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C#: Array
Array elements

Flatten array. A multidimensional array can be flattened. Its dimensions are reduced to one. This transformation yields a single-dimensional array—one that is simpler and faster. Flattened 2D arrays are also ideal for interop with other languages.

Flattened array index computation

array[(Y coordinate * width) + X coordinate]

2D array index computation

array[Y coordinate, X coordinate]

Intro. A 2D array is accessed with a Y and then X position. For rectangular arrays (including all 2D arrays and many jagged arrays) you can use a single array. You multiply the first coordinate by the width, and then add the second coordinate.

Star, asterisk character

Advantages: The advantages of using a flat array are improved performance and interoperability with C++ or other languages.

Note: To use a jagged array, you must have an array of references to arrays. 2D arrays have significant performance penalties.

2D ArraysJagged Arrays

Example. This example creates, assigns to and finally displays a 2D array and its equivalent flattened array. It is contained in a console program with a simple command-line interface. Specify a height of at least 4, and a width of at least 10.

C# program that uses flattened array

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());

	    //
	    // A. 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();

	    //
	    // B. 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();
	    }
	}
    }
}
Two-dimensional: 2D

The example has some complexity. Part A shows the 2D array with traditional syntax. Part B shows the flattened 1D array. Notice how we use multiplication always when accessing the oneDimensional flat array.

Next: We see some output from the program that demonstrates how the multiplication results in correct output.

Possible 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

C# programming language

Summary. We can create, assign values to, and display flattened arrays. This is useful for performance, memory reduction, and interoperability with other systems. In every application I have applied this technique, performance has improved.

And: Flattened arrays are ideal for hashtable bucket implementations as well as certain tree structures.