Cartesian product of two or more lists: Difference between revisions

 

<br>

=={{header|11l}}==

{{trans|Go}}

V p = [(0, 0)] * (a.len * b.len)

V i = 0

print(cart_prod([1, 2], [3, 4]))

print(cart_prod([3, 4], [1, 2]))

====Alternative version====

{{out}}

<pre>

[]

[]

</pre>

 

=={{header|AppleScript}}==

 

-- Two lists:

on unlines(xs)

intercalate(linefeed, xs)

{{Out}}

<pre>[[1, 3], [1, 4], [2, 3], [2, 4]]

 

[]</pre>

 

=={{header|C}}==

Recursive implementation for computing the Cartesian product of lists. In the pursuit of making it as interactive as possible, the parsing function ended up taking the most space. The product set expression must be supplied enclosed by double quotes. Prints out usage on incorrect invocation.

#include<string.h>

#include<stdlib.h>

return 0;

}

Invocation and output :

<pre>

{}

</pre>

public class Program

{

select acc.Concat(new [] { item }));

}

{{out}}

<pre>

{}</pre>

If the number of lists is known, LINQ provides an easier solution:

{

///...

select (a, b, c);

Console.WriteLine($"{{{string.Join(", ", cart2)}}}");

{{out}}

<pre>

{(1, 30, 500), (1, 30, 100), (2, 30, 500), (2, 30, 100), (3, 30, 500), (3, 30, 100)}

</pre>

 

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

"Compute the cartesian product of two sets represented as lists"

(loop for x in s1

nconc (loop for y in s2 collect (list x y))))

 

'''Output'''

 

CL-USER> (cartesian-product '(1 2) '(3 4))

((1 3) (1 4) (2 3) (2 4))

CL-USER> (cartesian-product '() '(1 2))

NIL

 

'''Extra credit:'''

 

"Compute the n-cartesian product of a list of sets (each of them represented as list).

Algorithm:

(loop for x in (car l)

nconc (loop for y in (n-cartesian-product (cdr l))

 

'''Output:'''

 

((1776 7 4 0) (1776 7 4 1) (1776 7 14 0) (1776 7 14 1) (1776 7 23 0) (1776 7 23 1) (1776 12 4 0) (1776 12 4 1) (1776 12 14 0) (1776 12 14 1) (1776 12 23 0) (1776 12 23 1) (1789 7 4 0) (1789 7 4 1) (1789 7 14 0) (1789 7 14 1) (1789 7 23 0) (1789 7 23 1) (1789 12 4 0) (1789 12 4 1) (1789 12 14 0) (1789 12 14 1) (1789 12 23 0) (1789 12 23 1))

CL-USER> (n-cartesian-product '((1 2 3) (30) (500 100)))

CL-USER> (n-cartesian-product '((1 2 3) () (500 100)))

NIL

 

=={{header|D}}==

 

void main() {

 

return Result();

 

{{out}}

[]

[]</pre>

 

=={{header|F Sharp|F#}}==

===The Task===

//Nigel Galloway February 12th., 2018

let cP2 n g = List.map (fun (n,g)->[n;g]) (List.allPairs n g)

{{out}}

<pre>

 

===Extra Credit===

//Nigel Galloway August 14th., 2018

{{out}}

<pre>

 

=={{header|Factor}}==

{ { { 1 3 } { 1 4 } } { { 2 3 } { 2 4 } } }

IN: scratchpad { 3 4 } { 1 2 } cartesian-product .

{ { } { } }

IN: scratchpad { } { 1 2 } cartesian-product .

 

=={{header|Fōrmulæ}}==

 

 

 

 

=={{header|Go}}==

'''Basic Task'''

 

import "fmt"

fmt.Println(cart2([]int{1, 2}, nil))

fmt.Println(cart2(nil, []int{1, 2}))

{{out}}

<pre>

 

This solution minimizes allocations and computes and fills the result sequentially.

 

import "fmt"

fmt.Println(cartN(nil))

fmt.Println(cartN())

{{out}}

<pre>

 

Code here is more compact, but with the cost of more garbage produced. It produces the same result as cartN above.

if len(a) == 0 {

return [][]int{nil}

}

return

'''Extra credit 3'''

 

This is a compact recursive version like Extra credit 2 but the result list is ordered differently. This is still a correct result if you consider a cartesian product to be a set, which is an unordered collection. Note that the set elements are still ordered lists. A cartesian product is an unordered collection of ordered collections. It draws attention though to the gloss of using list representations as sets. Any of the functions here will accept duplicate elements in the input lists, and then produce duplicate elements in the result.

if len(a) == 0 {

return [][]int{nil}

}

return

 

=={{header|Haskell}}==

Various routes can be taken to Cartesian products in Haskell.

For the product of two lists we could write:

cartProd xs ys =

[ (x, y)

| x <- xs

 

more directly:

 

applicatively:

 

parsimoniously:

 

We might test any of these with:

main =

mapM_ print $

uncurry cartProd <$>

{{Out}}

<pre>[(1,3),(1,4),(2,3),(2,4)]

 

For the n-ary Cartesian product of an arbitrary number of lists, we could apply the Prelude's standard '''sequence''' function to a list of lists,

cartProdN = sequence

 

main :: IO ()

{{Out}}

<pre>[[1,3,5],[1,3,6],[1,4,5],[1,4,6],[2,3,5],[2,3,6],[2,4,5],[2,4,6]]</pre>

 

or we could define ourselves an equivalent function over a list of lists in terms of a fold, for example as:

or, equivalently, as:

cartProdN = foldr

(\xs as ->

| x <- xs

, a <- as ])

testing any of these with something like:

main = do

mapM_ print $

print $ cartProdN [[1,2,3], [30], [500, 100]]

putStrLn ""

{{Out}}

<pre>[1776,7,4,0]

 

[]</pre>

=={{header|J}}==

The J primitive [http://code.jsoftware.com/wiki/Vocabulary/curlylf catalogue] <code>{</code> forms the Cartesian Product of two or more boxed lists. The result is a multi-dimensional array (which can be reshaped to a simple list of lists if desired).

┌────────────┬────────────┐

│1776 7 4 0 │1776 7 4 1 │

└───────┴────────┘

{ 1 2 3 ; '' ; 50 100 NB. result is an empty 3-dimensional array with shape 3 0 2

=={{header|Java}}==

{{works with|Java Virtual Machine|1.8}}

import static java.util.Arrays.asList;

import static java.util.Collections.emptyList;

}

}

 

 

 

 

 

 

 

 

 

 

 

{{Out}}

<pre>[[1,3],[1,4],[2,3],[2,4]]

 

 

 

 

// cartesianProduct :: [a] -> [b] -> [(a, b)]

 

 

 

// e.g. [(*2),(/2), sqrt] <*> [1,2,3]

 

// ap (<*>) :: [(a -> b)] -> [a] -> [b]

 

return [

]

.map(JSON.stringify)

.join('\n');

{{Out}}

<pre>[[1,3],[1,4],[2,3],[2,4]]

 

For the n-ary Cartesian product over a list of lists:

 

 

 

// bind :: [a] -> (a -> [b]) -> [b]

 

 

// intercalate :: String -> [a] -> String

 

// map :: (a -> b) -> [a] -> [b]

 

// show :: a -> String

const show = x => JSON.stringify(x);

 

{{Out}}

<pre>[1776,7,4,0]

Imperative implementations of Cartesian products are inevitably less compact and direct, but we can certainly write an iterative translation of a fold over nested applications of '''bind''' or '''concatMap''':

 

// n-ary Cartesian product of a list of lists

// ( Imperative implementation )

]))

]);

{{Out}}

<pre>[[1,4],[1,3],[2,4],[2,3]]

 

jq is stream-oriented and so we begin by defining a function that will emit a stream of the elements of the Cartesian product of two arrays:

def products: .[0][] as $x | .[1][] as $y | [$x,$y];

 

To generate an array of these arrays, one would in practice most likely simply write `[products]`, but to comply with the requirements of this article, we can define `product` as:

def product: [products];

 

For the sake of brevity, two illustrations should suffice:

 

And

[[1,2], []] | product

produces:

<pre>

Given an array of two or more arrays as input, `cartesians` as defined here produces a stream of the components of their Cartesian product:

 

def cartesians:

if length <= 2 then products

| [$x] + $y

end;

 

Again for brevity, in the following, we will just show the number of items in the Cartesian products:

[[1, 2, 3], [], [500, 100] ] | [cartesians] | length

# 0

=={{header|Julia}}==

# Product {1, 2} × {3, 4}

# Product {3, 4} × {1, 2}

# Product {1, 2} × {}

# Product {} × {1, 2}

# Product {1776, 1789} × {7, 12} × {4, 14, 23} × {0, 1}

# Product {1, 2, 3} × {30} × {500, 100}

# Product {1, 2, 3} × {} × {500, 100}

=={{header|Kotlin}}==

 

fun flattenList(nestList: List<Any>): List<Any> {

printNAryProduct(listOf(listOf(1, 2, 3), listOf<Int>(), listOf(500, 100)))

printNAryProduct(listOf(listOf(1, 2, 3), listOf(30), listOf('a', 'b')))

 

{{out}}

[3, 30, b]

]

</pre>

 

=== Functional ===

An iterator is created to output the product items.

local getn = function(t)return #t end

local const = function(k)return function(e) return k end end

print(i,a,b)

end

{{out}}

<pre>1 1 3

 

It is possible that specialising descend by depth may yield a further improvement in performance, but it would only be able to eliminate the lookup of ''sets[depth]'' and the if test, because the reference to ''result[depth]'' is required; I doubt the increase in complexity would be worth the (potential) improvement in performance.

local result = {}

local set_count = #sets

print(" " .. format_nested_list(product))

end

 

=== Imperative iterator ===

The functional implementation restated as an imperative iterator, also adjusted to not allocate a new result table on each iteration; this saves time, but makes mutating the returned table unsafe.

local item_counts = {}

local indices = {}

print(i, format_nested_list(product))

end

 

=={{header|Maple}}==

cartmulti := proc ()

local m, v;

end if;

end proc;

 

 

=={{header|Modula-2}}==

FROM FormatString IMPORT FormatString;

FROM Terminal IMPORT WriteString,WriteLn,ReadChar;

 

ReadChar

 

=={{header|OCaml}}==

''The double semicolons are necessary only for the toplevel''

 

match l1, l2 with

| [], _ | _, [] -> []

(*- : (int * 'a) list = []*)

product [] [1;2];;

 

let rec aux ~acc l1' l2' =

match l1', l2' with

(*- : (int * 'a) list = []*)

product' [] [1;2];;

 

(* We need to do the cross product of our current list and all the others

* so we define a helper function for that *)

*)

product'' [[1; 2; 3];[];[500; 100]];;

 

=== Better type ===

 

In the latter example, our function has this signature:

This lacks clarity as those two lists are not equivalent since one replaces a tuple. We can get a better signature by creating a tuple type:

 

let rec product'' (l:'a list tuple) =

 

type 'a tuple = 'a list

=={{header|Perl}}==

==== Iterative ====

Nested loops, with a short-circuit to quit early if any term is an empty set.

my $sets = shift @_;

for (@$sets) { return [] unless @$_ }

product([[1,2,3], [30], [500,100] ], '%1d %1d %3d' ).

product([[1,2,3], [], [500,100] ], '%1d %1d %3d' ).

{{out}}

<pre>(1 3) (1 4) (2 3) (2 4)

==== Glob ====

This being Perl, there's more than one way to do it. A quick demonstration of how <code>glob</code>, more typically used for filename wildcard expansion, can solve the task.

 

{{out}}

<pre>(1 30 500) (1 30 100) (2 30 500) (2 30 100) (3 30 500) (3 30 100)</pre>

==== Modules ====

A variety of modules can do this correctly for an arbitrary number of lists (each of independent length). Arguably using modules is very idiomatic Perl.

forsetproduct { say "@_" } [1,2,3],[qw/a b c/],[qw/@ $ !/];

 

 

use Algorithm::Loops qw/NestedLoops/;

=={{header|Phix}}==

{{out}}

<pre>

{}

</pre>

 

=={{header|PicoLisp}}==

(mapcan

'((I)

(cartesian (1 2 3) (30) (500 100)) )

(println

 

{{out}}

((1 30 500) (1 30 100) (2 30 500) (2 30 100) (3 30 500) (3 30 100))

NIL</pre>

 

=={{header|Python}}==

 

def cp(lsts):

print(lists, '=>')

pp(cp(lists), indent=2)

{{out}}

<pre>[[1, 2], [3, 4]] =>

(3, 30, 100)]

((1, 2, 3), (), (500, 100)) =>

 

=={{header|R}}==

 

one_w_many <- function(one, many) lapply(many, function(x) c(one,x))

 

prod = Reduce( '%p%', list(...) )

display_prod( prod ) }

 

Simple tests:

 

> display_prod( c(1, 2) %p% c(3, 4) )

1, 3

> display_prod( c(3, 4) %p% c() )

>

 

Tougher tests:

 

go( c(1776, 1789), c(7, 12), c(4, 14, 23), c(0, 1) )

go( c(1, 2, 3), c(30), c(500, 100) )

go( c(1, 2, 3), c(), c(500, 100) )

 

{{out}}

(1, 2, 3) * () * (500, 100)

</pre>

=={{header|Racket}}==

 

Racket has a built-in "cartesian-product" function:

 

(require rackunit

;; usually, included in "racket", but we're using racket/base so we

(cartesian-product '(1776 1789) '(7 12) '(4 14 23) '(0 1))

(cartesian-product '(1 2 3) '(30) '(500 100))

 

{{out}}

'((1 30 500) (1 30 100) (2 30 500) (2 30 100) (3 30 500) (3 30 100))

'()</pre>

 

=={{header|REXX}}==

===version 1===

@.= /*assign the default value to @. array*/

parse arg @.1 /*obtain the optional value of @.1 */

/* [↓] process each of the @.n values*/

do n=1 while @.n \= '' /*keep processing while there's a value*/

do #=1 until z=='' /*process each elements in first list. */

parse var z '{' x.# '}' z /*parse the list (contains elements). */

do j=i+1 for #-1 /* " " subsequent lists. */

do b=1 for words(x.j) /* " " elements of subsequent list*/

say 'Cartesian product of ' space(@.n) " is ───► {"substr($, 2)'}'

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

<pre>

 

===version 2===

Call cart '{1, 2} x {3, 4}'

Call cart '{3, 4} x {1, 2}'

End

Say ' '

{{out}}

<pre>{1, 2} x {3, 4}

 

{1, 2, 3} x {} x {500, 100}

=={{header|Ring}}==

# Project : Cartesian product of two or more lists

 

next

see nl

Output:

<pre>

(4, 1)

(4, 2)

</pre>

 

=={{header|Ruby}}==

"product" is a method of arrays. It takes one or more arrays as argument and results in the Cartesian product:

p [3, 4].product([1, 2])

p [1, 2].product([])

p [1, 2, 3].product([30], [500, 100])

p [1, 2, 3].product([], [500, 100])

{{out}}<pre>[[1, 3], [1, 4], [2, 3], [2, 4]]

[[3, 1], [3, 2], [4, 1], [4, 2]]

 

=={{header|Rust}}==

 

let mut list_iter = lists.iter();

}

for l in list_iter {

for r in res {

for &el in l {

res

}

}

}

 

 

 

 

 

 

</pre>

=={{header|Scala}}==

Function returning the n-ary product of an arbitrary number of lists, each of arbitrary length:

 

 

/**

}

}

and usage:

{{out}}

<pre>{(1, 3), (1, 4), (2, 3), (2, 4)}</pre>

 

{{out}}

<pre>{(3, 1), (3, 2), (4, 1), (4, 2)}</pre>

 

{{out}}

<pre>{}</pre>

 

{{out}}

<pre>{}</pre>

 

{{out}}

<pre>{(1776, 7, 4, 0), (1776, 7, 4, 1), (1776, 7, 14, 0), (1776, 7, 14, 1), (1776, 7, 23, 0), (1776, 7, 23, 1), (1776, 12, 4, 0), (1776, 12, 4, 1), (1776, 12, 14, 0), (1776, 12, 14, 1), (1776, 12, 23, 0), (1776, 12, 23, 1), (1789, 7, 4, 0), (1789, 7, 4, 1), (1789, 7, 14, 0), (1789, 7, 14, 1), (1789, 7, 23, 0), (1789, 7, 23, 1), (1789, 12, 4, 0), (1789, 12, 4, 1), (1789, 12, 14, 0), (1789, 12, 14, 1), (1789, 12, 23, 0), (1789, 12, 23, 1)}</pre>

 

{{out}}

<pre>{(1, 30, 500), (1, 30, 100), (2, 30, 500), (2, 30, 100), (3, 30, 500), (3, 30, 100)}</pre>

 

{{out}}

<pre>{}</pre>

 

=={{header|Sidef}}==

In Sidef, the Cartesian product of an arbitrary number of arrays is built-in as ''Array.cartesian()'':

 

Alternatively, a simple recursive implementation:

 

var c = []

 

return r

 

Completing the task:

{{out}}

<pre>

</pre>

The product of an empty list with any other list is empty:

{{out}}

<pre>

</pre>

Extra credit:

{{out}}

<pre>

</pre>

 

{{out}}

<pre>

[]

</pre>

=={{header|SQL}}==

If we create lists as tables with one column, cartesian product is easy.

create table L1 (value integer);

insert into L1 values (1);

insert into L2 values (4);

-- get the product

{{out}}

<pre> VALUE VALUE

1 4

2 3

Product with an empty list works as expected (using the tables created above):

{{out}}

<pre>no rows selected</pre>

insert into L2 values (30);

create table L3 (value integer);

insert into L3 values (100);

-- product works the same for as many "lists" as you'd like

{{out}}

<pre> VALUE VALUE VALUE

2 30 100

3 30 100</pre>

=={{header|Standard ML}}==

| prodList ((x::xs), ys) = map (fn y => (x,y)) ys @ prodList (xs, ys)

 

 

{{out}}

- naryProdList [[1, 2, 3], [], [500, 100]];

val it = [] : int list list</pre>

=={{header|Stata}}==

 

In Stata, the command '''[https://www.stata.com/help.cgi?fillin fillin]''' may be used to expand a dataset with all combinations of a number of variables. Thus it's easy to compute a cartesian product.

 

 

+-------+

3. | 2 3 1 |

4. | 2 4 0 |

 

The other way around:

 

 

+-------+

3. | 4 1 1 |

4. | 4 2 0 |

 

Note, however, that this is not equivalent to a cartesian product when one of the variables is "empty" (that is, only contains missing values).

 

 

+-------+

1. | 1 . 0 |

2. | 2 . 0 |

 

This command works also if the varaibles have different numbers of nonmissing elements. However, this requires additional code to remove the observations with missing values.

 

 

+-----------+

|---------------------|

6. | 3 5 6 1 |

 

=={{header|Tcl}}==

proc cartesianProduct {l1 l2} {

set result {}

puts "result: [cartesianNaryProduct {{1 2 3} {} {500 100}}]"

 

{{out}}

<pre>

result:

</pre>

 

 

=={{header|zkl}}==

Cartesian product is build into iterators or can be done with nested

loops.

L(L(1,3),L(1,4),L(2,3),L(2,4))

zkl: foreach a,b in (List(1,2),List(3,4)){ print("(%d,%d) ".fmt(a,b)) }

 

zkl: Walker.cproduct(List(3,4),List(1,2)).walk().println();

 

The walk method will throw an error if used on an empty iterator but the pump

method doesn't.

Exception thrown: TheEnd(Ain't no more)

 

L()

zkl: Walker.cproduct(List,List(3,4)).pump(List).println();

L(L(1776,7,4,0),L(1776,7,4,1),L(1776,7,14,0),L(1776,7,14,1),L(1776,7,23,0),L(1776,7,23,1),L(1776,12,4,0),L(1776,12,4,1),L(1776,12,14,0),L(1776,12,14,1),L(1776,12,23,0),L(1776,12,23,1),L(1789,7,4,0),L(1789,7,4,1),L(1789,7,14,0),L(1789,7,14,1),L(1789,7,23,0),L(1789,7,23,1),L(1789,12,4,0),L(1789,12,4,1),...)

 

 

zkl: Walker.cproduct(L(1,2,3),List,L(500,100)).pump(List).println();