How to combine two or more vectors of arbitrary types in C++

Question

I've got the following code that combines two vectors of arbitrary types into a combinatorial, i.e. std::vector<std::tuple<A, B>>.

template<class A, class B>
std::vector<std::tuple<A, B>> combine(const std::vector<A>& a, const std::vector<B>& b) {

    const auto combine_parts_ = [](const A& x, const B& y) {
        auto result = std::tuple_cat(std::make_tuple(x), std::make_tuple(y));
        return result;
    };

    std::vector<std::tuple<A, B>> results;

    for (const auto& x : a) {
        for (const auto& y : b) {
            results.push_back(combine_parts_(x, y));
        }
    }

    return results;
}

However, I'm unclear how to extend that to an arbitrary number of types/vectors. I don't care about duplicate types; in fact there may be two or more sets of the same type involved. That's okay.

Some example use cases, for instance:

const auto combinations = combine(
    std::vector<int>({1,2,3})
    , std::vector<int>({1,2,3})
);
const auto combinations2 = combine(
    std::vector<int>({1,2,3})
    , std::vector<int>({1,2,3})
    , std::vector<bool>({true,false})
);
const auto combinations3 = combine(
    std::vector<int>({1,2,3})
    , std::vector<int>({1,2,3})
    , std::vector<bool>({true,false})
    , std::vector<char>({'a','b','c','d','e'})
);

Chiefly, what I want to do is avoid the ugly nested for loop. At the same time, I want to combine some unit testing combinatorial use cases in order to work with the resulting std::tuple<...> as the test case.

Note, I am not talking about permutations of a homogeneous set here. That's been a point of confusion from prior questions.

I think it might have something to do with templates, variadics, std::tuple_cat, somewhere along the way, but I don't know.

Thoughts? Suggestions?

Answer 1

If you want to compute the Cartesian product of heterogeneous vectors, you may do something like:

template <std::size_t N>
bool increase(const std::array<std::size_t, N>& sizes, std::array<std::size_t, N>& it)
{
    for (std::size_t i = 0; i != N; ++i) {
        const std::size_t index = N - 1 - i;
        ++it[index];
        if (it[index] >= sizes[index]) {
            it[index] = 0;
        } else {
            return true;
        }
    }
    return false;
}

template <typename F, std::size_t ... Is, std::size_t N, typename Tuple>
void apply_impl(F&& f,
                std::index_sequence<Is...>,
                const std::array<std::size_t, N>& it,
                const Tuple& tuple)
{
    f(std::get<Is>(tuple)[it[Is]]...);
}

template <typename F, typename ... Ts>
void cartesian_product_apply(F&& f, const std::vector<Ts>&... vs)
{
    constexpr std::size_t N = sizeof...(Ts);
    std::array<std::size_t, N> sizes{{vs.size()...}};
    std::array<std::size_t, N> it{};

    do {
        apply_impl(f, std::index_sequence_for<Ts...>(), it, std::tie(vs...));
    } while (increase(sizes, it));
}

And finally:

template <typename ... Ts>
std::vector<std::tuple<Ts...>> cartesian_product(const std::vector<Ts>&... vs)
{
    std::vector<std::tuple<Ts...>> res;

    cartesian_product_apply([&res](const auto&... args) { res.emplace_back(args...); },
                            vs...);
    return res;
}

With usage similar to:

std::vector<int> v1 = {1, 2, 3};
std::vector<std::string> v2 = {" A "," B "};
std::vector<int> v3 = {4, 5};

const auto res = cartesian_product(v1, v2, v3);
for (const auto& t : res) {
    // ...
}

Demo