How to implement 2D vector array?

I'm not exactly sure what the problem is, as your example code has several errors and doesn't really make it clear what you're trying to do. But here's how you add to a specific row of a 2D vector:

// declare 2D vector
vector< vector<int> > myVector;
// make new row (arbitrary example)
vector<int> myRow(1,5);
myVector.push_back(myRow);
// add element to row
myVector[0].push_back(1);

Does this answer your question? If not, could you try to be more specific as to what you are having trouble with?

If you know the (maximum) number of rows and columns beforehand, you can use resize() to initialize a vector of vectors and then modify (and access) elements with operator[]. Example:

int no_of_cols = 5;
int no_of_rows = 10;
int initial_value = 0;

std::vector<std::vector<int>> matrix;
matrix.resize(no_of_rows, std::vector<int>(no_of_cols, initial_value));

// Read from matrix.
int value = matrix[1][2];

// Save to matrix.
matrix[3][1] = 5;

Another possibility is to use just one vector and split the id in several variables, access like vector[(row * columns) + column].