Difference between vector <int> V[] and vector< vector<int> > V

vector<int> V[] is an array of vectors.

vector< vector<int> > V is a vector of vectors.

Using arrays are C-style coding, using vectors are C++-style coding.

Quoting cplusplus.com ,

Vectors are sequence containers representing arrays that can change in size.

Just like arrays, vectors use contiguous storage locations for their elements, which means that their elements can also be accessed using offsets on regular pointers to its elements, and just as efficiently as in arrays. But unlike arrays, their size can change dynamically, with their storage being handled automatically by the container.

TL;DR:

When you want to work with a fixed number of std::vector elements, you can use vector <int> V[].

When you want to work with a dynamic array of std::vector, you can use vector< vector<int> > V.

One difference would be that although both can be initialized in the same way, e.g.

vector<int> V1[]        {{1,2,3}, {4,5,6}};
vector<vector<int>> V2  {{1,2,3}, {4,5,6}};

and accessed

cout << V1[0].back() << endl;
cout << V2[0].back() << endl;

the V1 can't grow. You cannot make V1.push_back(...) as its not a vector object. Its just an array. Second one is dynamic. You can grow it as you please.

vector<vector<int>> v(26); is a vector containing vectors. In this example, you have a vector with 26 vectors contained in it. The code v[1].push_back(x) means that x is pushed back to the first vector within the vectors.

vector<int> a[26]; is an array of vectors. In other words, a one-dimensional array containing 26 vectors of integers. The code a[1].push_back(x); has x being pushed back to the first index of the array.