Assuming that
- Nis some kind of integer,
- there is an #include <vector>somewhere,
- there is either a using namespace std;or ausing std::vector;somewhere...
This is the declaration of an object v, of type std::vector< int >, initialized to hold N objects (of type int), which are default-initialized (i.e., indeterminate, since int is a POD type for which no default initialization is defined).
Documentation of vector constructors -- this one is case (2).
Spiral rule -- which needs some adapting to C++ but is still a good start.
It is not "a dynamic array line vector v", it is a vector.
And no, it is not the same as vector v[N] (which would not even compile). It is also not the same as vector<int> v[N] -- that would be an array of N different vector<int> objects.
Now if it is the first one then what is vector< vector< int > > V(N) ?
Since it's not the first one, do I still have to answer this? :-D
vector< vector< int > > V(N);
That is the declaration of an object V of type vector< vector< int > >, i.e. "vector of int-vectors", initialized to hold N default-initialized objects...
...i.e., a vector holding N objects of vector< int > -- which are, in turn, empty (because "empty" is what default-initialized vectors are).
C++ has...
- The array (int v[N];), which works exactly like the C array.
- The std::vector (std::vector< int > v;), which is dynamic in size.
- The std::array (std::array< int, N >;), which is static in size like the C array, but does offer some of the niceties ofstd::vector.
You need to be exact about what you are referring to. These are quite distinct types with a distinct feature set.
UPDATE:
With your latest couple of edits, it became clear that your real question is:
What is a vector?
It's a C++ class template implementing a container that can hold contiguous elements of a given type (like a C array), but is dynamically-sized (unlike a C array).
See the documentation.
Generally speaking, you don't use C arrays in C++ code anymore, except for some really special cases. You use std::string for strings, and std::vector for (almost) everything else you used arrays for in C.