Problem-solving is one of the most fundamental skills in computer science. Before coding an actual program, a problem must be fully understood, broken down, and structured into a logical solution. This chapter explores key problem-solving strategies that are commonly used in algorithm design.
1. Understanding Problem-Solving in Computing
In computing, problem-solving is the process of identifying a problem, breaking it down into smaller components, and designing an effective solution using structured logic. Well-designed problem-solving methods lead to efficient algorithms that can be implemented in a programming language.
A structured approach to problem-solving ensures that solutions are:
- Clear and logical – Easy to understand and follow.
- Efficient – Minimizing redundant steps.
- Reusable – Can be applied to similar problems with minimal modifications.
The Four Steps of Problem-Solving in Computing
- Understanding the Problem – Identify what needs to be solved.
- Breaking the Problem Down (Decomposition) – Divide the problem into smaller, manageable parts.
- Designing a Solution – Develop a logical sequence of steps (algorithm).
- Testing and Improving – Run sample data through the solution and refine it.
2. Decomposition: Breaking Down a Complex Problem
What is Decomposition?
Decomposition is the process of breaking a large, complex problem into smaller, more manageable parts. Each part can then be solved individually before being combined into a complete solution. This strategy is widely used in both computational thinking and real-world problem-solving.
Why is Decomposition Important?
- Makes complex problems easier to handle – Instead of tackling an overwhelming task, decomposition allows us to solve one small part at a time.
- Increases efficiency – Each component can be optimized separately.
- Encourages reusability – Some components can be used for other tasks.
- Improves debugging – Errors are easier to find and fix when working with smaller sections.
Example: Organizing a School Event
Imagine you are planning a school event. Instead of trying to do everything at once, you can break the task into smaller steps:
- Invitations – Create and send out invitations.
- Venue Setup – Arrange seating, decorations, and technical setup.
- Scheduling – Create a timetable for performances and speeches.
- Food & Drinks – Arrange catering for attendees.
By solving each smaller problem individually, the entire event becomes easier to organize and execute.
Example: Decomposing a Computer Program
If you are designing a calculator program, you can break it down into smaller functions:
- User Input – Accept numbers and operators from the user.
- Processing – Perform calculations (addition, subtraction, multiplication, division).
- Output – Display the result.
Each function can be coded separately and tested before integrating them into the complete calculator.
3. Testing for Correctness
Once an algorithm has been designed, it must be tested to ensure it produces the correct results. Testing can reveal logical errors or inefficiencies in the algorithm.
Methods of Testing an Algorithm
- Dry-Run Testing – Manually step through the algorithm with sample inputs.
- Tracing Execution Flow – Follow how variables and logic behave in each step.
- Using Test Cases – Run the algorithm with multiple test cases to check for errors.
Example: Testing a Sorting Algorithm
Imagine you create an algorithm to sort a list of numbers. You can test it with different sets of numbers to check if the results are correct.
Test Cases:
|
Input List |
Expected Output |
|
[5, 2, 8, 3] |
[2, 3, 5, 8] |
|
[9, 1, 4, 7] |
[1, 4, 7, 9] |
By running these test cases, you can verify if your algorithm works correctly.
4. Combining Strategies for Stronger Solutions
Decomposition is useful, but it is often necessary to combine multiple problem-solving strategies to develop a robust solution.
Key Strategies to Combine
- Decomposition – Breaking down a problem into parts.
- Algorithmic Constructs – Using sequencing, selection, and iteration (covered in 7.2).
- Testing and Debugging – Ensuring correctness and efficiency.
By integrating these strategies, programmers create solutions that are both logical and effective.
Example: A Password Verification System
Suppose you need to design a system that checks if a user’s password meets certain criteria (e.g., contains numbers and symbols, has at least 8 characters). You can combine multiple strategies:
- Decomposition: Split the task into smaller checks (length check, character type check, etc.).
- Selection: Use if statements to verify each condition.
- Iteration: Use a loop to check each character in the password.
By applying these strategies together, you ensure the password system functions correctly.
5. The Importance of Critical Thinking in Problem-Solving
Even with structured strategies, problem-solving requires critical thinking.
Traits of a Good Problem-Solver in Computing
✔ Persistence – Not giving up if the first solution doesn’t work.
✔ Logical Analysis – Thinking through each step carefully.
✔ Creativity – Finding different ways to solve a problem.
✔ Attention to Detail – Catching errors before they become major issues.
Example: Debugging a Program
A student writes a program to calculate the area of a rectangle, but it gives incorrect results.
Problem:
length = input(“Enter length: “)
width = input(“Enter width: “)
area = length * width
print(“The area is:”, area)
Bug:
The program doesn’t multiply numbers correctly because input() returns a string, not a number.
Fix:
length = int(input(“Enter length: “))
width = int(input(“Enter width: “))
area = length * width
print(“The area is:”, area)
By analyzing and debugging the code, the error is corrected.
6. Summary
- Decomposition helps break down complex problems into smaller, solvable parts.
- Testing ensures an algorithm works correctly before implementing it in a program.
- Combining problem-solving strategies results in better solutions.
- Critical thinking is essential to solve problems efficiently and improve algorithms.
By mastering these skills, students will be better prepared for coding and algorithm development in future chapters.