Flatten array

A multidimensional array in C# can be flattened. This transformation yields a single-dimensional array—one that is simpler and faster.

Notes, 1D arrays

Flattened 2D arrays are ideal for interop with other languages. They can make method signatures simpler and easier to maintain.

An example

We introduce the To1DArray method, which receives a 2D int array and returns a flattened form. The result is a 1D array—we will need to access its elements with an expression.

using System;

class Program
{
    static int[] To1DArray(int[,] input)
    {
        // Step 1: get total size of 2D array, and allocate 1D array.
        int size = input.Length;
        int[] result = new int[size];

        // Step 2: copy 2D array elements into a 1D array.
        int write = 0;
        for (int i = 0; i <= input.GetUpperBound(0); i++)
        {
            for (int z = 0; z <= input.GetUpperBound(1); z++)
            {
                result[write++] = input[i, z];
            }
        }
        // Step 3: return the new array.
        return result;
    }

    static void Main()
    {
        int[,] elements = { { 10, 20, 30 }, { 40, 50, 60 } };

        // Convert 2D array to 1D array.
        int[] result = To1DArray(elements);

        // Write flat array.
        foreach (int value in result)
        {
            Console.WriteLine("ELEMENT: {0}", value);
        }
    }
}
ELEMENT: 10
ELEMENT: 20
ELEMENT: 30
ELEMENT: 40
ELEMENT: 50
ELEMENT: 60

Index multiplication

Here we consider how to access a flattened array as a 2D array. You multiply the first coordinate by the width, and then add the second coordinate.

using System;

class Program
{
    static void Main()
    {
        while (true)
        {
            Console.WriteLine("Enter height: [4+]");
            int height = int.Parse(Console.ReadLine());

            Console.WriteLine("Enter width: [10+]");
            int width = int.Parse(Console.ReadLine());

            //
            // TWO-DIMENSIONAL ARRAY
            //
            int[,] twoDimensional = new int[height, width];
            // Assign cell 1, 6
            twoDimensional[1, 6] = 5;
            // Assign cell 3, 9
            twoDimensional[3, 9] = 9;
            // Assign cell at 2, 3
            twoDimensional[2, 3] = 1;

            // Display
            for (int i = 0; i < height; i++)
            {
                for (int a = 0; a < width; a++)
                {
                    Console.Write(twoDimensional[i, a]);
                }
                Console.WriteLine();
            }
            Console.WriteLine();

            //
            // FLATTENED ARRAY
            //
            int[] oneDimensional = new int[width * height];
            // Assign cell 1, 6
            oneDimensional[1 * width + 6] = 5;
            // Assign cell 3, 9
            oneDimensional[3 * width + 9] = 9;
            // Assign cell at 2, 3
            oneDimensional[2 * width + 3] = 1;

            // Display
            for (int i = 0; i < height; i++)
            {
                for (int a = 0; a < width; a++)
                {
                    Console.Write(oneDimensional[i * width + a]);
                }
                Console.WriteLine();
            }
        }
    }
}

Notes, output

The example has some complexity. We see some output from the program that demonstrates how the multiplication results in correct output.

Enter height: [4+]
4
Enter width: [10+]
10
0000000000
0000005000
0001000000
0000000009

0000000000
0000005000
0001000000
0000000009

Enter height: [4+]
5
Enter width: [10+]
15
000000000000000
000000500000000
000100000000000
000000000900000
000000000000000

000000000000000
000000500000000
000100000000000
000000000900000
000000000000000

Enter height: [4+]
6
Enter width: [10+]
12
000000000000
000000500000
000100000000
000000000900
000000000000
000000000000

000000000000
000000500000
000100000000
000000000900
000000000000
000000000000

Notes, array access

Suppose we want to change the accesses of a 2D array into flattened, 1D array accesses. We can change them as shown in this table.

FLATTENED ARRAY:
array[(Y coordinate * width) + X coordinate]
2D ARRAY:
array[Y coordinate, X coordinate]

A summary

We can create, assign values to, and display flattened arrays. This is useful for performance, memory reduction, and interoperability with other systems.

Summary, continued

In every application I have applied this technique, performance has improved. Flattened arrays are ideal for hashtable buckets as well as tree structures.