Multi-Dimensional Arrays: Concepts and Applications

Multi-Dimensional Arrays
1. Definition
A multi-dimensional array is an array of arrays, where each element of the main
array can itself be an array. It allows you to store data in a table-like structure (2D
array) or even in a higher-dimensional structure (3D, 4D, etc.).

For example:

 A 2D array represents a matrix, where each element is accessed using two
indices: one for the row and one for the column.
 A 3D array represents a cube of data, where you need three indices to
access an element.



2. Two-Dimensional Arrays (2D Arrays)
A 2D array is an array of arrays, commonly used to represent a matrix (a table
with rows and columns). It can be thought of as a grid where each element is
accessible via two indices: one for the row and one for the column.

Declaration and Initialization (Example in Different Languages)
 C/C++: In C and C++, a 2D array is declared with two indices.

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

 Java: In Java, 2D arrays are objects and are accessed in a similar way.

int[][] arr = {
{1, 2, 3},
{4, 5, 6},

, {7, 8, 9}
};

 Python: Python doesn't have a built-in 2D array, but you can use lists to
create a 2D structure.

arr = [
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]

 JavaScript: JavaScript arrays can hold arrays as elements, so a 2D array is
created similarly.

let arr = [
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
];

Accessing Elements
To access elements in a 2D array, you use two indices (row and column).

 C/C++:

int value = arr[1][2]; // Access the element at row 1, column 2 (value 6)

 Python:

value = arr[1][2] # Access the element at row 1, column 2 (value 6)

 JavaScript:

let value = arr[1][2]; // Access the element at row 1, column 2 (value 6)