### Table of Contents

### Chpater 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 which 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 informs the compiler that we are
talking about an integer array. 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
so, 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 it is needed in
the evaluation of m_array[row][col] as has been described.
The reason is that 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.