Table of Contents

What are Multidimensional Arrays?

A multidimensional array in C is an array of arrays. The most common is the 2D array (matrix), but C supports 3D, 4D, or even higher dimensions.

Declaration Syntax

data_type array_name[size1][size2]...[sizeN];
// Examples
int matrix[3][4];      // 2D: 3 rows, 4 columns
float cube[2][3][4];   // 3D: 2 layers, 3 rows, 4 columns

2D Arrays (Most Common)

Declaration and Initialization

#include <stdio.h>
int main() {
// Method 1: Declare then assign
int matrix1[2][3];
matrix1[0][0] = 1;
matrix1[0][1] = 2;
matrix1[0][2] = 3;
matrix1[1][0] = 4;
matrix1[1][1] = 5;
matrix1[1][2] = 6;
// Method 2: Initialize at declaration
int matrix2[2][3] = {
{1, 2, 3},
{4, 5, 6}
};
// Method 3: Row-by-row (braces optional)
int matrix3[2][3] = {1, 2, 3, 4, 5, 6};
// Method 4: Partial initialization (rest become 0)
int matrix4[2][3] = {
{1, 2},
{4}
};
// Result: {{1,2,0}, {4,0,0}}
return 0;
}

Accessing Elements

#include <stdio.h>
int main() {
int matrix[3][4] = {
{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12}
};
// Access individual element
printf("Element at [1][2]: %d\n", matrix[1][2]);  // 7
// Change value
matrix[0][0] = 99;
printf("Modified: %d\n", matrix[0][0]);  // 99
return 0;
}

Traversing 2D Arrays (Nested Loops)

#include <stdio.h>
int main() {
int matrix[3][4] = {
{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12}
};
// Print all elements row by row
for(int i = 0; i < 3; i++) {        // Rows
for(int j = 0; j < 4; j++) {    // Columns
printf("%3d ", matrix[i][j]);
}
printf("\n");  // New line after each row
}
return 0;
}

Output:

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

Practical Example 1: Matrix Addition

#include <stdio.h>
int main() {
int A[2][3] = {{1, 2, 3}, {4, 5, 6}};
int B[2][3] = {{7, 8, 9}, {10, 11, 12}};
int C[2][3];  // Result matrix
// Add matrices
for(int i = 0; i < 2; i++) {
for(int j = 0; j < 3; j++) {
C[i][j] = A[i][j] + B[i][j];
}
}
// Display result
printf("Result of A + B:\n");
for(int i = 0; i < 2; i++) {
for(int j = 0; j < 3; j++) {
printf("%3d ", C[i][j]);
}
printf("\n");
}
return 0;
}

Output:

Result of A + B:
8  10  12
14  16  18

Practical Example 2: Matrix Multiplication

#include <stdio.h>
int main() {
int A[2][3] = {{1, 2, 3}, {4, 5, 6}};
int B[3][2] = {{7, 8}, {9, 10}, {11, 12}};
int C[2][2] = {{0, 0}, {0, 0}};  // Result: 2x2
// Matrix multiplication
for(int i = 0; i < 2; i++) {        // Rows of A
for(int j = 0; j < 2; j++) {    // Columns of B
for(int k = 0; k < 3; k++) { // Columns of A / Rows of B
C[i][j] += A[i][k] * B[k][j];
}
}
}
// Display result
printf("A (2x3) * B (3x2) = C (2x2):\n");
for(int i = 0; i < 2; i++) {
for(int j = 0; j < 2; j++) {
printf("%4d ", C[i][j]);
}
printf("\n");
}
return 0;
}

Output:

A (2x3) * B (3x2) = C (2x2):
58   64
139  154

3D Arrays

#include <stdio.h>
int main() {
// 3D array: 2 layers, 3 rows, 4 columns
int cube[2][3][4] = {
{ // Layer 0
{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12}
},
{ // Layer 1
{13, 14, 15, 16},
{17, 18, 19, 20},
{21, 22, 23, 24}
}
};
// Access element
printf("Element [1][2][3]: %d\n", cube[1][2][3]);  // 24
// Traverse 3D array
for(int i = 0; i < 2; i++) {        // Layers
printf("Layer %d:\n", i);
for(int j = 0; j < 3; j++) {    // Rows
for(int k = 0; k < 4; k++) { // Columns
printf("%3d ", cube[i][j][k]);
}
printf("\n");
}
printf("\n");
}
return 0;
}

Output:

Layer 0:
1   2   3   4
5   6   7   8
9  10  11  12
Layer 1:
13  14  15  16
17  18  19  20
21  22  23  24

Omitting Size in Function Parameters

When passing multidimensional arrays to functions, you must specify all dimensions except the first:

#include <stdio.h>
// CORRECT: First dimension can be omitted
void printMatrix(int rows, int cols, int matrix[][3]) {
for(int i = 0; i < rows; i++) {
for(int j = 0; j < cols; j++) {
printf("%3d ", matrix[i][j]);
}
printf("\n");
}
}
// Also correct using pointer notation
void printMatrix2(int rows, int cols, int (*matrix)[3]) {
for(int i = 0; i < rows; i++) {
for(int j = 0; j < cols; j++) {
printf("%3d ", matrix[i][j]);
}
printf("\n");
}
}
// WRONG: Cannot omit both dimensions
// void wrong(int matrix[][]) { }  // ERROR!
int main() {
int matrix[2][3] = {{1, 2, 3}, {4, 5, 6}};
printMatrix(2, 3, matrix);
return 0;
}

Practice Problem: Student Grades

#include <stdio.h>
int main() {
// 3 students, 4 subjects
int grades[3][4] = {
{85, 90, 78, 88},   // Student 0
{92, 88, 95, 89},   // Student 1
{76, 84, 91, 87}    // Student 2
};
// Calculate average for each student
for(int student = 0; student < 3; student++) {
int sum = 0;
for(int subject = 0; subject < 4; subject++) {
sum += grades[student][subject];
}
float avg = sum / 4.0;
printf("Student %d average: %.2f\n", student + 1, avg);
}
// Calculate average for each subject
for(int subject = 0; subject < 4; subject++) {
int sum = 0;
for(int student = 0; student < 3; student++) {
sum += grades[student][subject];
}
float avg = sum / 3.0;
printf("Subject %d average: %.2f\n", subject + 1, avg);
}
return 0;
}

Output:

Student 1 average: 85.25
Student 2 average: 91.00
Student 3 average: 84.50
Subject 1 average: 84.33
Subject 2 average: 87.33
Subject 3 average: 88.00
Subject 4 average: 88.00

Memory Layout (Row-Major Order)

C stores multidimensional arrays in row-major order (row by row in memory):

#include <stdio.h>
int main() {
int arr[2][3] = {{1, 2, 3}, {4, 5, 6}};
// Memory addresses are contiguous
printf("Address of arr[0][0]: %p\n", &arr[0][0]);
printf("Address of arr[0][1]: %p\n", &arr[0][1]);
printf("Address of arr[0][2]: %p\n", &arr[0][2]);
printf("Address of arr[1][0]: %p\n", &arr[1][0]);
// In memory: [1][2][3][4][5][6] sequentially
// Row 0 elements stored first, then row 1
return 0;
}

Quick Reference Table

Dimension	Declaration	Access	Loop Nesting
1D	`int arr[5]`	`arr[i]`	1 loop
2D	`int arr[3][4]`	`arr[i][j]`	2 loops
3D	`int arr[2][3][4]`	`arr[i][j][k]`	3 loops
4D	`int arr[2][3][4][5]`	`arr[i][j][k][l]`	4 loops

Common Operations Summary

// Declare a 3x4 matrix
int matrix[3][4];
// Initialize all to zero
int zero[3][4] = {0};
// Get total elements
int total = 3 * 4;  // Use rows * cols
// Copy matrix
for(int i = 0; i < rows; i++)
for(int j = 0; j < cols; j++)
dest[i][j] = src[i][j];
// Find max element
int max = matrix[0][0];
for(int i = 0; i < rows; i++)
for(int j = 0; j < cols; j++)
if(matrix[i][j] > max) max = matrix[i][j];

Key Points to Remember

Row-major order - Rows stored contiguously in memory
Index starts at 0 - First element is [0][0]
Size must be known except the first dimension in functions
Use nested loops for traversal
Memory allocation is static (size fixed at compile time)
Partial initialization sets remaining elements to 0

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C Functions, Arguments, Parameters & Flow

Mastering Functions in C – Complete Guide

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Function Arguments in C

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Explains how arguments are passed and used in function calls.

Function Parameters in C

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Explains defining inputs for functions and matching them with arguments.

Function Declarations in C

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Covers prototypes, syntax rules, and best practices.

Function Calls in C

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Explains execution flow and parameter handling during function calls.

Void Functions in C

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Explains functions that do not return values.

Return Values in C

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Explains different return types and how functions return results.

Pass-by-Value in C

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Explains how copies of variables are passed into functions.

Pass-by-Reference in C

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Explains using pointers to modify original variables.

C strstr() Function

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C Preprocessor & Macros

C Structures, Memory, Scope & Linkage

C Scope, Storage Classes & Typedef

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What are Multidimensional Arrays?

Declaration Syntax

2D Arrays (Most Common)

Declaration and Initialization

Accessing Elements

Traversing 2D Arrays (Nested Loops)

Practical Example 1: Matrix Addition

Practical Example 2: Matrix Multiplication

3D Arrays

Omitting Size in Function Parameters

Practice Problem: Student Grades

Memory Layout (Row-Major Order)

Quick Reference Table

Common Operations Summary

Key Points to Remember

Complete C Programming Guide + Compilers Collection

1. C srand() Function – Understanding Seed Initialization

2. C rand() Function Mechanics and Limitations

3. C log() Function

4. Mastering Date and Time in C

5. Mastering time_t Type in C

6. C exp() Function

7. C log() Function (Alternate Guide)

8. C log10() Function

9. C tan() Function

10. Random Numbers in C (Secure vs Predictable)

11. Free Online C Compiler

C Functions, Arguments, Parameters & Flow

Mastering Functions in C – Complete Guide

Function Arguments in C

Function Parameters in C

Function Declarations in C

Function Calls in C

Void Functions in C

Return Values in C

Pass-by-Value in C

Pass-by-Reference in C

C strstr() Function

C Preprocessor & Macros

C Structures, Memory, Scope & Linkage

C Scope, Storage Classes & Typedef

Extra Articles

Online Compilers

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