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🧩 ALGORITHM DESIGN & PROBLEM-SOLVING

1️⃣ Program Development Life Cycle (PDLC)

You must know the four stages and what happens in each.

🔹 1. Analysis​

This is understanding the problem.

Includes:

✅ Identifying the problem​

  • What needs to be solved?
  • Who will use the system?

✅ Requirements​

  • What inputs?
  • What outputs?
  • What processing?
  • What storage?

✅ Abstraction​

Removing unnecessary detail and focusing only on what matters.

Example:
If designing a student grading system:

  • Ignore student hobbies.
  • Focus on marks, names, averages.

✅ Decomposition​

Breaking a large problem into smaller sub-problems.

Example:
School system →

  • Input marks
  • Calculate average
  • Assign grade
  • Display result

🔹 2. Design​

Planning the solution before coding.

Includes:

  • Structure diagrams
  • Flowcharts
  • Pseudocode

You design:

  • Inputs
  • Processes
  • Outputs
  • Storage

🔹 3. Coding​

  • Writing the actual program.
  • Uses a programming language.
  • Includes iterative testing (testing as you code).

🔹 4. Testing​

  • Use test data.
  • Identify errors.
  • Fix bugs.

2️⃣ Sub-systems & Decomposition

🔹 Computer Systems Have Sub-systems​

Large systems are made of smaller systems.

Example: School system

  • Attendance system
  • Results system
  • Library system

Each can be broken down further.

🔹 Decomposition​

Breaking a problem into smaller parts makes it:

  • Easier to manage
  • Easier to test
  • Easier to debug

This is frequently examined.

3️⃣ Methods of Designing Algorithms

You must know three:

🔹 1. Structure Diagrams​

  • Show system broken into modules.
  • Hierarchical structure.
  • No logic shown.

🔹 2. Flowcharts​

Use standard symbols:

SymbolMeaning
OvalStart/End
ParallelogramInput/Output
RectangleProcess
DiamondDecision
ArrowFlow line

🔹 3. Pseudocode​

  • Structured English.
  • Uses programming style.
  • Must be precise.

4️⃣ Inputs, Processes, Outputs, Storage (IPOS)

Every system includes:

Input​

Data entered.

Process​

What happens to the data.

Output​

Result produced.

Storage​

Data saved for later use.

5️⃣ Standard Methods of Solution (Very Important)

These are guaranteed exam areas.

🔹 1. Linear Search​

Searches through a list one item at a time.

Algorithm:​

Used when:

  • Data is unsorted.

🔹 2. Bubble Sort​

Sorts by repeatedly swapping adjacent values.

Steps:​

  1. Compare first two values.
  2. Swap if wrong order.
  3. Repeat.
  4. Largest value "bubbles" to end.

🔹 3. Totalling​

Adds values together.

🔹 4. Counting​

Counts occurrences.

🔹 5. Maximum / Minimum​

Maximum:​

🔹 6. Average​

6️⃣ Validation & Verification

Very common 6-mark question.

🔹 Validation

Checks that data is sensible and acceptable.

Types:

TypeMeaning
Range checkValue within limits
Length checkCorrect number of characters
Type checkCorrect data type
Presence checkNot left blank
Format checkCorrect pattern (e.g. email)
Check digitMathematical check (e.g. barcodes)

🔹 Verification

Checks data was entered correctly.

Types:

TypeMeaning
Visual checkHuman checks data
Double entryData entered twice and compared

⚠️ Key difference:

Validation → Is data sensible?
Verification → Was data entered correctly?

7️⃣ Test Data

You must know 4 types.

🔹 Normal Data​

Valid input within range.

Example:
Age 18 (range 0–120)

🔹 Abnormal Data​

Invalid data.

Example:
Age = -5

🔹 Extreme Data​

Largest/smallest acceptable value.

If range 0–120:

  • 0
  • 120

🔹 Boundary Data​

Largest/smallest acceptable AND corresponding rejected.

If range 0–120:

  • 0 (accepted)
  • -1 (rejected)
  • 120 (accepted)
  • 121 (rejected)

Boundary questions are common.

8️⃣ Trace Tables & Dry Runs

Used to:

  • Track variables
  • Identify logic errors

Trace tables include:

| Step | Variable | Output |

You simulate the algorithm manually.

9️⃣ Errors in Algorithms

You must identify and correct:

🔹 Logical Errors​

Program runs but wrong output.

🔹 Syntax Errors​

Wrong structure (in code).

🔹 Runtime Errors​

Occurs during execution (e.g. divide by zero).

🔟 Writing Algorithms

When writing pseudocode, always include:

  • Variables
  • User prompts
  • Inputs
  • Processing
  • Outputs

Example:

⚠️ Precision Rules (Exam Critical)

Correct:

Use symbols:

✏️ Exam Strategy Tips

🔹 1. For 6–8 Mark Algorithm Questions​

Include:

  • Initialization of variables
  • Clear loops
  • Proper indentation
  • End statements (ENDIF, NEXT)

🔹 2. For Test Data Questions​

Always provide:

  • Value
  • Expected result

🔹 3. For Trace Tables​

Be slow and careful.
Marks are often 4–6 here.

🔹 4. Always Initialize Variables​

📌 Quick Revision Summary

You must confidently understand:

✅ PDLC stages
✅ Decomposition
✅ Structure diagrams
✅ Flowcharts
✅ Pseudocode
✅ Linear search
✅ Bubble sort
✅ Totalling, counting
✅ Max, min, average
✅ Validation vs Verification
✅ Test data types
✅ Trace tables
✅ Error correction