A-Level Computer Science 9618 / Topic 10 / AS

Many values, one name.

An array stores a fixed number of values of the same data type under one identifier, each reached by its index. One index gives a list; two give a table. Learn the vocabulary examiners use, then process whole arrays with loops.

Full-screen labPseudocode lab → Topic 10All data types and structures lessons →

The key idea

An array is a fixed-length data structure of elements that all have the same data type, held under one identifier. Each element is reached by its index (subscript). The lower bound is the index of the first element and the upper bound the index of the last, so ARRAY[1:30] has 30 elements. A 1D array is a list with one index; a 2D array is a table reached by [row, column]. Arrays are processed one element at a time with a FOR loop; a 2D array needs nested loops.

Fig. 1: a 1D array of six integers and a 2D array of 3 rows by 4 columns

Section 01

One dimension.

Declare the array with its bounds and data type, then use a loop variable as the index to visit every element in turn.

Element: one value stored in the array, such as Scores[3], which holds 7 in Fig. 1.
Index (subscript): the integer in square brackets that picks out an element. It can be an expression, such as Scores[i + 1].
Lower and upper bound: the first and last valid index. Number of elements = upper − lower + 1, so ARRAY[0:9] has 10.
Fixed length, one type: the size is set when the array is declared and every element has the declared data type.

DECLARE Scores : ARRAY[1:6] OF INTEGER
DECLARE Max : INTEGER
DECLARE MaxIndex : INTEGER
DECLARE i : INTEGER
Max ← Scores[1]
MaxIndex ← 1
FOR i ← 2 TO 6
    IF Scores[i] > Max THEN
        Max ← Scores[i]
        MaxIndex ← i
    ENDIF
NEXT i
OUTPUT "Highest ", Max, " at position ", MaxIndex

Worked example Trace table

Scores holds 12, 31, 7, 31, 25, 9 (Fig. 1). Trace the pseudocode above and state the output.

Before the loop: Max = 12, MaxIndex = 1.
i = 2: 31 > 12 is TRUE, so Max = 31, MaxIndex = 2.
i = 3: 7 > 31 is FALSE. i = 4: 31 > 31 is FALSE (not strictly greater), so MaxIndex stays 2.
i = 5: 25 > 31 FALSE. i = 6: 9 > 31 FALSE. The loop ends.

Answer:

i	Scores[i]	Scores[i] > Max	Max	MaxIndex
			12	1
2	31	TRUE	31	2
3	7	FALSE
4	31	FALSE
5	25	FALSE
6	9	FALSE

Output: Highest 31 at position 2. Because the test is > and not >=, the first position of a tied maximum is kept.

Your turn

Write a FOR loop that sets every element of Names : ARRAY[1:30] OF STRING to the empty string.

FOR Index ← 1 TO 30 / Names[Index] ← "" / NEXT Index. The guide does not allow Names[1 TO 30] ← "": each element is assigned separately.

Examiner trap

Start the maximum at the first element, Max ← Scores[1], not at 0: if every value were negative, a start of 0 would give the wrong answer.

Section 02

Two dimensions.

In the lab, run the 2D array program: it fills a 2 by 3 table with nested loops and totals each row. Watch the inner loop finish all its columns before the outer loop moves to the next row.

DECLARE Marks : ARRAY[1:3, 1:4] OF INTEGER
DECLARE Row : INTEGER
DECLARE Column : INTEGER
DECLARE RowTotal : INTEGER
FOR Row ← 1 TO 3
    RowTotal ← 0
    FOR Column ← 1 TO 4
        RowTotal ← RowTotal + Marks[Row, Column]
    NEXT Column
    OUTPUT "Student ", Row, ": ", RowTotal
NEXT Row

Two indices: Marks[Row, Column]. In Fig. 1, Marks[2, 3] is 10: row 2, column 3.
Size: rows × columns, so ARRAY[1:3, 1:4] has 12 elements and the inner statement above runs 12 times.
Reset in the right place: RowTotal is set to 0 inside the outer loop, so each student starts from zero.

Worked example Row totals

Marks holds the values in Fig. 1 (rows 5 8 6 9 / 7 7 10 4 / 3 9 8 6). State the output of the pseudocode above.

Row 1: 5 + 8 + 6 + 9 = 28.
Row 2: 7 + 7 + 10 + 4 = 28.
Row 3: 3 + 9 + 8 + 6 = 26.

Answer: Student 1: 28, Student 2: 28, Student 3: 26

Your turn

Swap the loops so that the outer loop is FOR Column ← 1 TO 4. What total is output for column 3?

Examiner trap

Keep the index order the same as the declaration. If the array is [1:3, 1:4], then Marks[4, 2] is out of range: there is no row 4.

Stage 1 · Learn

Check what the sim just showed you

Four quick checks. Each correct answer earns XP and records this skill on your profile.

Quick check+10 XP

How many elements does DECLARE Data : ARRAY[0:15] OF INTEGER create?

Quick check+10 XP

In the lab's 2D array program the table has 2 rows and 3 columns. How many times does the statement inside the inner loop run?

Quick check+10 XP

Using Marks in Fig. 1, what is the value of Marks[3, 2]?

Quick check+10 XP

What is the upper bound of an array?

Section 03

Choosing a structure.

Examiners ask you to select a 1D or 2D array and justify it. Ask: is the data a single list, or does each value belong to a row and a column? And is it all the same data type?

Data	Choice	Declaration
Rainfall for each day of one year	1D: one list of 365 values	`ARRAY[1:365] OF REAL`
Rainfall for each day of each of 52 weeks	2D: week (row) and day (column)	`ARRAY[1:52, 1:7] OF REAL`
Which seats in a 10-row, 20-seat cinema are booked	2D of BOOLEAN	`ARRAY[1:10, 1:20] OF BOOLEAN`
Name, age and fee for 30 members	1D array of records (mixed types)	`ARRAY[1:30] OF MemberRecord`

Same type only: a 2D array cannot hold names in one column and ages in another as different types; use a record, or parallel 1D arrays that share an index.
Justify: link the dimensions to the data, for example "2D because each value is identified by a row number and a seat number".

Worked example Select and declare

A noughts and crosses game stores 'X', 'O' or a space in each square of a 3 by 3 board. Choose and declare a suitable array, and write a statement that places an O in the middle square.

Each square is found by a row and a column, so a 2D array.
Each square holds one character, so the data type is CHAR.
Declaration: DECLARE Board : ARRAY[1:3, 1:3] OF CHAR.
The middle square is row 2, column 2.

Answer: Board[2, 2] ← 'O'

Examiner trap

Do not mix data types in one array. "A 2D array with a column of names and a column of marks" would need every element to be STRING, so the marks could not be used in arithmetic without conversion.

Stage 2 · Exam

Exam-style questions

Unlocks once the four checks above are done. Worth more XP, written to AS Paper 1 and Paper 2 standard.

Finish the four checks above to unlock the exam questions

Exam style+20 XP

Which declaration is correct for an 8 by 8 board where each square holds one character?

Exam style+20 XP

Values holds 4, 9, 2, 7, 5 in elements 1 to 5. After Total ← 0 and FOR i ← 2 TO 5 STEP 2 / Total ← Total + Values[i] / NEXT i, what is Total?

Exam style+20 XP

Which data is best stored in a 2D array?

Exam style+20 XP

Nums is declared as ARRAY[1:10] OF INTEGER. A loop runs FOR i ← 0 TO 10 and outputs Nums[i]. What happens?

Skill unlocked

1D and 2D arrays, mastered.

This skill is now recorded on your profile. Keep the chain going.

-Rank -Level -Score -Topics

Go deeper · practice

Six original Cambridge-style questions

Array terms, declaring and processing 1D and 2D arrays with loops, tracing array code and choosing a suitable array for a task.