Multidimensional Arrays
Multidimensional arrays with two dimensions are often used to represent tables of values consisting of information arranged in rows and columns. To identify a particular table element, we must specify two indices. By convention, the first identifies the element's row and the second its column. Arrays that require two indices to identify a particular element are called two-dimensional arrays. (Multidimensional arrays can have more than two dimensions.) Java does not support multidimensional arrays directly, but it does allow the programmer to specify one-dimensional arrays whose elements are also one-dimensional arrays, thus achieving the same effect. Figure 7.16 illustrates a two-dimensional array a that contains three rows and four columns (i.e., a three-by-four array). In general, an array with m rows and n columns is called an m-by-n array.
Figure 7.16. Two-dimensional array with three rows and four columns.
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Every element in array a is identified in Fig. 7.16 by an array-access expression of the form a [ row ][ column ]; a is the name of the array, and row and column are the indices that uniquely identify each element in array a by row and column number. Note that the names of the elements in row 0 all have a first index of 0, and the names of the elements in column 3 all have a second index of 3.
Arrays of One-Dimensional Arrays
Like one-dimensional arrays, multidimensional arrays can be initialized with array initializers in declarations. A two-dimensional array b with two rows and two columns could be declared and initialized with nested array initializers as follows:
int b[][] = { { 1, 2 }, { 3, 4 } };
The initializer values are grouped by row in braces. So 1 and 2 initialize b[ 0 ][ 0 ] and b[ 0 ][ 1 ], respectively, and 3 and 4 initialize b[ 1 ][ 0 ] and b[ 1 ][ 1 ], respectively. The compiler counts the number of nested array initializers (represented by sets of braces within the outer braces) in the array declaration to determine the number of rows in array b. The compiler counts the initializer values in the nested array initializer for a row to determine the number of columns in that row. As we will see momentarily, this means that rows can have different lengths.
Multidimensional arrays are maintained as arrays of one-dimensional arrays. Therefore array b in the preceding declaration is actually composed of two separate one-dimensional arraysone containing the values in the first nested initializer list { 1, 2 } and one containing the values in the second nested initializer list { 3, 4 }. Thus, array b itself is an array of two elements, each a one-dimensional array of int values.
Two-Dimensional Arrays with Rows of Different Lengths
The manner in which multidimensional arrays are represented makes them quite flexible. In fact, the lengths of the rows in array b are not required to be the same. For example,
int b[][] = { { 1, 2 }, { 3, 4, 5 } };
creates integer array b with two elements (determined by the number of nested array initializers) that represent the rows of the two-dimensional array. Each element of b is a reference to a one-dimensional array of int variables. The int array for row 0 is a one-dimensional array with two elements (1 and 2), and the int array for row 1 is a one-dimensional array with three elements (3, 4 and 5).
Creating Two-Dimensional Arrays with Array-Creation Expressions
A multidimensional array with the same number of columns in every row can be created with an array-creation expression. For example, the following lines declare array b and assign it a reference to a three-by-four array:
int b[][]; b = new int [ 3 ][ 4 ];
In this case, we use the literal values 3 and 4 to specify the number of rows and number of columns, respectively, but this is not required. Programs can also use variables to specify array dimensions. As with one-dimensional arrays, the elements of a multidimensional array are initialized when the array object is created.
A multidimensional array in which each row has a different number of columns can be created as follows:
int b[][]; b = new int[ 2 ][ ]; // create 2 rows b[ 0 ] = new int[ 5 ]; // create 5 columns for row 0 b[ 1 ] = new int[ 3 ]; // create 3 columns for row 1
The preceding statements create a two-dimensional array with two rows. Row 0 has five columns, and row 1 has three columns.
Two-Dimensional Array Example: Displaying Element Values
Figure 7.17 demonstrates initializing two-dimensional arrays with array initializers and using nested for loops to traverse the arrays (i.e., manipulate every element of each array).
Figure 7.17. Initializing two-dimensional arrays.
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1 // Fig. 7.17: InitArray.java 2 // Initializing two-dimensional arrays. 3 4 public class InitArray 5 { 6 // create and output two-dimensional arrays 7 public static void main( String args[] ) 8 { 9 int array1[][] = { { 1, 2, 3 }, { 4, 5, 6 } }; 10 int array2[][] = { { 1, 2 }, { 3 }, { 4, 5, 6 } }; 11 12 System.out.println( "Values in array1 by row are" ); 13 outputArray( array1 ); // displays array1 by row 14 15 System.out.println( " Values in array2 by row are" ); 16 outputArray( array2 ); // displays array2 by row 17 } // end main 18 19 // output rows and columns of a two-dimensional array 20 public static void outputArray( int array[][] ) 21 { 22 // loop through array's rows 23 for ( int row = 0; row < array.length; row++ ) 24 { 25 // loop through columns of current row 26 for ( int column = 0; column < array[ row ].length; column++ ) 27 System.out.printf( "%d ", array[ row ][ column ] ); 28 29 System.out.println(); // start new line of output 30 } // end outer for 31 } // end method outputArray 32 } // end class InitArray
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Class InitArray's main declares two arrays. The declaration of array1 (line 9) uses nested array initializers to initialize the first row of the array to the values 1, 2 and 3, and the second row to the values 4, 5 and 6. The declaration of array2 (line 10) uses nested initializers of different lengths. In this case, the first row is initialized to have two elements with values 1 and 2, respectively. The second row is initialized to have one element with value 3. The third row is initialized to have three elements with the values 4, 5 and 6, respectively.
Lines 13 and 16 call method outputArray (lines 2031) to output the elements of array1 and array2, respectively. Method outputArray specifies the array parameter as int array[][] to indicate that the method receives a two-dimensional array. The for statement (lines 2330) outputs the rows of a two-dimensional array. In the loop-continuation condition of the outer for statement, the expression array.length determines the number of rows in the array. In the inner for statement, the expression array[ row ].length determines the number of columns in the current row of the array. This condition enables the loop to determine the exact number of columns in each row.
Common Multidimensional-Array Manipulations Performed with for Statements
Many common array manipulations use for statements. As an example, the following for statement sets all the elements in row 2 of array a in Fig. 7.16 to zero:
for ( int column = 0; column < a[ 2 ].length; column++) a[ 2 ][ column ] = 0;
We specified row 2; therefore, we know that the first index is always 2 (0 is the first row, and 1 is the second row). This for loop varies only the second index (i.e., the column index). The preceding for statement is equivalent to the assignment statements
a[ 2 ][ 0 ] = 0; a[ 2 ][ 1 ] = 0; a[ 2 ][ 2 ] = 0; a[ 2 ][ 3 ] = 0;
The following nested for statement totals the values of all the elements in array a:
int total = 0; for ( int row = 0; row < a.length; row++ ) { for ( int column = 0; column < a[ row ].length; column++ ) total += a[ row ][ column ]; } // end outer for
This nested for statements total the array elements one row at a time. The outer for statement begins by setting the row index to 0 so that the first row's elements may be totaled by the inner for statement. The outer for then increments row to 1 so that the second row can be totaled. Then, the outer for increments row to 2 so that the third row can be totaled. The variable total can be displayed when the outer for statement terminates. In the next example, we show how to process a two-dimensional array in a similar manner using nested enhanced for statements.