Demystifying Arrays of Arrays in C++

As a C++ developer, you‘ve likely encountered the need to store tabular data at some point. Perhaps you wanted to represent a grid, matrix, or table of values in your program. This is where arrays of arrays, also known as multidimensional arrays, come in handy…

What Are Arrays of Arrays?

An array of arrays is an array that contains other arrays as its elements…

Declaring Multidimensional Arrays

Now let‘s explore how to actually declare an array of arrays in C++ code…

Initializing Multidimensional Arrays

When an array of arrays is declared, the inner arrays are uninitialized by default, containing garbage values left over in memory…

Accessing Elements

To access an item in an array of arrays, simply append two index values…

Modifying Array Values

Updating values follows the same indexing conventions…

Passing Arrays of Arrays to Functions

You can pass multidimensional arrays to functions just like normal arrays. The parameter declaration specifies two dimensions to match…

Dynamic Allocation

The arrays we‘ve looked at so far have been static – their sizes must be set at compile time. For more flexibility, you can dynamically allocate multidimensional arrays using new, just like with normal arrays…

Multidimensional Array Applications

Now that you understand the fundamentals of arrays of arrays, let‘s look at some practical examples of how they can be used to model real-world data…

Understanding Memory Layout

Now that we‘ve covered the basics, let‘s dive deeper and unpack what‘s actually happening in memory when you declare and initialize a multidimensional array…

As you can see in the diagram, the outer array contains integers representing the starting memory address for each inner array. Accessing an element requires first dereferencing that base pointer to get the inner block, then adding an offset.

There is unused padding between the rows inserted for alignment purposes. So while convenient, arrays of arrays are memory inefficient compared to tightly packed formats.

Knowing these internals helps explain why…

• There is unused space between rows
• Address calculation is more complex than single array
• Row lengths are fixed uniform

And guides optimization decisions when leveraging arrays of arrays.

For example, iterating through elements accessing each inner array pointer every time can add noticeable overhead compared to computing offsets manually. Compact storage formats like RGB8 pack data more efficiently.

Now let‘s look at some standard operations and how arrays of arrays impact efficiency…

Performance vs Other Data Structures

Operation	Array	Vector	Linked List
Indexing	O(1)	O(1)	O(n)
Insert	O(n)	O(1) amortized	O(1)

Vector tends to have better characteristics for data requiring frequent changes. But arrays allow fixed indexing without shifts.

Benchmark of 25×25 matrix multiplication on i7-9700K processor:

So while less flexible, arrays of arrays offer top tier performance for static datasets leveraging their cache coherence and predictability.

Now let‘s look at transforming array data…

Transforming Array Data In-Place

Since memory is preallocated, arrays of arrays enable fast in-place data transformations not possible with other formats:

const int size = 100;
int matrix[size][size]; 

// In-place transform
for(int i = 0; i < size; i++) {
  for(int j = 0; j < size; j++) {
    matrix[i][j] *= 2; 
  }
} 

By modifying the values directly, you skip the cost of creating new storage and copying data.

This works well for things like image filters, audio sample adjustments, physics integrations, etc.

Downside is of course that you lose the original data once transformed unless you copy it first.

Now let‘s look at sorting…

Fast Column Sorting

Columns in an array of arrays are contiguous blocks that can be sorted directly using fast algorithms:

int scores[100][5]; // 100 students x 5 assignments

// Sort exam column ascending   
std::sort(&scores[0][3], &scores[99][3] + 1); 

By passing pointers to start and end of the column, C++‘s std::sort can optimize leveraging locality.

Iterating rows then gives you a sorted view without shuffling other columns around expensively.

Game Engine Usage

Arrays of arrays are readily used in game engine scene graphs and spatial partitions. Grouped storage allows related data to reside sequentially in memory for efficient iteration and lookup.

For example a chunked LOD (level of detail) system:

const int gridSize = 16; // 1km world partitioned into 16x16 grids 

struct Cell {
  std::vector<Mesh*> contents; 
  float lodMultiplier;
};

Cell worldGrid[gridSize][gridSize]; // 16x16 chunk array

void RenderCell(Entity& camera, Cell& cell) {

  // Fetch all contents in cell 
  foreach(Mesh* mesh in cell.contents) {   
    // Render mesh simplified based on LOD  
  }

}

World broken into uniform cells, then array lookup used to batch query visible geometry per region. Nearby cells can prefetch optimally.

Now let‘s explore syntax options for higher dimensionality…

Beyond 2D Arrays

C++ supports arrays with more than two dimensions without issue:

int rgbHistogram[256][256][256]; // 3D RGB histogram

rgbHistogram[r][g][b]++; // Increment bucket 

int fourDArray[10][5][8][2]; // 4D array declaration

But manipulating beyond 3D gets very cumbersome:

fourDArray[3][2][7][1] = 100; // Set value

So higher dimension cases are often better served by encapsulating dimensions:

struct HistogramCell {

  int rBucket;
  int gBucket; 
  int bBucket;

  void Increment() {
    count++;
  }

  int count;

};

HistogramCell histogram[256][256][256]; 

histogram[100][200][150].Increment(); // Encapsulate data & operations

This maintains the useful array storage, while making the multidimensional data easier to handle.

Now, an very insightful look at arrays vs pointers when we start adding dimensions…

Array vs Pointer Duality

In C++, arrays have an equivalence with pointers to their first element. This means an array can decay to a pointer when passed to a function:

void PrintValues(int array[], int size) {
  // Can iterate array using pointer  
}

int values[100];
PrintValues(values, 100); // Array decays to pointer

For multidimensional arrays, this decay applies only to the first dimension:

void ShowMatrix(int matrix[][10], int nrows) {

  // 10 is fixed second dimension

}

int matrix[5][10];
ShowMatrix(matrix, 5); // First dimension decays to pointer

So when passing arrays of arrays, bear in mind that decay behavior to avoid confusion and bugs!

Finally, let‘s summarize everything we learned…

Key Takeaways (Expanded)

• Declare row-major layout using consecutive brackets per dimension
• Access elements through successive array and offset dereferences
• Expect unused padding between rows; iterate columns for optimal locality
• Achieve excellent 1D access performance, but insertion/deletion can get costly
• Utilize in-place transformations when persisting original data not needed
• Sort columns directly for fast stable rearrangement by row attribute
• Group related data in arrays of structures for high performance access
• Encapsulate dimensions using classes as you extend beyond 3D matrices
• Remember array-pointer duality and decay implications

For frequently changing tabular data, linked lists or vectors may be more flexible. But for focused lookup and transformation of grid-like datasets, properly leveraging arrays delivers speed and efficiency in a natural C++ native format.

I hope this advanced analysis provides even more depth on successfully applying arrays of arrays within your C++ programs! Let me know if you have any other questions.