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Explain the concept of a jagged array.

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A jagged array is a type of array in which the elements of the main array are arrays themselves, and these subarrays can be of different sizes. Unlike a regular multi-dimensional array where each row has the same number of elements, a jagged array allows for more flexibility by permitting different lengths for each row.

The term "jagged" comes from the uneven or jagged lengths of the subarrays within the main array. Each element of the main array is an array, and these subarrays can have different lengths. This makes jagged arrays useful in scenarios where a regular multi-dimensional array would be impractical due to varying data sizes.

Here's an example in C#:

int[][] jaggedArray = new int[3][];
jaggedArray[0] = new int[] { 1, 2, 3 };
jaggedArray[1] = new int[] { 4, 5 };
jaggedArray[2] = new int[] { 6, 7, 8, 9 };

// Accessing elements
int value = jaggedArray[1][0]; // Accessing the first element of the second subarray
 

In this example, jaggedArray is a jagged array with three subarrays, and each subarray has a different length. The first subarray has three elements, the second has two, and the third has four.

Jagged arrays are more memory-efficient than regular multi-dimensional arrays when the size of subarrays varies, as they only allocate memory for the actual data. They are particularly useful in scenarios where you have a collection of arrays with different sizes, such as representing a table where the number of elements in each row may differ.

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