| | | Multi-Dimensional arrays |
We have seen that we can create arrays to hold objects of any type, either basic data types like int and double, or instances of objects such as Image and DrawableInterface. Nothing stops us from defining arrays of arrays. To declare an array, each of whose elements is an array of int:
int[][] twoDArray;
While it is normally written without parentheses, we can think of the above declaration as defining twoDArray as having type (int []) []. Thus each element of twoDArray is an array of ints.
Despite the fact that Java will treat this as an array of arrays, we
usually think about this as a two-dimensional array, with
the elements arranged in a two-dimensional table so that twoDArray[i][j] can be seen as the element in the ith row and jth
column. For example here is the layout for a two-dimensional array
a with 6 rows (numbered 0 to 5) and 4 columns:
Viewed in this way, our two-dimensional array is a grid, much like a
map or a spreadsheet. This is a natural way to store things like
tables of data or matrices.
0 1 2 3
0 a[0][0] a[0][1] a[0][2] a[0][3]
1 a[1][0] a[1][1] a[1][2] a[1][3]
2 a[2][0] a[2][1] a[2][2] a[2][3]
3 a[3][0] a[3][1] a[3][2] a[3][3]
4 a[4][0] a[4][1] a[4][2] a[4][3]
5 a[5][0] a[5][1] a[5][2] a[5][3]
We access elements of two-dimensional arrays in a manner similar to that used for one dimensional arrays, except that we must provide both the row and column to access an element, giving the row number first.
We create a two-dimensional array by providing the number of rows and columns. Thus we can create the two-dimensional array above by writing:
int[][] a = new int[6][4];
Of course, in real life, we would usually define constants for the number of rows and the number of columns.
A nested for loop is the most common way to access or update the elements of a two-dimensional array. One loop walks through the rows and the other walks through the columns. For example, if we wanted to assign a unique number to each cell of our two-dimensional array, we could do the following:
for (int row = 0; row < 6; row++) {
for (int col = 0; col < 4; col++) {
a[row][col] = 4*row + col + 1;
}
}
This assigns the numbers 1 through 24 to the elements of array a. The array is filled by assigning values to the elements in the first row, then the second row, etc. and results in:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
You could modify the above to be slightly more interesting by computing a multiplication table.
We could just as well process all the elements of column 0 first, then all of column 1, etc., by swapping the order of our loops:
for (int col = 0; col < 4; col++)
for (int row = 0; row < 6; row++)
...
For the most part, it doesn't matter which order you choose, though for large arrays it is generally a good idea to traverse the array in the same order that your programming language will store the values in memory. For Java (and C, C++), the data is stored by rows, known as row major order. However, a two-dimensional array in FORTRAN is stored in column major order. You will certainly see this again if you go on and take courses like Computer Organization or Operating Systems.
| | | Multi-Dimensional arrays |