Three-Dimensional Array in C

A Three Dimensional Array or 3D array in C is a collection of two-dimensional arrays. It can be visualized as multiple 2D arrays stacked on top of each other.

Declaration of Three-Dimensional Array in C

We can declare a 3D array with x 2D arrays each having y rows and z columns using the syntax shown below.

Syntax:

data_type array_name[x][y][z];

• data_type: Type of data to be stored in each element.
• array_name: name of the array
• x: Number of 2D arrays.
• y: Number of rows in each 2D array.
• z: Number of columns in each 2D array.

Example:

int array[3][3][3];

Initialization of Three-Dimensional Array in C

Initialization in a 3D array is the same as that of 2D arrays. The difference is as the number of dimensions increases so the number of nested braces will also increase.

A 3D array in C can be initialized by using:

1. Initializer List
2. Loops

Initialization of 3D Array using Initializer List

Method 1:

int x[2][3][4] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 
                 11, 12, 13, 14, 15, 16, 17, 18, 19,
                 20, 21, 22, 23};

Method 2(Better):  

int x[2][3][4] = 
 { 
   { {0,1,2,3}, {4,5,6,7}, {8,9,10,11} },
   { {12,13,14,15}, {16,17,18,19}, {20,21,22,23} }
 };

Again, just like the 2D arrays, we can also declare the 3D arrays without specifying the size of the first dimensions if we are using initializer list for initialization. The compiler will automatically deduce the size of the first dimension. But we still need to specify the rest of the dimensions.

data_type array_name[][y][z] = {....};

Initialization of 3D Array using Loops

It is also similar to that of 2D array with one more nested loop for accessing one more dimension.

int x[2][3][4];

for (int i=0; i<2; i++) {
    for (int j=0; j<3; j++) {
        for (int k=0; k<4; k++) {
            x[i][j][k] = (some_value);
        }
    }
}

Accessing elements in Three-Dimensional Array in C

Accessing elements in 3D Arrays is also similar to that of 2D Arrays. The difference is we have to use three loops instead of two loops for one additional dimension in 3D Arrays.

Syntax:

array_name[x][y][z]

where,

• x: Index of 2D array.
• y: Index of that 2D array row.
• z: Index of that 2D array column.

In similar ways, we can create arrays with any number of dimensions. However, the complexity also increases as the number of dimensions increases. The most used multidimensional array is the Two-Dimensional Array.

Arrays are also closely related to pointers in C language. To know more about the Relationship of Arrays with Pointers in C, refer to this article.

Prerequisite: Arrays in C

A multi-dimensional array can be termed as an array of arrays that stores homogeneous data in tabular form. Data in multidimensional arrays is generally stored in row-major order in the memory.

The general form of declaring N-dimensional arrays is shown below.

Syntax:

data_type array_name[size1][size2]....[sizeN];

• data_type: Type of data to be stored in the array.
• array_name: Name of the array.
• size1, size2,…, sizeN: Size of each dimension.

Examples:

Two dimensional array: int two_d[10][20];

Three dimensional array: int three_d[10][20][30];

Size of Multidimensional Arrays:

The total number of elements that can be stored in a multidimensional array can be calculated by multiplying the size of all the dimensions.
For example:

• The array int x[10][20] can store total (10*20) = 200 elements.
• Similarly array int x[5][10][20] can store total (5*10*20) = 1000 elements.

To get the size of the array in bytes, we multiply the size of a single element with the total number of elements in the array.
For example:

• Size of array int x[10][20] = 10 * 20 * 4  = 800 bytes.      (where int = 4 bytes)
• Similarly, size of int x[5][10][20] = 5 * 10 * 20 * 4 = 4000 bytes.      (where int = 4 bytes)

The most commonly used forms of the multidimensional array are:

1. Two Dimensional Array
2. Three Dimensional Array