# Multi-dimensional arrays

suggest changeThe C programming language allows multidimensional arrays. Here is the general form of a multidimensional array declaration −

`type name[size1][size2]...[sizeN];`

For example, the following declaration creates a three dimensional (5 x 10 x 4) integer array:

`int arr[5][10][4];`

**Two-dimensional Arrays**

The simplest form of multidimensional array is the two-dimensional array. A two-dimensional array is, in essence, a list of one-dimensional arrays. To declare a two-dimensional integer array of dimensions m x n, we can write as follows:

`type arrayName[m][n];`

Where `type`

can be any valid C data type (`int`

, `float`

, etc.) and `arrayName`

can be any valid C identifier. A two-dimensional array can be visualized as a table with `m`

rows and `n`

columns. **Note**: The order *does* matter in C. The array `int a[4][3]`

is not the same as the array `int a[3][4]`

. The number of rows comes first as C is a *row*-major language.

A two-dimensional array `a`

, which contains three rows and four columns can be shown as follows:

Thus, every element in the array `a`

is identified by an element name of the form `a[i][j]`

, where `a`

is the name of the array, `i`

represents which row, and `j`

represents which column. Recall that rows and columns are zero indexed. This is very similar to mathematical notation for subscripting 2-D matrices.

**Initializing Two-Dimensional Arrays**

Multidimensional arrays may be initialized by specifying bracketed values for each row. The following define an array with 3 rows where each row has 4 columns.

```
int a[3][4] = {
{0, 1, 2, 3} , /* initializers for row indexed by 0 */
{4, 5, 6, 7} , /* initializers for row indexed by 1 */
{8, 9, 10, 11} /* initializers for row indexed by 2 */
};
```

The nested braces, which indicate the intended row, are optional. The following initialization is equivalent to the previous example:

`int a[3][4] = {0,1,2,3,4,5,6,7,8,9,10,11};`

While the method of creating arrays with nested braces is optional, it is strongly encouraged as it is more readable and clearer.

**Accessing Two-Dimensional Array Elements**

An element in a two-dimensional array is accessed by using the subscripts, i.e., row index and column index of the array. For example −

`int val = a[2][3];`

The above statement will take the 4th element from the 3rd row of the array. Let us check the following program where we have used a nested loop to handle a two-dimensional array:

```
#include <stdio.h>
int main () {
/* an array with 5 rows and 2 columns*/
int a[5][2] = { {0,0}, {1,2}, {2,4}, {3,6},{4,8}};
int i, j;
/* output each array element's value */
for ( i = 0; i < 5; i++ ) {
for ( j = 0; j < 2; j++ ) {
printf("a[%d][%d] = %d\n", i,j, a[i][j] );
}
}
return 0;
}
```

When the above code is compiled and executed, it produces the following result:

```
a[0][0]: 0
a[0][1]: 0
a[1][0]: 1
a[1][1]: 2
a[2][0]: 2
a[2][1]: 4
a[3][0]: 3
a[3][1]: 6
a[4][0]: 4
a[4][1]: 8
```

**Three-Dimensional array:**

A 3D array is essentially an array of arrays of arrays: it’s an array or collection of 2D arrays, and a 2D array is an array of 1D arrays.

**3D array memory map:**

**Initializing a 3D Array:**

```
double cprogram[3][2][4]={
{{-0.1, 0.22, 0.3, 4.3}, {2.3, 4.7, -0.9, 2}},
{{0.9, 3.6, 4.5, 4}, {1.2, 2.4, 0.22, -1}},
{{8.2, 3.12, 34.2, 0.1}, {2.1, 3.2, 4.3, -2.0}}
};
```

We can have arrays with any number of dimensions, although it is likely that most of the arrays that are created will be of one or two dimensions.