Logic and Algorithm

Developing an algorithm

• To help the initial analysis, the problem should be divided into 3 separate components:

1. Input: a list of the source data provided to the problem

2. Output: a list of the outputs required3. Processing: a list of actions needed to

produce the required outputs.

Example 1. Add three numbers

A program is required to read three numbers, add them together and print their total.

Solution:

1. Underline the nouns and adjectives used in the specification establish the input, output component and any object that are required.

A program is required to read three numbers, add them together and print their total.

• Defining diagram

Input Processing Output

Number1Number2Number3

total

2. Underline the verbs and adverbs used in the specification establish the action required.

A program is required to read three numbers, add them together and print their total.

• Defining diagram

Input Processing Output

Number1Number2Number3

Read three numbersAdd numbers togetherPrint total number

total

3. Writing down the processing steps in an algorithm,

Read three numbersAdd numbers togetherPrint total number

Solution Algorithm

• Add_three_numbersRead number1, number2, number3Total = number1 + number2 + number3Print total

END

Example 2. Find average temperature• A program is required to prompt the

terminal operator for the 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.

Step 1• A program is required to prompt the

terminal operator for the 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.

• Defining diagram

Input Processing OutputMax_tempMin_temp

Avg_temp

Step 2• A program is required to prompt the

terminal operator for the 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.

• Defining diagram

Input Processing OutputMax_tempMin_temp

Prompt for temperaturesGet temperaturesCalculate average temperatureDisplay average temperature

Avg_temp

Solution Algorithm

• Find average_temperaturePrompt operator for max_temp, min_tempGet max_temp, min_tempAvg_temp= (max_Temp + min_temp)/2Output avg_temp to the screen

END

Example 3. Compute Mowing Time A program is required to read from the

screen the lenght and widht of a rectangular house block, and the lenght 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

Step 1• A program is required to read from the

screen the lenght and widht of a rectangular house block, and the lenght 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.

• Defining diagram

Input Processing Output

Block_lenghtBlock_widthHouse_lenghtHouse_width

Mowing_time

Step 2• A program is required to read from the

screen the lenght and widht of a rectangular house block, and the lenght 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.

• Defining diagram

Input Processing OutputBlock_lenghtBlock_widthHouse_lenghtHouse_width

Prompt for block measurementsGet block measurementsPrompt for house measurementsGet house measurementsCalculate mowing areaCalculate mowing time

Mowing_time

Solution AlgorithmCalculate_mowing_time

Prompt operator for block_lenght, block_widthGet block_length, block_widthblock_area = block_lenght*block_widthPrompt operator for house_lenght, house_widthGet house_lenght, house_widthhouse_area=house_lenght*house_widthMowing_area=block_area-house_areaMowing_time=mowing_area/2Output mowing_time to screen

END

Desk Checking

Checking the solution algorithm(Desk Checking)

• Tracing through the logic of the algorithm with some chosen data..

Step in desk Checking an algorithm

1. Choose valid simple input test case (2-3 enough)2. Establish what the expected result should be.3. Make a table of relevant variable names4. Checking the test case line by line, step by step5. Repeat process 4 for other test case6. Check if expected result 2 matches with actual

result 5

Example 4. Desk Chek for example 1

A program is required to read three numbers, add them together and print their total.

Solution Algorithm

• Add_three_numbersRead number1, number2, number3Total = number1 + number2 + number3Print total

END

Desk Checking

1. Choose two sets input test data. Set 1: 10,20, 30 and Set 2: 40, 41, 42

Data Set 1 Data Set 2

Number 1 10 40

Number 2 20 41

Number 3 30 42

2. Establish the expected result for each test case

Data Set 1 Data Set 2

Total 60 123

3. Set up a table of relevant variable names, and pass each test data set statement by statement.

Statement number

number1 number2 number3 total

First Pass

1 10 20 30

2 60

3 Print

Second Pass1 40 41 42

2 123

3 Print

4. Check the expected results (60 and 123) match the actual results.

Desk Check of Example 2.

• A program is required to prompt the terminal operator for the 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.

Solution Algorithm

• Find average_temperaturePrompt operator for max_temp, min_tempGet max_temp, min_tempAvg_temp= (max_Temp + min_temp)/2Output avg_temp to the screen

END

Desk Checking

1. Choose two sets input test data. Set 1: 30, 10 and Set 2: 40, 20

Data Set 1 Data Set 2

Max_temp 30 40

Min_temp 10 20

2. Establish the expected result for each test case

Data Set 1 Data Set 2

Avg_temp 20 30

3. Set up a table of relevant variable names, and pass each test data set statement by statement.

Statement number

Max_temp Min_temp Avg_temp

First Pass

1,2 30 10

3 20

4 0utput

Second Pass

1,2 40 20

3 30

4 output

4. Check the expected results match the actual results.

Assignment 2:Desk Checking for

Compute mowing time

• A program is required to read from the screen the lenght and widht of a rectangular house block, and the lenght 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.

Solution AlgorithmCalculate_mowing_time

Prompt operator for block_lenght, block_widthGet block_length, block_widthblock_area = block_lenght*block_widthPrompt operator for house_lenght, house_widthGet house_lenght, house_widthhouse_area=house_lenght*house_widthMowing_area=block_area-house_areaMowing_time=mowing_area/2Output mowing_time to screen

END

Assignment 3 – Desk Checking for Mowing_time which now contains a logic error

Calculate_mowing_timePrompt operator for block_lenght, block_widthGet block_length, block_widthblock_area = block_lenght * block_widthPrompt operator for house_lenght, house_widthGet house_lenght, house_widthhouse_area=block_lenght * block_widthMowing_area=block_area - house_areaMowing_time=mowing_area/2Output mowing_time to screen

END

Assignment 2 Review: Calculate_mowing_time1 Prompt operator for block_lenght, block_width2 Get block_length, block_width3 block_area = block_lenght*block_width4 Prompt operator for house_lenght, house_width5 Get house_lenght, house_width6 house_area=house_lenght*house_width7 Mowing_area=block_area-house_area8 Mowing_time=mowing_area/29 Output mowing_time to screen

END

Desk Checking

1. Input data:

Data Set 1 Data Set 2

Block_lenght 30 40

Block_widht 30 20

House_lenght 20 20

House_width 20 10

2. Expected result:

Data Set 1 Data Set 2

Mowing_time 250 minutes 300 minutes

3. Set up a table of relevant variable names, and pass each test data set statement by statement.

Statement number

Block_lenght Block_width House_lenght House_width Block_area

House_area Mowing_area

Mowing_time

First Pass

1,2 30 30

3 900

4,5 20 20

6 400

7 500

8 250

9 Output

Second Pass

1,2 40 20

3 800

4,5 20 10

6 200

7 600

8 300

9 Output

4. Check the expected results match the actual results.