The 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 twodimensional 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.