Multidimensional Arrays

2D Arrays (Matrices)

A 2D array is an array of arrays, often used to represent tabular data like matrices.

In standard C++, the dimensions of a built-in multidimensional array must be compile-time constants.

Example

// Declaration
int matrix[3][4]; // 3 rows, 4 columns

// Initialization
int grid[2][3] = {
  {1, 2, 3}, // Row 0
  {4, 5, 6}  // Row 1
};

ℹ️ Note: C++ stores multidimensional arrays in contiguous memory using row-major order (entire row 0, then row 1, etc.).

Accessing Elements

Visualization of grid[2][3]:

⚠️ Warning: Accessing outside the valid index range is undefined behavior.

Example

// Get element at row 1, column 2
int value = grid[1][2]; // 6

// Modify element at row 0, column 1
grid[0][1] = 9;

Row	Column 0	Column 1	Column 2
0	1	9	3
1	4	5	6

Nested Loops for 2D Arrays

Example

#include <iostream>
using namespace std;

int main() {
  int grid[2][3] = { {1, 9, 3}, {4, 5, 6} };
  for (int row = 0; row < 2; row++) {
    for (int col = 0; col < 3; col++) {
      cout << grid[row][col] << " ";
    }
    cout << '\n';
  }
}

Output

1 9 3 
4 5 6

3D and Higher Dimensions

C++ supports arrays with more than two dimensions. For example, a 3D array can represent volumetric data or RGB images.

⚠️ Warning: The memory cost of higher-dimensional arrays grows quickly. Large objects may not fit on the stack; prefer dynamic storage or containers for large datasets.

Example

// 3D array (e.g., for RGB image data)
int image[480][640][3]; // Height × Width × Color channels

// Accessing pixel at (10,20)
int red   = image[10][20][0];
int green = image[10][20][1];
int blue  = image[10][20][2];

Passing Multidimensional Arrays to Functions

All but the first dimension must be known in the parameter type. Alternatives include references to arrays or passing a flat pointer with explicit row/column counts.

⚠️ Warning: A built-in 2D array like int[2][3] is not interchangeable with int**. Their memory layouts differ.

Example

// Dimension after the first must be fixed in the parameter type
void print(const int a[][3], int rows) {
  for (int r = 0; r < rows; ++r) {
    for (int c = 0; c < 3; ++c) {
      std::cout << a[r][c] << ' ';
    }
    std::cout << '\n';
  }
}

// Or pass a flat pointer with sizes and index manually
void printFlat(const int* a, int rows, int cols) {
  for (int r = 0; r < rows; ++r) {
    for (int c = 0; c < cols; ++c) {
      std::cout << a[r * cols + c] << ' ';
    }
    std::cout << '\n';
  }
}

int main() {
  int grid[2][3] = { {1,2,3}, {4,5,6} };
  print(grid, 2);
  printFlat(&grid[0][0], 2, 3);
}

Memory Layout & Indexing

For a 2D array int a[R][C], the address of a[r][c] equals &a[0][0] + (r * C + c). This is why the second dimension (C) must be known for correct indexing.

Row-major layout: all columns of row 0, then all columns of row 1, and so on.

ℹ️ Note: To handle dynamic sizes or safer ownership, prefer std::vector<std::vector<int>> (jagged) or a flat std::vector<int> of size R*C with manual indexing.

Real-World Applications

- Representing game boards (chess, tic-tac-toe)

- Image and video processing

- Scientific computing (matrices, tensors)

- Tabular data storage

- 3D graphics and voxel-based data

Multidimensional Arrays

2D Arrays (Matrices)

A 2D array is an array of arrays, often used to represent tabular data like matrices.

In standard C++, the dimensions of a built-in multidimensional array must be compile-time constants.

Example

// Declaration
int matrix[3][4]; // 3 rows, 4 columns

// Initialization
int grid[2][3] = {
  {1, 2, 3}, // Row 0
  {4, 5, 6}  // Row 1
};

ℹ️ Note: C++ stores multidimensional arrays in contiguous memory using row-major order (entire row 0, then row 1, etc.).

Accessing Elements

Visualization of grid[2][3]:

⚠️ Warning: Accessing outside the valid index range is undefined behavior.

Example

// Get element at row 1, column 2
int value = grid[1][2]; // 6

// Modify element at row 0, column 1
grid[0][1] = 9;

Row	Column 0	Column 1	Column 2
0	1	9	3
1	4	5	6

Nested Loops for 2D Arrays

Example

#include <iostream>
using namespace std;

int main() {
  int grid[2][3] = { {1, 9, 3}, {4, 5, 6} };
  for (int row = 0; row < 2; row++) {
    for (int col = 0; col < 3; col++) {
      cout << grid[row][col] << " ";
    }
    cout << '\n';
  }
}

Output

1 9 3 
4 5 6

3D and Higher Dimensions

C++ supports arrays with more than two dimensions. For example, a 3D array can represent volumetric data or RGB images.

⚠️ Warning: The memory cost of higher-dimensional arrays grows quickly. Large objects may not fit on the stack; prefer dynamic storage or containers for large datasets.

Example

// 3D array (e.g., for RGB image data)
int image[480][640][3]; // Height × Width × Color channels

// Accessing pixel at (10,20)
int red   = image[10][20][0];
int green = image[10][20][1];
int blue  = image[10][20][2];

Passing Multidimensional Arrays to Functions

All but the first dimension must be known in the parameter type. Alternatives include references to arrays or passing a flat pointer with explicit row/column counts.

⚠️ Warning: A built-in 2D array like int[2][3] is not interchangeable with int**. Their memory layouts differ.

Example

// Dimension after the first must be fixed in the parameter type
void print(const int a[][3], int rows) {
  for (int r = 0; r < rows; ++r) {
    for (int c = 0; c < 3; ++c) {
      std::cout << a[r][c] << ' ';
    }
    std::cout << '\n';
  }
}

// Or pass a flat pointer with sizes and index manually
void printFlat(const int* a, int rows, int cols) {
  for (int r = 0; r < rows; ++r) {
    for (int c = 0; c < cols; ++c) {
      std::cout << a[r * cols + c] << ' ';
    }
    std::cout << '\n';
  }
}

int main() {
  int grid[2][3] = { {1,2,3}, {4,5,6} };
  print(grid, 2);
  printFlat(&grid[0][0], 2, 3);
}

Memory Layout & Indexing

For a 2D array int a[R][C], the address of a[r][c] equals &a[0][0] + (r * C + c). This is why the second dimension (C) must be known for correct indexing.

Row-major layout: all columns of row 0, then all columns of row 1, and so on.

ℹ️ Note: To handle dynamic sizes or safer ownership, prefer std::vector<std::vector<int>> (jagged) or a flat std::vector<int> of size R*C with manual indexing.

Real-World Applications

- Representing game boards (chess, tic-tac-toe)

- Image and video processing

- Scientific computing (matrices, tensors)

- Tabular data storage

- 3D graphics and voxel-based data

C++ Basics

C++ Functions

C++ Classes

C++ Quiz

Multidimensional Arrays

2D Arrays (Matrices)

Accessing Elements

Nested Loops for 2D Arrays

3D and Higher Dimensions

Passing Multidimensional Arrays to Functions

Memory Layout & Indexing

Real-World Applications

Multidimensional Arrays

2D Arrays (Matrices)

Accessing Elements

Nested Loops for 2D Arrays

3D and Higher Dimensions

Passing Multidimensional Arrays to Functions

Memory Layout & Indexing

Real-World Applications