Create a type list combination of types in C++

Question

Im trying to create some tool to create a list of types based on combinations of other types.

Lets say we have three types

struct A{};
struct B{};
struct C{};

I want to get a list of tuples which has every possible combination of N types A,B or C.

For a N=2 case, this would be

std::tuple<A,A>
std::tuple<A,B>
std::tuple<A,C>
std::tuple<B,A>
std::tuple<B,B>
std::tuple<B,C>
std::tuple<C,A>
std::tuple<C,B>
std::tuple<C,C>

The idea is to create a tuple which holds a container for all those types, so I can later store any of those types inside the container list.

template <typename ...Combinations>
using CombinationList = std::tuple<std::vector<Combinations>...>;

I already have a mechanism to inserting a particupar element inside the container in which it fits, but I have no clue on how to create the combinatios.

On the comments people has suggestes using std::vector<Combination<std::variant<A,C,B>, std::variant<A,B,C>>>. Althought this technically solve the problem, I prefer not to use it, as A, B C and has very different sizes and I dont want to visit the variants at runtime. Also, at some point I will need to upload the all the data in the containers in

std::tuple<std::vector<Combination>...>

to the GPU, so I cant use std::variant here.

How could I do this?

Thanks!

PD: This is related to this question Combination explosion of an enum value (729 combinations...) In that question I asked how I could generate easily the types that would go inside the container. Now I need to generate the containers .

Answer 1

I already have a mechanism to inserting a particupar element inside the container in which it fits, but I have no clue on how to create the combinatios.

Suppose you have a list of types (say A, B, C) and an unsigned integer N, I propose a using

template <std::size_t N, typename ... Ts>
using Combinations = ???

that is defined as a std::tuple containing a list of std::tuples with all combinations.

So, by example,

Combinations<2u, A, B, C>

become

  std::tuple<
      std::tuple<A,A>, std::tuple<A,B>, std::tuple<A,C>,
      std::tuple<B,A>, std::tuple<B,B>, std::tuple<B,C>,
      std::tuple<C,A>, std::tuple<C,B>, std::tuple<C,C>>

The following is a full compiling C++11 example

#include <tuple>
#include <vector>
#include <type_traits>

struct A {};
struct B {};
struct C {};

template <typename T, typename ... Ts>
constexpr std::tuple<T, Ts...> addTupleType (std::tuple<Ts...>);

template <typename T, typename ... Ts>
constexpr auto addType ()
   -> std::tuple<decltype(addTupleType<T>(std::declval<Ts>()))...>;

template <typename ... Ts, typename ... Us>
constexpr auto getCombinations (std::integral_constant<std::size_t, 0u>,
                                std::tuple<Ts...> t, std::tuple<Us ...> u)
   -> decltype( u );

template <std::size_t N, typename ... Ts, typename ... Us,
          typename std::enable_if<(N > 0u), bool>::type = true>
constexpr auto getCombinations (std::integral_constant<std::size_t, N>,
                                std::tuple<Ts...> t, std::tuple<Us ...>)
   -> decltype (getCombinations(
         std::integral_constant<std::size_t, N-1u>{}, t,
         std::tuple_cat(addType<Ts, Us...>()...)));

template <std::size_t N, typename ... Ts>
using Combinations
   = decltype(getCombinations(
         std::integral_constant<std::size_t, N-1u>{},
         std::declval<std::tuple<Ts...>>(),
         std::declval<std::tuple<std::tuple<Ts>...>>()));

template <typename ... Ts>
constexpr auto CombListHelper (std::tuple<Ts...>)
   -> std::tuple<std::vector<Ts>...>;

template <typename T>
using CombinationList = decltype(CombListHelper(std::declval<T>()));


int main()
 {
   using type_1 = Combinations<2u, A, B, C>;
   using type_2 = std::tuple<
      std::tuple<A,A>, std::tuple<A,B>, std::tuple<A,C>,
      std::tuple<B,A>, std::tuple<B,B>, std::tuple<B,C>,
      std::tuple<C,A>, std::tuple<C,B>, std::tuple<C,C>>;

   static_assert( std::is_same<type_1, type_2>::value, "!" );

   using type_3 = CombinationList<Combinations<2u, A, B, C>>;
   using type_4 = std::tuple<
      std::vector<std::tuple<A,A>>, std::vector<std::tuple<A,B>>,
      std::vector<std::tuple<A,C>>, std::vector<std::tuple<B,A>>,
      std::vector<std::tuple<B,B>>, std::vector<std::tuple<B,C>>,
      std::vector<std::tuple<C,A>>, std::vector<std::tuple<C,B>>,
      std::vector<std::tuple<C,C>>>;

   static_assert( std::is_same<type_3, type_4>::value, "!" );
 }

Answer 2

Using the analogy with storing two dimensional matrix in linear storage, all possible pairs of A, B and C are labeled by one dimensional integers 0,1,...,8 like this:

0 -> (0/3, 0%3) = (0,0) -> std::tuple<A,A>
1 -> (1/3, 1%3) = (0,1) -> std::tuple<A,B>
...
8 -> (8/3, 8%3) = (2,2) -> std::tuple<C,C>

Thus we can construct the list of pairs as follows. These functions work in C++14 and over. For instance, Combinations<A,B,C>::types is equal to std::tuple<std::vector<std::tuple<A,A>>, std::vector<std::tuple<A,B>>, ...>:

Live DEMO

template<std::size_t I, typename Tuple>
struct make_pair_vector
{
    static constexpr std::size_t  left_index = I/std::tuple_size<Tuple>::value;
    static constexpr std::size_t right_index = I%std::tuple_size<Tuple>::value;

    using type = std::vector<
                    std::tuple<typename std::tuple_element< left_index, Tuple>::type,
                               typename std::tuple_element<right_index, Tuple>::type>>;
};

template <typename T, typename Is>
struct make_combinations;

template <typename Tuple, std::size_t... Is>
struct make_combinations<Tuple, std::index_sequence<Is...>>
{
    using tuples = std::tuple<typename make_pair_vector<Is, Tuple>::type...>;
};

template<typename ...Args>
struct Combinations
{
    using types = typename make_combinations
                    <std::tuple<Args...>,
                     std::make_index_sequence<(sizeof...(Args))*(sizeof...(Args))>>
                    ::tuples;
};