Problem Analysis Charts

A Problem Analysis Chart (PAC) is a structured tool used to break down a problem into key components. It helps to systematically understand the problem, identify necessary data, and develop a structured approach to solve it. In the context of algorithms and flowcharts, PACs serve as the initial step in problem-solving by organising information that will be used to visualise and implement the solution.

Let us take a simple case to find the area of a regular geometry. We will break the problem into small components so that we can arrive at a solution.

PACs for Different Geometries

We will start our discussion with a simple method to find the area of the case of a square. The PAC breaks the problem into smaller parts. It helps us to bring a logical sequence to our thought process and help us arrive at better solutions. For now, let us see how we can bring out a solution.

Finding the Area of a Square

For a regular geometry, we will need some parameters about the same. For instance, we know that a square has all right angles and it is a four-sided figure. We also know that to find the area of a square, we will need the information about the length of one side

Problem Analysis Chart: Area of a Square

Identifier	Use Case Example	Input	Output
Given Data	Side length of the square	Side length (s)	Area (A)
Required Results	Calculate the area	Side length (s)	Area (A = s2)
Processing	Formula for area	s	A = s2
Solution Alternatives	Use different units	Centimeters, Inches, Meters	Area in given unit

You will find that the logical steps are the same for many similar problems. You please try to develop a problem analysis chart for finding the area of a circle and then a rectangle. Although the solution is given, try to work on it independently.

Finding the Area of a Circle

Problem Analysis Chart: Area of a Circle

Identifier	Use Case Example	Input	Output
Given Data	Radius of the circle	Radius (r)	Area (A)
Required Results	Calculate the area	Radius (r)	Area (A = πr2)
Processing	Formula for area	r	A = πr2
Solution Alternatives	Use different units	Centimeters, Inches, Meters	Area in given unit

Finding the Area of a Rectangle

Problem Analysis Chart: Area of a Rectangle

Identifier	Use Case Example	Input	Output
Given Data	Length and width of the rectangle	Length (l), Width (w)	Area (A)
Required Results	Calculate the area	Length (l), Width (w)	Area (A = l * w)
Processing	Formula for area	l, w	A = l * w
Solution Alternatives	Use different units	Centimeters, Inches, Meters	Area in given unit

Interactive Activity: Compute Area of a Rectangle

Is using a formula the only way to compute areas, actually - No. You will find that you could also divide the rectangle into strips. Adding the areas of these strips should also give you the area of the figure. Here is a visual demonstration of the same.

Enter the length and width of the rectangle (integers only). When you press compute, the figure will be filled with strips, and their areas will be summed to give the total area.

Compute

 

Problem Analysis Chart and Flowchart for Area of a Rectangle through Addition

Problem Analysis Chart: Area of a Rectangle through Addition

Identifier	Use Case Example	Input	Output
Given Data	Length and width of the rectangle	Length (l), Width (w)	Area (A)
Required Results	Calculate the area through a series of additions	Length (l), Width (w)	Area (A = l * w)
Processing	Add width repeatedly, length times	l, w	A = w + w + ... (l times)
Solution Alternatives	Use different units	Centimeters, Inches, Meters	Area in given unit

    flowchart TD
        A(["Start"]) --> B["Enter length (l) and width (w)"]
        B --> C[Initialize area = 0]
        C --> D{Is length > 0?}
        D -->|Yes| E[Add width to area]
        E --> F[Decrement length]
        F --> D
        D -->|No| G(["End - Display Area"])
    

We know that there is more than one method to solve a problem. Each problem comes with a cost. For instance, if we do not know the range of values that can be true, using a binary search might not be really possible. In any case, in my experience, when we use a program to solve a problem, we will be able to tackle more complex problems.

How PACs, Algorithms, and Flowcharts Interrelate

PACs, algorithms, and flowcharts are interconnected in problem-solving:

• PACs provide a structured approach to analyse the problem by identifying inputs, outputs, processes, and alternative solutions.
• Flowcharts visually represent the steps and decision points outlined in the PAC, making it easier to understand and communicate the solution process.
• Algorithms are step-by-step procedures derived from the PAC and visualised through flowcharts. They provide a logical sequence of operations to solve the problem.

By integrating PACs, algorithms, and flowcharts, we can systematically analyse problems, visualise the solution process, and implement efficient solutions. This structured approach enhances our problem-solving skills and ensures that solutions are well-organized, efficient, and easy to understand. The interactive activity demonstrates how a simple algorithm can be visualised and implemented, reinforcing the concepts of PACs and flowcharts in a practical context.