Multi-Dimensional Arrays

Arrays can also have additional arrays inside them. Such arrays are called Multi-Dimensional Arrays. These are useful when we want to store the data in a tabular form, with rows and columns, or in the form of a matrix.

We can declare a two-dimensional array using the following syntax:

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datatype[][] arrayName = new datatype[lengthX, lengthY];

The array created using the above syntax will have the length (size) equal to lengthX and each element will be an array of size lengthY. For-example:

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int[,] numbers = new int[3,3];

In the above case, we create a new two-dimensional matrix of 3x3 size. It means that it can hold 9 integer numbers. We can initialize a 2D array using the following syntax:

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datatype [,] arrayName = {
    { element1, element2, ... },
    { element1, element2, ...},
    ...
};

For-example:

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int[,] numbers = {
    { 1, 2, 3, 4 },
    { 5, 6, 7, 8 },
    { 9, 10, 11, 12 }
};

The above is a 3x4 matrix and it can store 12 elements. The following illustration shows a 3x3 matrix in a visualized form:

Indexing in multidimensional arrays is similar to the normal arrays. We simply mention the row and the column index.

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arrayName[row, column];

For example, if we want to access 6 from the numbers array (shown in the illustration), we will access the 2nd row and the 3rd column:

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Console.WriteLine(numbers[1, 2]); // Output: 6

Higher dimensional arrays are also possible by adding extra commas to the declaration syntax:

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int[,,] myArray3D = new int[3, 4, 5];
int[,,,] myArray4D = new int[5, 4, 9, 10];
// Similarly more complex ones are possible as well using the same pattern

In the above code myArray3D will have 60 elements (3x4x5), while ``myArray4Dwill have1800` elements (5x4x9x10).

Following is how you would initialize a 3D array:

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int[,,] numbers =
{
    { {1, 2, 3}, { 4, 5, 6 }, {7, 8, 9} },
    { {10, 11, 12}, {13, 14, 15}, {16, 17, 18} },
    { {19, 20, 21}, {22, 23, 24}, {25, 26, 27} }
};

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