## CHAPTER 7: More on Multi-Dimensional Arrays

In the previous chapter we noted that given
#define ROWS 5
#define COLS 10
int multi[ROWS][COLS];

we can access individual elements of the array **multi **using
either:
multi[row][col]

or
*(*(multi + row) + col)

To understand more fully what is going on, let us replace
*(multi + row)

with ** X** as in:
*(X + col)

Now, from this we see that **X** is like a pointer since the
expression is de-referenced and we know that **col** is an integer.
Here the arithmetic being used is of a special kind called
"pointer arithmetic" is being used. That means that, since we
are talking about an integer array, the address pointed to by
(i.e. value of) **X + col + 1** must be greater than the address
**X + col** by and amount equal to **sizeof(int)**.
Since we know the memory layout for 2 dimensional arrays, we
can determine that in the expression **multi + row** as used
above, **multi + row + 1** must increase by value an amount
equal to that needed to "point to" the next row, which in this
case would be an amount equal to **COLS * sizeof(int)**.

That says that if the expression ***(*(multi + row) + col)**
is to be evaluated correctly at run time, the compiler must
generate code which takes into consideration the value of **COLS**,
i.e. the 2nd dimension. Because of the equivalence of the two
forms of expression, this is true whether we are using the
pointer expression as here or the array expression
**multi[row][col]**.

Thus, to evaluate either expression, a total of 5 values must be
known:

- The address of the first element of the array, which is
returned by the expression
**multi**, i.e., the name of the
array.
- The size of the type of the elements of the array, in
this case
**sizeof(int)**.
- The 2nd dimension of the array
- The specific index value for the first dimension,
**row**
in this case.
- The specific index value for the second dimension,
**col**
in this case.

Given all of that, consider the problem of designing a
function to manipulate the element values of a previously
declared array. For example, one which would set all the elements
of the array **multi** to the value 1.
void set_value(int m_array[][COLS])
{
int row, col;
for (row = 0; row < ROWS; row++)
{
for (col = 0; col < COLS; col++)
{
m_array[row][col] = 1;
}
}
}

And to call this function we would then use:
set_value(multi);

Now, within the function we have used the values #defined by ROWS and
COLS that set the limits on the for loops. But, these #defines are just constants
as far as the compiler is concerned, i.e. there is nothing to connect them to the
array size within the function. **row** and **col** are local variables, of course. The
formal parameter definition permits the compiler to determine the characteristics
associated with the pointer value that will be passed at run time. We really
don’t need the first dimension and, as will be seen later, there are occasions
where we would prefer not to define it within the parameter definition, out
of habit or consistency, I have not used it here. But, the second dimension
must be used as has been shown in the expression for the parameter. The
reason is that we need this in the evaluation of **m_array[row][col]** as has been
described. While the parameter defines the data type (**int** in this case) and the
automatic variables for row and column are defined in the for loops, only one
value can be passed using a single parameter. In this case, that is the value
of **multi** as noted in the call statement, i.e. the address of the first element, often
referred to as a pointer to the array. Thus, the only way we have of informing
the compiler of the 2nd dimension is by explicitly including it in the parameter definition.
In fact, in general all dimensions of higher order than one
are needed when dealing with multi-dimensional arrays. That is
if we are talking about 3 dimensional arrays, the 2nd **and** 3rd
dimension must be specified in the parameter definition.

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