4.1.2 Arrays of Arrays (``Multidimensional'' Arrays)

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When we said that ``Arrays are not limited to type int; you can have arrays of... any other type,'' we meant that more literally than you might have guessed. If you have an ``array of int,'' it means that you have an array each of whose elements is of type int. But you can have an array each of whose elements is of type x, where x is any type you choose. In particular, you can have an array each of whose elements is another array! We can use these arrays of arrays for the same sorts of tasks as we'd use multidimensional arrays in other computer languages (or matrices in mathematics). Naturally, we are not limited to arrays of arrays, either; we could have an array of arrays of arrays, which would act like a 3-dimensional array, etc.

The declaration of an array of arrays looks like this:

	int a2[5][7];

You have to read complicated declarations like these ``inside out.'' What this one says is that a2 is an array of 5 somethings, and that each of the somethings is an array of 7 ints. More briefly, ``a2 is an array of 5 arrays of 7 ints,'' or, ``a2 is an array of array of int.'' In the declaration of a2, the brackets closest to the identifier a2 tell you what a2 first and foremost is. That's how you know it's an array of 5 arrays of size 7, not the other way around. You can think of a2 as having 5 ``rows'' and 7 ``columns,'' although this interpretation is not mandatory. (You could also treat the ``first'' or inner subscript as ``x'' and the second as ``y.'' Unless you're doing something fancy, all you have to worry about is that the subscripts when you access the array match those that you used when you declared it, as in the examples below.)

To illustrate the use of multidimensional arrays, we might fill in the elements of the above array a2 using this piece of code:

	int i, j;
	for(i = 0; i < 5; i = i + 1)
		{
		for(j = 0; j < 7; j = j + 1)
			a2[i][j] = 10 * i + j;
		}

This pair of nested loops sets a[1][2] to 12, a[4][1] to 41, etc. Since the first dimension of a2 is 5, the first subscripting index variable, i, runs from 0 to 4. Similarly, the second subscript varies from 0 to 6.

We could print a2 out (in a two-dimensional way, suggesting its structure) with a similar pair of nested loops:

	for(i = 0; i < 5; i = i + 1)
		{
		for(j = 0; j < 7; j = j + 1)
			printf("%d\t", a2[i][j]);
		printf("\n");
		}

(The character \t in the printf string is the tab character.)

Just to see more clearly what's going on, we could make the ``row'' and ``column'' subscripts explicit by printing them, too:

	for(j = 0; j < 7; j = j + 1)
		printf("\t%d:", j);
	printf("\n");

	for(i = 0; i < 5; i = i + 1)
		{
		printf("%d:", i);
		for(j = 0; j < 7; j = j + 1)
			printf("\t%d", a2[i][j]);
		printf("\n");
		}

This last fragment would print

        0:      1:      2:      3:      4:      5:      6:
0:      0       1       2       3       4       5       6
1:      10      11      12      13      14      15      16
2:      20      21      22      23      24      25      26
3:      30      31      32      33      34      35      36
4:      40      41      42      43      44      45      46

Finally, there's no reason we have to loop over the ``rows'' first and the ``columns'' second; depending on what we wanted to do, we could interchange the two loops, like this:

	for(j = 0; j < 7; j = j + 1)
		{
		for(i = 0; i < 5; i = i + 1)
			printf("%d\t", a2[i][j]);
		printf("\n");
		}

Notice that i is still the first subscript and it still runs from 0 to 4, and j is still the second subscript and it still runs from 0 to 6.

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