Question

Exercises 21-60 are programs or shortanswer questions. Write a pseudocode algorithm that reads in three values and writes out the result of subtracting the second value from the sum of the first and third values.

Short answer

The algorithm sums the first and third values, subtracts the second, and outputs the result.

Step-by-step solution

Define the Problem

We are tasked to write a pseudocode algorithm that takes three values, calculates the sum of the first and third values, subtracts the second value from this sum, and outputs the result.

Introduce Input Variables

Identify variables to store the input values. Let's name them as: Input1, Input2, and Input3. These variables will be used to store the three values provided by the user.

Calculate the Sum of First and Third Values

Add the first and third input numbers. The result will be stored in a new variable called Sum13. Pseudocode: Sum13 = Input1 + Input3

Subtract the Second Value

Subtract the second input number (Input2) from the calculated sum (Sum13). Store this result in a variable called Result. Pseudocode: Result = Sum13 - Input2

Output the Result

Display the value stored in the Result variable. This is the final output of the algorithm. Pseudocode: PRINT Result

Key concepts

Algorithm Design

Designing a simple algorithm involves breaking down the problem into smaller, manageable steps that outline the necessary actions to achieve the desired outcome. The main structure of an algorithm should be logical and efficient. When designing an algorithm in pseudocode, focus on clarity and ease of understanding. Simplifying complex processes and clearly defining each step will help ensure that anyone reading the pseudocode can understand its intent and functionality.

• Start by clearly defining what the problem is and what the final output should be.
• Identify the necessary inputs that the algorithm will need to process.
• Break down the required operations or calculations.
• Combine these operations into a coherent step-by-step structure.
• Conclude with an output step that displays the desired result.

For our example, the algorithm design process involves stating the task of subtracting values and outputting the result, defining the inputs, and laying out operations like addition and subtraction to achieve the final result.

Problem-Solving

Problem-solving is about understanding what needs to be achieved and finding the most effective way to get there. For our pseudocode problem, we start by comprehending the task: computing a result based on provided numbers. This requires a structured approach:

• Analyze the problem: What is the relationship between the input numbers? Which operations are needed?
• Develop a strategy: Decide the sequence of operations. In this case, sum the first and third numbers, then subtract the second.
• Implement the plan: Convert your strategy into pseudocode, ensuring each line represents a step of the solution.
• Verify the results: Ensure the algorithm correctly implements the solution and produces the correct output.

Effective problem-solving lays the groundwork for constructing a suitable algorithm, ensuring that all the logic and processes follow the intended path to resolve the problem.

Programming Logic

Programming logic is the backbone of creating an effective algorithm. It involves using logical structures to process data and achieve the desired outcome. In pseudocode, the logic should be presented in a clear and precise manner. For instance, this exercise's logic takes the steps:

• Initialize and assign values to variables to represent input data.
• Perform arithmetic operations: First, add values and store the result, then make a subtraction.
• Use clear instructions (like PRINT) to show final results.

Understanding programming logic is crucial for transforming input data through each processing step to the final output. By breaking down operations like addition and subtraction into logical steps, anyone reading can grasp what the code is expected to do.

Mathematical Operations

Mathematical operations are fundamental to the pseudocode that solves computational problems. Recognizing what calculations are necessary is the first step in implementing effective pseudocode. This exercise uses simple arithmetic operations: addition and subtraction.

• Identify what operations must be conducted. Here, the expression involves the sum of two numbers with another number subtracted.
• Represent these operations in a format understandable by anyone familiar with basic math.

Example: To calculate a result where the second value is subtracted from the sum of the first and third, use these steps:
1. Compute the sum: \( \text{Sum13} = \text{Input1} + \text{Input3} \)
2. Compute the result: \( \text{Result} = \text{Sum13} - \text{Input2} \)
Mathematical proficiency ensures that operations in the pseudocode are correct and that the logic flows naturally from start to finish.