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C# Flatten Array: Transform 2D Array Into 1D Array

This C# article shows how to flatten 2D arrays into 1D arrays. It provides a benchmark.
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.Optimization
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.

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(); } } } }
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
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.

Array
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