TOPIC 8 PROBLEM SOLVING

Problem solving is an important skill in Computer Science that involves identifying a problem, analyzing it, and developing a logical solution. Computers solve problems by following instructions provided in a systematic manner.

I. CONCEPT OF PROBLEM SOLVING

Problem solving is the process of finding a solution to a given problem by following logical and systematic steps. In computer science, problems are solved using algorithms and computer programs.

Example: Using a computer to calculate student results instead of doing it manually.

Practical Activity

Identify one school problem that can be solved using a computer.

Scenario Activity

Explain why computers cannot solve problems without instructions.

II. IDENTIFICATION OF A PROBLEM

Problem identification involves clearly recognizing and defining the problem to be solved. A problem must be well understood before attempting to find a solution. Example: Identifying that manual calculation of marks causes delays and errors.

Practical Activity

List three problems in daily life that can be suitable for computer solutions.

Scenario Activity

Explain the effects of poorly defined problems in computer problem solving.

III. ANALYSIS OF A PROBLEM

Problem analysis involves breaking a problem into smaller manageable parts. This includes identifying inputs, processes, and outputs.

Example:

Input: Student marks

Process: Add marks and divide by number of subjects

Output: Average marks

Practical Activity

Analyze the steps required to calculate total marks for a class.

Scenario Activity

Why is problem analysis important before designing a solution?

IV. DESIGNING A SOLUTION

Designing a solution involves planning how the problem will be solved before writing a computer program. This is done using algorithms, pseudocode, and flowcharts.

A. ALGORITHM

An algorithm is a finite, step-by-step set of logical instructions used to solve a problem. It must be clear, precise, and arranged in logical order.

Characteristics of a good algorithm

i. It must have a clear start and end.

ii. Each step must be clear and unambiguous.

iii. It must produce a result.

iv. It must be finite.

v. Steps must follow logical order.

Example 1: Algorithm to add two numbers

i. Start

ii. Input first number A

iii. Input second number B

iv. Add A and B

v. Display the sum

vi. End

Example 2: Algorithm to calculate student average

i. Start

ii. Input marks for all subjects

iii. Calculate total marks

iv. Divide total by number of subjects

v. Display average

vi. End

Practical Activity

Write an algorithm to calculate the area of a triangle.

Scenario Activity

Explain what may happen if algorithm steps are not arranged correctly.

B. CONSTRUCTION OF AN ALGORITHM

Algorithm construction refers to the process of developing an algorithm by identifying inputs, processes, and outputs.

i. Identify the problem to be solved.

ii. Determine the required inputs.

iii. Identify processing steps.

iv. Determine the expected output.

v. Arrange steps logically.

Example:

Problem: Calculate total marks

Input: Subject marks

Process: Add all marks

Output: Total marks

Practical Activity

Construct an algorithm to determine whether a number is even or odd.

C. REPRESENTATION OF ALGORITHMS USING PSEUDOCODE

Pseudocode is a structured English description of an algorithm. It is not written in a programming language.

Example 1: Pseudocode to add two numbers

START

INPUT A

INPUT B

SUM = A + B

DISPLAY SUM

END

Example 2: Pseudocode to calculate student average

START

INPUT total Marks

INPUT number Of Subjects

average = total Marks / number Of Subjects

DISPLAY average

END

Practical Activity

Write pseudocode to calculate the perimeter of a rectangle.

D. CONTROL STRUCTURES IN ALGORITHMS

Control structures determine the order in which instructions are executed.

I. SEQUENCE CONTROL STRUCTURE

Sequence executes instructions in order.

Example Algorithm

START

INPUT length

INPUT width

area = length × width

DISPLAY area

END

Flowchart Diagram (Sequence)

┌─────────┐

│ START │

└────┬────┘

│

┌────▼────┐

│ INPUT │

│ length │

└────┬────┘

│

┌────▼────┐

│ INPUT │

│ width │

└────┬────┘

│

┌────▼────┐

│ PROCESS │

│ area = │

│ length× │

│ width │

└────┬────┘

│

┌────▼────┐

│ DISPLAY │

│ area │

└────┬────┘

│

┌────▼────┐

│ END │

└─────────┘

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II. SELECTION CONTROL STRUCTURE

Selection allows decision making based on conditions. Example Algorithm

START

INPUT marks

IF marks ≥ 50

DISPLAY PASS

ELSE

DISPLAY FAIL

END IF

END

Flowchart Diagram (Selection)

┌─────────┐

│ START │

└────┬────┘

│

┌────▼────┐

│ INPUT │

│ marks │

└────┬────┘

│

┌────▼────┐

│ DECISION│

│ marks ≥50? │

└────┬────┘

YES │ NO

┌───▼───┐ ┌───▼───┐

│ DISPLAY│ │ DISPLAY│

│ PASS │ │ FAIL │

└───┬───┘ └───┬───┘

│ │

└─────────┘

│

┌──▼──┐

│ END │

└─────┘

III. ITERATION CONTROL STRUCTURE

Iteration allows repetition of steps until a condition is met.

Example Algorithm

START

SET total = 0

FOR i = 1 TO 5

INPUT mark

total = total + mark

END FOR

DISPLAY total

END

Flowchart Diagram (Iteration)

┌─────────┐

│ START │

└────┬────┘

│

┌───────▼────────┐

│ total = 0, i=1 │

└───────┬────────┘

│

┌────▼────┐

│ INPUT │

│ mark │

└────┬────┘

│

┌────▼────┐

│ PROCESS │

│ total= │

│ total+mark│

└────┬────┘

│

┌────▼────┐

│ i = i+1 │

└────┬────┘

│

┌────▼────┐

Practical Activity

│ DECISION│

│ i ≤ 5 ? │

└───┬─────┘ YES │ NO

┌───▼───┐ │ REPEAT │

└───┬───┘ │

┌▼┐

│DISPLAY│

│ total │

└──┬───┘

│

┌──▼──┐

│ END │

└─────┘

Write an algorithm using iteration to display numbers from 1 to 10.

E. FLOWCHART SYMBOLS USED IN PROBLEM SOLVING

i. Oval represents Start or End

ii. Parallelogram represents Input or Output

iii. Rectangle represents Processing

iv. Diamond represents Decision

v. Arrow represents Flow of control

Scenario Activity

Explain why flowcharts are important in solving complex problems.

V. IMPLEMENTATION OF THE SOLUTION

Implementation involves converting the designed solution into a computer program. Example: Writing a program in Scratch or Python to calculate grades.

Practical Activity

Write simple instructions to display your name on the screen.

Scenario Activity

What problems may occur if a solution is poorly implemented?

VI. TESTING AND DEBUGGING

Testing checks whether a program works correctly, while debugging removes errors.

i. Syntax errors occur due to incorrect commands.

ii. Logic errors occur when output is incorrect.

iii. Runtime errors occur during program execution.

Practical Activity

Test a simple program and identify errors.

Scenario Activity

Explain why testing is important before using a program.

vii. DOCUMENTATION AND MAINTENANCE

Documentation records how a solution works, while maintenance involves updating and improving it.

Documentation helps users understand the solution.
Maintenance ensures the solution continues to meet needs.

Example: Updating a school system to include new subjects.

Practical Activity

Write short documentation for a simple algorithm.

Scenario Activity

Why is maintenance important after problem solving?