Introduction to Problem Solving

What is Problem Solving?

Problem-solving is the process of analyzing a problem, designing a solution, and implementing it using a programming language. In Python, problem-solving involves writing structured and logical code to achieve a desired outcome.

Steps in Problem Solving:

1. Understanding the Problem: Identify the requirements and constraints.
2. Devising a Plan: Develop a step-by-step strategy to solve the problem.
3. Writing the Algorithm: Create a sequence of instructions to solve the problem.
4. Writing the Pseudocode: Represent the solution in a high-level structured format before coding.
5. Converting Algorithm to Code: Write the Python program based on the algorithm.
6. Testing and Debugging: Run the program, check for errors, and refine the solution.

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Algorithm, Pseudocode, and Flowchart

What is an Algorithm?

An algorithm is a step-by-step procedure or a set of well-defined rules used to solve a specific problem or perform a computation. It takes some input, processes it, and produces an output.

Key Characteristics of an Algorithm:

1. Well-Defined Steps – The algorithm should follow a clear sequence of steps.
2. Input – It may take zero or more inputs.
3. Output – It should produce at least one output.
4. Definiteness – Each step must be unambiguous and precise.
5. Finiteness – The algorithm must terminate after a finite number of steps.
6. Effectiveness – The steps should be simple enough to be executed in a reasonable amount of time.

Example of an Algorithm:

Algorithm to Add Two Numbers:

1. Start
2. Take two numbers as input
3. Add the numbers
4. Display the sum
5. Stop

What is Pseudocode?

Pseudocode is a simplified, language-independent way of writing an algorithm using plain English and programming-like constructs.

Example of Pseudocode:

BEGIN
    PRINT "Enter first number"
    READ num1
    PRINT "Enter second number"
    READ num2
    sum_result ← num1 + num2
    PRINT "The sum is: ", sum_result
END

Pseudocode helps in understanding the logic before implementing it in an actual programming language.

What is a Flowchart?

A flowchart is a visual representation of an algorithm using symbols and arrows to show the flow of execution.

Flowchart Symbols:

• Oval: Start/End
• Parallelogram: Input/Output
• Rectangle: Process (Operations like addition, subtraction, etc.)
• Diamond: Decision-making

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Writing a Simple Python Program

Now, let’s convert the algorithm into a Python program.

Python Code:

# Program to add two numbers
num1 = int(input("Enter first number: "))
num2 = int(input("Enter second number: "))

# Calculate sum
sum_result = num1 + num2

# Display result
print("The sum is:", sum_result)

Explanation:

• The input() function takes user input.
• The numbers are converted to integers using int().
• The sum is calculated and displayed using print().

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Decomposition in Problem Solving

Decomposition is the process of breaking a complex problem into smaller, manageable sub-problems.

Example:

Consider a program that calculates the average of three numbers. Instead of writing a single block of code, we can:

1. Take three numbers as input
2. Calculate the sum
3. Divide by three to get the average
4. Display the result

This approach makes debugging and modification easier.

Python Code for Average Calculation:

# Program to calculate the average of three numbers
num1 = float(input("Enter first number: "))
num2 = float(input("Enter second number: "))
num3 = float(input("Enter third number: "))

# Compute average
average = (num1 + num2 + num3) / 3

# Display result
print("The average is:", average)

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Conclusion

• Problem-solving involves understanding a problem, designing an algorithm, and implementing a solution in Python.
• Pseudocode helps in structuring the logic before coding.
• Algorithms and flowcharts help in structuring the solution before coding.
• Breaking down complex problems into smaller tasks makes them easier to solve.