# Multidimensional Arrays

In Java, multidimensional arrays are actually arrays of arrays. For example, the following declares a two-dimensional array variable called `twoD`.

``````
int twoD[][] = new int[4][5];
``````

This allocates a 4-by-5 array and assigns it to twoD. This array will look like the one shown in the following:

``````
[leftIndex][rightIndex]

[0][0] [0][1] [0][2] [0][3] [0][4]
[1][0] [1][1] [1][2] [1][3] [1][4]
[2][0] [2][1] [2][2] [2][3] [2][4]
[3][0] [3][1] [3][2] [3][3] [3][4]
``````
The wrong way to think about multi-dimension arrays
``````
+----+----+----+
|   1|   2|   3|
+----+----+----+
|   4|   5|   6|
+----+----+----+
|   7|   8|   9|
+----+----+----+
``````
right way to think about multi-dimension arrays
``````
+--+        +----+----+----+
|  |--------|   1|   2|   3|
+--+        +----+----+----+     +----+----+----+
|  |-----------------------------|   4|   5|   6|
+--+   +----+----+----+          +----+----+----+
|  |---|   7|   8|   9|
+--+   +----+----+----+
``````
An irregular multi-dimension array
``````
+--+        +----+----+
|  |--------|   1|   2|
+--+        +----+----+          +----+----+----+
|  |-----------------------------|   4|   5|   6|
+--+   +----+----+----+----+     +----+----+----+
|  |---|   7|   8|   9|  10|
+--+   +----+----+----+----+
``````

The following code use nested for loop to assign values to a two-dimensional array.

``````
public class Main {
public static void main(String args[]) {
int twoD[][] = new int[4][5];
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 5; j++) {
twoD[i][j] = i*j;
}
}
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 5; j++) {
System.out.print(twoD[i][j] + " ");
}
System.out.println();
}
}
}

``````

This program generates the following output:

``````
0 0 0 0 0
0 1 2 3 4
0 2 4 6 8
0 3 6 9 12 ``````

## Three-dimensional array

The following program creates a 3 by 4 by 5, three-dimensional array.

``````
public class Main {
public static void main(String args[]) {
int threeD[][][] = new int[3][4][5];

for (int i = 0; i < 3; i++)
for (int j = 0; j < 4; j++)
for (int k = 0; k < 5; k++)
threeD[i][j][k] = i * j * k;

for (int i = 0; i < 3; i++) {
for (int j = 0; j < 4; j++) {
for (int k = 0; k < 5; k++)
System.out.print(threeD[i][j][k] + " ");
System.out.println();
}
System.out.println();
}
}
}

``````

This program generates the following output:

``````
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0

0 0 0 0 0
0 1 2 3 4
0 2 4 6 8
0 3 6 9 12

0 0 0 0 0
0 2 4 6 8
0 4 8 12 16
0 6 12 18 24 ``````