Cartesian product of two or more lists

From Rosetta Code
Task
Cartesian product of two or more lists
You are encouraged to solve this task according to the task description, using any language you may know.
Task

Show one or more idiomatic ways of generating the Cartesian product of two arbitrary lists in your language.

Demonstrate that your function/method correctly returns:

{1, 2} × {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}

and, in contrast:

{3, 4} × {1, 2} = {(3, 1), (3, 2), (4, 1), (4, 2)}

Also demonstrate, using your function/method, that the product of an empty list with any other list is empty.

{1, 2} × {} = {}
{} × {1, 2} = {}

For extra credit, show or write a function returning the n-ary product of an arbitrary number of lists, each of arbitrary length. Your function might, for example, accept a single argument which is itself a list of lists, and return the n-ary product of those lists.

Use your n-ary Cartesian product function to show the following products:

{1776, 1789} × {7, 12} × {4, 14, 23} × {0, 1}
{1, 2, 3} × {30} × {500, 100}
{1, 2, 3} × {} × {500, 100}


11l[edit]

Translation of: Go
F cart_prod(a, b)
   V p = [(0, 0)] * (a.len * b.len)
   V i = 0
   L(aa) a
      L(bb) b
         p[i++] = (aa, bb)
   R p

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

Alternative version[edit]

F cart_prod(a, b)
   R multiloop(a, b, (aa, bb) -> (aa, bb))
Output:
[(1, 3), (1, 4), (2, 3), (2, 4)]
[(3, 1), (3, 2), (4, 1), (4, 2)]
[]
[]

Action![edit]

DEFINE MAX_COUNT="10"
DEFINE MAX_RESULT="100"

DEFINE PTR="CARD"

PROC PrintInput(PTR ARRAY a INT count)
  INT i,j,n
  INT ARRAY tmp

  FOR i=0 TO count-1
  DO
    tmp=a(i) n=tmp(0)
    Put('[)
    FOR j=1 TO n
    DO
      PrintI(tmp(j))
      IF j<n THEN Put(',) FI
    OD
    Put('])
    IF i<count-1 THEN Put('x) FI
  OD
RETURN

PROC PrintOutput(INT ARRAY a INT groups,count)
  INT i,j,k

  Put('[)
  k=0
  FOR i=0 TO groups-1
  DO
    Put('()
    FOR j=0 TO count-1
    DO
      PrintI(a(k)) k==+1
      IF j<count-1 THEN Put(',) FI
    OD
    Put('))
    IF i<groups-1 THEN Put(',) FI
  OD
  Put('])
RETURN

PROC Product(PTR ARRAY a INT count
  INT ARRAY r INT POINTER groups)
  INT ARRAY ind(MAX_COUNT),tmp
  INT i,j,k

  IF count>MAX_COUNT THEN Break() FI
  groups^=1
  FOR i=0 TO count-1
  DO
    ind(i)=1 tmp=a(i)
    groups^==*tmp(0)
  OD
  IF groups^=0 THEN RETURN FI
  
  j=count-1 k=0
  DO
    FOR i=0 TO count-1
    DO
      tmp=a(i)
      r(k)=tmp(ind(i)) k==+1
    OD

    DO
      tmp=a(j)
      IF ind(j)<tmp(0) THEN
        ind(j)==+1
        FOR i=j+1 TO count-1
        DO
          ind(i)=1
        OD
        j=count-1
        EXIT
      ELSE
        IF j=0 THEN RETURN FI
        j==-1
      FI
    OD
  OD
RETURN

PROC Test(PTR ARRAY a INT count)
  INT ARRAY r(MAX_RESULT)
  INT groups

  IF count<2 THEN Break() FI
  Product(a,count,r,@groups)
  PrintInput(a,count)
  Put('=)
  PrintOutput(r,groups,count)
  PutE()
RETURN

PROC Main()
  INT ARRAY
    a1=[2 1 2],a2=[2 3 4],a3=[0],
    a4=[2 1776 1789],a5=[2 7 12],
    a6=[3 4 14 23],a7=[2 0 1],
    a8=[3 1 2 3],a9=[1 30],a10=[2 500 100]
  PTR ARRAY a(4)

  a(0)=a1 a(1)=a2 Test(a,2)
  a(0)=a2 a(1)=a1 Test(a,2)
  a(0)=a1 a(1)=a3 Test(a,2)
  a(0)=a3 a(1)=a1 Test(a,2) PutE()
  a(0)=a4 a(1)=a5 a(2)=a6 a(3)=a7 Test(a,4) PutE()
  a(0)=a8 a(1)=a9 a(2)=a10 Test(a,3) PutE()
  a(0)=a8 a(1)=a3 a(2)=a10 Test(a,3)
RETURN
Output:

Screenshot from Atari 8-bit computer

[1,2]x[3,4]=[(1,3),(1,4),(2,3),(2,4)]
[3,4]x[1,2]=[(3,1),(3,2),(4,1),(4,2)]
[1,2]x[]=[]
[]x[1,2]=[]
[1776,1789]x[7,12]x[4,14,23]x[0,1]=[(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)]
[1,2,3]x[30]x[500,100]=[(1,30,500),(1,30,100),(2,30,500),(2,30,100),(3,30,500),(3,30,100)]
[1,2,3]x[]x[500,100]=[]

Ada[edit]

with Ada.Text_IO;  use Ada.Text_Io;
with Ada.Containers.Doubly_Linked_Lists;
with Ada.Strings.Fixed;

procedure Cartesian is

   type Element_Type is new Long_Integer;

   package Lists is
      new Ada.Containers.Doubly_Linked_Lists (Element_Type);
   package List_Lists is
      new Ada.Containers.Doubly_Linked_Lists (Lists.List, Lists."=");

   subtype List      is Lists.List;
   subtype List_List is List_Lists.List;

   function "*" (Left, Right : List) return List_List is
      Result : List_List;
      Sub    : List;
   begin
      for Outer of Left loop
         for Inner of Right loop
            Sub.Clear;
            Sub.Append (Outer);
            Sub.Append (Inner);
            Result.Append (Sub);
         end loop;
      end loop;
      return Result;
   end "*";

   function "*" (Left  : List_List;
                 Right : List) return List_List
   is
      Result : List_List;
      Sub    : List;
   begin
      for Outer of Left loop
         for Inner of Right loop
            Sub := Outer;
            Sub.Append (Inner);
            Result.Append (Sub);
         end loop;
      end loop;
      return Result;
   end "*";

   procedure Put (L : List) is
      use Ada.Strings;
      First : Boolean := True;
   begin
      Put ("(");
      for E of L loop
         if not First then
            Put (",");
         end if;
         Put (Fixed.Trim (E'Image, Left));
         First := False;
      end loop;
      Put (")");
   end Put;

   procedure Put (LL : List_List) is
      First : Boolean := True;
   begin
      Put ("{");
      for E of LL loop
         if not First then
            Put (",");
         end if;
         Put (E);
         First := False;
      end loop;
      Put ("}");
   end Put;

   function "&" (Left : List; Right : Element_Type) return List is
      Result : List := Left;
   begin
      Result.Append (Right);
      return Result;
   end "&";

   Nil        : List renames Lists.Empty_List;
   List_1_2   : constant List := Nil & 1 & 2;
   List_3_4   : constant List := Nil & 3 & 4;
   List_Empty : constant List := Nil;
   List_1_2_3 : constant List := Nil & 1 & 2 & 3;
begin
   Put (List_1_2 * List_3_4); New_Line;

   Put (List_3_4 * List_1_2); New_Line;

   Put (List_Empty * List_1_2); New_Line;

   Put (List_1_2 * List_Empty); New_Line;

   Put (List'(Nil & 1776 & 1789) * List'(Nil & 7 & 12) *
          List'(Nil & 4 & 14 & 23) * List'(Nil & 0 & 1)); New_Line;

   Put (List_1_2_3 * List'(Nil & 30) * List'(Nil & 500 & 100)); New_Line;

   Put (List_1_2_3 * List_Empty * List'(Nil & 500 & 100)); New_Line;
end Cartesian;
Output:
{(1,3),(1,4),(2,3),(2,4)}
{(3,1),(3,2),(4,1),(4,2)}
{}
{}
{(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)}
{(1,30,500),(1,30,100),(2,30,500),(2,30,100),(3,30,500),(3,30,100)}
{}

APL[edit]

APL has a built-in outer product operator: X ∘.F Y will get you an ⍴X-by-⍴Y matrix containing every corresponding value of x F y for all x∊X, y∊Y.

The Cartesian product can therefore be expressed as ∘.,, but as that would return a matrix, and the task is asking for a list, you also need to ravel the result.

cart  ,∘.,
Output:
      1 2 cart 3 4
 1 3  1 4  2 3  2 4 
      3 4 cart 1 2
 3 1  3 2  4 1  4 2 
      1 2 cart ⍬   ⍝ empty output

      ⍬ cart 1 2   ⍝ empty output again

This can be reduced over a list of lists to generate the Cartesian product of an arbitrary list of lists.

nary_cart  (,∘.,)/
Output:

The items are listed on separate lines (using ↑) for clarity.

      ↑nary_cart (1776 1789)(7 12)(4 14 23)(0 1)
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
      ↑nary_cart(1 2 3)(,30)(50 100)
1 30  50
1 30 100
2 30  50
2 30 100
3 30  50
3 30 100
      ↑nary_cart(1 2 3)(⍬)(50 100)  ⍝ empty output

AppleScript[edit]

-- CARTESIAN PRODUCTS ---------------------------------------------------------

-- Two lists:

-- cartProd :: [a] -> [b] -> [(a, b)]
on cartProd(xs, ys)
    script
        on |λ|(x)
            script
                on |λ|(y)
                    [[x, y]]
                end |λ|
            end script
            concatMap(result, ys)
        end |λ|
    end script
    concatMap(result, xs)
end cartProd

-- N-ary – a function over a list of lists:

-- cartProdNary :: [[a]] -> [[a]]
on cartProdNary(xss)
    script
        on |λ|(accs, xs)
            script
                on |λ|(x)
                    script
                        on |λ|(a)
                            {x & a}
                        end |λ|
                    end script
                    concatMap(result, accs)
                end |λ|
            end script
            concatMap(result, xs)
        end |λ|
    end script
    foldr(result, {{}}, xss)
end cartProdNary

-- TESTS ----------------------------------------------------------------------
on run
    set baseExamples to unlines(map(show, ¬
        [cartProd({1, 2}, {3, 4}), ¬
            cartProd({3, 4}, {1, 2}), ¬
            cartProd({1, 2}, {}), ¬
            cartProd({}, {1, 2})]))
    
    set naryA to unlines(map(show, ¬
        cartProdNary([{1776, 1789}, {7, 12}, {4, 14, 23}, {0, 1}])))
    
    set naryB to show(cartProdNary([{1, 2, 3}, {30}, {500, 100}]))
    
    set naryC to show(cartProdNary([{1, 2, 3}, {}, {500, 100}]))
    
    intercalate(linefeed & linefeed, {baseExamples, naryA, naryB, naryC})
end run


-- GENERIC FUNCTIONS ----------------------------------------------------------

-- concatMap :: (a -> [b]) -> [a] -> [b]
on concatMap(f, xs)
    set lst to {}
    set lng to length of xs
    tell mReturn(f)
        repeat with i from 1 to lng
            set lst to (lst & |λ|(item i of xs, i, xs))
        end repeat
    end tell
    return lst
end concatMap

-- foldr :: (a -> b -> a) -> a -> [b] -> a
on foldr(f, startValue, xs)
    tell mReturn(f)
        set v to startValue
        set lng to length of xs
        repeat with i from lng to 1 by -1
            set v to |λ|(v, item i of xs, i, xs)
        end repeat
        return v
    end tell
end foldr

-- intercalate :: Text -> [Text] -> Text
on intercalate(strText, lstText)
    set {dlm, my text item delimiters} to {my text item delimiters, strText}
    set strJoined to lstText as text
    set my text item delimiters to dlm
    return strJoined
end intercalate

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
    tell mReturn(f)
        set lng to length of xs
        set lst to {}
        repeat with i from 1 to lng
            set end of lst to |λ|(item i of xs, i, xs)
        end repeat
        return lst
    end tell
end map

-- Lift 2nd class handler function into 1st class script wrapper 
-- mReturn :: Handler -> Script
on mReturn(f)
    if class of f is script then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn

-- show :: a -> String
on show(e)
    set c to class of e
    if c = list then
        script serialized
            on |λ|(v)
                show(v)
            end |λ|
        end script
        
        "[" & intercalate(", ", map(serialized, e)) & "]"
    else if c = record then
        script showField
            on |λ|(kv)
                set {k, ev} to kv
                "\"" & k & "\":" & show(ev)
            end |λ|
        end script
        
        "{" & intercalate(", ", ¬
            map(showField, zip(allKeys(e), allValues(e)))) & "}"
    else if c = date then
        "\"" & iso8601Z(e) & "\""
    else if c = text then
        "\"" & e & "\""
    else if (c = integer or c = real) then
        e as text
    else if c = class then
        "null"
    else
        try
            e as text
        on error
            ("«" & c as text) & "»"
        end try
    end if
end show

-- unlines :: [String] -> String
on unlines(xs)
    intercalate(linefeed, xs)
end unlines
Output:
[[1, 3], [1, 4], [2, 3], [2, 4]]
[[3, 1], [3, 2], [4, 1], [4, 2]]
[]
[]

[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]

[[1, 30, 500], [1, 30, 100], [2, 30, 500], [2, 30, 100], [3, 30, 500], [3, 30, 100]]

[]

Arturo[edit]

Translation of: Ruby
loop [
    [[1 2][3 4]] 
    [[3 4][1 2]]
    [[1 2][]]
    [[][1 2]] 
    [[1776 1789][7 12][4 14 23][0 1]]
    [[1 2 3][30][500 100]] 
    [[1 2 3][][500 100]] 
] 'lst [
    print as.code product.cartesian lst
]
Output:
[[1 3] [1 4] [2 3] [2 4]]
[[3 1] [3 2] [4 1] [4 2]]
[]
[]
[[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]]
[[1 30 500] [1 30 100] [2 30 500] [2 30 100] [3 30 500] [3 30 100]]
[]

AutoHotkey[edit]

example := [
(join,
[[1, 2], [3, 4]]
[[3, 4], [1, 2]]
[[1, 2], []]
[[], [1, 2]]
[[1776, 1789], [7, 12], [4, 14, 23], [0, 1]]
[[1, 2, 3], [30] , [500, 100]]
[[1, 2, 3], [] , [500, 100]]
)]

for i, obj in example
{
    Product := CartesianProduct(obj)
    out := dispRes(Product)
    result .= out "`n`n"
}
MsgBox % result
return

dispRes(Product){
    for i, o in Product
    {
        for j, v in o
            output .= v ", "
        
        output := Trim(output, ", ")
        output .= "], ["
    }
    return "[[" trim(output, ", []") "]]"
}

CartesianProduct(obj){
    CP(obj, Product:=[], [])
    return Product
}

CP(obj, Product, stack, v:=""){
    oClone := obj.clone()
    oClone.RemoveAt(1)
    stack.= v ","
    
    for i, o in obj
    {
        for j, v in o
            CP(oClone, Product, stack, v)
        return
    }
    stack := trim(stack, ",")
    oTemp := []
    for i, v in StrSplit(stack, ",")
        oTemp.Push(v)
    Product.push(oTemp)
}
Output:
[[1, 3], [1, 4], [2, 3], [2, 4]]
[[3, 1], [3, 2], [4, 1], [4, 2]]
[]
[]
[[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]]
[[1, 30, 500], [1, 30, 100], [2, 30, 500], [2, 30, 100], [3, 30, 500], [3, 30, 100]]
[]

Bracmat[edit]

( ( mul
  =   R a b A B
    .   :?R
      & !arg:(.?A) (.?B)
      & (   !A
          :   ?
              ( %@?a
              &   !B
                :   ?
                    ( (%@?b|(.?b))
                    & !R (.!a !b):?R
                    & ~
                    )
                    ?
              )
              ?
        | (.!R)
        )
  )
& ( cartprod
  =   a
    .   !arg:%?a %?arg&mul$(!a cartprod$!arg)
      | !arg
  )
&   out
  $ ( cartprod
    $ ( (.1776 1789)
        (.7 12)
        (.4 14 23)
        (.0 1)
      )
    )
& out$(cartprod$((.1 2 3) (.30) (.500 100)))
& out$(cartprod$((.1 2 3) (.) (.500 100)))
)
.   (.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)

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

C[edit]

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>
#include<stdio.h>

void cartesianProduct(int** sets, int* setLengths, int* currentSet, int numSets, int times){
	int i,j;
	
	if(times==numSets){
		printf("(");
		for(i=0;i<times;i++){
			printf("%d,",currentSet[i]);
		}
		printf("\b),");
	}
	else{
		for(j=0;j<setLengths[times];j++){
			currentSet[times] = sets[times][j];
			cartesianProduct(sets,setLengths,currentSet,numSets,times+1);
		}
	}
}

void printSets(int** sets, int* setLengths, int numSets){
	int i,j;
	
	printf("\nNumber of sets : %d",numSets);
	
	for(i=0;i<numSets+1;i++){
		printf("\nSet %d : ",i+1);
		for(j=0;j<setLengths[i];j++){
			printf(" %d ",sets[i][j]);
		}
	}
}

void processInputString(char* str){
	int **sets, *currentSet, *setLengths, setLength, numSets = 0, i,j,k,l,start,counter=0;
	char *token,*holder,*holderToken;
	
	for(i=0;str[i]!=00;i++)
		if(str[i]=='x')
			numSets++;
		
	if(numSets==0){
			printf("\n%s",str);
			return;
	}
		
	currentSet = (int*)calloc(sizeof(int),numSets + 1);
	
	setLengths = (int*)calloc(sizeof(int),numSets + 1);
	
	sets = (int**)malloc((numSets + 1)*sizeof(int*));
	
	token = strtok(str,"x");
	
	while(token!=NULL){
		holder = (char*)malloc(strlen(token)*sizeof(char));
		
		j = 0;
		
		for(i=0;token[i]!=00;i++){
			if(token[i]>='0' && token[i]<='9')
				holder[j++] = token[i];
			else if(token[i]==',')
				holder[j++] = ' ';
		}
		holder[j] = 00;
		
		setLength = 0;
		
		for(i=0;holder[i]!=00;i++)
			if(holder[i]==' ')
				setLength++;
			
		if(setLength==0 && strlen(holder)==0){
			printf("\n{}");
			return;
		}
		
		setLengths[counter] = setLength+1;
		
		sets[counter] = (int*)malloc((1+setLength)*sizeof(int));
		
		k = 0;
		
		start = 0;
		
		for(l=0;holder[l]!=00;l++){
			if(holder[l+1]==' '||holder[l+1]==00){
				holderToken = (char*)malloc((l+1-start)*sizeof(char));
				strncpy(holderToken,holder + start,l+1-start);
				sets[counter][k++] = atoi(holderToken);
				start = l+2;
			}
		}
		
		counter++;
		token = strtok(NULL,"x");
	}
	
	printf("\n{");
	cartesianProduct(sets,setLengths,currentSet,numSets + 1,0);
	printf("\b}");
	
}

int main(int argC,char* argV[])
{
	if(argC!=2)
		printf("Usage : %s <Set product expression enclosed in double quotes>",argV[0]);
	else
		processInputString(argV[1]);
	
	return 0;
}

Invocation and output :

C:\My Projects\threeJS>cartesianProduct.exe "{1,2} x {3,4}"

{(1,3),(1,4),(2,3),(2,4)}
C:\My Projects\threeJS>cartesianProduct.exe "{3,4} x {1,2}"

{(3,1),(3,2),(4,1),(4,2)}
C:\My Projects\threeJS>cartesianProduct.exe "{1,2} x {}"

{}
C:\My Projects\threeJS>cartesianProduct.exe "{} x {1,2}"

{}
C:\My Projects\threeJS>cartesianProduct.exe "{1776, 1789} x {7, 12} x {4, 14, 23} x {0, 1}"

{(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),(1789,9,12,14,1),(1789,12,23,0),(1789,12,23,1)}
C:\My Projects\threeJS>cartesianProduct.exe "{1, 2, 3} x {30} x {500, 100}"

{(1,30,500),(1,30,100),(2,30,500),(2,30,100),(3,30,500),(3,30,100)}
C:\My Projects\threeJS>cartesianProduct.exe "{1, 2, 3} x {} x {500, 100}"

{}

C#[edit]

using System;
public class Program
{
    public static void Main()
    {
        int[] empty = new int[0];
        int[] list1 = { 1, 2 };
        int[] list2 = { 3, 4 };
        int[] list3 = { 1776, 1789 };
        int[] list4 = { 7, 12 };
        int[] list5 = { 4, 14, 23 };
        int[] list6 = { 0, 1 };
        int[] list7 = { 1, 2, 3 };
        int[] list8 = { 30 };
        int[] list9 = { 500, 100 };
        
        foreach (var sequenceList in new [] {
            new [] { list1, list2 },
            new [] { list2, list1 },
            new [] { list1, empty },
            new [] { empty, list1 },
            new [] { list3, list4, list5, list6 },
            new [] { list7, list8, list9 },
            new [] { list7, empty, list9 }
        }) {
            var cart = sequenceList.CartesianProduct()
                .Select(tuple => $"({string.Join(", ", tuple)})");
            Console.WriteLine($"{{{string.Join(", ", cart)}}}");
        }
    }
}

public static class Extensions
{
    public static IEnumerable<IEnumerable<T>> CartesianProduct<T>(this IEnumerable<IEnumerable<T>> sequences) {
        IEnumerable<IEnumerable<T>> emptyProduct = new[] { Enumerable.Empty<T>() };
        return sequences.Aggregate(
            emptyProduct,
            (accumulator, sequence) =>
            from acc in accumulator
            from item in sequence
            select acc.Concat(new [] { item }));
    }
}
Output:
{(1, 3), (1, 4), (2, 3), (2, 4)}
{(3, 1), (3, 2), (4, 1), (4, 2)}
{}
{}
{(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)}
{(1, 30, 500), (1, 30, 100), (2, 30, 500), (2, 30, 100), (3, 30, 500), (3, 30, 100)}
{}

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

public static void Main()
{
    ///...
    var cart1 =
        from a in list1
        from b in list2
        select (a, b); // C# 7.0 tuple
    Console.WriteLine($"{{{string.Join(", ", cart1)}}}");
        
    var cart2 =
        from a in list7
        from b in list8
        from c in list9
        select (a, b, c);
    Console.WriteLine($"{{{string.Join(", ", cart2)}}}");
}
Output:
{(1, 3), (1, 4), (2, 3), (2, 4)}
{(1, 30, 500), (1, 30, 100), (2, 30, 500), (2, 30, 100), (3, 30, 500), (3, 30, 100)}

C++[edit]

#include <iostream>
#include <vector>
#include <algorithm>

void print(const std::vector<std::vector<int>>& v) {
  std::cout << "{ ";
  for (const auto& p : v) {
    std::cout << "(";
    for (const auto& e : p) {
      std::cout << e << " ";
    }
    std::cout << ") ";
  }
  std::cout << "}" << std::endl;
}

auto product(const std::vector<std::vector<int>>& lists) {
  std::vector<std::vector<int>> result;
  if (std::find_if(std::begin(lists), std::end(lists), 
    [](auto e) -> bool { return e.size() == 0; }) != std::end(lists)) {
    return result;
  }
  for (auto& e : lists[0]) {
    result.push_back({ e });
  }
  for (size_t i = 1; i < lists.size(); ++i) {
    std::vector<std::vector<int>> temp;
    for (auto& e : result) {
      for (auto f : lists[i]) {
        auto e_tmp = e;
        e_tmp.push_back(f);
        temp.push_back(e_tmp);
      }
    }
    result = temp;
  }
  return result;
}

int main() {
  std::vector<std::vector<int>> prods[] = {
    { { 1, 2 }, { 3, 4 } },
    { { 3, 4 }, { 1, 2} },
    { { 1, 2 }, { } },
    { { }, { 1, 2 } },
    { { 1776, 1789 }, { 7, 12 }, { 4, 14, 23 }, { 0, 1 } },
    { { 1, 2, 3 }, { 30 }, { 500, 100 } },
    { { 1, 2, 3 }, { }, { 500, 100 } }
  };
  for (const auto& p : prods) {
    print(product(p));
  }
  std::cin.ignore();
  std::cin.get();
  return 0;
}
Output:
{ (1 3) (1 4) (2 3) (2 4) }
{ (3 1) (3 2) (4 1) (4 2) }
{ }
{ }
{ (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) }
{ (1 30 500) (1 30 100) (2 30 500) (2 30 100) (3 30 500) (3 30 100) }
{ }

Clojure[edit]

 (ns clojure.examples.product
	(:gen-class)
	(:require [clojure.pprint :as pp]))

(defn cart [colls]
  "Compute the cartesian product of list of lists"
  (if (empty? colls)
    '(())
    (for [more (cart (rest colls))
          x (first colls)]
      (cons x more))))

Output

(doseq [lst [   [[1,2],[3,4]], 
                [[3,4],[1,2]], [[], [1, 2]], 
                [[1, 2], []],
                [[1776, 1789],  [7, 12], [4, 14, 23], [0, 1]],
                [[1, 2, 3], [30,], [500, 100]],
                [[1, 2, 3], [], [500, 100]]
            ]
        ]
    (println lst "=>")
    (pp/pprint (cart lst)))
[[1 2] [3 4]] =>
((1 3) (2 3) (1 4) (2 4))
[[3 4] [1 2]] =>
((3 1) (4 1) (3 2) (4 2))
[[] [1 2]] =>
()
[[1 2] []] =>
()
[[1776 1789] [7 12] [4 14 23] [0 1]] =>
((1776 7 4 0)
 (1789 7 4 0)
 (1776 12 4 0)
 (1789 12 4 0)
 (1776 7 14 0)
 (1789 7 14 0)
 (1776 12 14 0)
 (1789 12 14 0)
 (1776 7 23 0)
 (1789 7 23 0)
 (1776 12 23 0)
 (1789 12 23 0)
 (1776 7 4 1)
 (1789 7 4 1)
 (1776 12 4 1)
 (1789 12 4 1)
 (1776 7 14 1)
 (1789 7 14 1)
 (1776 12 14 1)
 (1789 12 14 1)
 (1776 7 23 1)
 (1789 7 23 1)
 (1776 12 23 1)
 (1789 12 23 1))
[[1 2 3] [30] [500 100]] =>
((1 30 500) (2 30 500) (3 30 500) (1 30 100) (2 30 100) (3 30 100))
[[1 2 3] [] [500 100]] =>
()

Common Lisp[edit]

(defun cartesian-product (s1 s2)
  "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 '(3 4) '(1 2))
((3 1) (3 2) (4 1) (4 2))
CL-USER> (cartesian-product '(1 2) '())
NIL
CL-USER> (cartesian-product '() '(1 2))
NIL

Extra credit:

(defun n-cartesian-product (l)
  "Compute the n-cartesian product of a list of sets (each of them represented as list).
   Algorithm:
     If there are no sets, then produce an empty set of tuples;
     otherwise, for all the elements x of the first set, concatenate the sets obtained by
     inserting x at the beginning of each tuple of the n-cartesian product of the remaining sets."
  (if (null l)
      (list nil)
      (loop for x in (car l)
            nconc (loop for y in (n-cartesian-product (cdr l))  
                        collect (cons x y)))))

Output:

CL-USER> (n-cartesian-product '((1776 1789) (7 12) (4 14 23) (0 1)))
((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)))
((1 30 500) (1 30 100) (2 30 500) (2 30 100) (3 30 500) (3 30 100))
CL-USER> (n-cartesian-product '((1 2 3) () (500 100)))
NIL

Crystal[edit]

The first function is the basic task. The version overloaded for one argument is the extra credit task, implemented using recursion.

def cartesian_product(a, b)
    return a.flat_map { |i| b.map { |j| [i, j] } }
end


def cartesian_product(l)
    if l.size <= 1
        return l
    elsif l.size == 2
        return cartesian_product(l[0], l[1])
    end

    return l[0].flat_map { |i| 
        cartesian_product(l[1..]).map { |j|
            [i, j].flatten
        }
    }
end


tests = [ [[1, 2], [3, 4]],
          [[3, 4], [1, 2]],
          [[1, 2], [] of Int32],
          [[] of Int32, [1, 2]],
          [[1, 2, 3], [30], [500, 100]],
          [[1, 2, 3], [] of Int32, [500, 100]],
          [[1776, 1789], [7, 12], [4, 14, 23], [0, 1]] ]

tests.each { |test|
    puts "#{test.join(" x ")} ->"
    puts "    #{cartesian_product(test)}"
    puts ""
}
Output:
[1, 2] x [3, 4] ->
    [[1, 3], [1, 4], [2, 3], [2, 4]]

[3, 4] x [1, 2] ->
    [[3, 1], [3, 2], [4, 1], [4, 2]]

[1, 2] x [] ->
    []

[] x [1, 2] ->
    []

[1, 2, 3] x [30] x [500, 100] ->
    [[1, 30, 500], [1, 30, 100], [2, 30, 500], [2, 30, 100], [3, 30, 500], [3, 30, 100]]

[1, 2, 3] x [] x [500, 100] ->
    []

[1776, 1789] x [7, 12] x [4, 14, 23] x [0, 1] ->
    [[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]]

D[edit]

import std.stdio;

void main() {
    auto a = listProduct([1,2], [3,4]);
    writeln(a);

    auto b = listProduct([3,4], [1,2]);
    writeln(b);

    auto c = listProduct([1,2], []);
    writeln(c);

    auto d = listProduct([], [1,2]);
    writeln(d);
}

auto listProduct(T)(T[] ta, T[] tb) {
    struct Result {
        int i, j;

        bool empty() {
            return i>=ta.length
                || j>=tb.length;
        }

        T[] front() {
            return [ta[i], tb[j]];
        }

        void popFront() {
            if (++j>=tb.length) {
                j=0;
                i++;
            }
        }
    }

    return Result();
}
Output:
[[1, 3], [1, 4], [2, 3], [2, 4]]
[[3, 1], [3, 2], [4, 1], [4, 2]]
[]
[]

Delphi[edit]

Translation of: Go
program Cartesian_product_of_two_or_more_lists;

{$APPTYPE CONSOLE}

uses
  System.SysUtils;

type
  TList = TArray<Integer>;

  TLists = TArray<TList>;

  TListHelper = record helper for TList
    function ToString: string;
  end;

  TListsHelper = record helper for TLists
    function ToString(BreakLines: boolean = false): string;
  end;

function cartN(arg: TLists): TLists;
var
  b, n: TList;
  argc: Integer;
begin
  argc := length(arg);

  var c := 1;
  for var a in arg do
    c := c * length(a);

  if c = 0 then
    exit;

  SetLength(result, c);
  SetLength(b, c * argc);
  SetLength(n, argc);

  var s := 0;
  for var i := 0 to c - 1 do
  begin
    var e := s + argc;
    var Resi := copy(b, s, e - s);
    Result[i] := Resi;

    s := e;
    for var j := 0 to high(n) do
    begin
      var nj := n[j];
      Resi[j] := arg[j, nj];
    end;

    for var j := high(n) downto 0 do
    begin
      inc(n[j]);
      if n[j] < Length(arg[j]) then
        Break;
      n[j] := 0;
    end;
  end;
end;

{ TListHelper }

function TListHelper.ToString: string;
begin
  Result := '[';
  for var i := 0 to High(self) do
  begin
    Result := Result + self[i].ToString;
    if i < High(self) then
      Result := Result + ' ';
  end;
  Result := Result + ']';
end;

{ TListsHelper }

function TListsHelper.ToString(BreakLines: boolean = false): string;
begin
  Result := '[';
  for var i := 0 to High(self) do
  begin
    Result := Result + self[i].ToString;
    if i < High(self) then
    begin
      if BreakLines then
        Result := Result + #10
      else
        Result := Result + ' ';
    end;
  end;
  Result := Result + ']';
end;

begin
  writeln(#10, cartN([[1, 2], [3, 4]]).ToString);
  writeln(#10, cartN([[3, 4], [1, 2]]).ToString);
  writeln(#10, cartN([[1, 2], []]).ToString);
  writeln(#10, cartN([[], [1, 2]]).ToString);

  writeln(#10, cartN([[1776, 1789], [17, 12], [4, 14, 23], [0, 1]]).ToString(True));

  writeln(#10, cartN([[1, 2, 3], [30], [500, 100]]).ToString);

  writeln(#10, cartN([[1, 2, 3], [], [500, 100]]).ToString);

  {$IFNDEF UNIX} readln; {$ENDIF}
end.
Output:
[[1 3] [1 4] [2 3] [2 4]]

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

[]

[]

[[1776 17 4 0]
[1776 17 4 1]
[1776 17 14 0]
[1776 17 14 1]
[1776 17 23 0]
[1776 17 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 17 4 0]
[1789 17 4 1]
[1789 17 14 0]
[1789 17 14 1]
[1789 17 23 0]
[1789 17 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]]

[[1 30 500] [1 30 100] [2 30 500] [2 30 100] [3 30 500] [3 30 100]]

[]

F#[edit]

The Task[edit]

//Nigel Galloway February 12th., 2018
let cP2 n g = List.map (fun (n,g)->[n;g]) (List.allPairs n g)
Output:
cP2 [1;2] [3;4] -> [[1; 3]; [1; 4]; [2; 3]; [2; 4]]
cP2 [3;4] [1;2] -> [[3; 1]; [3; 2]; [4; 1]; [4; 2]]
cP2 [1;2] []    -> []
cP2 [] [1;2]    -> []

Extra Credit[edit]

//Nigel Galloway August 14th., 2018
let cP ng=Seq.foldBack(fun n g->[for n' in n do for g' in g do yield n'::g']) ng [[]]
Output:
cP [[1;2];[3;4]] -> [[1; 3]; [1; 4]; [2; 3]; [2; 4]]
cP [[3;4];[1;2]] -> [[3; 1]; [3; 2]; [4; 1]; [4; 2]]
cP [[3;4];[]] ->[]
cP [[];[1;2]] ->[]
cP [[1776;1789];[7;12];[4;14;23];[0;1]] -> [[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]]
cP [[1;2;3];[30];[500;100]] -> [[1; 30; 500]; [1; 30; 100]; [2; 30; 500]; [2; 30; 100]; [3; 30; 500]; [3; 30; 100]]
cP [[1;2;3];[];[500;100]] -> []

Factor[edit]

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

Fortran[edit]

This implementation is hard to extend to n-ary products but it is simple and works well for binary products of lists of any length.

 ! Created by simon on 29/04/2021.
  
 ! ifort -o cartesian_product cartesian_product.f90 -check all
 
 module tuple
    implicit none
    private
    public :: tuple_t, operator(*), print
 
    type tuple_t(n)
        integer, len     :: n
        integer, private :: v(n)
    contains
        procedure, public :: print => print_tuple_t
        generic, public :: assignment(=) => eq_tuple_t
        procedure, public :: eq_tuple_t
    end type tuple_t
 
    interface print
        module procedure print_tuple_a_t
    end interface print
    interface operator(*)
        module procedure tup_times_tup
    end interface
 
 contains
    subroutine eq_tuple_t(this, src)
        class(tuple_t(*)), intent(inout) :: this
        integer, intent(in)              :: src(:)
        this%v = src
    end subroutine eq_tuple_t

    pure function tup_times_tup(a, b) result(r)
        type(tuple_t(*)), intent(in)  :: a
        type(tuple_t(*)), intent(in)  :: b
        type(tuple_t(2)), allocatable :: r(:)
        integer :: i, j, k
 
        allocate(r(a%n*b%n))
        k = 0
        do i=1,a%n
            do j=1,b%n
                k = k + 1
                r(k)%v = [a%v(i),b%v(j)]
            end do
        end do
    end function tup_times_tup
 
    subroutine print_tuple_t(this)
        class(tuple_t(*)), intent(in) :: this
        integer :: i
        write(*,fmt='(a)',advance='no') '{'
        do i=1,size(this%v)
            write(*,fmt='(i0)',advance='no') this%v(i)
            if (i < size(this%v)) write(*,fmt='(a)',advance='no') ','
        end do
        write(*,fmt='(a)',advance='no') '}'
    end subroutine print_tuple_t
 
    subroutine print_tuple_a_t(r)
        type(tuple_t(*)), intent(in) :: r(:)
        integer :: i
        write(*,fmt='(a)',advance='no') '{'
        do i=1,size(r)
            call r(i)%print
            if (i < size(r)) write(*,fmt='(a)',advance='no') ','
        end do
        write(*,fmt='(a)') '}'
    end subroutine print_tuple_a_t
 end module tuple
 
 program cartesian_product
    use tuple
 
    implicit none
    type(tuple_t(2)) :: a, b
    type(tuple_t(0)) :: z
 
    a = [1,2]
    b = [3,4]
 
    call print_product(a, b)
    call print_product(b, a)
    call print_product(z, a)
    call print_product(a, z)
 
    stop
 contains
    subroutine print_product(s, t)
        type(tuple_t(*)), intent(in) :: s
        type(tuple_t(*)), intent(in) :: t
        call s%print
        write(*,fmt='(a)',advance='no') ' x '
        call t%print
        write(*,fmt='(a)',advance='no') ' = '
        call print(s*t)
    end subroutine print_product
 end program cartesian_product

Output:

{1,2} x {3,4} = {{1,3},{1,4},{2,3},{2,4}}
{3,4} x {1,2} = {{3,1},{3,2},{4,1},{4,2}}
{1,2} x {} = {}
{} x {1,2} = {}

Go[edit]

Basic Task

package main

import "fmt"

type pair [2]int

func cart2(a, b []int) []pair {
    p := make([]pair, len(a)*len(b))
    i := 0
    for _, a := range a {
        for _, b := range b {
            p[i] = pair{a, b}
            i++
        }
    }
    return p
}

func main() {
    fmt.Println(cart2([]int{1, 2}, []int{3, 4}))
    fmt.Println(cart2([]int{3, 4}, []int{1, 2}))
    fmt.Println(cart2([]int{1, 2}, nil))
    fmt.Println(cart2(nil, []int{1, 2}))
}
Output:
[[1 3] [1 4] [2 3] [2 4]]
[[3 1] [3 2] [4 1] [4 2]]
[]
[]

Extra credit 1

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

package main

import "fmt"

func cartN(a ...[]int) [][]int {
    c := 1
    for _, a := range a {
        c *= len(a)
    }
    if c == 0 {
        return nil
    }
    p := make([][]int, c)
    b := make([]int, c*len(a))
    n := make([]int, len(a))
    s := 0
    for i := range p {
        e := s + len(a)
        pi := b[s:e]
        p[i] = pi
        s = e
        for j, n := range n {
            pi[j] = a[j][n]
        }
        for j := len(n) - 1; j >= 0; j-- {
            n[j]++
            if n[j] < len(a[j]) {
                break
            }
            n[j] = 0
        }
    }
    return p
}

func main() {
    fmt.Println(cartN([]int{1, 2}, []int{3, 4}))
    fmt.Println(cartN([]int{3, 4}, []int{1, 2}))
    fmt.Println(cartN([]int{1, 2}, nil))
    fmt.Println(cartN(nil, []int{1, 2}))

    fmt.Println()
    fmt.Println("[")
    for _, p := range cartN(
        []int{1776, 1789},
        []int{7, 12},
        []int{4, 14, 23},
        []int{0, 1},
    ) {
        fmt.Println(" ", p)
    }
    fmt.Println("]")
    fmt.Println(cartN([]int{1, 2, 3}, []int{30}, []int{500, 100}))
    fmt.Println(cartN([]int{1, 2, 3}, []int{}, []int{500, 100}))

    fmt.Println()
    fmt.Println(cartN(nil))
    fmt.Println(cartN())
}
Output:
[[1 3] [1 4] [2 3] [2 4]]
[[3 1] [3 2] [4 1] [4 2]]
[]
[]

[
  [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]
]
[[1 30 500] [1 30 100] [2 30 500] [2 30 100] [3 30 500] [3 30 100]]
[]

[]
[[]]

Extra credit 2

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

func cartN(a ...[]int) (c [][]int) {
    if len(a) == 0 {
        return [][]int{nil}
    }
    r := cartN(a[1:]...)
    for _, e := range a[0] {
        for _, p := range r {
            c = append(c, append([]int{e}, p...))
        }
    }
    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.

func cartN(a ...[]int) (c [][]int) {
    if len(a) == 0 {
        return [][]int{nil}
    }
    last := len(a) - 1
    l := cartN(a[:last]...)
    for _, e := range a[last] {
        for _, p := range l {
            c = append(c, append(p, e))
        }
    }
    return
}

Groovy[edit]

Solution:
The following CartesianCategory class allows for modification of regular Iterable interface behavior, overloading Iterable's multiply (*) operator to perform a Cartesian Product when the second operand is also an Iterable.

class CartesianCategory {
    static Iterable multiply(Iterable a, Iterable b) {
        assert [a,b].every { it != null }
        def (m,n) = [a.size(),b.size()]
        (0..<(m*n)).inject([]) { prod, i -> prod << [a[i.intdiv(n)], b[i%n]].flatten() }
    }
}

Test:
The mixin method call is necessary to make the multiply (*) operator work.

Iterable.metaClass.mixin CartesianCategory

println "\nCore Solution:"
println "[1, 2] × [3, 4] = ${[1, 2] * [3, 4]}"
println "[3, 4] × [1, 2] = ${[3, 4] * [1, 2]}"
println "[1, 2] × [] = ${[1, 2] * []}"
println "[] × [1, 2] = ${[] * [1, 2]}"

println "\nExtra Credit:"
println "[1776, 1789] × [7, 12] × [4, 14, 23] × [0, 1] = ${[1776, 1789] * [7, 12] * [4, 14, 23] * [0, 1]}"
println "[1, 2, 3] × [30] × [500, 100] = ${[1, 2, 3] * [30] * [500, 100]}"
println "[1, 2, 3] × [] × [500, 100] = ${[1, 2, 3] * [] * [500, 100]}"

println "\nNon-Numeric Example:"
println "[John,Paul,George,Ringo] × [Emerson,Lake,Palmer] × [Simon,Garfunkle] = ["
( ["John","Paul","George","Ringo"] * ["Emerson","Lake","Palmer"] * ["Simon","Garfunkle"] ).each { println "\t${it}," }
println "]"

Output:

Core Solution:
[1, 2] × [3, 4] = [[1, 3], [1, 4], [2, 3], [2, 4]]
[3, 4] × [1, 2] = [[3, 1], [3, 2], [4, 1], [4, 2]]
[1, 2] × [] = []
[] × [1, 2] = []

Extra Credit:
[1776, 1789] × [7, 12] × [4, 14, 23] × [0, 1] = [[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]]
[1, 2, 3] × [30] × [500, 100] = [[1, 30, 500], [1, 30, 100], [2, 30, 500], [2, 30, 100], [3, 30, 500], [3, 30, 100]]
[1, 2, 3] × [] × [500, 100] = []

Non-Numeric Example:
[John,Paul,George,Ringo] × [Emerson,Lake,Palmer] × [Simon,Garfunkle] = [
	[John, Emerson, Simon],
	[John, Emerson, Garfunkle],
	[John, Lake, Simon],
	[John, Lake, Garfunkle],
	[John, Palmer, Simon],
	[John, Palmer, Garfunkle],
	[Paul, Emerson, Simon],
	[Paul, Emerson, Garfunkle],
	[Paul, Lake, Simon],
	[Paul, Lake, Garfunkle],
	[Paul, Palmer, Simon],
	[Paul, Palmer, Garfunkle],
	[George, Emerson, Simon],
	[George, Emerson, Garfunkle],
	[George, Lake, Simon],
	[George, Lake, Garfunkle],
	[George, Palmer, Simon],
	[George, Palmer, Garfunkle],
	[Ringo, Emerson, Simon],
	[Ringo, Emerson, Garfunkle],
	[Ringo, Lake, Simon],
	[Ringo, Lake, Garfunkle],
	[Ringo, Palmer, Simon],
	[Ringo, Palmer, Garfunkle],
]

Haskell[edit]

Various routes can be taken to Cartesian products in Haskell. For the product of two lists we could write:

cartProd :: [a] -> [b] -> [(a, b)]
cartProd xs ys =
  [ (x, y)
  | x <- xs 
  , y <- ys ]

more directly:

cartProd :: [a] -> [b] -> [(a, b)]
cartProd xs ys = xs >>= \x -> ys >>= \y -> [(x, y)]

applicatively:

cartProd :: [a] -> [b] -> [(a, b)]
cartProd xs ys = (,) <$> xs <*> ys

parsimoniously:

cartProd :: [a] -> [b] -> [(a, b)]
cartProd = (<*>) . fmap (,)

We might test any of these with:

main :: IO ()
main =
  mapM_ print $
  uncurry cartProd <$>
  [([1, 2], [3, 4]), ([3, 4], [1, 2]), ([1, 2], []), ([], [1, 2])]
Output:
[(1,3),(1,4),(2,3),(2,4)]
[(3,1),(3,2),(4,1),(4,2)]
[]
[]


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 :: [[a]] -> [[a]]
cartProdN = sequence

main :: IO ()
main = print $ cartProdN [[1, 2], [3, 4], [5, 6]]
Output:
[[1,3,5],[1,3,6],[1,4,5],[1,4,6],[2,3,5],[2,3,6],[2,4,5],[2,4,6]]

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

cartProdN :: [[a]] -> [[a]]
cartProdN = foldr (\xs as -> xs >>= (<$> as) . (:)) [[]]

or, equivalently, as:

cartProdN :: [[a]] -> [[a]]
cartProdN = foldr
    (\xs as ->
        [ x : a
        | x <- xs
        , a <- as ])
    [[]]

testing any of these with something like:

main :: IO ()
main = do
  mapM_ print $ 
    cartProdN [[1776, 1789], [7,12], [4, 14, 23], [0,1]]
  putStrLn ""
  print $ cartProdN [[1,2,3], [30], [500, 100]]
  putStrLn ""
  print $ cartProdN [[1,2,3], [], [500, 100]]
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]

[[1,30,500],[1,30,100],[2,30,500],[2,30,100],[3,30,500],[3,30,100]]

[]

J[edit]

The J primitive catalogue { 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 1789 ; 7 12 ; 4 14 23 ; 0 1   NB. result is 4 dimensional array with shape 2 2 3 2
┌────────────┬────────────┐
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 01776 12 14 1
├────────────┼────────────┤
1776 12 23 01776 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 01789 12 14 1
├────────────┼────────────┤
1789 12 23 01789 12 23 1
└────────────┴────────────┘
   { 1 2 3 ; 30 ; 50 100    NB. result is a 2-dimensional array with shape 2 3
┌───────┬────────┐
1 30 501 30 100
├───────┼────────┤
2 30 502 30 100
├───────┼────────┤
3 30 503 30 100
└───────┴────────┘
   { 1 2 3 ; '' ; 50 100    NB. result is an empty 3-dimensional array with shape 3 0 2

Java[edit]

Works with: Java Virtual Machine version 1.8
import static java.util.Arrays.asList;
import static java.util.Collections.emptyList;
import static java.util.Optional.of;
import static java.util.stream.Collectors.toList;

import java.util.List;

public class CartesianProduct {

    public List<?> product(List<?>... a) {
        if (a.length >= 2) {
            List<?> product = a[0];
            for (int i = 1; i < a.length; i++) {
                product = product(product, a[i]);
            }
            return product;
        }

        return emptyList();
    }

    private <A, B> List<?> product(List<A> a, List<B> b) {
        return of(a.stream()
                .map(e1 -> of(b.stream().map(e2 -> asList(e1, e2)).collect(toList())).orElse(emptyList()))
                .flatMap(List::stream)
                .collect(toList())).orElse(emptyList());
    }
}

Using a generic class with a recursive function

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class CartesianProduct<V> {

	public List<List<V>> product(List<List<V>> lists) {
		List<List<V>> product = new ArrayList<>();

		// We first create a list for each value of the first list
		product(product, new ArrayList<>(), lists);

		return product;
	}

	private void product(List<List<V>> result, List<V> existingTupleToComplete, List<List<V>> valuesToUse) {
		for (V value : valuesToUse.get(0)) {
			List<V> newExisting = new ArrayList<>(existingTupleToComplete);
			newExisting.add(value);

			// If only one column is left
			if (valuesToUse.size() == 1) {
				// We create a new list with the exiting tuple for each value with the value
				// added
				result.add(newExisting);
			} else {
				// If there are still several columns, we go into recursion for each value
				List<List<V>> newValues = new ArrayList<>();
				// We build the next level of values
				for (int i = 1; i < valuesToUse.size(); i++) {
					newValues.add(valuesToUse.get(i));
				}

				product(result, newExisting, newValues);
			}
		}
	}

	public static void main(String[] args) {
		List<Integer> list1 = new ArrayList<>(Arrays.asList(new Integer[] { 1776, 1789 }));
		List<Integer> list2 = new ArrayList<>(Arrays.asList(new Integer[] { 7, 12 }));
		List<Integer> list3 = new ArrayList<>(Arrays.asList(new Integer[] { 4, 14, 23 }));
		List<Integer> list4 = new ArrayList<>(Arrays.asList(new Integer[] { 0, 1 }));

		List<List<Integer>> input = new ArrayList<>();
		input.add(list1);
		input.add(list2);
		input.add(list3);
		input.add(list4);

		CartesianProduct<Integer> cartesianProduct = new CartesianProduct<>();
		List<List<Integer>> product = cartesianProduct.product(input);
		System.out.println(product);
	}
}

JavaScript[edit]

ES6[edit]

Functional[edit]

Cartesian products fall quite naturally out of concatMap (Array.flatMap), and its argument-flipped twin bind.

For the Cartesian product of just two lists:

(() => {
    // CARTESIAN PRODUCT OF TWO LISTS ---------------------

    // cartProd :: [a] -> [b] -> [[a, b]]
    const cartProd = xs => ys =>
        xs.flatMap(x => ys.map(y => [x, y]))


    // TEST -----------------------------------------------
    return [
        cartProd([1, 2])([3, 4]),
        cartProd([3, 4])([1, 2]),
        cartProd([1, 2])([]),
        cartProd([])([1, 2]),
    ].map(JSON.stringify).join('\n');
})();
Output:
[[1,3],[1,4],[2,3],[2,4]]
[[3,1],[3,2],[4,1],[4,2]]
[]
[]


Abstracting a little more, we can define the cartesian product quite economically in terms of a general applicative operator:

(() => {

    // CARTESIAN PRODUCT OF TWO LISTS ---------------------

    // cartesianProduct :: [a] -> [b] -> [(a, b)]
    const cartesianProduct = xs =>
        ap(xs.map(Tuple));


    // GENERIC FUNCTIONS ----------------------------------

    // e.g. [(*2),(/2), sqrt] <*> [1,2,3]
    // -->  ap([dbl, hlf, root], [1, 2, 3])
    // -->  [2,4,6,0.5,1,1.5,1,1.4142135623730951,1.7320508075688772]

    // Each member of a list of functions applied to each
    // of a list of arguments, deriving a list of new values.

    // ap (<*>) :: [(a -> b)] -> [a] -> [b]
    const ap = fs => xs =>
        // The sequential application of each of a list
        // of functions to each of a list of values.
        fs.flatMap(
            f => xs.map(f)
        );

    // Tuple (,) :: a -> b -> (a, b)
    const Tuple = a => b => [a, b];

    // TEST -----------------------------------------------
    return [
            cartesianProduct([1, 2])([3, 4]),
            cartesianProduct([3, 4])([1, 2]),
            cartesianProduct([1, 2])([]),
            cartesianProduct([])([1, 2]),
        ]
        .map(JSON.stringify)
        .join('\n');
})();
Output:
[[1,3],[1,4],[2,3],[2,4]]
[[3,1],[3,2],[4,1],[4,2]]
[]
[]

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

(() => {
    const main = () => {
        // n-ary Cartesian product of a list of lists.

        // cartProdN :: [[a]] -> [[a]]
        const cartProdN = foldr(
            xs => as =>
            bind(as)(
                x => bind(xs)(
                    a => [
                        [a].concat(x)
                    ]
                )
            )
        )([
            []
        ]);

        // TEST -------------------------------------------
        return intercalate('\n\n')([
            map(show)(
                cartProdN([
                    [1776, 1789],
                    [7, 12],
                    [4, 14, 23],
                    [0, 1]
                ])
            ).join('\n'),
            show(cartProdN([
                [1, 2, 3],
                [30],
                [50, 100]
            ])),
            show(cartProdN([
                [1, 2, 3],
                [],
                [50, 100]
            ]))
        ])
    };

    // GENERIC FUNCTIONS ----------------------------------

    // bind ::  [a] -> (a -> [b]) -> [b]
    const bind = xs => f => xs.flatMap(f);

    // foldr :: (a -> b -> b) -> b -> [a] -> b
    const foldr = f => a => xs =>
        xs.reduceRight((a, x) => f(x)(a), a);

    // intercalate :: String -> [a] -> String
    const intercalate = s => xs => xs.join(s);

    // map :: (a -> b) -> [a] -> [b]
    const map = f => xs => xs.map(f);

    // show :: a -> String
    const show = x => JSON.stringify(x);

    return main();
})();
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]

[[1,30,50],[1,30,100],[2,30,50],[2,30,100],[3,30,50],[3,30,100]]

[]

Imperative[edit]

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 )

    // cartProd :: [a] -> [b] -> [[a, b]]
    const cartProd = lists => {
        let ps = [],
            acc = [
                []
            ],
            i = lists.length;
        while (i--) {
            let subList = lists[i],
                j = subList.length;
            while (j--) {
                let x = subList[j],
                    k = acc.length;
                while (k--) ps.push([x].concat(acc[k]))
            };
            acc = ps;
            ps = [];
        };
        return acc.reverse();
    };

    // GENERIC FUNCTIONS ------------------------------------------------------

    // intercalate :: String -> [a] -> String
    const intercalate = (s, xs) => xs.join(s);

    // map :: (a -> b) -> [a] -> [b]
    const map = (f, xs) => xs.map(f);

    // show :: a -> String
    const show = x => JSON.stringify(x);

    // unlines :: [String] -> String
    const unlines = xs => xs.join('\n');

    // TEST -------------------------------------------------------------------
    return intercalate('\n\n', [show(cartProd([
            [1, 2],
            [3, 4]
        ])),
        show(cartProd([
            [3, 4],
            [1, 2]
        ])),
        show(cartProd([
            [1, 2],
            []
        ])),
        show(cartProd([
            [],
            [1, 2]
        ])),
        unlines(map(show, cartProd([
            [1776, 1789],
            [7, 12],
            [4, 14, 23],
            [0, 1]
        ]))),
        show(cartProd([
            [1, 2, 3],
            [30],
            [50, 100]
        ])),
        show(cartProd([
            [1, 2, 3],
            [],
            [50, 100]
        ]))
    ]);
})();
Output:
[[1,4],[1,3],[2,4],[2,3]]

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

[]

[]

[1776,12,4,1]
[1776,12,4,0]
[1776,12,14,1]
[1776,12,14,0]
[1776,12,23,1]
[1776,12,23,0]
[1776,7,4,1]
[1776,7,4,0]
[1776,7,14,1]
[1776,7,14,0]
[1776,7,23,1]
[1776,7,23,0]
[1789,12,4,1]
[1789,12,4,0]
[1789,12,14,1]
[1789,12,14,0]
[1789,12,23,1]
[1789,12,23,0]
[1789,7,4,1]
[1789,7,4,0]
[1789,7,14,1]
[1789,7,14,0]
[1789,7,23,1]
[1789,7,23,0]

[[1,30,50],[1,30,100],[2,30,50],[2,30,100],[3,30,50],[3,30,100]]

[]

jq[edit]

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:

   [ [1,2], [3,4] ] | products

produces the stream:

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

And

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

produces:

[]

n-way Cartesian Product[edit]

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
  else .[0][] as $x
  | (.[1:] | cartesians) as $y
  | [$x] + $y
  end;

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

   [ [1776, 1789], [7, 12], [4, 14, 23], [0, 1]] | [cartesians] | length
   # 24
   [[1, 2, 3], [30], [500, 100] ] | [cartesians] | length
   # 6
   [[1, 2, 3], [], [500, 100] ] | [cartesians] | length
   # 0

Julia[edit]

Run in REPL.

# Product {1, 2} × {3, 4}
collect(Iterators.product([1, 2], [3, 4]))
# Product {3, 4} × {1, 2}
collect(Iterators.product([3, 4], [1, 2]))
 
# Product {1, 2} × {}
collect(Iterators.product([1, 2], []))
# Product {} × {1, 2}
collect(Iterators.product([], [1, 2]))
 
# Product {1776, 1789} × {7, 12} × {4, 14, 23} × {0, 1}
collect(Iterators.product([1776, 1789], [7, 12], [4, 14, 23], [0, 1]))
# Product {1, 2, 3} × {30} × {500, 100}
collect(Iterators.product([1, 2, 3], [30], [500, 100]))
# Product {1, 2, 3} × {} × {500, 100}
collect(Iterators.product([1, 2, 3], [], [500, 100]))

Kotlin[edit]

// version 1.1.2

fun flattenList(nestList: List<Any>): List<Any> {
    val flatList = mutableListOf<Any>()

    fun flatten(list: List<Any>) {
        for (e in list) {
            if (e !is List<*>)
                flatList.add(e)
            else
                @Suppress("UNCHECKED_CAST")
                flatten(e as List<Any>)
        }
    }

    flatten(nestList)
    return flatList
}

operator fun List<Any>.times(other: List<Any>): List<List<Any>> {
    val prod = mutableListOf<List<Any>>()
    for (e in this) {
        for (f in other) {
            prod.add(listOf(e, f))
        }
    }
    return prod
}

fun nAryCartesianProduct(lists: List<List<Any>>): List<List<Any>> {
    require(lists.size >= 2)
    return lists.drop(2).fold(lists[0] * lists[1]) { cp, ls -> cp * ls }.map { flattenList(it) }
}

fun printNAryProduct(lists: List<List<Any>>) {
    println("${lists.joinToString(" x ")} = ")
    println("[")
    println(nAryCartesianProduct(lists).joinToString("\n    ", "    "))
    println("]\n")
}

fun main(args: Array<String>) {
   println("[1, 2] x [3, 4] = ${listOf(1, 2) * listOf(3, 4)}")
   println("[3, 4] x [1, 2] = ${listOf(3, 4) * listOf(1, 2)}")
   println("[1, 2] x []     = ${listOf(1, 2) * listOf()}")
   println("[]     x [1, 2] = ${listOf<Any>() * listOf(1, 2)}")
   println("[1, a] x [2, b] = ${listOf(1, 'a') * listOf(2, 'b')}")
   println()
   printNAryProduct(listOf(listOf(1776, 1789), listOf(7, 12), listOf(4, 14, 23), listOf(0, 1)))
   printNAryProduct(listOf(listOf(1, 2, 3), listOf(30), listOf(500, 100)))
   printNAryProduct(listOf(listOf(1, 2, 3), listOf<Int>(), listOf(500, 100)))
   printNAryProduct(listOf(listOf(1, 2, 3), listOf(30), listOf('a', 'b')))
}
Output:
[1, 2] x [3, 4] = [[1, 3], [1, 4], [2, 3], [2, 4]]
[3, 4] x [1, 2] = [[3, 1], [3, 2], [4, 1], [4, 2]]
[1, 2] x []     = []
[]     x [1, 2] = []
[1, a] x [2, b] = [[1, 2], [1, b], [a, 2], [a, b]]

[1776, 1789] x [7, 12] x [4, 14, 23] x [0, 1] = 
[
    [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]
]

[1, 2, 3] x [30] x [500, 100] = 
[
    [1, 30, 500]
    [1, 30, 100]
    [2, 30, 500]
    [2, 30, 100]
    [3, 30, 500]
    [3, 30, 100]
]

[1, 2, 3] x [] x [500, 100] = 
[
    
]

[1, 2, 3] x [30] x [a, b] = 
[
    [1, 30, a]
    [1, 30, b]
    [2, 30, a]
    [2, 30, b]
    [3, 30, a]
    [3, 30, b]
]

langur[edit]

We could use mapX() to map each set of values to a function, but this assignment only requires an array of arrays, so we use the X() function.

Works with: langur version 0.8.3
writeln X([1, 2], [3, 4]) == [[1, 3], [1, 4], [2, 3], [2, 4]]
writeln X([3, 4], [1, 2]) == [[3, 1], [3, 2], [4, 1], [4, 2]]
writeln X([1, 2], []) == []
writeln X([], [1, 2]) == []
writeln()

writeln X [1776, 1789], [7, 12], [4, 14, 23], [0, 1]
writeln()

writeln X [1, 2, 3], [30], [500, 100]
writeln()

writeln X [1, 2, 3], [], [500, 100]
writeln()
Output:
true
true
true
true

[[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]]

[[1, 30, 500], [1, 30, 100], [2, 30, 500], [2, 30, 100], [3, 30, 500], [3, 30, 100]]

[]

Lua[edit]

Functional[edit]

An iterator is created to output the product items.

  local pk,upk = table.pack, table.unpack
  local getn = function(t)return #t end
  local const = function(k)return function(e) return k end end
  local function attachIdx(f)-- one-time-off function modifier
    local idx = 0
    return function(e)idx=idx+1 ; return f(e,idx)end
  end  
  
  local function reduce(t,acc,f)
    for i=1,t.n or #t do acc=f(acc,t[i])end
    return acc
  end
  local function imap(t,f)
    local r = {n=t.n or #t, r=reduce, u=upk, m=imap}
    for i=1,r.n do r[i]=f(t[i])end
    return r
  end

  local function prod(...)
    local ts = pk(...)
    local limit = imap(ts,getn)
    local idx, cnt = imap(limit,const(1)),  0
    local max = reduce(limit,1,function(a,b)return a*b end)
    local function ret(t,i)return t[idx[i]] end
    return function()
      if cnt>=max then return end -- no more output
      if cnt==0 then -- skip for 1st
        cnt = cnt + 1 
      else
        cnt, idx[#idx] = cnt + 1, idx[#idx] + 1 
        for i=#idx,2,-1 do -- update index list
          if idx[i]<=limit[i] then 
            break -- no further update need
          else -- propagate limit overflow
            idx[i],idx[i-1] = 1, idx[i-1]+1
          end        
        end        
      end
      return cnt,imap(ts,attachIdx(ret)):u()
    end    
  end
--- test
  for i,a,b in prod({1,2},{3,4}) do
    print(i,a,b)
  end
  print()
  for i,a,b in prod({3,4},{1,2}) do
    print(i,a,b)
  end
Output:
1	1	3
2	1	4
3	2	3
4	2	4

1	3	1
2	3	2
3	4	1
4	4	2

Using coroutines[edit]

I have not benchmarked this, but I believe that this should run faster than the functional implementation and also likely the imperative implementation, it has significantly fewer function calls per iteration, and only the stack changes during iteration (no garbage collection during iteration). On the other hand due to avoiding garbage collection, result is reused between returns, so mutating the returned result is unsafe.

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 function cartesian_product(sets)
  local result = {}
  local set_count = #sets
--[[ I believe that this should make the below go very slightly faster, because it doesn't need to lookup yield in coroutine each time it
     yields, though perhaps the compiler optimises the lookup away? ]]
  local yield = coroutine.yield 
  local function descend(depth)
    if depth == set_count then
      for k,v in pairs(sets[depth]) do
        result[depth] = v
        yield(result)
      end
    else
      for k,v in pairs(sets[depth]) do
        result[depth] = v
        descend(depth + 1)
      end
    end
  end
  return coroutine.wrap(function() descend(1) end)
end

--- tests
local test_cases = {
  {{1, 2}, {3, 4}},
  {{3, 4}, {1, 2}},
  {{1776, 1789}, {7, 12}, {4, 14, 23}, {0,1}},
  {{1,2,3}, {30}, {500, 100}},
  {{1,2,3}, {}, {500, 100}}
}

local function format_nested_list(list)
  if list[1] and type(list[1]) == "table" then
    local formatted_items = {}
    for i, item in ipairs(list) do
      formatted_items[i] = format_nested_list(item)
    end
    return format_nested_list(formatted_items)
  else
    return "{" .. table.concat(list, ",") .. "}"
  end
end

for _,test_case in ipairs(test_cases) do
  print(format_nested_list(test_case))
  for product in cartesian_product(test_case) do
    print("  " .. format_nested_list(product))
  end
end

Imperative iterator[edit]

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 function cartesian_product(sets)
  local item_counts = {}
  local indices = {}
  local results = {}
  local set_count = #sets
  local combination_count = 1
  
  for set_index=set_count, 1, -1 do
    local set = sets[set_index]
    local item_count = #set
    item_counts[set_index] = item_count
    indices[set_index] = 1
    results[set_index] = set[1]
    combination_count = combination_count * item_count
  end
  
  local combination_index = 0
  
  return function()
    if combination_index >= combination_count then return end -- no more output

    if combination_index == 0 then goto skip_update end -- skip first index update
    
    indices[set_count] = indices[set_count] + 1
    
    for set_index=set_count, 1, -1 do -- update index list
      local set = sets[set_index]
      local index = indices[set_index]
      if index <= item_counts[set_index] then
        results[set_index] = set[index]
        break -- no further update needed
      else -- propagate item_counts overflow
        results[set_index] = set[1]
        indices[set_index] = 1
        if set_index > 1 then
          indices[set_index - 1] = indices[set_index - 1] + 1
        end
      end
    end
    
    ::skip_update::
    
    combination_index = combination_index + 1
    
    return combination_index, results
  end
end
--- tests
local test_cases = {
  {{1, 2}, {3, 4}},
  {{3, 4}, {1, 2}},
  {{1776, 1789}, {7, 12}, {4, 14, 23}, {0,1}},
  {{1,2,3}, {30}, {500, 100}},
  {{1,2,3}, {}, {500, 100}}
}

local function format_nested_list(list)
  if list[1] and type(list[1]) == "table" then
    local formatted_items = {}
    for i, item in ipairs(list) do
      formatted_items[i] = format_nested_list(item)
    end
    return format_nested_list(formatted_items)
  else
    return "{" .. table.concat(list, ",") .. "}"
  end
end

for _,test_case in ipairs(test_cases) do
  print(format_nested_list(test_case))
  for i, product in cartesian_product(test_case) do
    print(i, format_nested_list(product))
  end
end

Functional-esque (non-iterator)[edit]

Motivation: If a list-of-lists is passed into the cartesian product, then wouldn't a list-of-lists be the expected return type? Of course this is just personal opinion/preference, other implementations are fine as-is if you'd rather have an iterator.

-- support:
function T(t) return setmetatable(t, {__index=table}) end
table.clone = function(t) local s=T{} for k,v in ipairs(t) do s[k]=v end return s end
table.reduce = function(t,f,acc) for i=1,#t do acc=f(t[i],acc) end return acc end

-- implementation:
local function cartprod(sets)
  local temp, prod = T{}, T{}
  local function descend(depth)
    for _,v in ipairs(sets[depth]) do
      temp[depth] = v
      if (depth==#sets) then prod[#prod+1]=temp:clone() else descend(depth+1) end
    end
  end
  descend(1)
  return prod
end

-- demonstration:
tests = {
  { {1, 2}, {3, 4} },
  { {3, 4}, {1, 2} },
  { {1, 2}, {} },
  { {}, {1, 2} },
  { {1776, 1789}, {7, 12}, {4, 14, 23}, {0, 1} },
  { {1, 2, 3}, {30}, {500, 100} },
  { {1, 2, 3}, {}, {500, 100} }
}
for _,test in ipairs(tests) do
  local cp = cartprod(test)
  print("{"..cp:reduce(function(t,a) return (a=="" and a or a..", ").."("..t:concat(", ")..")" end,"").."}")
end
Output:
{(1, 3), (1, 4), (2, 3), (2, 4)}
{(3, 1), (3, 2), (4, 1), (4, 2)}
{}
{}
{(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)}
{(1, 30, 500), (1, 30, 100), (2, 30, 500), (2, 30, 100), (3, 30, 500), (3, 30, 100)}
{}

Maple[edit]

cartmulti := proc ()
 local m, v;
 if [] in {args} then
 return [];
 else 
m := Iterator:-CartesianProduct(args);
 for v in m do
 printf("%{}a\n", v);
 end do;
 end if;
 end proc;

Mathematica/Wolfram Language[edit]

cartesianProduct[args__] := Flatten[Outer[List, args], Length[{args}] - 1]

Modula-2[edit]

MODULE CartesianProduct;
FROM FormatString IMPORT FormatString;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;

PROCEDURE WriteInt(a : INTEGER);
VAR buf : ARRAY[0..9] OF CHAR;
BEGIN
    FormatString("%i", buf, a);
    WriteString(buf)
END WriteInt;

PROCEDURE Cartesian(a,b : ARRAY OF INTEGER);
VAR i,j : CARDINAL;
BEGIN
    WriteString("[");
    FOR i:=0 TO HIGH(a) DO
        FOR j:=0 TO HIGH(b) DO
            IF (i>0) OR (j>0) THEN
                WriteString(",");
            END;
            WriteString("[");
            WriteInt(a[i]);
            WriteString(",");
            WriteInt(b[j]);
            WriteString("]")
        END
    END;
    WriteString("]");
    WriteLn
END Cartesian;

TYPE
    AP = ARRAY[0..1] OF INTEGER;
    E = ARRAY[0..0] OF INTEGER;
VAR
    a,b : AP;
BEGIN
    a := AP{1,2};
    b := AP{3,4};
    Cartesian(a,b);

    a := AP{3,4};
    b := AP{1,2};
    Cartesian(a,b);

    (* If there is a way to create an empty array, I do not know of it *)

    ReadChar
END CartesianProduct.

Nim[edit]

Task: product of two lists[edit]

To compute the product of two lists (Nim arrays or sequences), we use an iterator. Obtaining a sequence from an iterator is easily done using "toSeq" from the module “sequtils” of the standard library.

The procedure allows to mix sequences of different types, for instance integers and characters.

In order to display the result using mathematical formalism, we have created a special procedure “$$” for the sequences and have overloaded the procedure “$” for tuples.

iterator product[T1, T2](a: openArray[T1]; b: openArray[T2]): tuple[a: T1, b: T2] =
  # Yield the element of the cartesian product of "a" and "b".
  # Yield tuples rather than arrays as it allows T1 and T2 to be different.
  
  for x in a:
    for y in b:
      yield (x, y)

#———————————————————————————————————————————————————————————————————————————————————————————————————

when isMainModule:

  from seqUtils import toSeq
  import strformat
  from strutils import addSep

  #-------------------------------------------------------------------------------------------------

  proc `$`[T1, T2](t: tuple[a: T1, b: T2]): string =
    ## Overloading of `$` to display a tuple without the field names.
    &"({t.a}, {t.b})"

  proc `$$`[T](s: seq[T]): string =
    ## New operator to display a sequence using mathematical set notation.
    result = "{"
    for item in s:
      result.addSep(", ", 1)
      result.add($item)
    result.add('}')

#-------------------------------------------------------------------------------------------------

  const Empty = newSeq[int]()   # Empty list of "int".

  for (a, b) in [(@[1, 2], @[3, 4]),
                 (@[3, 4], @[1, 2]),
                 (@[1, 2],  Empty ),
                 ( Empty,  @[1, 2])]:

    echo &"{$$a} x {$$b} = {$$toSeq(product(a, b))}"
Output:
1, 2} x {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}
{3, 4} x {1, 2} = {(3, 1), (3, 2), (4, 1), (4, 2)}
{1, 2} x {} = {}
{} x {1, 2} = {}

Extra credit: product of n list[edit]

Recursive procedure[edit]

As iterators cannot be recursive, we have to use a procedure which returns the whole sequence. And as we don’t know the number of sequences, we use a “varargs”. So all the sequences must contain the same type of values, values which are returned as sequences and not tuples.

Note that there exists in the standard module “algorithm” a procedure which computes the product of sequences of a same type. It is not recursive and, so, likely more efficient that the following version.

proc product[T](a: varargs[seq[T]]): seq[seq[T]] =
  ## Return the product of several sets (sequences).

  if a.len == 1:
    for x in a[0]:
      result.add(@[x])
  else:
    for x in a[0]:
      for s in product(a[1..^1]):
        result.add(x & s)

#———————————————————————————————————————————————————————————————————————————————————————————————————

when isMainModule:

  import strformat
  
  let
    a = @[1, 2]
    b = @[3, 4]
    c = @[5, 6]
  echo &"{a} x {b} x {c} = {product(a, b, c)}"
Output:
@[1, 2] x @[3, 4] x @[5, 6] = @[@[1, 3, 5], @[1, 3, 6], @[1, 4, 5], @[1, 4, 6], @[2, 3, 5], @[2, 3, 6], @[2, 4, 5], @[2, 4, 6]]

Using a macro[edit]

Another way to compute the product consists to use a macro. It would be possible to create an iterator but it’s somewhat easier to produce the code to build the whole sequence. No recursion here: we generate nested loops, so the algorithm is the simplest possible.

With a macro, we are able to mix several value types: the “varrags” is no longer a problem as being used at compile time it may contain sequences of different types. And we are able to return tuples of n values instead of sequences of n values.

import macros

macro product(args: varargs[typed]): untyped =
  ## Macro to generate the code to build the product of several sequences.

  let t = args[0].getType()
  if t.kind != nnkBracketExpr or t[0].kind != nnkSym or $t[0] != "seq":
    error("Arguments must be sequences", args)

  # Build the result type i.e. a tuple with "args.len" elements.
  # Fields are named "f0", "f1", etc.
  let tupleTyNode = newNimNode(nnkTupleTy)
  for idx, arg in args:
    let identDefsNode = newIdentDefs(ident('f' & $idx), arg.getType()[1])
    tupleTyNode.add(identDefsNode)

  # Build the nested for loops with counter "i0", "i1", etc.
  var stmtListNode = newStmtList()
  let loopsNode = nnkForStmt.newTree(ident("i0"), ident($args[0]), stmtListNode)
  var idx = 0
  for arg in args[1..^1]:
    inc idx
    let loopNode = nnkForStmt.newTree(ident('i' & $idx), ident($arg))
    stmtListNode.add(loopNode)
    stmtListNode = newStmtList()
    loopNode.add(stmtListNode)

  # Build the instruction "result.add(i1, i2,...)".
  let parNode = newPar()
  let addNode = newCall(newDotExpr(ident("result"), ident("add")), parNode)
  for i, arg in args:
    parNode.add(ident('i' & $i))
  stmtListNode.add(addNode)

  # Build the tree.
  result = nnkStmtListExpr.newTree(
             nnkVarSection.newTree(
               newIdentDefs(
                 ident("result"),
                 nnkBracketExpr.newTree(ident("seq"), tupleTyNode))),
               loopsNode,
             ident("result"))

#———————————————————————————————————————————————————————————————————————————————————————————————————

when isMainModule:

  import strformat
  import strutils

  #-------------------------------------------------------------------------------------------------

  proc `$`[T: tuple](t: T): string =
    ## Overloading of `$` to display a tuple without the field names.
    result = "("
    for f in t.fields:
      result.addSep(", ", 1)
      result.add($f)
    result.add(']')

  proc `$$`[T](s: seq[T]): string =
    ## New operator to display a sequence using mathematical set notation.
    result = "{"
    for item in s:
      result.addSep(", ", 1)
      result.add($item)
    result.add('}')

  #-------------------------------------------------------------------------------------------------

  var a = @[1, 2]
  var b = @['a', 'b']
  var c = @[false, true]
  echo &"{$$a} x {$$b} x {$$c} = {$$product(a, b, c)}"
Output:
{1, 2} x {a, b} x {false, true} = {(1, a, false], (1, a, true], (1, b, false], (1, b, true], (2, a, false], (2, a, true], (2, b, false], (2, b, true]}

OCaml[edit]

The double semicolons are necessary only for the toplevel

Naive but more readable version
let rec product l1 l2 = 
    match l1, l2 with
    | [], _ | _, [] -> []
    | h1::t1, h2::t2 -> (h1,h2)::(product [h1] t2)@(product t1 l2)
;;

product [1;2] [3;4];;
(*- : (int * int) list = [(1, 3); (1, 4); (2, 3); (2, 4)]*)
product [3;4] [1;2];;
(*- : (int * int) list = [(3, 1); (3, 2); (4, 1); (4, 2)]*)
product [1;2] [];;
(*- : (int * 'a) list = []*)
product [] [1;2];;
(*- : ('a * int) list = []*)

Implementation with a bit more tail-call optimization, introducing a helper function. The order of the result is changed but it should not be an issue for most uses.

let product' l1 l2 = 
    let rec aux ~acc l1' l2' = 
        match l1', l2' with
        | [], _ | _, [] -> acc
        | h1::t1, h2::t2 -> 
            let acc = (h1,h2)::acc in
            let acc = aux ~acc t1 l2' in
            aux ~acc [h1] t2
    in aux [] l1 l2
;;

product' [1;2] [3;4];;
(*- : (int * int) list = [(1, 4); (2, 4); (2, 3); (1, 3)]*)
product' [3;4] [1;2];;
(*- : (int * int) list = [(3, 2); (4, 2); (4, 1); (3, 1)]*)
product' [1;2] [];;
(*- : (int * 'a) list = []*)
product' [] [1;2];;
(*- : ('a * int) list = []*)

Implemented using nested folds:

let cart_prod l1 l2 =
  List.fold_left (fun acc1 ele1 ->
    List.fold_left (fun acc2 ele2 -> (ele1,ele2)::acc2) acc1 l2) [] l1 ;;

cart_prod [1; 2; 3] ['a'; 'b'; 'c'] ;;
(*- : (int * char) list = [(3, 'c'); (3, 'b'); (3, 'a'); (2, 'c'); (2, 'b'); (2, 'a'); (1, 'c'); (1, 'b'); (1, 'a')]*)
cart_prod [1; 2; 3] [] ;;
(*- : ('a * int) list = [] *)

Extra credit function. Since in OCaml a function can return only one type, and because tuples of different arities are different types, this returns a list of lists rather than a list of tuples. Since lists are homogeneous this version is restricted to products over a single type, eg integers.

let rec product'' l = 
    (* We need to do the cross product of our current list and all the others
     * so we define a helper function for that *)
    let rec aux ~acc l1 l2 = match l1, l2 with
    | [], _ | _, [] -> acc
    | h1::t1, h2::t2 -> 
        let acc = (h1::h2)::acc in
        let acc = (aux ~acc t1 l2) in
        aux ~acc [h1] t2
    (* now we can do the actual computation *)
    in match l with
    | [] -> []
    | [l1] -> List.map (fun x -> [x]) l1
    | l1::tl ->
        let tail_product = product'' tl in
        aux ~acc:[] l1 tail_product


product'' [[1;2];[3;4]];;
(*- : int list list = [[1; 4]; [2; 4]; [2; 3]; [1; 3]]*)
product'' [[3;4];[1;2]];;
(*- : int list list = [[3; 2]; [4; 2]; [4; 1]; [3; 1]]*)
product'' [[1;2];[]];;
(*- : int list list = []*)
product'' [[];[1;2]];;
(*- : int list list = []*)
product'' [[1776; 1789];[7; 12];[4; 14; 23];[0; 1]];;
(*
- : int list list =

[[1776; 7; 4; 1]; [1776; 12; 4; 1]; [1776; 12; 14; 1]; [1776; 12; 23; 1];
 [1776; 12; 23; 0]; [1776; 12; 14; 0]; [1776; 12; 4; 0]; [1776; 7; 14; 1];
 [1776; 7; 23; 1]; [1776; 7; 23; 0]; [1776; 7; 14; 0]; [1789; 7; 4; 1];
 [1789; 12; 4; 1]; [1789; 12; 14; 1]; [1789; 12; 23; 1]; [1789; 12; 23; 0];
 [1789; 12; 14; 0]; [1789; 12; 4; 0]; [1789; 7; 14; 1]; [1789; 7; 23; 1];
 [1789; 7; 23; 0]; [1789; 7; 14; 0]; [1789; 7; 4; 0]; [1776; 7; 4; 0]]
*)
product'' [[1; 2; 3];[30];[500; 100]];;
(*
- : int list list =

[[1; 30; 500]; [2; 30; 500]; [3; 30; 500]; [3; 30; 100]; [2; 30; 100];
 [1; 30; 100]]
*)
product'' [[1; 2; 3];[];[500; 100]];;
(*- : int list list = []*)

Better type[edit]

In the latter example, our function has this signature:

val product'' : 'a list list -> 'a list list = <fun>

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:

type 'a tuple = 'a list

let rec product'' (l:'a list tuple) =
    (* We need to do the cross product of our current list and all the others
     * so we define a helper function for that *)
    let rec aux ~acc l1 l2 = match l1, l2 with
    | [], _ | _, [] -> acc
    | h1::t1, h2::t2 ->
        let acc = (h1::h2)::acc in
        let acc = (aux ~acc t1 l2) in
        aux ~acc [h1] t2
    (* now we can do the actual computation *)
    in match l with
    | [] -> []
    | [l1] -> List.map ~f:(fun x -> ([x]:'a tuple)) l1
    | l1::tl ->
        let tail_product = product'' tl in
        aux ~acc:[] l1 tail_product
;;

type 'a tuple = 'a list
val product'' : 'a list tuple -> 'a tuple list = <fun>

Perl[edit]

Iterative[edit]

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

sub cartesian {
    my $sets = shift @_;
    for (@$sets) { return [] unless @$_ }

    my $products = [[]];
    for my $set (reverse @$sets) {
        my $partial = $products;
        $products = [];
        for my $item (@$set) {
            for my $product (@$partial) {
                push @$products, [$item, @$product];
            }
        }
    }
    $products;
}

sub product {
    my($s,$fmt) = @_;
    my $tuples;
    for $a ( @{ cartesian( \@$s ) } ) { $tuples .= sprintf "($fmt) ", @$a; }
    $tuples . "\n";
}

print 
product([[1, 2],      [3, 4]                  ], '%1d %1d'        ).
product([[3, 4],      [1, 2]                  ], '%1d %1d'        ).
product([[1, 2],      []                      ], '%1d %1d'        ).
product([[],          [1, 2]                  ], '%1d %1d'        ).
product([[1,2,3],     [30],   [500,100]       ], '%1d %1d %3d'    ).
product([[1,2,3],     [],     [500,100]       ], '%1d %1d %3d'    ).
product([[1776,1789], [7,12], [4,14,23], [0,1]], '%4d %2d %2d %1d')
Output:
(1 3) (1 4) (2 3) (2 4)
(3 1) (3 2) (4 1) (4 2)


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

(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)

Glob[edit]

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

$tuples = [ map { [split /:/] } glob '{1,2,3}:{30}:{500,100}' ];

for $a (@$tuples) { printf "(%1d %2d %3d) ", @$a; }
Output:
(1 30 500) (1 30 100) (2 30 500) (2 30 100) (3 30 500) (3 30 100)

Modules[edit]

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.

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

use Set::Product qw/product/;
product { say "@_" } [1,2,3],[qw/a b c/],[qw/@ $ !/];

use Math::Cartesian::Product;
cartesian { say "@_" } [1,2,3],[qw/a b c/],[qw/@ $ !/];

use Algorithm::Loops qw/NestedLoops/;
NestedLoops([[1,2,3],[qw/a b c/],[qw/@ $ !/]], sub { say "@_"; });

Phix[edit]

with javascript_semantics
function cart(sequence s)
    sequence res = {}
    for n=2 to length(s) do
        for i=1 to length(s[1]) do
            for j=1 to length(s[2]) do
                res = append(res,s[1][i]&s[2][j])
            end for
        end for
        if length(s)=2 then exit end if
        s[1..2] = {res}
        res = {}
    end for
    return res
end function
 
?cart({{1,2},{3,4}})
?cart({{3,4},{1,2}})
?cart({{1,2},{}})
?cart({{},{1,2}})
?cart({{1776, 1789},{7, 12},{4, 14, 23},{0, 1}})
?cart({{1, 2, 3},{30},{500, 100}})
?cart({{1, 2, 3},{},{500, 100}})
Output:
{{1,3},{1,4},{2,3},{2,4}}
{{3,1},{3,2},{4,1},{4,2}}
{}
{}
{{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}}
{{1,30,500},{1,30,100},{2,30,500},{2,30,100},{3,30,500},{3,30,100}}
{}

Phixmonti[edit]

include ..\Utilitys.pmt

def cart
    ( ) var res
    -1 get var ta -1 del
    -1 get var he -1 del
    ta "" != he "" != and if
        he len nip for
            he swap get var h drop
            ta len nip for
                ta swap get var t drop
                ( h t ) flatten res swap 0 put var res
            endfor
        endfor
        len if res 0 put cart endif
    endif
enddef

/# ---------- MAIN ---------- #/

( ( 1 2 ) ( 3 4 ) ) cart
drop res print nl nl

( ( 1776 1789 ) ( 7 12 ) ( 4 14 23 ) ( 0 1 ) ) cart
drop res print nl nl

( ( 1 2 3 ) ( 30 ) ( 500 100 ) ) cart
drop res print nl nl

( ( 1 2 ) ( ) ) cart
drop res print nl nl

PicoLisp[edit]

(de 2lists (L1 L2)
   (mapcan
      '((I)
         (mapcar
            '((A) ((if (atom A) list cons) I A))
            L2 ) )
      L1 ) )
(de reduce (L . @)
   (ifn (rest) L (2lists L (apply reduce (rest)))) )
(de cartesian (L . @)
   (and L (rest) (pass reduce L)) )

(println
   (cartesian (1 2)) )
(println
   (cartesian NIL (1 2)) )
(println
   (cartesian (1 2) (3 4)) )
(println
   (cartesian (3 4) (1 2)) )
(println
   (cartesian (1776 1789) (7 12) (4 14 23) (0 1)) )
(println
   (cartesian (1 2 3) (30) (500 100)) )
(println
   (cartesian (1 2 3) NIL (500 100)) )
Output:
NIL
NIL
((1 3) (1 4) (2 3) (2 4))
((3 1) (3 2) (4 1) (4 2))
((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))
((1 30 500) (1 30 100) (2 30 500) (2 30 100) (3 30 500) (3 30 100))
NIL

Prolog[edit]

product([A|_], Bs, [A, B]) :- member(B, Bs).
product([_|As], Bs, X) :- product(As, Bs, X).
Output:
?- findall(X, product([1,2],[3,4],X), S).
S = [[1, 3], [1, 4], [2, 3], [2, 4]].

?- findall(X, product([3,4],[1,2],X), S).
S = [[3, 1], [3, 2], [4, 1], [4, 2]].

?- findall(X, product([1,2,3],[],X), S).
S = [].

?- findall(X, product([],[1,2,3],X), S).
S = [].

Python[edit]

Using itertools[edit]

import itertools

def cp(lsts):
    return list(itertools.product(*lsts))

if __name__ == '__main__':
    from pprint import pprint as pp
    
    for lists in [[[1,2],[3,4]], [[3,4],[1,2]], [[], [1, 2]], [[1, 2], []],
                  ((1776, 1789),  (7, 12), (4, 14, 23), (0, 1)),
                  ((1, 2, 3), (30,), (500, 100)),
                  ((1, 2, 3), (), (500, 100))]:
        print(lists, '=>')
        pp(cp(lists), indent=2)
Output:
[[1, 2], [3, 4]] =>
[(1, 3), (1, 4), (2, 3), (2, 4)]
[[3, 4], [1, 2]] =>
[(3, 1), (3, 2), (4, 1), (4, 2)]
[[], [1, 2]] =>
[]
[[1, 2], []] =>
[]
((1776, 1789), (7, 12), (4, 14, 23), (0, 1)) =>
[ (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)]
((1, 2, 3), (30,), (500, 100)) =>
[ (1, 30, 500),
  (1, 30, 100),
  (2, 30, 500),
  (2, 30, 100),
  (3, 30, 500),
  (3, 30, 100)]
((1, 2, 3), (), (500, 100)) =>
[]

Using the 'Applicative' abstraction[edit]

This task calls for alternative approaches to defining cartesian products, and one particularly compact alternative route to a native cartesian product (in a more mathematically reasoned idiom of programming) is through the Applicative abstraction (see Applicative Functor), which is slightly more general than the possibly better known monad structure. Applicative functions are provided off-the-shelf by languages like Agda, Idris, Haskell and Scala, and can usefully be implemented in any language, including Python, which supports higher-order functions.

If we write ourselves a re-usable Python ap function for the case of lists (applicative functions for other 'data containers' can also be written – this one applies a list of functions to a list of values):

# ap (<*>) :: [(a -> b)] -> [a] -> [b]
def ap(fs):
    return lambda xs: foldl(
        lambda a: lambda f: a + foldl(
            lambda a: lambda x: a + [f(x)])([])(xs)
    )([])(fs)

then one simple use of it will be to define the cartesian product of two lists (of possibly different type) as:

ap(map(Tuple, xs))

where Tuple is a constructor, and xs is bound to the first of two lists. The returned value is a function which can be applied to a second list.

For an nAry product, we can then use a fold (catamorphism) to lift the basic function over two lists cartesianProduct :: [a] -> [b] -> [(a, b)] to a function over a list of lists:

# nAryCartProd :: [[a], [b], [c] ...] -> [(a, b, c ...)]
def nAryCartProd(xxs):
    return foldl1(cartesianProduct)(
        xxs
    )

For example:

# Two lists -> list of tuples


# cartesianProduct :: [a] -> [b] -> [(a, b)]
def cartesianProduct(xs):
    return ap(map(Tuple, xs))


# List of lists -> list of tuples

# nAryCartProd :: [[a], [b], [c] ...] -> [(a, b, c ...)]
def nAryCartProd(xxs):
    return foldl1(cartesianProduct)(
        xxs
    )


# main :: IO ()
def main():
    # Product of lists of different types
    print (
        'Product of two lists of different types:'
    )
    print(
        cartesianProduct(['a', 'b', 'c'])(
            [1, 2]
        )
    )

    # TESTS OF PRODUCTS OF TWO LISTS

    print(
        '\nSpecified tests of products of two lists:'
    )
    print(
        cartesianProduct([1, 2])([3, 4]),
        ' <--> ',
        cartesianProduct([3, 4])([1, 2])
    )
    print (
        cartesianProduct([1, 2])([]),
        ' <--> ',
        cartesianProduct([])([1, 2])
    )

    # TESTS OF N-ARY CARTESIAN PRODUCTS

    print('\nSpecified tests of nAry products:')
    for xs in nAryCartProd([[1776, 1789], [7, 12], [4, 14, 23], [0, 1]]):
        print(xs)

    for xs in (
        map_(nAryCartProd)(
            [
                [[1, 2, 3], [30], [500, 100]],
                [[1, 2, 3], [], [500, 100]]
            ]
        )
    ):
        print(
            xs
        )

# GENERIC -------------------------------------------------


# Applicative function for lists

# ap (<*>) :: [(a -> b)] -> [a] -> [b]
def ap(fs):
    return lambda xs: foldl(
        lambda a: lambda f: a + foldl(
            lambda a: lambda x: a + [f(x)])([])(xs)
    )([])(fs)


# foldl :: (a -> b -> a) -> a -> [b] -> a
def foldl(f):
    def go(v, xs):
        a = v
        for x in xs:
            a = f(a)(x)
        return a
    return lambda acc: lambda xs: go(acc, xs)


# foldl1 :: (a -> a -> a) -> [a] -> a
def foldl1(f):
    return lambda xs: foldl(f)(xs[0])(
        xs[1:]
    ) if xs else None


# map :: (a -> b) -> [a] -> [b]
def map_(f):
    return lambda xs: list(map(f, xs))


# Tuple :: a -> b -> (a, b)
def Tuple(x):
    return lambda y: (
        x + (y,)
    ) if tuple is type(x) else (x, y)


# TEST ----------------------------------------------------
if __name__ == '__main__':
    main()
Output:
Product of two lists of different types:
[('a', 1), ('a', 2), ('b', 1), ('b', 2), ('c', 1), ('c', 2)]

Specified tests of products of two lists:
[(1, 3), (1, 4), (2, 3), (2, 4)]  <-->  [(3, 1), (3, 2), (4, 1), (4, 2)]
[]  <-->  []

Specified tests of nAry products:
(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)
[(1, 30, 500), (1, 30, 100), (2, 30, 500), (2, 30, 100), (3, 30, 500), (3, 30, 100)]
[]

Quackery[edit]

  [ [] unrot
    swap witheach
      [ over witheach
          [ over nested 
            swap nested join 
            nested dip rot join 
            unrot ]
      drop ] drop ]             is cartprod ( [ [ --> [ )

  ' [ 1 2 ] ' [ 3 4 ] cartprod echo cr
  ' [ 3 4 ] ' [ 1 2 ] cartprod echo cr
  ' [ 1 2 ] ' [     ] cartprod echo cr
  ' [     ] ' [ 1 2 ] cartprod echo cr
Output:
[ [ 1 3 ] [ 1 4 ] [ 2 3 ] [ 2 4 ] ]
[ [ 3 1 ] [ 3 2 ] [ 4 1 ] [ 4 2 ] ]
[ ]
[ ]

R[edit]

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

# Let's define an infix operator to perform a cartesian product.

"%p%" <- function( a, b ) {
  p = c( sapply(a, function (x) one_w_many(x, b) ) )
  if (is.null(unlist(p))) list() else p}

display_prod <-
  function (xs) { for (x in xs) cat( paste(x, collapse=", "), "\n" ) }

fmt_vec <- function(v) sprintf("(%s)", paste(v, collapse=', '))

go <- function (...) {
  cat("\n", paste( sapply(list(...),fmt_vec), collapse=" * "), "\n")
  prod = Reduce( '%p%', list(...) )
  display_prod( prod ) }

Simple tests:

> display_prod(  c(1, 2) %p% c(3, 4)  )
1, 3
1, 4
2, 3
2, 4
> display_prod(  c(3, 4) %p% c(1, 2)  )
3, 1
3, 2
4, 1
4, 2
> 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) )
Output:
 (1776, 1789) * (7, 12) * (4, 14, 23) * (0, 1)
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

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

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

Racket[edit]

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

#lang racket/base
(require rackunit
         ;; usually, included in "racket", but we're using racket/base so we
         ;; show where this comes from
         (only-in racket/list cartesian-product))
;; these tests will pass silently
(check-equal? (cartesian-product '(1 2) '(3 4))
             '((1 3) (1 4) (2 3) (2 4)))
(check-equal? (cartesian-product '(3 4) '(1 2))
             '((3 1) (3 2) (4 1) (4 2)))
(check-equal? (cartesian-product '(1 2) '()) '())
(check-equal? (cartesian-product '() '(1 2)) '())

;; these will print
(cartesian-product '(1776 1789) '(7 12) '(4 14 23) '(0 1))
(cartesian-product '(1 2 3) '(30) '(500 100))
(cartesian-product '(1 2 3) '() '(500 100))
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))
'((1 30 500) (1 30 100) (2 30 500) (2 30 100) (3 30 500) (3 30 100))
'()

Raku[edit]

(formerly Perl 6)

Works with: Rakudo version 2017.06

The cross meta operator X will return the cartesian product of two lists. To apply the cross meta-operator to a variable number of lists, use the reduce cross meta operator [X].

# cartesian product of two lists using the X cross meta-operator
say (1, 2) X (3, 4);
say (3, 4) X (1, 2);
say (1, 2) X ( );
say ( )    X ( 1, 2 );

# cartesian product of variable number of lists using
# the [X] reduce cross meta-operator
say [X] (1776, 1789), (7, 12), (4, 14, 23), (0, 1);
say [X] (1, 2, 3), (30), (500, 100);
say [X] (1, 2, 3), (),   (500, 100);
Output:
((1 3) (1 4) (2 3) (2 4))
((3 1) (3 2) (4 1) (4 2))
()
()
((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))
((1 30 500) (1 30 100) (2 30 500) (2 30 100) (3 30 500) (3 30 100))
()

REXX[edit]

version 1[edit]

This REXX version isn't limited by the number of lists or the number of sets within a list.

/*REXX program  calculates  the   Cartesian product   of two  arbitrary-sized  lists.   */
@.=                                              /*assign the default value to  @. array*/
parse arg @.1                                    /*obtain the optional value of  @.1    */
if @.1=''  then do;  @.1= "{1,2} {3,4}"          /*Not specified?  Then use the defaults*/
                     @.2= "{3,4} {1,2}"          /* "      "         "   "   "      "   */
                     @.3= "{1,2} {}"             /* "      "         "   "   "      "   */
                     @.4= "{}    {3,4}"          /* "      "         "   "   "      "   */
                     @.5= "{1,2} {3,4,5}"        /* "      "         "   "   "      "   */
                end
                                                 /* [↓]  process each of the  @.n values*/
  do n=1  while @.n \= ''                        /*keep processing while there's a value*/
  z= translate( space( @.n, 0),  ,  ',')         /*translate the  commas  to blanks.    */
     do #=1  until z==''                         /*process each elements in first list. */
     parse var  z   '{'  x.#  '}'   z            /*parse the list  (contains elements). */
     end   /*#*/
  $=
     do       i=1   for #-1                      /*process the subsequent lists.        */
       do     a=1   for words(x.i)               /*obtain the elements of the first list*/
         do   j=i+1 for #-1                      /*   "    "  subsequent lists.         */
           do b=1   for words(x.j)               /*   "    " elements of subsequent list*/
           $=$',('word(x.i, a)","word(x.j, b)')' /*append partial Cartesian product ──►$*/
           end   /*b*/
         end     /*j*/
       end       /*a*/
     end         /*i*/
  say 'Cartesian product of '       space(@.n)       " is ───► {"substr($, 2)'}'
  end            /*n*/                           /*stick a fork in it,  we're all done. */
output   when using the default lists:
Cartesian product of  {1,2} {3,4}  is ───► {(1,3),(1,4),(2,3),(2,4)}
Cartesian product of  {3,4} {1,2}  is ───► {(3,1),(3,2),(4,1),(4,2)}
Cartesian product of  {1,2} {}  is ───► {}
Cartesian product of  {} {3,4}  is ───► {}
Cartesian product of  {1,2} {3,4,5}  is ───► {(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)}

version 2[edit]

/* REXX computes the Cartesian Product of up to 4 sets */
Call cart '{1, 2} x {3, 4}'
Call cart '{3, 4} x {1, 2}'
Call cart '{1, 2} x {}'
Call cart '{} x {1, 2}'
Call cart '{1776, 1789} x {7, 12} x {4, 14, 23} x {0, 1}'
Call cart '{1, 2, 3} x {30} x {500, 100}'
Call cart '{1, 2, 3} x {} x {500, 100}'
Exit

cart:
  Parse Arg sl
  Say sl
  Do i=1 By 1 while pos('{',sl)>0
    Parse Var sl '{' list '}' sl
    Do j=1 By 1 While list<>''
      Parse Var list e.i.j . ',' list
      End
    n.i=j-1
    If n.i=0 Then Do /* an empty set */
      Say '{}'
      Say ''
      Return
      End
    End
  n=i-1
  ct2.=0
  Do i=1 To n.1
    Do j=1 To n.2
      z=ct2.0+1
      ct2.z=e.1.i e.2.j
      ct2.0=z
      End
    End
  If n<3 Then
    Return output(2)
  ct3.=0
  Do i=1 To ct2.0
    Do k=1 To n.3
      z=ct3.0+1
      ct3.z=ct2.i e.3.k
      ct3.0=z
      End
    End
  If n<4 Then
    Return output(3)
  ct4.=0
  Do i=1 To ct3.0
    Do l=1 To n.4
      z=ct4.0+1
      ct4.z=ct3.i e.4.l
      ct4.0=z
      End
    End
  Return output(4)

output:
  Parse Arg u
  Do v=1 To value('ct'u'.0')
    res='{'translate(value('ct'u'.'v),',',' ')'}'
    Say res
    End
  Say ' '
  Return 0
Output:
{1, 2} x {3, 4}
{1,3}
{1,4}
{2,3}
{2,4}

{3, 4} x {1, 2}
{3,1}
{3,2}
{4,1}
{4,2}

{1, 2} x {}
{}

{} x {1, 2}
{}

{1776, 1789} x {7, 12} x {4, 14, 23} x {0, 1}
{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}

{1, 2, 3} x {30} x {500, 100}
{1,30,500}
{1,30,100}
{2,30,500}
{2,30,100}
{3,30,500}
{3,30,100}

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

Ring[edit]

# Project : Cartesian product of two or more lists

list1 = [[1,2],[3,4]]
list2 = [[3,4],[1,2]]
cartesian(list1)
cartesian(list2)

func cartesian(list1)
     for n = 1 to len(list1[1])
         for m = 1 to len(list1[2])
             see "(" + list1[1][n] + ", " + list1[2][m] + ")" + nl
         next
      next
      see nl

Output:

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

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

Ruby[edit]

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

p [1, 2].product([3, 4]) 
p [3, 4].product([1, 2])
p [1, 2].product([])
p [].product([1, 2]) 
p [1776, 1789].product([7, 12], [4, 14, 23], [0, 1])
p [1, 2, 3].product([30], [500, 100]) 
p [1, 2, 3].product([], [500, 100])
Output:
[[1, 3], [1, 4], [2, 3], [2, 4]]

[[3, 1], [3, 2], [4, 1], [4, 2]] [] [] [[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]] [[1, 30, 500], [1, 30, 100], [2, 30, 500], [2, 30, 100], [3, 30, 500], [3, 30, 100]] []

Rust[edit]

fn cartesian_product(lists: &Vec<Vec<u32>>) -> Vec<Vec<u32>> {
    let mut res = vec![];

    let mut list_iter = lists.iter();
    if let Some(first_list) = list_iter.next() {
        for &i in first_list {
            res.push(vec![i]);
        }
    }
    for l in list_iter {
        let mut tmp = vec![];
        for r in res {
            for &el in l {
                let mut tmp_el = r.clone();
                tmp_el.push(el);
                tmp.push(tmp_el);
            }
        }
        res = tmp;
    }
    res
}
 
fn main() {
    let cases = vec![
        vec![vec![1, 2], vec![3, 4]],
        vec![vec![3, 4], vec![1, 2]],
        vec![vec![1, 2], vec![]],
        vec![vec![], vec![1, 2]],
        vec![vec![1776, 1789], vec![7, 12], vec![4, 14, 23], vec![0, 1]],
        vec![vec![1, 2, 3], vec![30], vec![500, 100]],
        vec![vec![1, 2, 3], vec![], vec![500, 100]],
    ];
    for case in cases {
        println!(
            "{}\n{:?}\n",
            case.iter().map(|c| format!("{:?}", c)).collect::<Vec<_>>().join(" × "),
            cartesian_product(&case)
        )
    }
}
Output:
[1, 2] × [3, 4]

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

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

[1, 2] × [] []

[] × [1, 2] []

[1776, 1789] × [7, 12] × [4, 14, 23] × [0, 1] [[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]]

[1, 2, 3] × [30] × [500, 100] [[1, 30, 500], [1, 30, 100], [2, 30, 500], [2, 30, 100], [3, 30, 500], [3, 30, 100]]

[1, 2, 3] × [] × [500, 100] []

Scala[edit]

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

def cartesianProduct[T](lst: List[T]*): List[List[T]] = {

  /**
    * Prepend single element to all lists of list
    * @param e single elemetn
    * @param ll list of list
    * @param a accumulator for tail recursive implementation
    * @return list of lists with prepended element e
    */
  def pel(e: T,
          ll: List[List[T]],
          a: List[List[T]] = Nil): List[List[T]] =
    ll match {
      case Nil => a.reverse
      case x :: xs => pel(e, xs, (e :: x) :: a )
    }

  lst.toList match {
    case Nil => Nil
    case x :: Nil => List(x)
    case x :: _ =>
      x match {
        case Nil => Nil
        case _ =>
          lst.par.foldRight(List(x))( (l, a) =>
            l.flatMap(pel(_, a))
          ).map(_.dropRight(x.size))
      }
  }
}

and usage:

cartesianProduct(List(1, 2), List(3, 4))
  .map(_.mkString("(", ", ", ")")).mkString("{",", ","}")
Output:
{(1, 3), (1, 4), (2, 3), (2, 4)}
cartesianProduct(List(3, 4), List(1, 2))
  .map(_.mkString("(", ", ", ")")).mkString("{",", ","}")
Output:
{(3, 1), (3, 2), (4, 1), (4, 2)}
cartesianProduct(List(1, 2), List.empty)
  .map(_.mkString("(", ", ", ")")).mkString("{",", ","}")
Output:
{}
cartesianProduct(List.empty, List(1, 2))
  .map(_.mkString("(", ", ", ")")).mkString("{",", ","}")
Output:
{}
cartesianProduct(List(1776, 1789), List(7, 12), List(4, 14, 23), List(0, 1))
  .map(_.mkString("(", ", ", ")")).mkString("{",", ","}")
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)}
cartesianProduct(List(1, 2, 3), List(30), List(500, 100))
  .map(_.mkString("(", ", ", ")")).mkString("{",", ","}")
Output:
{(1, 30, 500), (1, 30, 100), (2, 30, 500), (2, 30, 100), (3, 30, 500), (3, 30, 100)}
cartesianProduct(List(1, 2, 3), List.empty, List(500, 100))
  .map(_.mkString("[", ", ", "]")).mkString("\n")
Output:
{}

Scheme[edit]

(define cartesian-product (lambda (xs ys)
 (if (or (zero? (length xs)) (zero? (length ys)))
     '()
     (fold append (map (lambda (x) (map (lambda (y) (list x y)) ys)) xs)))))

(define nary-cartesian-product (lambda (ls)
 (if (fold (lambda (a b) (or a b)) (map (compose zero? length) ls))
     '()
     (map flatten (fold cartesian-product ls)))))

> (cartesian-product '(1 2) '(3 4))
((1 3) (1 4) (2 3) (2 4))
> (cartesian-product '(3 4) '(1 2))
((3 1) (3 2) (4 1) (4 2))
> (cartesian-product '(1 2) '())
()
> (cartesian-product '() '(1 2))
()
> (nary-cartesian-product '((1 2)(a b)(x y)))
((1 a x) (1 a y) (1 b x) (1 b y) (2 a x) (2 a y) (2 b x) (2 b y))

Sidef[edit]

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

cartesian([[1,2], [3,4], [5,6]]).say
cartesian([[1,2], [3,4], [5,6]], {|*arr| say arr })

Alternatively, a simple recursive implementation:

func cartesian_product(*arr) {

    var c = []
    var r = []

    func {
        if (c.len < arr.len) {
            for item in (arr[c.len]) {
                c.push(item)
                __FUNC__()
                c.pop
            }
        }
        else {
            r.push([c...])
        }
    }()

    return r
}

Completing the task:

say cartesian_product([1,2], [3,4])
say cartesian_product([3,4], [1,2])
Output:
[[1, 3], [1, 4], [2, 3], [2, 4]]
[[3, 1], [3, 2], [4, 1], [4, 2]]

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

say cartesian_product([1,2], [])
say cartesian_product([], [1,2])
Output:
[]
[]

Extra credit:

cartesian_product([1776, 1789], [7, 12], [4, 14, 23], [0, 1]).each{ .say }
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]
say cartesian_product([1, 2, 3], [30], [500, 100])
say cartesian_product([1, 2, 3], [], [500, 100])
Output:
[[1, 30, 500], [1, 30, 100], [2, 30, 500], [2, 30, 100], [3, 30, 500], [3, 30, 100]]
[]

SQL[edit]

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

-- set up list 1
create table L1 (value integer);
insert into L1 values (1);
insert into L1 values (2);
-- set up list 2
create table L2 (value integer);
insert into L2 values (3);
insert into L2 values (4);
-- get the product
select * from L1, L2;
Output:
     VALUE      VALUE
---------- ----------
         1          3
         1          4
         2          3
         2          4
You should be able to be more explicit should get the same result:
select * from L1 cross join L2;

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

delete from L2;
select * from L1, L2;
Output:
no rows selected
I don't think "extra credit" is meaningful here because cartesian product is so hard-baked into SQL, so here's just one of the extra credit examples (again using the tables created above):
insert into L1 values (3);
insert into L2 values (30);
create table L3 (value integer);
insert into L3 values (500);
insert into L3 values (100);
-- product works the same for as many "lists" as you'd like
select * from L1, L2, L3;
Output:
     VALUE      VALUE      VALUE
---------- ---------- ----------
         1         30        500
         2         30        500
         3         30        500
         1         30        100
         2         30        100
         3         30        100

Standard ML[edit]

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

fun naryProdList zs = foldl (fn (xs, ys) => map op:: (prodList (xs, ys))) [[]] (rev zs)
Output:
- prodList ([1, 2], [3, 4]);
val it = [(1,3),(1,4),(2,3),(2,4)] : (int * int) list
- prodList ([3, 4], [1, 2]);
val it = [(3,1),(3,2),(4,1),(4,2)] : (int * int) list
- prodList ([1, 2], []);
stdIn:8.1-8.22 Warning: type vars not generalized because of
   value restriction are instantiated to dummy types (X1,X2,...)
val it = [] : (int * ?.X1) list
- naryProdList [[1776, 1789], [7, 12], [4, 14, 23], [0, 1]];
val it =
  [[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]]
  : int list list
- naryProdList [[1, 2, 3], [30], [500, 100]];
val it = [[1,30,500],[1,30,100],[2,30,500],[2,30,100],[3,30,500],[3,30,100]]
  : int list list
- naryProdList [[1, 2, 3], [], [500, 100]];
val it = [] : int list list

Stata[edit]

In Stata, the command 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.

. list

     +-------+
     | a   b |
     |-------|
  1. | 1   3 |
  2. | 2   4 |
     +-------+

. fillin a b
. list

     +-----------------+
     | a   b   _fillin |
     |-----------------|
  1. | 1   3         0 |
  2. | 1   4         1 |
  3. | 2   3         1 |
  4. | 2   4         0 |
     +-----------------+

The other way around:

. list

     +-------+
     | a   b |
     |-------|
  1. | 3   1 |
  2. | 4   2 |
     +-------+

. fillin a b
. list

     +-----------------+
     | a   b   _fillin |
     |-----------------|
  1. | 3   1         0 |
  2. | 3   2         1 |
  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).

. list

     +-------+
     | a   b |
     |-------|
  1. | 1   . |
  2. | 2   . |
     +-------+

. fillin a b
. list

     +-----------------+
     | a   b   _fillin |
     |-----------------|
  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.

. list

     +-----------+
     | a   b   c |
     |-----------|
  1. | 1   4   6 |
  2. | 2   5   . |
  3. | 3   .   . |
     +-----------+

. fillin a b c
. list

     +---------------------+
     | a   b   c   _fillin |
     |---------------------|
  1. | 1   4   6         0 |
  2. | 1   4   .         1 |
  3. | 1   5   6         1 |
  4. | 1   5   .         1 |
  5. | 1   .   6         1 |
     |---------------------|
  6. | 1   .   .         1 |
  7. | 2   4   6         1 |
  8. | 2   4   .         1 |
  9. | 2   5   6         1 |
 10. | 2   5   .         0 |
     |---------------------|
 11. | 2   .   6         1 |
 12. | 2   .   .         1 |
 13. | 3   4   6         1 |
 14. | 3   4   .         1 |
 15. | 3   5   6         1 |
     |---------------------|
 16. | 3   5   .         1 |
 17. | 3   .   6         1 |
 18. | 3   .   .         0 |
     +---------------------+

. foreach var of varlist _all {
          quietly drop if missing(`var')
  }

. list

     +---------------------+
     | a   b   c   _fillin |
     |---------------------|
  1. | 1   4   6         0 |
  2. | 1   5   6         1 |
  3. | 2   4   6         1 |
  4. | 2   5   6         1 |
  5. | 3   4   6         1 |
     |---------------------|
  6. | 3   5   6         1 |
     +---------------------+

Swift[edit]

Translation of: Scala
func + <T>(el: T, arr: [T]) -> [T] {
  var ret = arr

  ret.insert(el, at: 0)

  return ret
}

func cartesianProduct<T>(_ arrays: [T]...) -> [[T]] {
  guard let head = arrays.first else {
    return []
  }

  let first = Array(head)

  func pel(
    _ el: T,
    _ ll: [[T]],
    _ a: [[T]] = []
  ) -> [[T]] {
    switch ll.count {
    case 0:
      return a.reversed()
    case _:
      let tail = Array(ll.dropFirst())
      let head = ll.first!

      return pel(el, tail, el + head + a)
    }
  }

  return arrays.reversed()
    .reduce([first], {res, el in el.flatMap({ pel($0, res) }) })
    .map({ $0.dropLast(first.count) })
}


print(cartesianProduct([1, 2], [3, 4]))
print(cartesianProduct([3, 4], [1, 2]))
print(cartesianProduct([1, 2], []))
print(cartesianProduct([1776, 1789], [7, 12], [4, 14, 23], [0, 1]))
print(cartesianProduct([1, 2, 3], [30], [500, 100]))
print(cartesianProduct([1, 2, 3], [], [500, 100])
Output:
[[1, 3], [1, 4], [2, 3], [2, 4]]
[[3, 1], [3, 2], [4, 1], [4, 2]]
[]
[[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]]
[[1, 30, 500], [1, 30, 100], [2, 30, 500], [2, 30, 100], [3, 30, 500], [3, 30, 100]]
[]

Tailspin[edit]

'{1,2}x{3,4} = $:[by [1,2]..., by [3,4]...];
' -> !OUT::write

'{3,4}x{1,2} = $:[by [3,4]..., by [1,2]...];
' -> !OUT::write

'{1,2}x{} = $:[by [1,2]..., by []...];
' -> !OUT::write

'{}x{1,2} = $:[by []..., by [1,2]...];
' -> !OUT::write

'{1776, 1789} × {7, 12} × {4, 14, 23} × {0, 1} = $:[by [1776, 1789]..., by [7, 12]..., by [4, 14, 23]..., by [0, 1]...];
' -> !OUT::write

'{1, 2, 3} × {30} × {500, 100} = $:[by [1, 2, 3] ..., by [30]..., by [500, 100]...];
' -> !OUT::write

'{1, 2, 3} × {} × {500, 100} = $:[by [1, 2, 3]..., by []..., by [500, 100]...];
' -> !OUT::write

// You can also generate structures with named fields
'year {1776, 1789} × month {7, 12} × day {4, 14, 23} = $:{by [1776, 1789]... -> (year:$), by [7, 12]... -> (month:$), by [4, 14, 23]... -> (day:$)};
' -> !OUT::write
Output:
{1,2}x{3,4} = [1, 3][2, 3][1, 4][2, 4]
{3,4}x{1,2} = [3, 1][4, 1][3, 2][4, 2]
{1,2}x{} = 
{}x{1,2} = 
{1776, 1789} × {7, 12} × {4, 14, 23} × {0, 1} = [1776, 7, 4, 0][1789, 7, 4, 0][1776, 12, 4, 0][1789, 12, 4, 0][1776, 7, 14, 0][1789, 7, 14, 0][1776, 12, 14, 0][1789, 12, 14, 0][1776, 7, 23, 0][1789, 7, 23, 0][1776, 12, 23, 0][1789, 12, 23, 0][1776, 7, 4, 1][1789, 7, 4, 1][1776, 12, 4, 1][1789, 12, 4, 1][1776, 7, 14, 1][1789, 7, 14, 1][1776, 12, 14, 1][1789, 12, 14, 1][1776, 7, 23, 1][1789, 7, 23, 1][1776, 12, 23, 1][1789, 12, 23, 1]
{1, 2, 3} × {30} × {500, 100} = [1, 30, 500][2, 30, 500][3, 30, 500][1, 30, 100][2, 30, 100][3, 30, 100]
{1, 2, 3} × {} × {500, 100} = 
year {1776, 1789} × month {7, 12} × day {4, 14, 23} = {day=4, month=7, year=1776}{day=4, month=7, year=1789}{day=4, month=12, year=1776}{day=4, month=12, year=1789}{day=14, month=7, year=1776}{day=14, month=7, year=1789}{day=14, month=12, year=1776}{day=14, month=12, year=1789}{day=23, month=7, year=1776}{day=23, month=7, year=1789}{day=23, month=12, year=1776}{day=23, month=12, year=1789}

Tcl[edit]

proc cartesianProduct {l1 l2} {
  set result {}
  foreach el1 $l1 {
    foreach el2 $l2 {
      lappend result [list $el1 $el2]
    }
  }
  return $result
}

puts "simple"
puts "result: [cartesianProduct {1 2} {3 4}]"
puts "result: [cartesianProduct {3 4} {1 2}]"
puts "result: [cartesianProduct {1 2} {}]"
puts "result: [cartesianProduct {} {3 4}]"

proc cartesianNaryProduct {lists} {
  set result {{}}
  foreach l $lists {
    set res {}
    foreach comb $result {
      foreach el $l {
        lappend res [linsert $comb end $el]
      }
    }
    set result $res
  }
  return $result
}

puts "n-ary"
puts "result: [cartesianNaryProduct {{1776 1789} {7 12} {4 14 23} {0 1}}]"
puts "result: [cartesianNaryProduct {{1 2 3} {30} {500 100}}]"
puts "result: [cartesianNaryProduct {{1 2 3} {} {500 100}}]"
Output:
simple
result: {1 3} {1 4} {2 3} {2 4}
result: {3 1} {3 2} {4 1} {4 2}
result: 
result: 
n-ary
result: {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}
result: {1 30 500} {1 30 100} {2 30 500} {2 30 100} {3 30 500} {3 30 100}
result: 

UNIX Shell[edit]

The UNIX shells don't allow passing or returning arrays from functions (other than pass-by-name shenanigans), but as pointed out in the Perl entry, wildcard brace expansion (in bash, ksh, zsh) does a Cartesian product if there's more than one set of alternatives. It doesn't handle the empty-list case (an empty brace expansion item is treated as a single item that is equal to the empty string), but otherwise it works:

   $ printf '%s' "("{1,2},{3,4}")"; printf '\n'
   (1,3)(1,4)(2,3)(2,4)
   $ printf '%s' "("{3,4},{1,2}")"; printf '\n'
   (3,1)(3,2)(4,1)(4,2)

More than two lists is not a problem:

   $ printf '%s\n' "("{1776,1789},{7,12},{4,14,23},{0,1}")"
   (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)
   $ printf '%s\n' "("{1,2,3},30,{500,100}")"
   (1,30,500)
   (1,30,100)
   (2,30,500)
   (2,30,100)
   (3,30,500)
   (3,30,100)

Visual Basic .NET[edit]

Translation of: C#
Imports System.Runtime.CompilerServices

Module Module1

    <Extension()>
    Function CartesianProduct(Of T)(sequences As IEnumerable(Of IEnumerable(Of T))) As IEnumerable(Of IEnumerable(Of T))
        Dim emptyProduct As IEnumerable(Of IEnumerable(Of T)) = {Enumerable.Empty(Of T)}
        Return sequences.Aggregate(emptyProduct, Function(accumulator, sequence) From acc In accumulator From item In sequence Select acc.Concat({item}))
    End Function

    Sub Main()
        Dim empty(-1) As Integer
        Dim list1 = {1, 2}
        Dim list2 = {3, 4}
        Dim list3 = {1776, 1789}
        Dim list4 = {7, 12}
        Dim list5 = {4, 14, 23}
        Dim list6 = {0, 1}
        Dim list7 = {1, 2, 3}
        Dim list8 = {30}
        Dim list9 = {500, 100}

        For Each sequnceList As Integer()() In {
            ({list1, list2}),
            ({list2, list1}),
            ({list1, empty}),
            ({empty, list1}),
            ({list3, list4, list5, list6}),
            ({list7, list8, list9}),
            ({list7, empty, list9})
        }
            Dim cart = sequnceList.CartesianProduct().Select(Function(tuple) $"({String.Join(", ", tuple)})")
            Console.WriteLine($"{{{String.Join(", ", cart)}}}")
        Next
    End Sub

End Module
Output:
{(1, 3), (1, 4), (2, 3), (2, 4)}
{(3, 1), (3, 2), (4, 1), (4, 2)}
{}
{}
{(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)}
{(1, 30, 500), (1, 30, 100), (2, 30, 500), (2, 30, 100), (3, 30, 500), (3, 30, 100)}
{}

Wren[edit]

Translation of: Kotlin
Library: Wren-seq
import "/seq" for Lst

var prod2 = Fn.new { |l1, l2|
    var res = []
    for (e1 in l1) {
        for (e2 in l2) res.add([e1, e2])
    }
    return res
}

var prodN = Fn.new { |ll|
    if (ll.count < 2) Fiber.abort("There must be at least two lists.")
    var p2 = prod2.call(ll[0], ll[1])
    return ll.skip(2).reduce(p2) { |acc, l| prod2.call(acc, l) }.map { |l| Lst.flatten(l) }.toList
}

var printProdN = Fn.new { |ll|
    System.print("%(ll.join(" x ")) = ")
    System.write("[\n    ")
    System.print(prodN.call(ll).join("\n    "))
    System.print("]\n")
}

System.print("[1, 2] x [3, 4] = %(prodN.call([ [1, 2], [3, 4] ]))")
System.print("[3, 4] x [1, 2] = %(prodN.call([ [3, 4], [1, 2] ]))")
System.print("[1, 2] x []     = %(prodN.call([ [1, 2], [] ]))")
System.print("[]     x [1, 2] = %(prodN.call([ [], [1, 2] ]))")
System.print("[1, a] x [2, b] = %(prodN.call([ [1, "a"], [2, "b"] ]))")
System.print()
printProdN.call([ [1776, 1789], [7, 12], [4, 14, 23], [0, 1] ])
printProdN.call([ [1, 2, 3], [30], [500, 100] ])
printProdN.call([ [1, 2, 3], [], [500, 100] ])
printProdN.call([ [1, 2, 3], [30], ["a", "b"] ])
Output:
[1, 2] x [3, 4] = [[1, 3], [1, 4], [2, 3], [2, 4]]
[3, 4] x [1, 2] = [[3, 1], [3, 2], [4, 1], [4, 2]]
[1, 2] x []     = []
[]     x [1, 2] = []
[1, a] x [2, b] = [[1, 2], [1, b], [a, 2], [a, b]]

[1776, 1789] x [7, 12] x [4, 14, 23] x [0, 1] = 
[
    [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]
]

[1, 2, 3] x [30] x [500, 100] = 
[
    [1, 30, 500]
    [1, 30, 100]
    [2, 30, 500]
    [2, 30, 100]
    [3, 30, 500]
    [3, 30, 100]
]

[1, 2, 3] x [] x [500, 100] = 
[
    
]

[1, 2, 3] x [30] x [a, b] = 
[
    [1, 30, a]
    [1, 30, b]
    [2, 30, a]
    [2, 30, b]
    [3, 30, a]
    [3, 30, b]
]

zkl[edit]

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

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

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

The walk method will throw an error if used on an empty iterator but the pump method doesn't.

zkl: Walker.cproduct(List(3,4),List).walk().println();
Exception thrown: TheEnd(Ain't no more)

zkl: Walker.cproduct(List(3,4),List).pump(List).println();
L()
zkl: Walker.cproduct(List,List(3,4)).pump(List).println();
L()
zkl: Walker.cproduct(L(1776,1789),L(7,12),L(4,14,23),L(0,1)).walk().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),L(30),L(500,100)).walk().println();
L(L(1,30,500),L(1,30,100),L(2,30,500),L(2,30,100),L(3,30,500),L(3,30,100))

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