🔢 Demystifying 2D Arrays in C: Row-Major vs Column-Major

 

Hey Code Explorers! 👋

Welcome to Part 3 of our C Arrays Series.

We’ve learned 1D arrays, explored boundaries, and now we’re diving into 2D arrays — the grid-like arrays you see in matrices.

Today we’ll also see how memory can be arranged differently: row-major vs column-major. 🧠💡

🧱 What is a 2D Array?

A 2D array is a table of elements with rows and columns, declared like this:

data_type array_name[rows][columns];

Example:

int matrix[2][3]; // 2 rows × 3 columns

It has 6 elements in total.

✨ Initialization and Access

You can initialize like this:

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

Access elements using two indices: matrix[row][column].

printf("%d", matrix[1][2]); // prints 6

✅ Expected Output: 6

🧠 Row-Major Order (C Default)

Row-major order stores one row after another in memory.

Example:

matrix[2][3] = {{1,2,3},{4,5,6}}

Memory layout in C (row-major): 1 2 3 4 5 6

Example: Printing Addresses in C

#include <stdio.h>

int main() {
    int matrix[2][3] = {{10,20,30},{40,50,60}};
    for(int i=0;i<2;i++){
        for(int j=0;j<3;j++){
            printf("Address of matrix[%d][%d] = %p\n", i,j,&matrix[i][j]);
        }
    }
    return 0;
}

📍 Addresses increase row by row: matrix[0][0], matrix[0][1], matrix[0][2], matrix[1][0], matrix[1][1], matrix[1][2]

🧩 Column-Major Order (Other Languages)

Some languages like Fortran and MATLAB use column-major order, where one column is stored after another.

Example: matrix[2][3] = {{1,2,3},{4,5,6}}

Memory layout in column-major: 1 4 2 5 3 6

• First column → matrix[0][0], matrix[1][0]
• Second column → matrix[0][1], matrix[1][1]
• Third column → matrix[0][2], matrix[1][2]

💡 In C, this does not happen by default, but it’s useful to know for interfacing with other languages or linear algebra libraries.

🧠 Visual Comparison

Index — Row-Major (C) vs Column-Major (Fortran / MATLAB)

Index	Row-Major (C)	Column-Major (Fortran / MATLAB)
matrix[0][0]	1	1
matrix[0][1]	2	4
matrix[0][2]	3	2
matrix[1][0]	4	5
matrix[1][1]	5	3
matrix[1][2]	6	6

🔍 Key Takeaways

✅ C arrays use row-major order by default
✅ Memory is contiguous, even though you see a 2D grid
✅ Column-major order exists in other languages — keep it in mind for cross-language programming.

🧠 Mini Assignments

🎯 Assignment 1:
Declare a 3x2 integer matrix in C, fill values, and print each element with its memory address.
Observe how row-major order is followed.

🎯 Assignment 2:
Imagine the same matrix in column-major order. Write down manually the order in which memory would be stored.

🎯 Assignment 3:
Write a program to calculate the sum of each row and sum of each column of a 2x3 matrix.

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💬 Share your outputs and observations with the ProgVeda Community! 🌟
Understanding memory layout helps you write faster, safer code and is essential for future topics like pointers and dynamic arrays.