Traits class to extract container's value_type from a back_insert_iterator

The answer by @Rapptz is correct but for generic code (i.e. when it is not clear a priori whether one deals with a raw T* or a back_insert_iterator or one of the Standard Library's other output iterators), a more systematic approach is necessary.

To that effect, below a definition of a class template output_iterator_traits in a user-defined namespace xstd.

#include <iterator>             // iterator, iterator_traits, input_iterator_tag, output_iterator_tag, random_access_iterator_tag
                                // back_insert_iterator, front_insert_iterator, insert_iterator, ostream_iterator, ostreambuf_iterator
#include <memory>               // raw_storage_iterator

namespace xstd {

template<class T>
struct output_iterator_traits
:
        std::iterator_traits<T>
{};

template< class OutputIt, class T>
struct output_iterator_traits<std::raw_storage_iterator<OutputIt, T>>
:
        std::iterator<std::output_iterator_tag, T>
{};

template<class Container>
struct output_iterator_traits<std::back_insert_iterator<Container>>
:
        std::iterator<std::output_iterator_tag, typename Container::value_type>
{};

template<class Container>
struct output_iterator_traits<std::front_insert_iterator<Container>>
:
        std::iterator<std::output_iterator_tag, typename Container::value_type>
{};

template<class Container>
struct output_iterator_traits<std::insert_iterator<Container>>
:
        std::iterator<std::output_iterator_tag, typename Container::value_type>
{};

template <class T, class charT, class traits>
struct output_iterator_traits<std::ostream_iterator<T, charT, traits>>
:
        std::iterator<std::output_iterator_tag, T>
{};

template <class charT, class traits>
struct output_iterator_traits<std::ostreambuf_iterator<charT, traits>>
:
        std::iterator<std::output_iterator_tag, charT>
{};

} // namespace xstd

The unspecialized version simply inherits from std::iterator_traits<T>, but for the 6 output iterators defined in the <iterator> and <memory> headers, the specializations inherit from std::iterator<std::output_iterator_tag, V> where V is the type appearing as an argument of the iterator's operator=(const V&).

For the insert iterators, this corresponds to typename Container::value_type, for raw storage iterators to T, and for ostream and ostreambuf iterators to T and charT, respectively.

A generic algorithm of the form

template<class InputIt, class OutputIt>
auto my_fancy_algorithm(InputIt first, InputIt last, OutputIt dest)
{
     using T = typename xstd::output_iterator_traits<OutputIt>::value_type;
     for (; first != last; ++first) {
         // ... construct arguments from *first
         *dest++ = T{ /* arguments */ };
     }
}

will then transparantly work with both raw pointers and the Standard Library's output iterators.

You could just use container_type that it has:

#include <iterator>
#include <type_traits>
#include <vector>

template<typename T>
struct outit_v {
    using container_type = typename T::container_type;
    using value_type = typename container_type::value_type;
};

int main()
{
    std::vector<int> v;
    auto it = std::back_inserter(v);
    static_assert(std::is_same<outit_v<decltype(it)>::value_type, int>::value, "");
}

Live Example