursala}}==

The powerset function is a standard library function,

but could be defined as shown below.

test program:

 

{{out}}

<pre>{

=={{header|V}}==

V has a built in called powerlist

 

its implementation in std.v is (like joy)

[null?]

[unitlist]

[dup swapd [cons] map popd swoncat]

linrec].

 

=={{header|VBA}}==

Private Function power_set(ByRef st As Collection) As Collection

Dim subset As Collection, pwset As New Collection

Debug.Print print_set(power_set(rcset))

Debug.Print

<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}}

{{}}

 

=={{header|VBScript}}==

q = n

Dec2Bin = ""

End Function

 

{{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}}==

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.

 

var sets = [ [1, 2, 3, 4], [], [[]] ]

for (set in sets) {

System.print("The power set of %(set) is:")

System.print()

 

{{out}}

<pre>

The power set of [1, 2, 3, 4] is:

 

The power set of [] is:

The power set of [[]] is:

[[], [[]]]

</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)

ps:=pwerSet((1).pump(n,List)); ps.println(" Size = ",ps.len());

{{out}}

<pre>