Use the technical terms associated with arrays

10.2 Arrays – Technical Terminology

What is an Array?

An array is a collection of elements of the same data type stored in contiguous memory locations and accessed by a numeric index (or subscript).

Key Terms

• Element – a single value stored in an array.
• Index / Subscript – the integer used to locate an element. In most A‑Level languages the first element has index 0 (zero‑based indexing).
• Bounds – the lowest and highest valid indices of an array (lower bound and upper bound).
• Length / Size – the total number of elements an array can hold.
• Dimension – the number of indices required to access an element (1‑D, 2‑D, …).
• Static Array – an array whose size is fixed at compile time.
• Dynamic Array – an array whose size can be created or altered at run time (e.g., using new in Java).
• Row‑major order – storage order where rows are stored contiguously (used by Java, C, Python).
• Column‑major order – storage order where columns are stored contiguously (used by Fortran).
• Declaration – the statement that defines an array’s type and size.
• Initialization – assigning values to an array at the point of declaration or later.
• Access / Retrieval – reading the value of an element using its index.
• Assignment / Update – writing a new value to an element using its index.
• Iteration – repeatedly processing elements, typically with a for loop.
• Bounds checking – runtime verification that an index lies within the array’s bounds.
• Out‑of‑bounds error – an exception or undefined behaviour caused by using an illegal index.

Array Declaration and Initialization Examples

Java (static, zero‑based):

int[] scores = new int[5]; // declaration, length 5

int[] ages = {12, 15, 17, 19, 21}; // declaration + initialization

Python (dynamic, zero‑based):

scores = [0] * 5 # list of length 5

ages = [12, 15, 17, 19, 21]

Address Calculation (One‑Dimensional)

When an array is stored in contiguous memory, the address of element i can be computed as:

\$\$

\text{address}(i) = \text{baseAddress} + i \times \text{elementSize}

\$\$

where i is the zero‑based index.

Address Calculation (Two‑Dimensional, Row‑major)

For an array A with R rows and C columns, the address of element A[i][j] is:

\$\$

\text{address}(i,j) = \text{baseAddress} + \bigl(i \times C + j\bigr) \times \text{elementSize}

\$\$

In column‑major order the formula swaps the roles of i and j.

Common Operations

1. Declare an array.
2. Initialize the array (explicit values or default).
3. Access an element: value = array[index];
4. Update an element: array[index] = new \cdot alue;
5. Iterate using a loop, ensuring 0 ≤ index < length.

Summary Table of Terms

Suggested Diagram