One- and Two-Dimensional Arrays — Cambridge IGCSE CS (0478)

🎯 Syllabus & Goals 3 min

Cambridge 8.2 · Arrays Paper 2 · Algorithms, Programming and Logic

By the end of this lesson you can:

Declare a one-dimensional and a two-dimensional array in pseudocode, and create the equivalent list in Python.
Use an index (or a row and column index) to read and write a single element.
Use a loop — or nested loops for 2-D — to write data into an array and read it back out.

Textbook: Chapter 8, §8.2 (pp. 329–333)

Recap / Warm-Up 5 min

Last lesson: scope, library routines and maintainable code. Every variable so far has held one value. Today: one name for many values.

Quick starter

You need to store 30 students' marks, then output those above the class average. Why is 30 separate variables (Mark1, Mark2, …) a bad idea?

Reveal the answer

You would need 30 declarations and 30 input lines, and you could not use a loop to process them. An array stores all 30 under one name, and a loop can visit each one using its index.

🧠 Key Concept 14 min

1 · One-dimensional arrays (a list)

A 1-D array is like a single row of numbered lockers. The first index can be 0 or 1 — most languages, including Python, start at 0.

Seven elements, all of type REAL, one identifier. Temperatures[3] is the fourth element, because counting starts at 0.

A declaration gives the name, the first index, the last index and the data type:

Cambridge pseudocode

DECLARE Temperatures : ARRAY[0:6] OF REAL
Temperatures[3] ← 25
OUTPUT Temperatures[3]
FOR Day ← 0 TO 6
  OUTPUT "Enter temperature: "
  INPUT Temperatures[Day]
NEXT Day

The same in Python

temperatures = [0.0] * 7            # 7 elements, all 0.0
temperatures[3] = 25
print(temperatures[3])
for day in range(0, 7):
    temperatures[day] = float(input("Enter temperature: "))

# or fill it when it is created:
temperatures = [21, 23, 19, 25, 24, 18, 22]

Key point: the loop counter is the index. As Day goes 0, 1, 2 … 6, the same statement INPUT Temperatures[Day] fills a different element each time. This is how iteration writes to and reads from an array.

2 · Two-dimensional arrays (a table)

A 2-D array has rows and columns. Each element needs two indexes: [row, column].

Three students (rows) each sat four tests (columns). This array has 3 × 4 = 12 elements.

Cambridge pseudocode

DECLARE Scores : ARRAY[0:2, 0:3] OF INTEGER
FOR Student ← 0 TO 2
  FOR Test ← 0 TO 3
    OUTPUT "Enter score: "
    INPUT Scores[Student, Test]
  NEXT Test
NEXT Student
OUTPUT Scores[1, 2]

The same in Python

# Python has no true arrays: a 2-D array is a list of lists
scores = [[12, 15, 18, 11],     # row 0
          [20, 17, 19, 16],     # row 1
          [9, 14, 10, 13]]      # row 2
print(scores[1][2])

Examiner tip: read the declaration before you trace. ARRAY[1:30] starts at 1, so a loop FOR Index ← 0 TO 29 would try to use a position that does not exist. Also keep the order [row, column] — swapping them is the most common 2-D error.

Real world: a weather station keeps a year of daily rainfall in a 1-D array of 365 elements. A cinema's booking system stores its seats as a 2-D array — row letter by seat number — with a BOOLEAN for "booked". A spreadsheet is, at heart, one big 2-D array.

Worked Example 12 min

Example 1 · 1-D array — which days were above average?

Input 7 daily temperatures, output the average to 1 decimal place, then list every day above the average. The data must be kept, because it is used twice — this is why an array is needed.

Cambridge pseudocode

CONSTANT Days ← 7
DECLARE Temperatures : ARRAY[0:6] OF REAL
DECLARE Day : INTEGER
DECLARE Total, Average : REAL
// write to the array
FOR Day ← 0 TO Days - 1
  OUTPUT "Temperature for day ", Day, ": "
  INPUT Temperatures[Day]
NEXT Day
// read from the array to total it
Total ← 0
FOR Day ← 0 TO Days - 1
  Total ← Total + Temperatures[Day]
NEXT Day
Average ← Total / Days
OUTPUT "Average: ", ROUND(Average, 1)
// read it again to compare
FOR Day ← 0 TO Days - 1
  IF Temperatures[Day] > Average
    THEN
      OUTPUT "Day ", Day, " was above average at ", Temperatures[Day]
  ENDIF
NEXT Day

The same in Python

# Daily high temperatures for one week, stored in a list (array)
DAYS = 7
temperatures = [0.0] * DAYS            # 7 elements, indexes 0 to 6
for day in range(0, DAYS):             # writing to the array
    temperatures[day] = float(input("Temperature for day " + str(day) + ": "))
total = 0
for day in range(0, DAYS):             # reading from the array
    total = total + temperatures[day]
average = total / DAYS
print("Average:", round(average, 1))
for day in range(0, DAYS):             # reading it again
    if temperatures[day] > average:
        print("Day", day, "was above average at", temperatures[day])

Temperature for day 0: 21
Temperature for day 1: 23
Temperature for day 2: 19
Temperature for day 3: 25
Temperature for day 4: 24
Temperature for day 5: 18
Temperature for day 6: 22
Average: 21.7
Day 1 was above average at 23.0
Day 3 was above average at 25.0
Day 4 was above average at 24.0
Day 6 was above average at 22.0

First loop: Day goes 0 → 6, filling one element per pass.writing to an array with iteration.
Second loop totals the elements: 21 + 23 + 19 + 25 + 24 + 18 + 22 = 152; 152 ÷ 7 = 21.714… → 21.7.reading from an array with iteration.
Third loop compares each element with 21.714…: days 1, 3, 4 and 6 are above it.without the array, the first six values would already be lost.

Example 2 · 2-D array — row totals with nested loops

The Scores array above already holds 3 students × 4 tests. Output each student's total and average.

Cambridge pseudocode

CONSTANT Students ← 3
CONSTANT Tests ← 4
DECLARE Student, Test, StudentTotal : INTEGER
FOR Student ← 0 TO Students - 1
  StudentTotal ← 0
  FOR Test ← 0 TO Tests - 1
    StudentTotal ← StudentTotal + Scores[Student, Test]
  NEXT Test
  OUTPUT "Student ", Student, " total: ", StudentTotal, " average: ", StudentTotal / Tests
NEXT Student
OUTPUT "Student 1, test 2 scored ", Scores[1, 2]

The same in Python

# Test scores: 3 students (rows) x 4 tests (columns)
scores = [[12, 15, 18, 11],
          [20, 17, 19, 16],
          [9, 14, 10, 13]]
STUDENTS = 3
TESTS = 4
for student in range(0, STUDENTS):
    student_total = 0
    for test in range(0, TESTS):
        student_total = student_total + scores[student][test]
    print("Student", student, "total:", student_total, "average:", student_total / TESTS)
print("Student 1, test 2 scored", scores[1][2])

Student 0 total: 56 average: 14.0
Student 1 total: 72 average: 18.0
Student 2 total: 46 average: 11.5
Student 1, test 2 scored 19

Student	Test	Scores[Student, Test]	StudentTotal	OUTPUT
0			0
	0	12	12
	1	15	27
	2	18	45
	3	11	56	Student 0 total: 56 average: 14
1			0
	0 … 3	20, 17, 19, 16	72	Student 1 total: 72 average: 18

The outer loop picks a row; the inner loop walks along that row's columns. To total a column (one test for all students), swap which loop is outside.

Try It Yourself 12 min

🟢 Easy

Goal: Declare MyList : ARRAY[0:9] OF INTEGER, fill it with a FOR loop from the keyboard, then output the element at index 4. Do the same in Python.

🟡 Medium

Goal: Using the Temperatures array, output the highest temperature and the day it happened. (Start with Highest ← Temperatures[0].)

🔴 Stretch

Goal: A 2-D array Names : ARRAY[1:10, 1:2] OF STRING holds a first name (column 1) and a family name (column 2) for 10 people. Write pseudocode to output each full name, then sort the rows into family-name order before outputting them.

Hint

Outputting needs one loop over the rows. For sorting, adapt the Unit 7 bubble sort: compare Names[Index, 2] with Names[Index + 1, 2], and when they are out of order swap both columns using a temporary variable.

📝 Exam Practice 10 min

Define[2]

Define the terms array and index.

Mark scheme

Array: a data structure holding several elements of the same data type under one identifier (1).
Index: the number that identifies the position of an element in the array (1).

Write[2]

Write the pseudocode to declare a 2-D array Seats of BOOLEAN values with 12 rows and 20 columns, using 1 as the first index for both.

Mark scheme

DECLARE Seats : ARRAY[1:12, 1:20] — correct bounds, rows then columns (1)
OF BOOLEAN (1)

Write[5]

The array Price : ARRAY[1:50] OF REAL holds the prices of 50 items. Write pseudocode to output how many prices are over $20 and the total of all 50 prices.

Mark scheme

Count and total initialised to 0 (1).
FOR Index ← 1 TO 50 … NEXT Index (1).
Total ← Total + Price[Index] (1).
IF Price[Index] > 20 THEN Count ← Count + 1 (1).
Both outputs after the loop, with messages (1).

Explain[2]

Explain why nested loops are used to fill a two-dimensional array.

Mark scheme

Each element needs two indexes — a row and a column (1)…
…so one loop moves through the rows and the inner loop moves through every column of each row (1).

🗝️ Recap & Key Terms 3 min

An array stores many values of one type under one name. A 1-D array uses one index; a 2-D array uses [row, column]. A loop counter used as the index lets one statement process every element — nested loops for 2-D. Python uses lists (and lists of lists) and always starts at 0.

Array: A data structure containing several elements of the same data type, accessed using the same identifier name.
Element: One individual item stored in an array.
Index: Identifies the position of an element in an array.
One-dimensional array: An array that can be thought of as a list; each element has one index.
Two-dimensional array: An array that can be thought of as a table of rows and columns; each element has a row index and a column index.

Homework 1 min

Task (≤ 15 min): Write pseudocode to input 300 names into the array Name[1:300], then input a name to search for and output its position, or "Not found". [5]

Model answer

DECLARE Name : ARRAY[1:300] OF STRING
DECLARE Index, Position : INTEGER
DECLARE Target : STRING
FOR Index ← 1 TO 300
  OUTPUT "Enter name ", Index, ": "
  INPUT Name[Index]
NEXT Index
OUTPUT "Name to find: "
INPUT Target
Position ← 0
Index ← 1
WHILE Position = 0 AND Index <= 300 DO
  IF Name[Index] = Target
    THEN
      Position ← Index
  ENDIF
  Index ← Index + 1
ENDWHILE
IF Position > 0
  THEN
    OUTPUT Target, " is at position ", Position
  ELSE
    OUTPUT "Not found"
ENDIF

Marks: FOR loop inputs into the array (1); search target input (1); loop comparing each element (1); stops when found or at the end (1); correct outputs (1).

🎯 Syllabus & Goals 3 min

Cambridge 8.2 · Arrays Paper 2 · Algorithms, Programming and Logic

By the end of this lesson you can:

Declare a one-dimensional and a two-dimensional array in pseudocode, and create the equivalent list in Python.
Use an index (or a row and column index) to read and write a single element.
Use a loop — or nested loops for 2-D — to write data into an array and read it back out.

Textbook: Chapter 8, §8.2 (pp. 329–333)

Recap / Warm-Up 5 min

Last lesson: scope, library routines and maintainable code. Every variable so far has held one value. Today: one name for many values.

Quick starter

You need to store 30 students' marks, then output those above the class average. Why is 30 separate variables (Mark1, Mark2, …) a bad idea?

Reveal the answer

You would need 30 declarations and 30 input lines, and you could not use a loop to process them. An array stores all 30 under one name, and a loop can visit each one using its index.

🧠 Key Concept 14 min

1 · One-dimensional arrays (a list)

A 1-D array is like a single row of numbered lockers. The first index can be 0 or 1 — most languages, including Python, start at 0.

Seven elements, all of type REAL, one identifier. Temperatures[3] is the fourth element, because counting starts at 0.

A declaration gives the name, the first index, the last index and the data type:

Cambridge pseudocode

DECLARE Temperatures : ARRAY[0:6] OF REAL
Temperatures[3] ← 25
OUTPUT Temperatures[3]
FOR Day ← 0 TO 6
  OUTPUT "Enter temperature: "
  INPUT Temperatures[Day]
NEXT Day

The same in Python

temperatures = [0.0] * 7            # 7 elements, all 0.0
temperatures[3] = 25
print(temperatures[3])
for day in range(0, 7):
    temperatures[day] = float(input("Enter temperature: "))

# or fill it when it is created:
temperatures = [21, 23, 19, 25, 24, 18, 22]

2 · Two-dimensional arrays (a table)

A 2-D array has rows and columns. Each element needs two indexes: [row, column].

Three students (rows) each sat four tests (columns). This array has 3 × 4 = 12 elements.

Cambridge pseudocode

DECLARE Scores : ARRAY[0:2, 0:3] OF INTEGER
FOR Student ← 0 TO 2
  FOR Test ← 0 TO 3
    OUTPUT "Enter score: "
    INPUT Scores[Student, Test]
  NEXT Test
NEXT Student
OUTPUT Scores[1, 2]

The same in Python

# Python has no true arrays: a 2-D array is a list of lists
scores = [[12, 15, 18, 11],     # row 0
          [20, 17, 19, 16],     # row 1
          [9, 14, 10, 13]]      # row 2
print(scores[1][2])

Worked Example 12 min

Example 1 · 1-D array — which days were above average?

Input 7 daily temperatures, output the average to 1 decimal place, then list every day above the average. The data must be kept, because it is used twice — this is why an array is needed.

Cambridge pseudocode

CONSTANT Days ← 7
DECLARE Temperatures : ARRAY[0:6] OF REAL
DECLARE Day : INTEGER
DECLARE Total, Average : REAL
// write to the array
FOR Day ← 0 TO Days - 1
  OUTPUT "Temperature for day ", Day, ": "
  INPUT Temperatures[Day]
NEXT Day
// read from the array to total it
Total ← 0
FOR Day ← 0 TO Days - 1
  Total ← Total + Temperatures[Day]
NEXT Day
Average ← Total / Days
OUTPUT "Average: ", ROUND(Average, 1)
// read it again to compare
FOR Day ← 0 TO Days - 1
  IF Temperatures[Day] > Average
    THEN
      OUTPUT "Day ", Day, " was above average at ", Temperatures[Day]
  ENDIF
NEXT Day

The same in Python

# Daily high temperatures for one week, stored in a list (array)
DAYS = 7
temperatures = [0.0] * DAYS            # 7 elements, indexes 0 to 6
for day in range(0, DAYS):             # writing to the array
    temperatures[day] = float(input("Temperature for day " + str(day) + ": "))
total = 0
for day in range(0, DAYS):             # reading from the array
    total = total + temperatures[day]
average = total / DAYS
print("Average:", round(average, 1))
for day in range(0, DAYS):             # reading it again
    if temperatures[day] > average:
        print("Day", day, "was above average at", temperatures[day])

Temperature for day 0: 21
Temperature for day 1: 23
Temperature for day 2: 19
Temperature for day 3: 25
Temperature for day 4: 24
Temperature for day 5: 18
Temperature for day 6: 22
Average: 21.7
Day 1 was above average at 23.0
Day 3 was above average at 25.0
Day 4 was above average at 24.0
Day 6 was above average at 22.0

First loop: Day goes 0 → 6, filling one element per pass.writing to an array with iteration.
Second loop totals the elements: 21 + 23 + 19 + 25 + 24 + 18 + 22 = 152; 152 ÷ 7 = 21.714… → 21.7.reading from an array with iteration.
Third loop compares each element with 21.714…: days 1, 3, 4 and 6 are above it.without the array, the first six values would already be lost.

Example 2 · 2-D array — row totals with nested loops

The Scores array above already holds 3 students × 4 tests. Output each student's total and average.

Cambridge pseudocode

CONSTANT Students ← 3
CONSTANT Tests ← 4
DECLARE Student, Test, StudentTotal : INTEGER
FOR Student ← 0 TO Students - 1
  StudentTotal ← 0
  FOR Test ← 0 TO Tests - 1
    StudentTotal ← StudentTotal + Scores[Student, Test]
  NEXT Test
  OUTPUT "Student ", Student, " total: ", StudentTotal, " average: ", StudentTotal / Tests
NEXT Student
OUTPUT "Student 1, test 2 scored ", Scores[1, 2]

The same in Python

# Test scores: 3 students (rows) x 4 tests (columns)
scores = [[12, 15, 18, 11],
          [20, 17, 19, 16],
          [9, 14, 10, 13]]
STUDENTS = 3
TESTS = 4
for student in range(0, STUDENTS):
    student_total = 0
    for test in range(0, TESTS):
        student_total = student_total + scores[student][test]
    print("Student", student, "total:", student_total, "average:", student_total / TESTS)
print("Student 1, test 2 scored", scores[1][2])

Student 0 total: 56 average: 14.0
Student 1 total: 72 average: 18.0
Student 2 total: 46 average: 11.5
Student 1, test 2 scored 19

Student	Test	Scores[Student, Test]	StudentTotal	OUTPUT
0			0
	0	12	12
	1	15	27
	2	18	45
	3	11	56	Student 0 total: 56 average: 14
1			0
	0 … 3	20, 17, 19, 16	72	Student 1 total: 72 average: 18

The outer loop picks a row; the inner loop walks along that row's columns. To total a column (one test for all students), swap which loop is outside.

Try It Yourself 12 min

🟢 Easy

Goal: Declare MyList : ARRAY[0:9] OF INTEGER, fill it with a FOR loop from the keyboard, then output the element at index 4. Do the same in Python.

🟡 Medium

Goal: Using the Temperatures array, output the highest temperature and the day it happened. (Start with Highest ← Temperatures[0].)

🔴 Stretch

Hint

📝 Exam Practice 10 min

Define[2]

Define the terms array and index.

Mark scheme

Array: a data structure holding several elements of the same data type under one identifier (1).
Index: the number that identifies the position of an element in the array (1).

Write[2]

Write the pseudocode to declare a 2-D array Seats of BOOLEAN values with 12 rows and 20 columns, using 1 as the first index for both.

Mark scheme

DECLARE Seats : ARRAY[1:12, 1:20] — correct bounds, rows then columns (1)
OF BOOLEAN (1)

Write[5]

The array Price : ARRAY[1:50] OF REAL holds the prices of 50 items. Write pseudocode to output how many prices are over $20 and the total of all 50 prices.

Mark scheme

Count and total initialised to 0 (1).
FOR Index ← 1 TO 50 … NEXT Index (1).
Total ← Total + Price[Index] (1).
IF Price[Index] > 20 THEN Count ← Count + 1 (1).
Both outputs after the loop, with messages (1).

Explain[2]

Explain why nested loops are used to fill a two-dimensional array.

Mark scheme

Each element needs two indexes — a row and a column (1)…
…so one loop moves through the rows and the inner loop moves through every column of each row (1).

🗝️ Recap & Key Terms 3 min

Array: A data structure containing several elements of the same data type, accessed using the same identifier name.
Element: One individual item stored in an array.
Index: Identifies the position of an element in an array.
One-dimensional array: An array that can be thought of as a list; each element has one index.
Two-dimensional array: An array that can be thought of as a table of rows and columns; each element has a row index and a column index.

Homework 1 min

Task (≤ 15 min): Write pseudocode to input 300 names into the array Name[1:300], then input a name to search for and output its position, or "Not found". [5]

Model answer

DECLARE Name : ARRAY[1:300] OF STRING
DECLARE Index, Position : INTEGER
DECLARE Target : STRING
FOR Index ← 1 TO 300
  OUTPUT "Enter name ", Index, ": "
  INPUT Name[Index]
NEXT Index
OUTPUT "Name to find: "
INPUT Target
Position ← 0
Index ← 1
WHILE Position = 0 AND Index <= 300 DO
  IF Name[Index] = Target
    THEN
      Position ← Index
  ENDIF
  Index ← Index + 1
ENDWHILE
IF Position > 0
  THEN
    OUTPUT Target, " is at position ", Position
  ELSE
    OUTPUT "Not found"
ENDIF

Marks: FOR loop inputs into the array (1); search target input (1); loop comparing each element (1); stops when found or at the end (1); correct outputs (1).