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7. Algorithm Design and Problem Solving

SECTION 2: ALGORITHMS, PROGRAMMING AND LOGIC

Important Note

These notes cover the main points for revision. They are great for reviewing key concepts, but for in-depth understanding, always keep your textbook nearby for reference.

Algorithm design and problem solving are fundamental skills in computer science. This chapter covers the Program Development Life Cycle, decomposition techniques, design tools (structure charts, flowcharts, pseudocode), and common algorithms for solving problems.

Table of Contents

7.1 Program Development Life Cycle

The Program Development Life Cycle (PDLC) consists of five key stages that guide the development of software from initial concept to final implementation and maintenance.

  1. 1. Analysis
  2. 2. Design
  3. 3. Coding
  4. 4. Testing
  5. 5. Maintenance (covered in Chapter 8)

7.1.1 Analysis

The purpose of analysis is to understand what the program needs to do. The result is a requirements specification — a clear definition of the program's goals.

Techniques used in analysis:

Abstraction

Focus only on important details, removing anything unnecessary.

Example: A map only shows roads, not trees or benches.

Decomposition

Break down a large problem into smaller parts.

Example: Getting dressed → Select clothes → Remove current clothes → Put on new clothes.

7.1.2 Design

Design converts the analysis into a plan for how to solve the problem. It outlines:

  • • Tasks to be completed
  • • How each task will be done
  • • How tasks interact

Common design tools:

Structure Charts

Show modular breakdown of a system

Flowcharts

Visual representation of algorithms

Pseudocode

English-like syntax describing steps

7.1.3 Coding and Iterative Testing

  • •Writing the program using a high-level language (e.g. Python, Java)
  • •Each module is developed and tested individually
  • •Iterative testing: Repeating testing and improving until the module works correctly

7.1.4 Testing (Final Stage)

  • •Testing the complete program using a variety of test data
  • •Ensures that all modules work together and meet the original specification

7.2 Computer Systems, Sub-systems and Decomposition

7.2.1 Computer Systems and Sub-systems

A computer system consists of:

  • • Hardware
  • • Software
  • • Data
  • • People
  • • Communications

Top-down design:

  • • Break system into smaller sub-systems
  • • Break sub-systems down further into subroutines
  • • Use structure diagrams to show hierarchy

Benefits:

  • • Multiple programmers can work in parallel
  • • Makes development faster and more manageable

7.2.2 Decomposing a Problem

All computer systems can be broken down into four parts:

1. Inputs

What data is entered into the system?

2. Processes

What operations need to be done?

3. Outputs

What information is produced?

4. Storage

What needs to be saved for future use?

Example: Alarm App

  • • Inputs: Set alarm time, press snooze, etc.
  • • Processes: Check current time, manage snooze logic
  • • Outputs: Sound the alarm
  • • Storage: Save alarm settings

7.3 Design Tools

Structure Diagrams

Note: Structure diagrams (also known as structure charts) show the hierarchical breakdown of a system into modules and subroutines. They illustrate how a system is decomposed from top to bottom.

Structure diagrams use boxes to represent modules, with lines showing the relationships between them. The top box represents the main program, and lower boxes represent subroutines or modules.

Key Point: A subroutine is a named block of code that performs a specific task and can be called from other parts of the program.

Structure Diagrams Example
Structure Diagram Example

Flowcharts

Flowcharts use standardized symbols to represent different operations in an algorithm:

Oval: Start/Stop

Rectangle: Process

Diamond: Decision

Parallelogram: Input/Output

Flowchart example diagram

Example: Calculate Total of First 10 Numbers

This flowchart demonstrates a common algorithm pattern using a loop with a decision to calculate the sum of numbers from 1 to 10.

Flowchart showing calculation of sum of first 10 numbers

7.4 Pseudocode

Pseudocode is a simplified method of writing algorithms using English-like syntax. It is not constrained by the strict syntax rules of programming languages but mimics their structure to make algorithms easy to understand.

1. Variables and Assignment

Variables in pseudocode are used to store data. Assignment is done using the ← symbol.

Example:

In the above example, the variable PRICE is assigned the value 100, and NAME is assigned "Kunal".

2. Input and Output

  • • Input: Used to receive data from the user
  • • Output: Used to display information to the user

Syntax:

Example:

Important Note for Exams:

In exam questions, especially in error detection questions, some past papers might use the word "print" instead of "OUTPUT". Please understand that this is NOT an error. Both terms mean the same thing - they are used to display information. When you see "print" in a question, treat it the same way you would treat "OUTPUT".

3. Conditional Statements (IF, ELSE)

Conditional statements are used to perform different actions based on a condition.

Syntax:

Example 1:

Example 2:

Example 3:

4. Case Statements (CASE, OTHERWISE)

CASE statements allow multi-way branching, selecting actions based on the value of a variable.

Syntax:

Example 1:

Example 2:

Difference Between CASE and Nested IF Statements

CASE OF Statement

Used when there are multiple possible values for a single variable. Cleaner and more readable.

CASE OF Grade
    "A": OUTPUT "Excellent"
    "B": OUTPUT "Good"
OTHERWISE
    OUTPUT "Improvement Needed"
ENDCASE
  • ✓ Cleaner and more readable
  • ✓ Faster to write
  • ✓ Easier to maintain
Nested IF Statement

More flexible, can handle complex conditions that don't rely on just one variable.

IF GRADE = 'A' THEN
    OUTPUT "EXCELLENT"
ELSE
    IF GRADE = 'B' THEN
        OUTPUT "GOOD"
    ELSE
        OUTPUT "Improvement Needed"
    ENDIF
ENDIF
  • ✗ More complex and less readable
  • ✗ More prone to errors
  • ✗ Requires more lines of code

Which to Use? Use CASE when comparing the same variable against different specific values. Use nested IF when you need to compare multiple conditions or perform different checks.

💡 Important: Also check the book for Validation and Verification - HIGHLY RECOMMENDED!

5. Loops (FOR, REPEAT, WHILE)

Loops are used to repeat sections of code.

FOR Loop (Count Controlled Loop)

Repeats a block of code a set number of times.

Syntax:
Example 1:
Example 2:
Example 3: Descending Order

Use STEP -1 to count downwards.

REPEAT UNTIL Loop (Postcondition/Exit Controlled)

Repeats until a condition becomes true. Always executes at least once.

Syntax:
Example 1:
Example 2:

WHILE Loop (Precondition/Entry Controlled)

Repeats while a condition is true. May not run at all if condition is false initially.

Syntax:
Example 1:
Example 2:

Difference Between REPEAT and WHILE Loops

REPEAT...UNTIL
  • • Always runs at least once
  • • Checks condition after executing code
  • • Exit controlled loop
WHILE
  • • May not run if condition is false initially
  • • Checks condition before executing code
  • • Entry controlled loop

Example: Password Verification

This example shows the same logic implemented with both loop types.

WHILE Loop
REPEAT...UNTIL Loop

6. Common Algorithms

Counting

Used to keep a count of occurrences.

Finding Maximum and Minimum

Used to find the largest or smallest values in a set.

Linear Search

Used to search for an item in a list.

String Manipulation in Pseudocode

Printing Characters Letter by Letter

Printing Adjacent Character Pairs

Menu-Driven Programs

Menu-driven programs use a REPEAT loop to display options and execute different actions based on user choice.

Past Paper Question: Algorithm Maintainability

Past Paper

Question (b): A programmer has written a program that will be maintained by another programmer. Explain how the program can be written to make sure it can be easily maintained by the other programmer.

Answer:

  • •Meaningful identifiers: Use descriptive names (e.g., using Number instead of N).
  • •Comments: Add explanations (e.g., // loops until the guess equals the number).
  • •Procedures/Functions: Break the algorithm into smaller subroutines/procedures.

7.5 Arrays

An array is a fixed-length structure that stores multiple items of the same data type.

Array Declaration

One-Dimensional Arrays

Two-Dimensional Arrays

Array Assignment

Single Element Assignment

Using Loops to Fill Arrays

Two-Dimensional Array Initialization

7.6 Validation and Verification

Validation

Validation checks whether data is reasonable before being processed.

Types of Validation Checks:

  • • Range checks
  • • Length checks
  • • Type checks
  • • Presence checks
  • • Format checks
  • • Check digits

Range Check

Example 1:
Example 2:

Length Check

Example 1:
Example 2:

Format Check Examples

Product Code Validation (Length = 6):
Product Code Validation (Must start with "PD"):
Alternative using WHILE:

Verification

Verification is checking that data has been accurately copied from one source to another – for instance, input into a computer or transferred from one part of a computer system to another.

Methods of Verification:

  • • Double entry: The data is entered twice and compared

  • • Screen/visual check: User visually checks the data on screen

7.7 Test Data

Before confirming that a program or system works correctly, it needs to be tested. Testing ensures that:

  • • The solution performs as expected
  • • Errors are detected and corrected before implementation

A set of test data is all the data items required to work through a solution.

Example: If a program calculates the average of 10 exam marks, a set of test data might include 10 values like 50, 60, 70, 80, 90, 50, 60, 70, 80, 90.

Testing must include multiple sets of data to fully check all possible cases.

Types of Test Data

TypePurposeExampleExpected Result
Normal DataData the program is expected to handle during normal operation50, 60, 70, 80, 90, 50, 60, 70, 80, 90Average = 70
Abnormal (Erroneous) DataData that should be rejected as invalid or not suitable-12, "eleven"Both rejected as invalid
Extreme DataData at the upper and lower limits of the valid range0, 100Both accepted as valid
Boundary DataData just inside and just outside the limits of the valid rangeFor 0–100 range: -1, 0-1 rejected, 0 accepted

Example Summary

For an algorithm to find average percentage marks (0–100):

  • • Normal data: 40, 50, 60 → expected average = 50
  • • Abnormal data: 5, 120 → should be rejected
  • • Extreme data: 0, 100 → accepted
  • • Boundary data: 1 rejected, 0 accepted; 100 accepted, 101 rejected

7.8 Sorting and Searching Algorithms

Bubble Sort

Bubble sort is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order.

Linear Search

Linear search checks each element in a list sequentially until the target item is found or the list is exhausted.

Chapter Summary

This chapter covered the Program Development Life Cycle (Analysis, Design, Coding, Testing, Maintenance), decomposition techniques, design tools (structure charts, flowcharts, pseudocode), common algorithms (counting, finding max/min, linear search, bubble sort), arrays, validation and verification, and test data types. Understanding these concepts is essential for IGCSE O Level Computer Science.

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