Two Dimensional Arrays in Java

A table organized in rows and columns is a very effective means for communicating many different types of information. E.g., to show high temperatures versus a date for different locations:

	10/2	10/3	10/4	10/5	10/6
Chicago	53	61	65	45	30
Detroit	42	56	63	68	46
St. Paul	60	63	42	30	25

Or distance table between cities in miles:

	LA	SF	San Jose	San Diego	Monterey
LA		600	500	150	450
SF	600		100	750	150
San Jose	500	100		650	50
San Diego	150	750	650		600
Monterey	450	150	50	600

Or, a tuition table:

	Day	Boarding
Grades 1-6	6,000	18,000
Grades 7-8	9,000	21,000
Grades 9-12	12,000	24,500

This is referred to as tabular format. In Java, we represent these as two dimensional arrays.

In Java, one declares a two dimensional array the same as in C or C++, but the memory allocation by the compiler is different. E.g., in C one declares a two-dimensional array of int as

int [ ][ ] table = new int[3][5];

The memory management system will allocate 60 (3*5*4) bytes of contiguous memory.  It will store the two dimensional array as row major.  This means it first stores the first row of the table, then the second row, etc: (table[0][0],table[0][1],table[0][2],table[0][3],table[0][4],table[1][0],table[1][1]…)

where table[i][j] means the element in the ith row and jth column.  

            The address of table[i][j] then is calculated as

address of table + i*4*5 + j*4

The 4*5 is because each row has 5 elements, each of 4 bytes.  So if the array is given having the following data:

2	6	-8	9	10
5	8	9	6	-8
4	3	5	7	8

In memory, it will look like, assuming the array starts at address 200:

200 204 208 212 216 220 224 228 232 236 240 244 248 252 256

2

6

-8

9

10

5

8

9

6

-8

4

3

5

7

8

So table[2][3] is at address 200+2*4*5+4*3 = 252.

            However, in Java, one allocates a table of addresses, just as for an array of objects.  I.e.,

int[ ][ ] table = new int[3][5];

in Java means

int[ ][ ] table;

table = new int[3][ ];

table[0] = new int[5];

table[1] = new int[5];

table[2] = new int[5];

which is equivalent to:

int[][] table;

table = new int[3][];

for(int i = 0; i < 3; i++)

table[i] = new int[5];

That is to say, table is a one-dimensional array, but each of its values is an address where a one dimensional array of size 5 can be found. In Java, we only have one dimensional array as a data structure. If we want to represent higher dimensional arrays, we must have one dimensional array, each element inside the array is pointing to another array.

Symbolically, it looks like:

The table on the left is table, while the three other tables are table [0], table [1], and table[2]. Each of the 15 boxes on the right represents a storage place for an int. Each of the 3 boxes on the right represents the storage place for an address.

We can also declare a two-dimensional array and initialize it as we do one dimensional arrays. Remember, that we can create a one-dimensional array in Java as

int [ ] list = {1,2,3,3,5};

which creates a one dimensional array of size 5, with list[0] = 1, list[1] = 2, list[3] = 3, and list[4] = 5. We can do the same with two dimensional arrays as

int [ ] [ ] list ={ {2,6,-8,9,10},{5,8,9,6,-8},{4,3,5,7,8}};

which creates a two dimensional array of size [3][5].

Note that one can have irregular dimensional two dimensional arrays in Java.  That is to say, the following can be done in Java:

int [ ][ ] table;

table = new int[3][ ];

table[0] = new int[4];

table[1] = new int[3];

table[2] = new int[5];

 We call such an array a ragged array.

Thus, row 0 has 4 elements, row 1 has 3, and row 2 has 5 elements.

Suppose we declare a two dimensional array

int [ ] [ ] table = new int [3][5];

Then what is table.length equal to? Remember that in Java all arrays are one-dimensional. To declare a two-dimensional array really means to declare a one-dimensional array each of whose elements is a one-dimensional array. Hence, there is no ambiguity of table.length. It is 3, as table is a one-dimensional array of 3 elements, each of whose elements happens to point to a 5 dimensional array. We refer to the dimensions of each of the elements of table by table[i].length, for i = 0, 1, or 2. Each of them is of length 5 in this case.

Notice in our ragged array above, table[0].length = 4, table[1].length =3, and table[2].length = 5.