Arrays in Computer Science (A-Level Computer Science 9618)

10.2 Selecting a Suitable Data Structure

Arrays are fundamental data structures used to store collections of elements of the same data type. Choosing the right type of array (1D or 2D) is crucial for efficiency and code clarity. This section explores when to use each type.

1. 1D Arrays

A 1D array is a linear collection of elements, accessed using a single index. It's suitable for representing sequences or lists where elements have a direct, ordered relationship.

• Use Cases:
• Storing a list of student names.
• Representing the scores of players in a game.
• Storing the pixels of an image in a row-major format.
• Implementing a stack or queue.

Example (Python):

my_array = [10, 20, 30, 40, 50]
print(my_array[0])  # Output: 10

2. 2D Arrays

A 2D array is an array of arrays, essentially representing a table or a grid. It's used to organize data into rows and columns.

• Use Cases:
• Representing a spreadsheet.
• Storing a chessboard.
• Representing a matrix in mathematics.
• Image representation (row-major or column-major).

Example (Python):

my_array = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
print(my_array[1][2])  # Output: 6

3. Choosing Between 1D and 2D Arrays

The choice between a 1D and a 2D array depends on how the data is structured and how it will be accessed.

Feature	1D Array	2D Array
Data Structure	Linear sequence	Table/Grid
Indexing	Single index	Two indices (row, column)
Memory Allocation	Contiguous memory	Contiguous memory
Accessing Elements	Efficient for sequential access	Efficient for accessing elements within a row or column
Use Cases	Lists, sequences, stacks, queues	Matrices, spreadsheets, grids, images

4. Mathematical Representation

In mathematics, a 2D array is often used to represent a matrix. A matrix is a rectangular array of numbers. The elements of a matrix are denoted by $a_{ij}$, where $i$ represents the row number and $j$ represents the column number.

For example, a matrix $A$ can be represented as:

$$ A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} $$

5. Considerations

When selecting an array, consider the following:

• Memory Efficiency: Arrays store elements of the same data type contiguously in memory, which is memory-efficient.
• Access Time: Accessing elements in an array is typically very fast due to the contiguous memory allocation.
• Code Readability: Using the appropriate array type can improve the readability and maintainability of your code.