Power set: Difference between revisions

{{task|Discrete math}}

{{omit from|GUISS}}

without any particular order, and no repeated values.

It corresponds with a finite set in mathematics.

A set can be implemented as an associative array (partial mapping)

in which the value of each key-value pair is ignored.

 

 

 

For a set which contains n elements, the corresponding power set has 2ⁿ elements, including the edge cases of [[wp:Empty_set|empty set]].<br />

 

The power set of the empty set is the set which contains itself (2⁰ = 1):<br />

And 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 (2¹ = 2):<br />

 

'''Extra credit: ''' Demonstrate that your language supports these last two powersets.

 

 

 

 

 

 

 

 

begin

 

{{out}}

 

 

=={{header|ALGOL 68}}==

 

Requires: ALGOL 68g mk14.1+

 

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

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

OD

{{out}}

<pre>

set[8] = (1, 2, 4);

</pre>

 

=={{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

}

 

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>

[ 3 2 1 ]

</pre>

 

=={{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]

#{#{}} coll))

 

 

=={{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

["b", "c"]

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

 

=={{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|Erlang}}==

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

</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>

( 1 2 3 4 )

</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}}

{{}, {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|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}}==

set add method. Adding elements with the add method ensures the uniqueness property.

 

 

import (

)

 

// implemented and stored in sets.

type elem interface {

}

 

 

func (i Int) Eq(e elem) bool {

}

 

func (i Int) String() string {

}

 

// uniqueness of elements can be ensured by using add method

func (s *set) add(e elem) {

}

 

func (s *set) has(e elem) bool {

}

 

// elem.Eq

func (s set) Eq(e elem) bool {

}

 

// elem.String

func (s set) String() string {

}

 

// method required for task

func (s set) powerSet() set {

}

 

func main() {

 

{{out}}

<pre>

s: {1,2,3,4} length: 4

𝑷(s): {∅,{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}} length: 16

empty: ∅ len: 0

𝑷(∅): {∅} len: 1

𝑷(𝑷(∅)): {∅,{∅}} len: 2

</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'''.

}

 

 

Test program:

 

{{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

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}}==

Uses a JSON stringifier from http://www.json.org/js.html

 

{{works with|SpiderMonkey}}

var ps = [[]];

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

 

load('json2.js');

 

{{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|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}}==

end

result

end

{{Out}}

<pre>

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

</pre>

 

=={{header|K}}==

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

Usage:

ps "ABC"

(""

"AB"

"ABC")

 

=={{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}}

{{},{a},{a,b},{a,b,c},{a,c},{b},{b,c},{c}}

</pre>

 

=={{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}}==

var h = 0

for i in x: h = h !& hash(i)

result = !$h

 

 

=={{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}}==

 

=={{header|Perl}}==

 

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>

 

=== Module: [https://metacpan.org/pod/ntheory ntheory] ===

{{out}}

 

for $k (0..@S) {

# Iterate over each $#S+1,$k combination.

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

}

{{out}}

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

 

=== Module: [https://metacpan.org/pod/Set::Object Set::Object] ===

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:

The technique shown above will work with arbitrarily large sets, and uses a trivial amount of memory.

 

{{out}}

{{out}}

 

=={{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}}==

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

* 06.01.2014 Walter Pachl translated from REXX

End;

 

{{out}}

<pre>{}

 

=={{header|PowerShell}}==

function power-set ($array) {

if($array) {

state ($set+@($array[$i])) ($i-1)

} else {

}

}

$power = 0..($set.Count-1) | foreach{@(0)}

$i = 0

$power | sort {$_.Count}

} else {@()}

 

}

<b>Output:</b>

<pre>

</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).

 

for(element in set){ #For each element in the set, take all subsets

for(subset in 1:length(ps)){ #by adding "element" to each of them.

temp[[subset]] = c(ps[[subset]],element)

}

}

}

 

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|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}}==

 

1 {}

2 {one}

15 {two,three,four}

16 {one,two,three,four}

</pre>

 

=={{header|Ruby}}==

# See the link if you want a shorter version.

class Array

# Adds a power_set method to every array, i.e.: [1, 2].power_set

p %w(one two three).func_power_set

 

{{out}}

<pre>

[[], ["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|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]")

 

=={{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}}

{2, 3, 4}

{1, 2, 3, 4}

</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|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

("")

(#() #(1) #(2) #(3) #(1 2) #(1 3) #(2 3) #(1 2 3))</pre>

 

=={{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|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|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>