AQA A-Level Computer Science: Data Structures – Arrays

AQA A-Level Computer Science: Data Structures - Arrays

1. Introduction to Arrays

Arrays are fundamental data structures in computer science. They provide a way to store and manage collections of data of the same data type. Think of an array as a structured container with a fixed number of compartments, each holding a single value.

2. Single-Dimensional Arrays

A single-dimensional array is like a list of elements, organized sequentially. Each element is accessed using its index, starting from 0.

Example:

array = [10, 20, 30, 40]

In this array, array[0] refers to the element at index 0, which is 10. array[1] is 20, and so on.

3. Memory Allocation and Indexing

Arrays are typically stored in contiguous memory locations, meaning the elements are placed one after another in memory. This allows for efficient access to any element using its index.

Example:

Let's say an array of integers is allocated in memory starting at address 1000. Each integer takes up 4 bytes.

To access array[2], the program calculates its address (1000 + 2 * 4 = 1008) and retrieves the value from that memory location.

4. Operations on Arrays

Arrays support various operations, including:

• Initialization: Assigning values to the array elements.
• Accessing: Retrieving the value at a specific index.
• Modification: Changing the value at a specific index.
• Traversing: Iterating through all elements of the array.
• Searching: Finding a specific element within the array.
• Sorting: Arranging the elements in a specific order.

5. Multi-Dimensional Arrays

Multi-dimensional arrays represent data organized in rows and columns. They can be visualized as tables or matrices.

Example:

A 2-dimensional array to store a 3x4 matrix:

matrix = [
    [1, 2, 3, 4],
    [5, 6, 7, 8],
    [9, 10, 11, 12]
]

Elements are accessed using multiple indices: matrix[1][2] refers to the element at row 1, column 2, which is 7.

6. Advantages of Arrays

• Efficiency: Arrays allow for fast access to elements based on their index.
• Organization: They provide a structured way to store collections of data.
• Memory Contiguity: Their contiguous memory allocation facilitates efficient processing.

7. Disadvantages of Arrays

• Fixed Size: Once declared, the size of an array cannot be changed dynamically.
• Data Type Restriction: All elements in an array must be of the same data type.

8. Applications of Arrays

Arrays are used extensively in computer programming for various tasks:

• Storing lists of data: Such as customer records, inventory items, or student grades.
• Representing matrices: For operations in linear algebra and image processing.
• Implementing other data structures: Like stacks, queues, and heaps.

9. Conclusion

Arrays are essential data structures that enable efficient storage, access, and manipulation of collections of data. Understanding their concepts and operations is crucial for building effective and efficient programs.