Why am I seeing different behavior between arrays allocated on the heap and the stack?

Question

I am inspecting the behavior of two 2D arrays in C++, one allocated from the stack, and one allocated from the heap.

I create two, 2D arrays of the same shape, and populate those arrays with some data. Then I attempt to read the arrays in two different methods, the first being with the simple array index format "Arr[ROW][COLUMN]". Then I read the arrays using a pointer dereference, and I get two different results for the heap allocated array, but identical results for the stack allocated array. I am trying to understand why the results differ. I would appreciate any clarification that someone can provide. Thanks in advance.

The code I am running is below:

#include <iostream>

using namespace std;

int main(){

    int rows = 6;
    int columns = 3;

    // allocate from the stack.
    double q[rows][columns];

    // allocate from the heap.
    double ** a;
    a = new double*[rows];

    for(int i = 0; i < rows; ++i){
        a[i] = new double[columns];
    }

    // populate the arrays.
    for(int i = 0; i < rows; ++i){
        for(int j = 0; j < columns; ++j){
            a[i][j] = columns*i+j;
            q[i][j] = columns*i+j;
        }
    }

    cout << "*****************" << endl;
    cout << "Array indexing method." << endl;
    cout << "*****************" << endl;

    // print the heap allocated array using array indexing.
    for(int i = 0; i < rows; ++i){
        for(int j = 0; j < columns; ++j){
            cout << a[i][j] << '\t';
        }
        cout << endl;
    }

    cout << "*****************" << endl;

    // print the stack allocated array using array indexing.
    for(int i = 0; i < rows; ++i){
        for(int j = 0; j < columns; ++j){
            cout << q[i][j] << '\t';
        }
        cout << endl;
    }

    cout << "*****************" << endl;
    cout << "Pointer dereferencing method." << endl;
    cout << "*****************" << endl;

    // print the heap allocated array.
    for(int i = 0; i < rows; ++i){
        for(int j = 0; j < columns; ++j){
            cout << *(&a[0][0] + columns*i + j) << '\t';
        }
        cout << endl;
    }

    cout << "*****************" << endl;

    // print the stack allocated array.
    for(int i = 0; i < rows; ++i){
        for(int j = 0; j < columns; ++j){
            cout << *(&q[0][0] + columns*i + j) << '\t';
        }
        cout << endl;
    }
    cout << "*****************" << endl;

    // release the memory allocated to the heap.
    for(int i = 0; i < rows; ++i){
        delete[] a[i];
    }

    delete a;

    return 0;
}

And the results I obtain are:

*****************
Array indexing method.
*****************
0       1       2
3       4       5
6       7       8
9       10      11
12      13      14
15      16      17
*****************
0       1       2
3       4       5
6       7       8
9       10      11
12      13      14
15      16      17
*****************
Pointer dereferencing method.
*****************
0       1       2
0       3       4
5       0       6
7       8       0
9       10      11
0       12      13
*****************
0       1       2
3       4       5
6       7       8
9       10      11
12      13      14
15      16      17
*****************

And I can see that in the third block of output, the heap allocated array isn't being read properly, but the stack allocated array is.

Thanks again.

Answer 1

&q[0][0] gives you a pointer to the first double in a block containing rowsxcolumns doubles. While &a[0][0] gives you a pointer the first double in a block containing columns doubles (you've allocated it using a[0] = new double[columns];, remember?). So accessing it columns*i + j will be out of bounds and will triggers Undefined Behavior.