AS · Practice questions · 1D and 2D arrays

Index into the table.

Six original Cambridge-style questions on 1D and 2D arrays, with a trace table and pseudocode mark points.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

Bounds, then loops.

Elements = upper bound − lower bound + 1; a 2D array has rows × columns.
Declare: DECLARE X : ARRAY[1:n] OF type or ARRAY[1:r, 1:c] OF type.
Process: a FOR loop for 1D; nested FOR loops for 2D, with totals reset in the right loop.
Choose: 2D when each value has a row and a column; records when the data types differ.

Recall

[3 marks]

An array is declared as DECLARE Temps : ARRAY[0:23] OF REAL. State (a) the lower bound, (b) the upper bound, (c) the number of elements.

(a) 0. ✓
(b) 23. ✓
(c) 23 − 0 + 1 = 24. ✓

Write

[3 marks]

Write pseudocode to declare a 1D array Names to hold 50 names, and to set every element to the empty string.

DECLARE Names : ARRAY[1:50] OF STRING. ✓
FOR Index ← 1 TO 50 ... NEXT Index. ✓
Names[Index] ← "" inside the loop. ✓

Trace

[4 marks]

Nums holds 3, 8, 2, 8, 5, 1 in elements 1 to 6. Complete a trace table for this pseudocode, state the output and describe what it does.

Count ← 0
Last ← Nums[1]
FOR i ← 2 TO 6
    IF Nums[i] > Last THEN
        Count ← Count + 1
    ENDIF
    Last ← Nums[i]
NEXT i
OUTPUT Count

i = 2: 8 > 3, Count = 1, Last = 8; i = 3: 2 > 8 FALSE, Last = 2. ✓
i = 4: 8 > 2, Count = 2, Last = 8; i = 5: 5 > 8 FALSE, Last = 5; i = 6: 1 > 5 FALSE, Last = 1. ✓
Output: 2. ✓
It counts how many values are greater than the value immediately before them. ✓

Write

[6 marks]

Sales : ARRAY[1:4, 1:12] OF REAL holds the sales of 4 shops (rows) for 12 months (columns). Write pseudocode to output the total sales for each month, and then the number of the month with the highest total.

Initialise BestTotal ← -1 (or the total of month 1) and BestMonth ← 1. ✓
Outer loop FOR Month ← 1 TO 12; set MonthTotal ← 0 inside it. ✓
Inner loop FOR Shop ← 1 TO 4 with MonthTotal ← MonthTotal + Sales[Shop, Month]. ✓
After the inner loop: OUTPUT Month, MonthTotal. ✓
IF MonthTotal > BestTotal THEN BestTotal ← MonthTotal, BestMonth ← Month. ✓
After the outer loop: OUTPUT BestMonth. ✓

Apply

[4 marks]

A theatre has 12 rows of 25 seats. The program records whether each seat is booked. (a) Choose a suitable data structure, justify your choice and write its declaration. (b) Write a statement to record that seat 17 in row 5 is booked.

(a) A 2D array, because each seat is identified by a row and a seat number. ✓
Of BOOLEAN, because each seat is either booked or not. ✓
DECLARE Seats : ARRAY[1:12, 1:25] OF BOOLEAN. ✓
(b) Seats[5, 17] ← TRUE. ✓

Analysis

[3 marks]

This pseudocode should output the total of all 48 values in Sales, but the output is wrong. Identify the error, explain its effect and write the correction.

FOR Shop ← 1 TO 4
    Total ← 0
    FOR Month ← 1 TO 12
        Total ← Total + Sales[Shop, Month]
    NEXT Month
NEXT Shop
OUTPUT Total

Total ← 0 is inside the outer loop. ✓
Total is reset for every shop, so only the total of shop 4 is output. ✓
Move Total ← 0 to before FOR Shop ← 1 TO 4. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.