What is a two-dimensional array in C language?

A two-dimensional array in C is a collection of elements arranged in rows and columns, forming a matrix-like structure. It is essentially an array of arrays, where each element is identified by two indices: row index and column index.

Syntax

datatype array_name[row_size][column_size];

Example: int matrix[3][4]; declares a 2D array with 3 rows and 4 columns.

Memory Layout

Two-dimensional arrays are stored in row-major order in memory. Here's how a 2x3 array looks −

Initialization Methods

Two-dimensional arrays can be initialized in two ways −

Method 1: Compile-time Initialization

#include <stdio.h>

int main() {
    int a[3][3] = {10, 20, 30, 40, 50, 60, 70, 80, 90};
    int i, j;
    
    printf("Elements of the array are:<br>");
    for (i = 0; i < 3; i++) {
        for (j = 0; j < 3; j++) {
            printf("%d\t", a[i][j]);
        }
        printf("<br>");
    }
    return 0;
}

Elements of the array are:
10	20	30	
40	50	60	
70	80	90	

Method 2: Runtime Initialization

This example shows how to read values from the user at runtime −

#include <stdio.h>

int main() {
    int a[2][2] = {{1, 2}, {3, 4}};  // Pre-initialized for demo
    int i, j;
    
    printf("Elements of the array are:<br>");
    for (i = 0; i < 2; i++) {
        for (j = 0; j < 2; j++) {
            printf("%d\t", a[i][j]);
        }
        printf("<br>");
    }
    return 0;
}

Elements of the array are:
1	2	
3	4	

Example: Matrix Operations

This example demonstrates addition and multiplication of two 2D arrays −

#include <stdio.h>

int main() {
    int A[2][2] = {{1, 2}, {3, 4}};
    int B[2][2] = {{5, 6}, {7, 8}};
    int sum[2][2], product[2][2];
    int i, j;
    
    /* Calculate sum */
    for (i = 0; i < 2; i++) {
        for (j = 0; j < 2; j++) {
            sum[i][j] = A[i][j] + B[i][j];
        }
    }
    
    /* Calculate element-wise product */
    for (i = 0; i < 2; i++) {
        for (j = 0; j < 2; j++) {
            product[i][j] = A[i][j] * B[i][j];
        }
    }
    
    printf("Sum array:<br>");
    for (i = 0; i < 2; i++) {
        for (j = 0; j < 2; j++) {
            printf("%d\t", sum[i][j]);
        }
        printf("<br>");
    }
    
    printf("Product array:<br>");
    for (i = 0; i < 2; i++) {
        for (j = 0; j < 2; j++) {
            printf("%d\t", product[i][j]);
        }
        printf("<br>");
    }
    
    return 0;
}

Sum array:
6	8	
10	12	
Product array:
5	12	
21	32	

Key Points

• Elements are accessed using array_name[row_index][column_index]
• Both indices start from 0
• Memory is allocated in row-major order
• Nested loops are commonly used to traverse 2D arrays

Conclusion

Two-dimensional arrays in C provide an efficient way to store and manipulate tabular data. They are essential for matrix operations, image processing, and any application requiring grid-based data storage.