Arrays (1D and 2D) and Lists

This lesson covers arrays and lists as required by OCR J277 Section 2.3. Arrays are data structures that store multiple values under a single name, accessed by an index. Understanding arrays is essential for working with collections of data and is heavily tested in the OCR GCSE Computer Science exam.

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What Is an Array?

An array is an ordered collection of elements, all of the same data type, stored under a single variable name. Each element is accessed by its index (position number). In most programming contexts (and in OCR pseudocode), arrays use zero-based indexing — the first element is at index 0.

OCR Pseudocode:

names = ["Alice", "Bob", "Charlie", "Diana", "Eve"]
print(names[0])    // Output: Alice
print(names[2])    // Output: Charlie
print(names[4])    // Output: Eve

Python:

names = ["Alice", "Bob", "Charlie", "Diana", "Eve"]
print(names[0])    # Output: Alice
print(names[2])    # Output: Charlie
print(names[4])    # Output: Eve

OCR Exam Tip: Arrays in OCR use zero-based indexing. The first element is at index 0, and the last element of an array with n elements is at index n-1. A very common exam mistake is being "off by one" — always check your indices carefully.

The relationship between an array, its zero-based indices, and the values stored in each slot can be drawn like this:

flowchart LR
    subgraph names["names array"]
        direction LR
        I0["[0]<br/>Alice"]
        I1["[1]<br/>Bob"]
        I2["[2]<br/>Charlie"]
        I3["[3]<br/>Diana"]
        I4["[4]<br/>Eve"]
    end
    A["names[2]"] --> I2
    I2 --> B["returns ’Charlie’"]

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Declaring and Using 1D Arrays

A one-dimensional (1D) array is a simple list of values arranged in a single row.

Creating an Array

OCR Pseudocode:

// Pre-populated array
scores = [85, 92, 78, 90, 88]

// Empty array with 5 elements
array results[5]

Python:

# Pre-populated list
scores = [85, 92, 78, 90, 88]

# Empty list
results = []

# List with 5 zeros
results = [0] * 5

Accessing and Modifying Elements

scores = [85, 92, 78, 90, 88]
print(scores[1])       // Output: 92
scores[2] = 95         // Change element at index 2 from 78 to 95
print(scores[2])       // Output: 95

Iterating Through an Array

OCR Pseudocode:

scores = [85, 92, 78, 90, 88]
total = 0
for i = 0 to scores.length - 1
    total = total + scores[i]
next i
average = total / scores.length
print("Average: " + str(average))

Python:

scores = [85, 92, 78, 90, 88]
total = 0
for i in range(len(scores)):
    total += scores[i]
average = total / len(scores)
print("Average:", average)

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2D Arrays

A two-dimensional (2D) array is an array of arrays — like a table with rows and columns. Each element is accessed using two indices: one for the row and one for the column.

OCR Pseudocode:

// A 3x3 grid (3 rows, 3 columns)
grid = [[1, 2, 3],
        [4, 5, 6],
        [7, 8, 9]]

print(grid[0][0])    // Output: 1 (row 0, column 0)
print(grid[1][2])    // Output: 6 (row 1, column 2)
print(grid[2][1])    // Output: 8 (row 2, column 1)

Python:

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

print(grid[0][0])    # Output: 1
print(grid[1][2])    # Output: 6
print(grid[2][1])    # Output: 8

Visualising a 2D Array

	Col 0	Col 1	Col 2
Row 0	1	2	3
Row 1	4	5	6
Row 2	7	8	9

grid[1][2] = Row 1, Column 2 = 6

Iterating Through a 2D Array

OCR Pseudocode:

for row = 0 to 2
    for col = 0 to 2
        print(grid[row][col])
    next col
next row

Python:

for row in range(3):
    for col in range(3):
        print(grid[row][col], end=" ")
    print()  # New line after each row

OCR Exam Tip: 2D array questions often appear on Paper 2. The key is knowing the syntax: array[row][column]. Always think "row first, then column". Drawing the 2D array as a table can help you trace through the code correctly.

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Practical Example: Class Register

OCR Pseudocode:

// 2D array: 5 students, each with [name, mark]
students = [["Alice", 85],
            ["Bob", 72],
            ["Charlie", 91],
            ["Diana", 68],
            ["Eve", 95]]

// Find the student with the highest mark
highestMark = 0
topStudent = ""

for i = 0 to 4
    if students[i][1] > highestMark then
        highestMark = students[i][1]
        topStudent = students[i][0]
    endif
next i

print("Top student: " + topStudent + " with " + str(highestMark))

Python:

students = [["Alice", 85], ["Bob", 72], ["Charlie", 91],
            ["Diana", 68], ["Eve", 95]]

highest_mark = 0
top_student = ""

for i in range(len(students)):
    if students[i][1] > highest_mark:
        highest_mark = students[i][1]
        top_student = students[i][0]

print(f"Top student: {top_student} with {highest_mark}")

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Summary

• A 1D array stores a list of values accessed by a single index.
• A 2D array stores a table of values accessed by two indices [row][column].
• Arrays use zero-based indexing — the first element is at index 0.
• Use for loops to iterate through arrays.
• .length gives the number of elements in an array.

OCR Exam Tip: When working with arrays in the exam, always write out the index numbers next to the values to avoid off-by-one errors. For the array [10, 20, 30, 40], write: index 0=10, index 1=20, index 2=30, index 3=40.

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Worked Example: Finding the Average and Highest of an Array

A class of 5 students has taken a test. Their marks are stored in a 1D array. Calculate the average mark and identify the highest mark.

OCR reference language pseudocode:

marks = [72, 85, 63, 91, 58]
total = 0
highest = marks[0]

for i = 0 to marks.length - 1
    total = total + marks[i]
    if marks[i] > highest then
        highest = marks[i]
    endif
next i

average = total / marks.length
print("Average: " + str(average))
print("Highest: " + str(highest))

Step-by-step trace: