Algorithmic Thinking: Creating Step-by-Step Solutions

This lesson covers algorithmic thinking, a core component of computational thinking as required by OCR J277 Section 2.1. Algorithmic thinking is about designing clear, logical, step-by-step solutions to problems.

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What Is an Algorithm?

An algorithm is a precise, step-by-step set of instructions for solving a problem or completing a task. An algorithm must be:

Property	Description
Finite	It must have a definite end — it cannot run forever
Precise	Each step must be clearly defined and unambiguous
Effective	Each step must be achievable (it can actually be carried out)
Ordered	The steps must be in the correct sequence

Everyday Algorithms

Algorithms are not just for computers — we use them in everyday life:

Task	Algorithm
Making tea	1. Boil water. 2. Put tea bag in cup. 3. Pour water into cup. 4. Wait 3 minutes. 5. Remove tea bag. 6. Add milk if desired.
Getting dressed	1. Choose clothes. 2. Put on underwear. 3. Put on shirt. 4. Put on trousers. 5. Put on socks. 6. Put on shoes.
Crossing the road	1. Stop at the kerb. 2. Look left. 3. Look right. 4. Look left again. 5. If road is clear, cross. 6. Otherwise, wait and repeat.

OCR Exam Tip: An algorithm is NOT a program. An algorithm is the plan (language-independent). A program is the implementation of an algorithm in a specific programming language. You can express an algorithm in English, pseudocode, or a flowchart.

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What Is Algorithmic Thinking?

Algorithmic thinking is the ability to define clear, step-by-step instructions for solving a problem. It involves:

1. Identifying the problem — What needs to be solved?
2. Planning the steps — What sequence of actions will solve the problem?
3. Considering edge cases — What happens with unusual or extreme inputs?
4. Ensuring correctness — Will the algorithm always produce the right output?
5. Optimising — Can the solution be made more efficient?

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Representing Algorithms

Algorithms can be represented in three main ways:

Method	Description	When Used
Written description	Plain English steps	Initial planning, explaining to non-technical people
Pseudocode	Structured, code-like language that is not tied to any programming language	Detailed design, OCR exam questions
Flowcharts	Visual diagrams using standard symbols	Visual learners, design documentation, OCR exam questions

We will cover pseudocode and flowcharts in detail in later lessons.

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Key Algorithmic Concepts

Sequence

Sequence means executing instructions one after another in order.

Step 1: Input the first number
Step 2: Input the second number
Step 3: Add the two numbers together
Step 4: Output the result

Selection (Decision Making)

Selection means choosing which instructions to execute based on a condition.

Step 1: Input the temperature
Step 2: IF temperature > 30 THEN
Step 3:     Output "It is hot"
Step 4: ELSE
Step 5:     Output "It is not hot"
Step 6: ENDIF

Iteration (Repetition / Loops)

Iteration means repeating a set of instructions, either a fixed number of times or until a condition is met.

Count-controlled loop (FOR loop):

FOR i = 1 TO 10
    Output i
NEXT i

Condition-controlled loop (WHILE loop):

WHILE answer != "quit"
    Input answer
ENDWHILE

Construct	Symbol	Purpose
Sequence	Instructions in order	Execute steps one after another
Selection	IF...THEN...ELSE	Make decisions based on conditions
Iteration	FOR / WHILE	Repeat instructions

OCR Exam Tip: Sequence, selection, and iteration are the three fundamental programming constructs. Every algorithm is built from combinations of these three. Make sure you can identify which construct is being used in a given piece of pseudocode or flowchart.

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Designing Algorithms: A Worked Example

Problem: Design an algorithm that asks the user for 5 numbers and outputs the largest.

Step-by-step design:

1. Set a variable largest to a very small number (or the first input).
2. Repeat 5 times: a. Ask the user to input a number. b. If the number is greater than largest, update largest.
3. Output largest.

In pseudocode:

largest = 0
FOR i = 1 TO 5
    INPUT number
    IF number > largest THEN
        largest = number
    ENDIF
NEXT i
OUTPUT largest

Identifying the constructs:

• Sequence — The overall flow from start to finish
• Iteration — The FOR loop repeating 5 times
• Selection — The IF statement comparing each number to the largest

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Common Algorithm Patterns

These patterns appear frequently in problems and exams:

Pattern	Description
Linear search	Check each item in a list one by one until you find the target
Counting	Use a counter variable to count how many items meet a condition
Totalling	Use a running total to add up values
Finding max/min	Track the largest or smallest value seen so far
Validation	Check that input meets certain criteria before accepting it
Authentication	Compare entered credentials against stored values

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Testing Algorithms

After designing an algorithm, you should test it with different inputs:

Test Type	Description	Example
Normal data	Typical, expected inputs	Numbers within the expected range
Boundary data	Values at the edge of acceptable ranges	The minimum and maximum allowed values
Erroneous data	Invalid or unexpected inputs	Text when a number is expected, negative values

OCR Exam Tip: When asked to design an algorithm, always consider what happens with unusual inputs. A good algorithm handles edge cases (e.g. what if the user enters a negative number, or the list is empty?). Mentioning this in your answer shows deeper understanding.

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Summary

Algorithmic thinking is the ability to design clear, step-by-step solutions to problems. Every algorithm uses sequence, selection, and iteration. Algorithms can be represented as written descriptions, pseudocode, or flowcharts. For the OCR J277 exam, practise designing algorithms for common problems (searching, counting, finding max/min) and testing them with normal, boundary, and erroneous data.

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Worked Example: Designing a PIN Login Algorithm

Problem: Design an algorithm for a cash machine login. The user must enter a four-digit PIN. If the PIN matches the stored PIN the user is granted access. If the PIN is wrong, the user gets up to three attempts in total, after which the card is retained.

Step 1 — Understand the requirements. What are the inputs, outputs, and edge cases?

• Inputs: the user's entered PIN, the stored PIN for the card.
• Outputs: an "access granted" message, a "try again" message, or a "card retained" message.
• Edge cases: what if the first attempt is correct? what if all three attempts fail? what if the user enters something that is not four digits?

Step 2 — Identify the constructs needed.

• Sequence for the overall flow.
• Iteration for "up to three attempts" — this is condition-controlled, so a WHILE loop fits naturally. We stop looping when either the PIN matches or the attempt counter reaches 3.
• Selection inside the loop, to decide whether the current entry matches.
• Selection after the loop, to decide which final message to display.

Step 3 — Draft pseudocode.

storedPIN = "4271"
attempts = 0
accessGranted = False