QUESTION 31 · Matrices and Dimensions

How is an element of int a[2][3] selected?

2 marks

Answer

Use a[row][col], with row in 0..1 and col in 0..2.

The declaration creates two rows of three int elements each.
Both subscripts must be valid independently.

Explain the declaration, initialisation and access of two-dimensional arrays.

5 marks

Answer in brief

A two-dimensional array is an array whose elements are themselves arrays. It naturally represents a table of rows and columns.

Declaration and initialisation

int a[2][3] = {
    {1, 2, 3},
    {4, 5, 6}
};

Access

a[0][0] is 1, a[0][2] is 3 and a[1][1] is 5. The first index selects a row array; the second selects an element within that row. Neither index may leave its own array bounds. a[0][3] is invalid even though another row follows in storage.

Row-major storage

C stores each row contiguously, followed by the next row. The example’s element order is 1, 2, 3, 4, 5, 6. This is called row-major order. A two-dimensional array is not the same type as a pointer to pointer.

Traversal

Use an outer loop for rows and an inner loop for columns. Print a newline after the inner loop to end each row. The program displays the two rows exactly as a table.

Complexity and memory

For r rows and c columns, there are r × c elements. Visiting every element once takes O(rc) time. The array occupies r × c × sizeof(element) C bytes; only loop counters add O(1) auxiliary space. A direct valid access uses O(1) time in the usual model.

Function connection

When passing such an array to a function, the row width must be described correctly so that indexing advances by a complete row. The final topic of this unit explains the fixed-width function form.

C program and output

Download .c Open compiler

/* CodeBhavya | PPS AR25 | Learning example */
#include <stdio.h>

int main(void)
{
    int a[2][3] = {{1, 2, 3}, {4, 5, 6}};
    for (int row = 0; row < 2; ++row) {
        for (int col = 0; col < 3; ++col) {
            if (col > 0) { putchar(' '); }
            printf("%d", a[row][col]);
        }
        putchar('\n');
    }
    return 0;
}

Sample input and output

This example uses values already written in the program.

Output

1 2 3
4 5 6