Is there a way to check if a sequence container is contiguous in memory? Something like:
#include <iostream>
#include <vector>
#include <deque>
#include <array>
int main()
{
    std::cout << std::boolalpha;
    std::cout << is_contiguous<std::vector<int>>::value   << '\n'  // true
    std::cout << is_contiguous<std::deque<int>>::value    << '\n'; // false
    std::cout << is_contiguous<std::array<int, 3>>::value << '\n'; // true
}
Clarification
This question is referring to type traits, rather than the properties of a specific instance of a type.
No, there is not compiletime trait for this.
The draft C++1z Standard defines contiguity as a runtime property of an iterator range. Note there is no compiletime std::contiguous_iterator_tag corresponding to this iterator category.
24.2 Iterator requirements [iterator.requirements]
24.2.1 In general [iterator.requirements.general]
5 Iterators that further satisfy the requirement that, for integral values
nand dereferenceable iterator valuesaand(a + n), *(a + n)is equivalent to*(addressof(*a) + n), are called contiguous iterators. [ Note: For example, the type “pointer to int” is a contiguous iterator, butreverse_iterator<int *>is not. For a valid iterator range[a,b)with dereferenceablea, the corresponding range denoted by pointers is[addressof(*a),addressof(*a) + (b - a));bmight not be dereferenceable. — end note ]
One way to test for this at runtime would be
#include <array>
#include <deque>
#include <list>
#include <iostream>
#include <iterator>
#include <map>
#include <memory>
#include <string>
#include <unordered_set>
#include <vector>
template<class I>
auto is_contiguous(I first, I last)
{ 
    auto test = true;
    auto const n = std::distance(first, last);
    for (auto i = 0; i < n && test; ++i) {
        test &= *(std::next(first, i)) == *(std::next(std::addressof(*first), i));
    }        
    return test;        
}
int main()
{
    auto l = std::list<int> { 1, 2, 3 };
    auto m = std::map<int, int>  { {1, 1}, {2,2}, {3,3} };
    auto u = std::unordered_multiset<int> { 1, 1, 1 };
    auto d = std::deque<int>(4000);
    int c[] = { 1, 2, 3 };
    auto a = std::array<int, 3> {{ 1, 2, 3 }};
    auto s = std::string {"Hello world!"};
    auto v = std::vector<int> { 1, 2, 3, };
    std::cout << std::boolalpha << is_contiguous(l.begin(), l.end()) << "\n";
    std::cout << std::boolalpha << is_contiguous(m.begin(), m.end()) << "\n";
    std::cout << std::boolalpha << is_contiguous(u.begin(), u.end()) << "\n";
    std::cout << std::boolalpha << is_contiguous(d.begin(), d.end()) << "\n";
    std::cout << std::boolalpha << is_contiguous(d.begin(), d.begin() + 1000) << "\n";
    std::cout << std::boolalpha << is_contiguous(std::begin(c), std::end(c)) << "\n";
    std::cout << std::boolalpha << is_contiguous(a.begin(), a.end()) << "\n";
    std::cout << std::boolalpha << is_contiguous(s.begin(), s.end()) << "\n";
    std::cout << std::boolalpha << is_contiguous(v.begin(), v.end()) << "\n";
    std::cout << std::boolalpha << is_contiguous(v.rbegin(), v.rend()) << "\n";
}
Live Example. This prints false for the list, map and unordered_multimap, and true for the C-array, and the std::array, string and vector. It prints true for small subranges within a deque and false for large subranges. It also prints false for an iterator range consisting of reverse iterators.
UPDATE: as commented by @T.C. the original N3884 proposal did have a
struct contiguous_iterator_tag : random_access_iterator_tag {};
so that tag-dispatching on iterator categories would not break. However, this would have broken non-idiomatic code with class template specializations on random_access_iterator_tag. The current draft hence does not contain a new iterator category tag.
No. The C++ Standard guarantees there are no false negatives. (i.e., std::vector, std::string, std::array, and basic arrays are promised to be stored contiguously).
However, the C++ Standard doesn't guarantee there are no false positives.
int main() {
   std::unique_ptr<Node> n1(new Node);
   std::unique_ptr<Node> n2(new Node);
   n1->next = n2; // n1 and n2 might be contiguous, but might not be
}
Thus, your type trait could be wrong some of the time. If it's wrong some of the time, it's not a type trait; rather, it's an instance trait.
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