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.

In many situations we will need to list some elements by their order.

Cartesian product of sets Cartesian product of sets A and B is denoted by A x B.
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. In Sidef, the Cartesian product of an arbitrary number of arrays is built-in as The product of an empty list with any other list is empty: method doesn't.

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

A cartesian product is an unordered collection of ordered collections. Product with an empty list works as expected (using the tables created above): B x A is the set of all possible ordered pairs between the elements of A and B such that the first coordinate is an element of B and the second coordinate is an element of A. This being Perl, there's more than one way to do it. It produces the same result as cartN above. result is an empty 3-dimensional array with shape 3 0 2// CARTESIAN PRODUCT OF TWO LISTS ---------------------// TEST -----------------------------------------------// CARTESIAN PRODUCT OF TWO LISTS ---------------------// GENERIC FUNCTIONS ----------------------------------// --> [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.// TEST -----------------------------------------------// TEST -------------------------------------------// GENERIC FUNCTIONS ----------------------------------// GENERIC FUNCTIONS ------------------------------------------------------// TEST -------------------------------------------------------------------"[] x [1, 2] = ${listOf() * listOf(1, 2)}""[1, a] x [2, b] = ${listOf(1, 'a') * listOf(2, 'b')}"--[[ 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(* If there is a way to create an empty array, I do not know of it *)(*- : (int * int) list = [(1, 3); (1, 4); (2, 3); (2, 4)]*)(*- : (int * int) list = [(3, 1); (3, 2); (4, 1); (4, 2)]*)(*- : (int * int) list = [(1, 4); (2, 4); (2, 3); (1, 3)]*)(*- : (int * int) list = [(3, 2); (4, 2); (4, 1); (3, 1)]*)(*- : (int * char) list = [(3, 'c'); (3, 'b'); (3, 'a'); (2, 'c'); (2, 'b'); (2, 'a'); (1, 'c'); (1, 'b'); (1, 'a')]*)(* We need to do the cross product of our current list and all the others(*- : int list list = [[1; 4]; [2; 4]; [2; 3]; [1; 3]]*)(*- : int list list = [[3; 2]; [4; 2]; [4; 1]; [3; 1]]*)(* We need to do the cross product of our current list and all the others# nAryCartProd :: [[a], [b], [c] ...] -> [(a, b, c ...)]# nAryCartProd :: [[a], [b], [c] ...] -> [(a, b, c ...)]# GENERIC -------------------------------------------------# TEST ----------------------------------------------------# cartesian product of two lists using the X cross meta-operator# cartesian product of variable number of lists using/*REXX program calculates the Cartesian product of two arbitrary-sized lists.

Recursive implementation for computing the Cartesian product of lists.

This is a compact recursive version like Extra credit 2 but the result list is ordered differently.
For the sake of brevity, two illustrations should suffice:

Verify thatC = {2}   2 is the one and only even prime number. 3:18. AxBxC 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. Find A x B and B x A and show that A x B ≠ B x A. In detail, a set should not be able to contain the same element multiple times, but the tuples in the return value are able to, so they shouldn't be stored in a type named Integer_Set. 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). result is 4 dimensional array with shape 2 2 3 2NB.
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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.

In many situations we will need to list some elements by their order.

Cartesian product of sets Cartesian product of sets A and B is denoted by A x B.
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. In Sidef, the Cartesian product of an arbitrary number of arrays is built-in as The product of an empty list with any other list is empty: method doesn't.

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

A cartesian product is an unordered collection of ordered collections. Product with an empty list works as expected (using the tables created above): B x A is the set of all possible ordered pairs between the elements of A and B such that the first coordinate is an element of B and the second coordinate is an element of A. This being Perl, there's more than one way to do it. It produces the same result as cartN above. result is an empty 3-dimensional array with shape 3 0 2// CARTESIAN PRODUCT OF TWO LISTS ---------------------// TEST -----------------------------------------------// CARTESIAN PRODUCT OF TWO LISTS ---------------------// GENERIC FUNCTIONS ----------------------------------// --> [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.// TEST -----------------------------------------------// TEST -------------------------------------------// GENERIC FUNCTIONS ----------------------------------// GENERIC FUNCTIONS ------------------------------------------------------// TEST -------------------------------------------------------------------"[] x [1, 2] = ${listOf() * listOf(1, 2)}""[1, a] x [2, b] = ${listOf(1, 'a') * listOf(2, 'b')}"--[[ 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(* If there is a way to create an empty array, I do not know of it *)(*- : (int * int) list = [(1, 3); (1, 4); (2, 3); (2, 4)]*)(*- : (int * int) list = [(3, 1); (3, 2); (4, 1); (4, 2)]*)(*- : (int * int) list = [(1, 4); (2, 4); (2, 3); (1, 3)]*)(*- : (int * int) list = [(3, 2); (4, 2); (4, 1); (3, 1)]*)(*- : (int * char) list = [(3, 'c'); (3, 'b'); (3, 'a'); (2, 'c'); (2, 'b'); (2, 'a'); (1, 'c'); (1, 'b'); (1, 'a')]*)(* We need to do the cross product of our current list and all the others(*- : int list list = [[1; 4]; [2; 4]; [2; 3]; [1; 3]]*)(*- : int list list = [[3; 2]; [4; 2]; [4; 1]; [3; 1]]*)(* We need to do the cross product of our current list and all the others# nAryCartProd :: [[a], [b], [c] ...] -> [(a, b, c ...)]# nAryCartProd :: [[a], [b], [c] ...] -> [(a, b, c ...)]# GENERIC -------------------------------------------------# TEST ----------------------------------------------------# cartesian product of two lists using the X cross meta-operator# cartesian product of variable number of lists using/*REXX program calculates the Cartesian product of two arbitrary-sized lists.

Recursive implementation for computing the Cartesian product of lists.

This is a compact recursive version like Extra credit 2 but the result list is ordered differently.
For the sake of brevity, two illustrations should suffice:

Verify thatC = {2}   2 is the one and only even prime number. 3:18. AxBxC 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. Find A x B and B x A and show that A x B ≠ B x A. In detail, a set should not be able to contain the same element multiple times, but the tuples in the return value are able to, so they shouldn't be stored in a type named Integer_Set. 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). result is 4 dimensional array with shape 2 2 3 2NB.
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cartesian product of 3 sets calculator


Note that the set elements are still ordered lists. Racket has a built-in "cartesian-product" function: Code here is more compact, but with the cost of more garbage produced. The cross product (Cartesian Product) is a vector product which yields another vector rather than a scalar.

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.

In many situations we will need to list some elements by their order.

Cartesian product of sets Cartesian product of sets A and B is denoted by A x B.
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. In Sidef, the Cartesian product of an arbitrary number of arrays is built-in as The product of an empty list with any other list is empty: method doesn't.

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

A cartesian product is an unordered collection of ordered collections. Product with an empty list works as expected (using the tables created above): B x A is the set of all possible ordered pairs between the elements of A and B such that the first coordinate is an element of B and the second coordinate is an element of A. This being Perl, there's more than one way to do it. It produces the same result as cartN above. result is an empty 3-dimensional array with shape 3 0 2// CARTESIAN PRODUCT OF TWO LISTS ---------------------// TEST -----------------------------------------------// CARTESIAN PRODUCT OF TWO LISTS ---------------------// GENERIC FUNCTIONS ----------------------------------// --> [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.// TEST -----------------------------------------------// TEST -------------------------------------------// GENERIC FUNCTIONS ----------------------------------// GENERIC FUNCTIONS ------------------------------------------------------// TEST -------------------------------------------------------------------"[] x [1, 2] = ${listOf() * listOf(1, 2)}""[1, a] x [2, b] = ${listOf(1, 'a') * listOf(2, 'b')}"--[[ 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(* If there is a way to create an empty array, I do not know of it *)(*- : (int * int) list = [(1, 3); (1, 4); (2, 3); (2, 4)]*)(*- : (int * int) list = [(3, 1); (3, 2); (4, 1); (4, 2)]*)(*- : (int * int) list = [(1, 4); (2, 4); (2, 3); (1, 3)]*)(*- : (int * int) list = [(3, 2); (4, 2); (4, 1); (3, 1)]*)(*- : (int * char) list = [(3, 'c'); (3, 'b'); (3, 'a'); (2, 'c'); (2, 'b'); (2, 'a'); (1, 'c'); (1, 'b'); (1, 'a')]*)(* We need to do the cross product of our current list and all the others(*- : int list list = [[1; 4]; [2; 4]; [2; 3]; [1; 3]]*)(*- : int list list = [[3; 2]; [4; 2]; [4; 1]; [3; 1]]*)(* We need to do the cross product of our current list and all the others# nAryCartProd :: [[a], [b], [c] ...] -> [(a, b, c ...)]# nAryCartProd :: [[a], [b], [c] ...] -> [(a, b, c ...)]# GENERIC -------------------------------------------------# TEST ----------------------------------------------------# cartesian product of two lists using the X cross meta-operator# cartesian product of variable number of lists using/*REXX program calculates the Cartesian product of two arbitrary-sized lists.

Recursive implementation for computing the Cartesian product of lists.

This is a compact recursive version like Extra credit 2 but the result list is ordered differently.
For the sake of brevity, two illustrations should suffice:

Verify thatC = {2}   2 is the one and only even prime number. 3:18. AxBxC 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. Find A x B and B x A and show that A x B ≠ B x A. In detail, a set should not be able to contain the same element multiple times, but the tuples in the return value are able to, so they shouldn't be stored in a type named Integer_Set. 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). result is 4 dimensional array with shape 2 2 3 2NB.

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