Multidimensional Arrays

Two-dimensional and multidimensional arrays in C

An array stores multiple values of the same data type. Based on the number of dimensions, arrays can be classified as one-dimensional, two-dimensional, and multidimensional arrays.

• One-dimensional array: Stores elements in a single sequence.
• Two-dimensional array: Stores elements in rows and columns, like a table.
• Multidimensional array: Has three or more dimensions, such as a three-dimensional array.

Two-dimensional array in C

Definition

A two-dimensional array is a collection of elements of the same data type arranged in rows and columns. Each element is accessed using two indexes: one for the row and one for the column.

For example, a two-dimensional array can represent students' marks in different subjects.

Visual representation: int a[2][3]

The first index identifies the row; the second identifies the column. Both indexes start at 0.

Declaration of a two-dimensional array

Syntax:

data_type array_name[rows][columns];

Example:

int a[2][3];

Here:
- int is the data type.
- a is the array name.
- 2 represents the number of rows.
- 3 represents the number of columns.
- Total elements = 2 × 3 = 6.

Initialization of a two-dimensional array

Method 1: Using nested braces

int a[2][3] = {
    {10, 20, 30},
    {40, 50, 60}
};

Method 2: Using a single list

int a[2][3] = {10, 20, 30, 40, 50, 60};

In both examples, the elements are initialized in row-major order: the first row is filled first, followed by the second row.

Accessing elements

Use two indexes to access an element.

a[0][0]   // First row, first column: 10
a[0][2]   // First row, third column: 30
a[1][1]   // Second row, second column: 50

For int a[2][3], valid row indexes are 0–1 and valid column indexes are 0–2.

Example: C Program to read and display a matrix

#include 

int main(void)
{
    int a[2][3];
    int i, j;

    printf("Enter 6 elements:\n");

    for (i = 0; i < 2; i++)
    {
        for (j = 0; j < 3; j++)
        {
            scanf("%d", &a[i][j]);
        }
    }

    printf("The matrix is:\n");

    for (i = 0; i < 2; i++)
    {
        for (j = 0; j < 3; j++)
        {
            printf("%d ", a[i][j]);
        }
        printf("\n");
    }

    return 0;
}

Sample input:

10 20 30
40 50 60

Output:

The matrix is:
10 20 30
40 50 60

How does it work?

1. The outer loop (i) controls the rows.
2. The inner loop (j) controls the columns.
3. scanf("%d", &a[i][j]) stores each input value.
4. The second pair of loops displays the array row by row.

Multidimensional arrays in C

Definition

A multidimensional array is an array with more than one dimension. In C, arrays can have two, three, or more dimensions.

Examples include:

int a[2][3];       // Two-dimensional array
int b[2][3][4];    // Three-dimensional array
int c[2][3][4][5]; // Four-dimensional array

Three-dimensional array

A three-dimensional array can be understood as a collection of two-dimensional tables or layers.

Visual representation: int a[2][2][3]
Each element is identified by three indexes: layer, row, and column.

Declaration and initialization

Syntax:

data_type array_name[size1][size2][size3];

Example:

int a[2][2][3] = {
    {
        {1, 2, 3},
        {4, 5, 6}
    },
    {
        {7, 8, 9},
        {10, 11, 12}
    }
};

Here:
- First dimension: 2 layers.
- Second dimension: 2 rows per layer.
- Third dimension: 3 columns per row.
- Total elements = 2 × 2 × 3 = 12.

To access the element 11, write:

a[1][1][1]

Example: C Program to display a three-dimensional array

#include 

int main(void)
{
    int a[2][2][3] = {
        {{1, 2, 3}, {4, 5, 6}},
        {{7, 8, 9}, {10, 11, 12}}
    };

    int i, j, k;

    for (i = 0; i < 2; i++)
    {
        printf("Layer %d:\n", i);

        for (j = 0; j < 2; j++)
        {
            for (k = 0; k < 3; k++)
            {
                printf("%d ", a[i][j][k]);
            }
            printf("\n");
        }
    }

    return 0;
}

Output:

Layer 0:
1 2 3
4 5 6
Layer 1:
7 8 9
10 11 12

The three nested loops traverse the layers, rows, and columns respectively.

Difference between two-dimensional and multidimensional arrays

Feature	Two-dimensional array	Three-dimensional array
Dimensions	2	3
Declaration	int a[2][3];	int a[2][3][4];
Indexes needed	2	3
Total elements	Rows × columns	Layers × rows × columns
Example application	Matrix of numbers	Multiple matrices or layered data

Index range checking

C does not automatically check whether array indexes are within bounds. The programmer must ensure that every index is valid.

For example:

int a[2][3];

Valid indexes:
- Row: 0 to 1
- Column: 0 to 2

This is valid:

if (i >= 0 && i < 2 && j >= 0 && j < 3)
{
    printf("%d", a[i][j]);
}

This is invalid:

printf("%d", a[2][0]);  // Row index is out of range

Accessing an element outside the array bounds causes undefined behavior.

Practice questions

1. Define a two-dimensional array. Explain its declaration, initialization, and accessing elements with an example.
2. Write a C program to read and display a matrix using a two-dimensional array.
3. What is a multidimensional array? Explain three-dimensional arrays with a suitable program.
4. Differentiate between one-dimensional, two-dimensional, and multidimensional arrays.
5. Explain index range checking for two-dimensional arrays with an example.