Algorithms

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Notes

What is an Algorithm?

An **algorithm** is a precise set of rules or instructions to solve a specific problem or task.
Algorithms can be designed using **structure diagrams**, **flowcharts**, or **pseudocode**.
A well-designed algorithm should be interpretable by a new user to explain its purpose.

Structure Diagrams

Structure diagrams show **hierarchical top-down design** in a visual form.
Each problem is divided into **sub-problems**, and each sub-problem is further divided.
At each level, the problem is broken down into more detailed tasks that can be implemented using a **single subroutine**.
Example: A mobile app structure diagram might show top-level modules like 'Login', 'Main Menu', and 'Settings', each with sub-tasks.

Flowcharts

Flowcharts use **shapes** to represent different functions (e.g., process, decision, input/output).
**Lines** show the flow of control between steps.
Common shapes: **oval** (start/end), **rectangle** (process), **diamond** (decision), **parallelogram** (input/output).
Example: A flowchart for age verification inputs age, checks if ≥18, and outputs appropriate message.

Pseudocode

Pseudocode is a **text-based** tool using short English words/statements to describe an algorithm.
It is more structured than plain English but very flexible.
Use **INPUT** and **OUTPUT** statements (not `print()` or `input()` with brackets).
Example: `INPUT Age` / `IF Age ≥ 18 THEN OUTPUT "Welcome"`.
Default to pseudocode when writing algorithms; use flowcharts only when asked.

Explaining Algorithms

To explain an algorithm, follow the instructions step by step to determine its purpose.
Look for **comments** in the code, consider the **context**, and **test with different inputs**.
The algorithm's purpose should become clear by tracing its logic.
Example: A REPEAT loop that inputs 10 numbers and outputs the total adds ten user-entered numbers.

Worked Example: Grade Assignment

Input marks are stored in an array `Score[]`.
Each mark is checked against boundaries (70, 60, 50, 40, 30) to assign a grade (A–F).
The grade is stored in `Grade[]` at the same index as the mark.
The algorithm repeats until 30 marks have been input and processed.

Example flowchart symbols: oval (start/end), rectangle (process), diamond (decision), parallelogram (input/output).

Practice questions

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1.What is an algorithm?
Easy
- AA precise set of rules or instructions to solve a specific problem
- BA type of computer hardware
- CA programming language
- DA data structure
2.Which of the following is NOT a method for designing an algorithm?
Easy
- AStructure diagrams
- BFlowcharts
- CPseudocode
- DBinary search
3.In a flowchart, which shape is used to represent a decision?
Easy
- ARectangle
- BDiamond
- COval
- DParallelogram
4.What does a structure diagram show?
Medium
- AThe flow of control through an algorithm
- BHierarchical top-down design, breaking a problem into sub-problems
- CThe exact syntax of a programming language
- DThe data types used in a program
5.In pseudocode, which of the following is the correct way to output a message?
Medium
- AOUTPUT 'Hello'
- Bprint('Hello')
- CPRINT 'Hello'
- DDISPLAY 'Hello'
6.Consider the following pseudocode: Count ← 1 Total ← 0 REPEAT INPUT Number Total ← Total + Number Count ← Count + 1 UNTIL Count > 10 OUTPUT Total What does this algorithm do?
Medium
- AIt outputs the sum of ten numbers entered by the user
- BIt outputs the average of ten numbers entered by the user
- CIt outputs the largest of ten numbers entered by the user
- DIt outputs the count of numbers entered
7.In the following pseudocode, what is stored in Grade[2] if the input Score[2] is 65? Count ← 0 REPEAT INPUT Score[Count] IF Score[Count] ≥ 70 THEN Grade[Count] ← 'A' ELSE IF Score[Count] ≥ 60 THEN Grade[Count] ← 'B' ELSE IF Score[Count] ≥ 50 THEN Grade[Count] ← 'C' ELSE IF Score[Count] ≥ 40 THEN Grade[Count] ← 'D' ELSE IF Score[Count] ≥ 30 THEN Grade[Count] ← 'E' ELSE Grade[Count] ← 'F' ENDIF ENDIF ENDIF ENDIF ENDIF Count ← Count + 1 UNTIL Count = 30
Hard
- A'B'
- B'A'
- C'C'
- D'D'
8.Which of the following is a characteristic of pseudocode?
Easy
- AIt uses strict syntax like a programming language
- BIt is a visual tool using shapes
- CIt uses short English words/statements to describe an algorithm
- DIt is written in binary

More questions

9.In a flowchart, what does a parallelogram represent?
Medium
- AInput/Output
- BProcess
- CDecision
- DStart/End
10.An algorithm uses a variable Total that is initialised to 0. The algorithm then inputs 5 numbers and adds each to Total. Finally it outputs Total divided by 5. What does this algorithm calculate?
Hard
- AThe sum of the numbers
- BThe average of the numbers
- CThe product of the numbers
- DThe maximum of the numbers
11.What is the purpose of a structure diagram?
Easy
- ATo show the flow of control in a program
- BTo break a problem into smaller sub-problems
- CTo write the exact code of a program
- DTo test the algorithm with different inputs
12.Which of the following is the correct pseudocode to input a value into a variable called Age?
Medium
- AINPUT Age
- BAge = input()
- CREAD Age
- DGET Age
13.A teacher uses the following algorithm to assign grades to 30 students. What grade is assigned to a student with a score of 55? Count ← 0 REPEAT INPUT Score[Count] IF Score[Count] ≥ 70 THEN Grade[Count] ← "A" ELSE IF Score[Count] ≥ 60 THEN Grade[Count] ← "B" ELSE IF Score[Count] ≥ 50 THEN Grade[Count] ← "C" ELSE IF Score[Count] ≥ 40 THEN Grade[Count] ← "D" ELSE IF Score[Count] ≥ 30 THEN Grade[Count] ← "E" ELSE Grade[Count] ← "F" ENDIF ENDIF ENDIF ENDIF ENDIF Count ← Count + 1 UNTIL Count = 30
Medium
- AA
- BB
- CC
- DD
14.What does a structure diagram represent?
Easy
- AThe flow of control in an algorithm
- BA hierarchical top-down decomposition of a problem
- CThe syntax of a programming language
- DThe input and output of a program
15.In a flowchart, which shape represents a decision?
Medium
- ARectangle
- BParallelogram
- CDiamond
- DOval
16.Consider the following pseudocode: Count ← 1 Total ← 0 REPEAT INPUT Number Total ← Total + Number Count ← Count + 1 UNTIL Count > 10 OUTPUT Total How many numbers are input in total?
Medium
- A9
- B10
- C11
- D1
17.Given the following pseudocode, what is the value of X after execution? X ← 0 FOR I ← 1 TO 4 FOR J ← 1 TO I X ← X + 1 NEXT J NEXT I
Hard
- A10
- B8
- C6
- D4
18.A flowchart uses a parallelogram shape. What does it represent?
Hard
- AProcess
- BInput/Output
- CDecision
- DStart/End
19.An algorithm uses a variable Total initialised to 0. It inputs 5 numbers and adds each to Total. Finally it outputs Total divided by 5. What does this algorithm do?
Medium
- ACalculates the sum of the numbers
- BCalculates the average of the numbers
- CCalculates the product of the numbers
- DCalculates the maximum of the numbers
20.What does a parallelogram represent in a flowchart?
Easy
- AInput/Output
- BProcess
- CDecision
- DStart/End
21.Given the following pseudocode, what is stored in Grade[2] if the input Score[2] is 65? Count ← 0 REPEAT INPUT Score[Count] IF Score[Count] ≥ 70 THEN Grade[Count] ← "A" ELSE IF Score[Count] ≥ 60 THEN Grade[Count] ← "B" ELSE IF Score[Count] ≥ 50 THEN Grade[Count] ← "C" ELSE IF Score[Count] ≥ 40 THEN Grade[Count] ← "D" ELSE IF Score[Count] ≥ 30 THEN Grade[Count] ← "E" ELSE Grade[Count] ← "F" ENDIF ENDIF ENDIF ENDIF ENDIF Count ← Count + 1 UNTIL Count = 30
Medium
- A"B"
- B"C"
- C"A"
- D"D"
22.Consider the following pseudocode: Count ← 1 Total ← 0 REPEAT INPUT Number Total ← Total + Number Count ← Count + 1 UNTIL Count > 10 OUTPUT Total How many times does the loop execute?
Hard
- A10
- B9
- C11
- D0
23.In the following pseudocode, what is stored in Grade[2] if the input Score[2] is 65? Count ← 0 REPEAT INPUT Score[Count] IF Score[Count] ≥ 70 THEN Grade[Count] ← 'A' ELSE IF Score[Count] ≥ 60 THEN Grade[Count] ← 'B' ELSE IF Score[Count] ≥ 50 THEN Grade[Count] ← 'C' ELSE Grade[Count] ← 'F' ENDIF ENDIF ENDIF Count ← Count + 1 UNTIL Count = 30
Medium
- A'B'
- B'A'
- C'C'
- D'F'
24.Consider the following pseudocode: Count ← 0 Total ← 0 REPEAT INPUT Number Total ← Total + Number Count ← Count + 1 UNTIL Count = 10 OUTPUT Total How many numbers does the user input?
Medium
- A9
- B10
- C11
- D0
25.Consider the following pseudocode: Count ← 0 REPEAT INPUT Score[Count] IF Score[Count] ≥ 70 THEN Grade[Count] ← 'A' ELSE IF Score[Count] ≥ 60 THEN Grade[Count] ← 'B' ELSE IF Score[Count] ≥ 50 THEN Grade[Count] ← 'C' ELSE IF Score[Count] ≥ 40 THEN Grade[Count] ← 'D' ELSE IF Score[Count] ≥ 30 THEN Grade[Count] ← 'E' ELSE Grade[Count] ← 'F' ENDIF ENDIF ENDIF ENDIF ENDIF Count ← Count + 1 UNTIL Count = 30 What is stored in Grade[2] if the input Score[2] is 65?
Medium
- A'A'
- B'B'
- C'C'
- D'D'
26.In a flowchart, what shape is used to represent a decision?
Easy
- ARectangle
- BDiamond
- CParallelogram
- DOval
27.Given the following pseudocode: Count ← 1 Total ← 0 REPEAT INPUT Number Total ← Total + Number Count ← Count + 1 UNTIL Count > 10 OUTPUT Total What does the algorithm output?
Hard
- AThe sum of the first 10 numbers input
- BThe sum of the first 11 numbers input
- CThe total of numbers input until a number >10 is entered
- DThe average of the numbers input
28.A teacher uses the following algorithm to assign grades to 30 students: Count ← 0 REPEAT INPUT Score[Count] IF Score[Count] ≥ 70 THEN Grade[Count] ← 'A' ELSE IF Score[Count] ≥ 60 THEN Grade[Count] ← 'B' ELSE IF Score[Count] ≥ 50 THEN Grade[Count] ← 'C' ELSE IF Score[Count] ≥ 40 THEN Grade[Count] ← 'D' ELSE IF Score[Count] ≥ 30 THEN Grade[Count] ← 'E' ELSE Grade[Count] ← 'F' ENDIF ENDIF ENDIF ENDIF ENDIF Count ← Count + 1 UNTIL Count = 30 What grade is assigned to a student with a score of 55?
Medium
- AA
- BB
- CC
- DD
29.Consider the following pseudocode: X ← 0 FOR I ← 1 TO 4 FOR J ← 1 TO I X ← X + 1 NEXT J NEXT I What is the value of X after execution?
Medium
- A10
- B16
- C4
- D6
30.An algorithm uses a variable Total initialised to 0. It inputs 5 numbers and adds each to Total. Finally it outputs Total divided by 5. What does this algorithm calculate?
Medium
- ASum of the numbers
- BAverage of the numbers
- CProduct of the numbers
- DCount of numbers
31.Consider the following pseudocode: Count ← 0 Total ← 0 REPEAT INPUT Number Total ← Total + Number Count ← Count + 1 UNTIL Count = 10 OUTPUT Total / Count What does this algorithm output?
Hard
- ASum of 10 numbers
- BAverage of 10 numbers
- CSum of 9 numbers
- DAverage of 9 numbers
32.Consider the following pseudocode: Total ← 0 FOR I ← 1 TO 3 INPUT N Total ← Total + N NEXT I OUTPUT Total If the user inputs 5, 10, and 15, what is the output?
Hard
- A30
- B25
- C20
- D35
33.In the following pseudocode, what is the purpose of the algorithm? Count ← 0 Total ← 0 REPEAT INPUT Number Total ← Total + Number Count ← Count + 1 UNTIL Count = 10 OUTPUT Total / Count
Medium
- AIt inputs 10 numbers and outputs the total
- BIt inputs 10 numbers and outputs the average
- CIt inputs numbers until a negative number is entered and outputs the sum
- DIt inputs 10 numbers and outputs the largest number
34.Which shape in a flowchart represents a process?
Easy
- AOval
- BRectangle
- CDiamond
- DParallelogram
35.Consider the following pseudocode: Total ← 0 FOR I ← 1 TO 5 FOR J ← 1 TO I Total ← Total + 1 NEXT J NEXT I OUTPUT Total What is output?
Hard
- A5
- B10
- C15
- D20
36.Which of the following is correct pseudocode to input a value into a variable called Age and then output it?
Medium
- AINPUT Age OUTPUT Age
- BAge = input() print(Age)
- CREAD Age WRITE Age
- DGET Age PUT Age
37.The pseudocode below is intended to find the highest number in a list of 10 numbers. However, it contains a logic error. What is the error? Max ← 0 Count ← 0 REPEAT INPUT Number IF Number > Max THEN Max ← Number ENDIF Count ← Count + 1 UNTIL Count = 10 OUTPUT Max
Hard
- AMax should be initialised to a very small number instead of 0
- BThe loop should repeat until Count > 10
- CThe IF condition should be Number < Max
- DThe variable Count should be initialised to 1
38.The following pseudocode searches an array Score[0..9] for a value Target. What is output if Target is 45 and Score contains {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}? Found ← False Index ← 0 REPEAT IF Score[Index] = Target THEN Found ← True ENDIF Index ← Index + 1 UNTIL Found = True OR Index = 10 IF Found = True THEN OUTPUT Index - 1 ELSE OUTPUT -1 ENDIF
Hard
- A3
- B4
- C-1
- D45
39.What does the diamond shape represent in a flowchart?
Easy
- AStart/End
- BProcess
- CDecision
- DInput/Output
40.Which of the following is the correct definition of an algorithm?
Easy
- AA precise set of rules or instructions to solve a specific problem or task
- BA high-level programming language
- CA diagram showing the flow of data in a system
- DA type of computer hardware

Slides

What is an Algorithm?

An algorithm is a precise set of rules or instructions to solve a specific problem or task.
There are three main ways to design an algorithm: structure diagrams, flowcharts, and pseudocode.
Structure diagrams show hierarchical top-down design, breaking problems into sub-problems.
Flowcharts use shapes to represent different functions and lines to show flow of control.
Pseudocode uses short English words/statements to describe an algorithm.

Which of the following is NOT a method for designing an algorithm?

Structure diagram
Flowchart
Pseudocode
Python code

Structure Diagrams

Structure diagrams show hierarchical top-down design in a visual form.
Each problem is divided into sub-problems, and each sub-problem is divided further.
At each level, the problem is broken down into more detailed tasks that can be implemented using a single subroutine.

A structure diagram shows ____ top-down design, where each problem is divided into ____.

Flowcharts

Flowcharts are a visual tool that uses shapes to represent different functions.
They show data input/output, processes, decisions, and repetition.
Lines (arrows) are used to show the flow of control.

In a flowchart, what shape is typically used for a decision?

Rectangle
Diamond
Parallelogram
Oval

Pseudocode

Pseudocode is a text-based tool that uses short English words/statements to describe an algorithm.
It is more structured than plain English but very flexible.
Do not use actual programming language syntax like print() or input() with brackets.
Use simple statements like: INPUT Age and OUTPUT 'Welcome'.

In pseudocode, to get a value from the user you write ____ Age. To display a message you write ____ 'Hello'.

Explaining Algorithms

A well-designed algorithm should be interpretable by a new user.
To understand a complex algorithm, look for comments, consider the context, or test with different inputs.
Algorithms can be written using flowcharts, pseudocode, or high-level programming language code.

Which of these are true about explaining algorithms?

Comments in code can help explain an algorithm.
Testing an algorithm with different inputs is not helpful.
The purpose of an algorithm is to solve a problem.
Algorithms can only be written in pseudocode.

Worked Example: Grade Assignment

The algorithm inputs marks into an array Score[].
It checks each mark against boundaries (70, 60, 50, 40, 30) and assigns a grade (A to F) to Grade[].
The process repeats for 30 students.

In the grade algorithm, what grade is assigned for a mark of 65?

Example: Adding Ten Numbers

The algorithm initializes Count=1, Number=0, Total=0.
It repeats: input a number, add to Total, increment Count.
The loop continues until Count > 10, then outputs Total.

In the algorithm, the variable ____ is used to count how many numbers have been entered. The loop continues until Count ____ 10.

Key Points to Remember

Use pseudocode by default when asked to write an algorithm.
Use flowcharts only when asked or when visual logic helps.
Examiners reward clarity, not decoration.
Always use simple statements like INPUT and OUTPUT.

When writing an algorithm for an exam, which method should you default to?

Flowchart
Pseudocode
Python code
Structure diagram

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