1. Developing an Algorithm

2. Simple Program Design, Fourth Edition Chapter 3
Objectives
In this chapter you will be able to:
Introduce methods of analyzing a problem and developing a solution
Develop simple algorithms using the sequence control structure
Introduce methods of manually checking the developed solution
Simple Program Design, Fourth Edition Chapter 3

3. Simple Program Design, Fourth Edition Chapter 3
Defining the Problem
To help with this initial analysis, the problem should be divided into three separate components:
Input: a list of the source data provided to the problem.
Output: a list of the outputs required.
Processing: a list of actions needed to produce the required outputs.
Input
Processing
Output
Simple Program Design, Fourth Edition Chapter 3

4. Simple Program Design, Fourth Edition Chapter 3
Defining the Problem
When dividing a problem into its three different components, you should simply analyze the actual words used in the specification, and divide them into those that are descriptive and those that imply actions
Simple Program Design, Fourth Edition Chapter 3

5. Example 3.1 Add Three Numbers
A program is required to read three numbers, add them together and print their total
Tackle this problem in two stages
First, underline the nouns and adjectives used in the specification
Input
Processing
Output
Number1
Number2
Number3
Total
Simple Program Design, Fourth Edition Chapter 3

6. Example 3.1 Add Three Numbers
Second, underline (in a different color) the verbs and adverbs used in the specification
A program is required to read three numbers, add them together and print their total
By looking at the underlined words, you can see that the processing verbs are ‘read,’ ‘add together,’ and ‘print’
Each action is described as a single verb followed by a two- word object
Each action is described as a single verb followed by a two- word object
Input
Processing
Output
Number1
Number2
Number3
Read three numbers
Add numbers together
Print total number
Total
Simple Program Design, Fourth Edition Chapter 3

7. Example 3.2 Find Average Temperature
A program is required to prompt the terminal operator for maximum and minimum temperature readings on a particular day, accept those readings as integers, and calculate and display to the screen the average temperature, calculated by (maximum temperature – minimum temperature)/2.
Simple Program Design, Fourth Edition Chapter 3

8. Example 3.2 Find Average Temperature
Establish input and output components
A program is required to prompt the terminal operator for maximum and minimum temperature readings on a particular day, accept those readings as integers, and calculate and display to the screen the average temperature, calculated by (maximum temperature – minimum temperature)/2.
Simple Program Design, Fourth Edition Chapter 3

9. Example 3.2 Find Average Temperature
Establish processing steps
A program is required to prompt the terminal operator for maximum and minimum temperature readings on a particular day, accept those readings as integers, and calculate and display to the screen the average temperature, calculated by (maximum temperature – minimum temperature)/2.
Simple Program Design, Fourth Edition Chapter 3

10. Example 3.2 Find Average Temperature
Defining diagram
Input
Processing
Output
Max_temp
Min_temp
Prompt for temperatures
Get temperatures
Calculate average temperature
Display average temperature
Avg_temp
Simple Program Design, Fourth Edition Chapter 3

11. Example 3.3 Compute Mowing Time
A program is required to read from the screen the length and width of a rectangular house block, and the length and width of the rectangular house that has been built on the block. The algorithm should then compute and display the mowing time required to cut the grass around the house, at the rate of two square metres per minute
Simple Program Design, Fourth Edition Chapter 3

12. Example 3.3 Compute Mowing Time
Input and Out components
A program is required to read from the screen the length and width of a rectangular house block, and the length and width of the rectangular house that has been built on the block. The algorithm should then compute and display the mowing time required to cut the grass around the house, at the rate of two square metres per minute
Simple Program Design, Fourth Edition Chapter 3

13. Example 3.3 Compute Mowing Time
Processing steps
A program is required to read from the screen the length and width of a rectangular house block, and the length and width of the rectangular house that has been built on the block. The algorithm should then compute and display the mowing time required to cut the grass around the house, at the rate of two square metres per minute
Simple Program Design, Fourth Edition Chapter 3

14. Example 3.3 Compute Mowing Time
Defining diagram
Input
Processing
Output
Block_length
Block_width
House_length
House_width
Prompt for block measurements
Get block measurements
Prompt for house measurements
Get house measurements
Calculate mowing area
Calculate mowing time
Mowing_time
Simple Program Design, Fourth Edition Chapter 3

15. Designing a Solution Algorithm
Designing a solution algorithm is the most challenging task in the life cycle of a program
Once the problem has been properly defined, you usually begin with a rough sketch of the steps required to solve the problem
The first attempt at designing a particular algorithm usually does not result in a finished product
Pseudocode is useful in this trial-and-error process, since it is relatively easy to add, delete, or alter an instruction
Simple Program Design, Fourth Edition Chapter 3

16. Designing a Solution Algorithm
Solution algorithm for Example 3.1
Input
Processing
Output
Number1
Number2
Number3
Read three numbers
Add numbers together
Print total number
Total
Add_three_numbers
Read number1, number2, number3
total = number1 + number2 + number 3
Print total
END
Simple Program Design, Fourth Edition Chapter 3

17. Designing a Solution Algorithm
Solution algorithm for Example 3.3
Input
Processing
Output
Max_temp
Min_temp
Prompt for temperatures
Get temperatures
Calculate average temperature
Display average temperature
Avg_temp
Calculate_mowing_time
Prompt operator for block_length, block_width
Get block_length, block_width
Prompt operator for house_length, house_width
Get house_length, house_width
house_area = house_length * house_width
mowning_area = block_area – house_area
mowing_time = mowing_area/2
Output mowing_time to screen
END
Simple Program Design, Fourth Edition Chapter 3

18. Checking the Solution Algorithm
After a solution algorithm has been established, it must be tested for correctness
This step is necessary because most major logic errors occur during the development of the algorithm, and if not detected, these errors can be passed on to the program
Desk checking involves tracing through the logic of the algorithm with some chosen test data
Simple Program Design, Fourth Edition Chapter 3

19. Simple Program Design, Fourth Edition Chapter 3
Selecting Test Data
When selecting test data to desk check an algorithm, you must look at the program specification and choose simple test cases only, based on the requirements of the specification, not the algorithm
By doing this, you will still be able to concentrate on what the program is supposed to do, not how
Simple Program Design, Fourth Edition Chapter 3

20. Steps in Desk Checking an Algorithm
There are six simple steps to follow when desk checking an algorithm listed on page 26 of the textbook
By desk checking an algorithm, you are attempting to detect early errors
It is a good idea for someone other than the author of the solution algorithm to design the test data for the program, as they are not influenced by the program logic
Simple Program Design, Fourth Edition Chapter 3

21. Checking the Solution Algorithm
Desk check Example 3.1
Add_three_numbers
Read number1, number2, number3
total = number1 + number2 + number 3
Print total
END
Test data
First dataset
Second dataset
number1 10 40
number2 20 41
number3 30 42
Expected Results
total 60
123
Simple Program Design, Fourth Edition Chapter 3

22. Checking the Solution Algorithm
Desk check Example 3.1
Add_three_numbers
Read number1, number2, number3
total = number1 + number2 + number 3
Print total
END
Statement #
number1
number2
number3
total
First pass 1 10 20 30 2 60 3
Print
Second pass 40 41 42
123
Simple Program Design, Fourth Edition Chapter 3

23. Simple Program Design, Fourth Edition Chapter 3
Summary
The first section of this chapter was devoted to methods of analyzing and defining a programming problem
You must fully understand a problem before you can attempt to find a solution
The method suggested was to analyze the actual words used in the specification with the aim of dividing the problem into three separate components: input, output, and processing
Simple Program Design, Fourth Edition Chapter 3

24. Simple Program Design, Fourth Edition Chapter 3
Summary
The second section was devoted to the establishment of a solution algorithm
After the initial analysis of the problem, you must attempt to find a solution and express the solution as an algorithm
The third section was concerned with checking the algorithm for correctness
Simple Program Design, Fourth Edition Chapter 3

25. Simple Program Design, Fourth Edition Chapter 3
Practice Problems
Construct an algorithm that will prompt an operator to input three characters, receive those three characters, and display a welcoming message to the screen such as ‘Hello xxx! We hope you have a nice day’.
Answer outline:
Define problem by constructing a defining diagram
Create a solution algorithm using pseudocode
Desk check the solution algorithm using two valid cases
Simple Program Design, Fourth Edition Chapter 3

26. Simple Program Design, Fourth Edition Chapter 3
Practice Problems
You require an algorithm that will receive an integer from the screen, add 5 to it, double it, subtract 7 from it, and display the final number to the screen.
Answer outline:
Define problem by constructing a defining diagram
Create a solution algorithm using pseudocode
Desk check the solution algorithm using two valid cases
Simple Program Design, Fourth Edition Chapter 3