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
Complete Guide to Core & Advanced C Programming Concepts (Functions, Strings, Arrays, Loops, I/O, Control Flow)
https://macronepal.com/bash/building-blocks-of-c-a-complete-guide-to-functions/
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https://macronepal.com/bash/the-heart-of-text-processing-a-complete-guide-to-strings-in-c-2/
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https://macronepal.com/bash/the-cornerstone-of-data-organization-a-complete-guide-to-arrays-in-c/
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https://macronepal.com/bash/mastering-iteration-a-complete-guide-to-the-for-loop-in-c/
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https://macronepal.com/bash/mastering-iteration-a-complete-guide-to-while-loops-in-c/
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https://macronepal.com/bash/mastering-conditional-logic-a-complete-guide-to-if-else-statements-in-c/
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https://macronepal.com/bash/mastering-the-fundamentals-a-complete-guide-to-arithmetic-operations-in-c/
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https://macronepal.com/bash/foundation-of-c-programming-a-complete-guide-to-basic-input-output/
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