dynamic allocation/deallocation of 2D & 3D arrays

Question

I know about algorithms to allocate/deallocate a 2D array dynamically, however I'm not too sure about the same for 3D arrays.
Using this knowledge and a bit of symmetry, I came up with the following code.
(I had a hard time visualizing in 3D during coding).

Please comment on the correctness and suggest any better alternative (efficiency-wise or intuitively), if any.
Also, I think both these 2D and 3D arrays can be accessed normally like static arrays like arr2D[2][3] and
arr3D[2][3][2]. Right?

Code for 2D

//allocate a 2D array
int** allocate2D(int rows,int cols)
{
    int **arr2D;
    int i;

    arr2D = (int**)malloc(rows*sizeof(int*));
    for(i=0;i<rows;i++)
    {
        arr2D[i] = (int*)malloc(cols*sizeof(int));
    }
}

//deallocate a 2D array
void deallocate2D(int** arr2D,int rows)
{
    int i;

    for(i=0;i<rows;i++)
    {
        free(arr2D[i]);
    }

    free(arr2D);
}  

Code for 3D

//allocate a 3D array
int*** allocate3D(int l,int m,int n)
{
int ***arr3D;
int i,j,k;

arr3D = (int***)malloc(l * sizeof(int **));

for(i=0;i<l;i++)
{
    arr3D[i] = (int**)malloc(m * sizeof(int*));
    for(j=0;j<m;j++)
    {
        arr3D[i][j] = (int*)malloc(n*sizeof(int));
    }
}

return arr3D;
}

//deallocate a 3D array
void deallocate3D(int arr3D,int l,int m)
{
    int i,j;

    for(i=0;i<l;i++)
    {
        for(int j=0;j<m;j++)
        {
            free(arr3D[i][j]);
        }
        free(arr3D[i]);
    }
    free(arr3D);
}

Answer 1

You can also allocate one array and compute individual indices. This requires fewer allocator calls and results in both less fragmentation and better cache use.

typedef struct {
  int a;
  int b;
  int* data;
} Int2d;

Int2d arr2d = { 2, 3 };
arr2d.data = malloc(arr2d.a * arr2d.b * sizeof *arr2d.data);

Now arr2d[r][c] becomes arr2d.data[r * arr2d.b + c]. Deallocation is a single free() away. As a bonus you're sure to always keep your dynamic array sizes with you.

Extrapolating to 3d:

typedef struct {
  int a;
  int b;
  int c;
  int* data;
} Int3d;

Int3d arr3d = { 2, 3, 4 };
arr3d.data = malloc(arr3d.a * arr3d.b * arr3d.c * sizeof *arr3d.data);

//arr3d[r][c][d]
// becomes:
arr3d.data[r * (arr3d.b * arr3d.c) + c * arr3d.c + d];

You should encapsulate these index operations (and the (de-)allocations for that matter) in a separate function or macro.

(The names for r, c, and d could be better—I was going for row, column, and depth. While a, b, and c are the limits of their corresponding dimensions, you might prefer something like n1, n2, n3 there, or even use an array for them.)