Developing a Solution

How to create the computer-based solution for a real-world problem.

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General Idea of This Lesson

Give you methodology

Example problems: “Find the optimum nozzle dimensions for …” “Solve for the optimum path for the robot …” “Find the range of temperatures adequate for …”

In EGR115, most tasks will be:

“Develop a program that ……”

General Terms

As a programmer, keep in mind there are 2 sides to a software The person who writes the software: the programmer The person who uses the software: the user (aka client)

As you (the student) develop software, you will constantly jump back and forth between the two roles.

Your goal as a programmer:

“The programmer should make the user’s life easy.”

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The 5 step process

Follow these steps in order:

1. State the problem clearly

2. Identify the givens vs. the results wanted This will be referred as the I/O diagram

3. Manually solve the problem

4. Computerize the solution

5. Test, test, test!!!

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Step 1. State the problem

However easy the problem may seem, it is crucial to fully understand the problem, and clarify details. It can help to put the problem in writing.

For example:

Write a program that “Computes the area of a triangle”

This might bring up questions – like “what do I know about the triangle?”

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Step 2. Identify the I/O

What do you know about the problem? How do you want to solve it?

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height

base

Step 2. Identify the I/O

What do you know about the problem? How do you want to solve it?

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side 1

side 2

angleheight

base

Step 2. Identify the I/O

Remember the Von Neumann architecture? CPU + memory + inputs/outputs devices

The I/O diagram determines which input and output devices the software uses, as well as decide which inputs and output variables are used.

The I/O diagram is a first step to organizing the brainstorming.

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General frame of an I/O diagram

Arrows indicate and names each given and result Purple boxes indicate which devices are used

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General frame of an I/O diagram

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INPUT SIDE

?

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General frame of an I/O diagram

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OUTPUT SIDE

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Applied to the area of triangle

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COMPUTE THE AREA OF TRIANGLE

Applied to the area of triangle

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COMPUTE THE AREA OF TRIANGLE

Sides 1 and 2

Angle

Each arrow represents the INPUTS

(=GIVENS)

Applied to the area of triangle

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AREA OF TRIANGLE

Sides 1 and 2

Angle

External interface – What DEVICE is used to enter the values of the givens

Keyboard

Each arrow represents the INPUTS

(=GIVENS)

Applied to the area of triangle

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COMPUTE THE AREA OF TRIANGLE

Sides 1 and 2

Angle

Keyboard

Each arrow represents the INPUTS

(=GIVENS)

area

Each arrow represents the OUTPUTS

(=RESULTS)

Applied to the area of triangle

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COMPUTE THE AREA OF TRIANGLE

Sides 1 and 2

Angle

External interface – What DEVICE is used to see the results

Keyboard

Each arrow represents the INPUTS

(=GIVENS)

Screenarea

Each arrow represents the OUTPUTS

(=RESULTS)

Applied to the area of triangle

Final I/O diagram

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COMPUTE THE AREA OF TRIANGLE

Sides 1 and 2

Angle

Keyboard Screenarea

Same problem: Option 2

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COMPUTE THE AREA OF TRIANGLE

Sides 1 and 2

Angle

Printer

Different input/output devices

area

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Microphone

… or option 3 …

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COMPUTE THE AREA OF TRIANGLE

base

height

Screenarea

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Keyboard

Different Inputs

Some Other More Complex Examples (and yet, the I/O is not so complex)

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ATM MACHINE

Some Other More Complex Examples (and yet, the I/O is not so complex)

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ATM MACHINE

Account numberCard

Some Other More Complex Examples (and yet, the I/O is not so complex)

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ATM MACHINEpin

Deposit/with-draw/transfer…

Touch Screen/ pin pad

Account numberCard

Some Other More Complex Examples (and yet, the I/O is not so complex)

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ATM MACHINEpin

Deposit/with-draw/transfer…

Touch Screen/ pin pad

Account numberCard

Money Slot

money

Some Other More Complex Examples (and yet, the I/O is not so complex)

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ATM MACHINEmoney Money Slotpin

Deposit/with-draw/transfer…

Touch Screen/ pin pad

Account numberCard

Money Slot

money

Some Other More Complex Examples (and yet, the I/O is not so complex)

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ATM MACHINEmoney Money Slotpin

Deposit/with-draw/transfer…

Touch Screen/ pin pad

Account numberCard

receiptReceipt Slot

Money Slot

money

Step3. Manually Solve Problem

Solving the area of a triangle is obvious (right?)

Height = 3 in Base = 2 in

Area = ½ * 2 * 3

= 3 in squared

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Step 4 and Step 5

These steps actually involve owning a computer and starting to type ‘lines of code’.

Realize that none of the steps before did this.

In short: Step 4 – Computerize the solution Step 5 – Test the software created

Remember: “SIMCT”(or: Small iPods Make Copying Tough)

1. S State the problem (clarify it if need be)

2. I Identify the Inputs and Outputs

3. M Manually solve the problem

4. C Computerize the solution1. Layout the algorithm

2. Provide the code that implements the algorithm

5. T test, Test, TEST!!

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1. S State the problem (clarify it if need be)

2. I Identify the Inputs and Outputs

3. M Manually solve the problem

4. C Computerize the solution1. Layout the algorithm

2. Provide the code that implements the algorithm

5. T Test, Test, TEST!!

Remember: “SIMCT”(or: Small iPods Make Copying Tough)

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Note: I and M are sometimes reversed. You may need to decide what method you will use to solve the problem before you can determine what inputs are needed and what outputs will be provided. In fact, sometimes the problem being solved gets changed. But we will assume the standard SIMCT model.

Developing a SolutionComplete Example

Development of software which finds the roots of any quadratic equation:

ax2 + bx + c = 0

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1: State the problem

The client says:

“I want a computer program that will find the roots of any quadratic equation”

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1 (cont.):

The programmer wonders:

Any quadratic equation?

Inputs:

What if the coefficient “a” is 0?

Outputs:

What if the roots are imaginary?

And the client re-considers..

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1 (cont.):

Client clarifies his requirements:

“I want a computer program that will find the REAL roots of a quadratic equation for all REAL coefficients a, b, and c such that a≠0.”

This shows a much more thorough consideration of the problem.

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2: Identify Inputs/Outputs What are the inputs for this problem?

In other words, what information is needed

FROM OUTSIDE THE PROGRAM

for the desired program to solve the problem?

In our programs, these inputs typically come from the user – but they don’t have to. Sensors and other programs can provide information, too.

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2 (cont.):

Inputs, continued…

The only information needed from outside the program are the values of the coefficients:

a?

b?

c?

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2 (cont.):

What is expected as output from this program?

The roots (x1, and x2) of course. But…

- what about error messages – when the user puts in bad information?

- what about an “imaginary roots found” message?

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2 (cont.):

Outputs, continued:

- The roots, if real

- Message if roots are imaginary

- Error if the user inputs bad values

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2 (cont.):

Final I/O diagram:

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*** magic ***

Coefficients a,b and c

Roots/ error message screenKeyboard

Step 3: Manually solve the problem

Not always practical to actually solve the problem…

e.g. can you manually launch the shuttle?

But…

a programmer must be able to solve the problem manually, assuming all the time and resources necessary were available. Otherwise, how could a programmer tell the computer how to do it???

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3 (cont.): For this problem, manually solve the quadratic

equation for various inputs. Pretend you are the program you will be writing. What should YOU do if the user provides:

- good data

- bad data

- data that gives real roots

- data that gives imaginary roots40

3 (cont.):

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Test case #1: enter a valid case (http://www.algebra1help.com/tutorials/math-worksheets-for-mean-mode-median-6th-grade.html

)

3 (cont.):

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Test case #2: enter 0 for a expect an error message

Test case #3: enter a=4, b=-2, c=0 expect "imaginary roots" message

http://www.videolife.tk/discriminant/

4: Computerize

4.1 Algorithm Describe the steps taken when the problem was

manually solved.

This is more difficult than it seems. Humans perform actions subconsciously – we’re not even aware we are doing them!

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4.1 (cont.):

Layout the algorithm in “skeleton” form:

% Collect the inputs from the user% Apply the inputs to the quadratic formula% Display the results

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4.1 (cont.): Now, “flesh it out”

% Collect the inputs from the user% Print error message if bad inputs% Apply the inputs to the quadratic formula% Compute the discriminant (b2-4ac)% If discriminant < 0

% display ‘Imaginary roots’% Otherwise

% compute real roots% Display the results

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4.2: code

For each step of the algorithm, write code (in this class, MATLAB code) that will perform the actions you have specified. Avoid proceeding to the next step until you feel certain the step has been accomplished. It is important to test as you go.

(Actual coding steps will be learned this semester)

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5: test, Test, TEST!!! It is provably impossible to write a computer

program to test another arbitrary computer program for correctness. And it’s usually too time consuming to write a program that specifically tests the program we’re writing – so we resort to manual testing.

For complicated programs, it is not possible to test a program too thoroughly because it is not possible to test all inputs. And it may be worth writing that test program after all…

Choose inputs to maximize confidence that the solution written will work correctly.

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5 (cont.):

For a quadratic solver, each set of input should be tested, which means:

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a<0, b<0, c<0a<0, b<0, c=0a<0, b<0, c>0a<0, b=0, c<0a<0, b=0, c=0a<0, b=0, c>0a<0, b>0, c<0a<0, b>0, c=0a<0, b>0, c>0

a=0, b<0, c<0a=0, b<0, c=0a=0, b<0, c>0a=0, b=0, c<0a=0, b=0, c=0a=0, b=0, c>0a=0, b>0, c<0a=0, b>0, c=0a=0, b>0, c>0

a>0, b<0, c<0a>0, b<0, c=0a>0, b<0, c>0a>0, b=0, c<0a>0, b=0, c=0a>0, b=0, c>0a>0, b>0, c<0a>0, b>0, c=0a>0, b>0, c>0

Step5 (cont.)

Of course, with human ingenuity, change the design of the program (i.e. modify the algorithm) to avoid some of these:

% If no error condition (such as a equal 0)% then compute the roots% Otherwise, just print the error message

With this sort of technique, we can avoid having to test nearly 1/3 of the possibilities!

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Step5 (cont.)

For a quadratic solver, each set of input should be tested, which means:

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a<0, b<0, c<0a<0, b<0, c=0a<0, b<0, c>0a<0, b=0, c<0a<0, b=0, c=0a<0, b=0, c>0a<0, b>0, c<0a<0, b>0, c=0a<0, b>0, c>0

a=0, b<0, c<0a=0, b<0, c=0a=0, b<0, c>0a=0, b=0, c<0a=0, b=0, c=0a=0, b=0, c>0a=0, b>0, c<0a=0, b>0, c=0a=0, b>0, c>0

a>0, b<0, c<0a>0, b<0, c=0a>0, b<0, c>0a>0, b=0, c<0a>0, b=0, c=0a>0, b=0, c>0a>0, b>0, c<0a>0, b>0, c=0a>0, b>0, c>0

% Collect the inputs from the user

% If no error condition

% Compute the discriminant (b2-4ac)

% If discriminant < 0

% display ‘Imaginary roots’

% Otherwise

% compute real roots

% Display the results

% Otherwise

% Print error message

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Develop your

algorithm first

% Collect the inputs from the usera = input(‘Enter coefficient a: ’);

% If no error condition

% Compute the discriminant (b2-4ac)

% If discriminant < 0

% display ‘Imaginary roots’

% Otherwise

% compute real roots

% Display the results

% Otherwise

% Print error message

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% Collect the inputs from the usera = input(‘Enter coefficient a: ’);b = input(‘Enter coefficient b: ’);c = input(‘Enter coefficient c: ’);

% If no error condition

% Compute the discriminant (b2-4ac)

% If discriminant < 0

% display ‘Imaginary roots’

% Otherwise

% compute real roots

% Display the results

% Otherwise

% Print error message

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% Collect the inputs from the usera = input(‘Enter coefficient a: ’);b = input(‘Enter coefficient b: ’);c = input(‘Enter coefficient c: ’);

% If no error conditionif a~=0 %means a not equal to zero, could have done (a<0 || a>0)

% Compute the discriminant (b2-4ac)

% If discriminant < 0

% display ‘Imaginary roots’

% Otherwise

% compute real roots

% Display the results

% Otherwiseelse

% Print error message

end54

% Collect the inputs from the usera = input(‘Enter coefficient a: ’);b = input(‘Enter coefficient b: ’);c = input(‘Enter coefficient c: ’);

% If no error conditionif a~=0 %means a not equal to zero, could have done (a<0 || a>0)

% Compute the discriminant (b2-4ac)

% If discriminant < 0

% display ‘Imaginary roots’

% Otherwise

% compute real roots

% Display the results

% Otherwiseelse

% Print error messagedisp(‘error: a invalid’)

end55

% Collect the inputs from the usera = input(‘Enter coefficient a: ’);b = input(‘Enter coefficient b: ’);c = input(‘Enter coefficient c: ’);

% If no error conditionif a~=0 %means a not equal to zero, could have done (a<0 || a>0)

% Compute the discriminant (b2-4ac)discriminant = b^2-4*a*c;

% If discriminant < 0

% display ‘Imaginary roots’

% Otherwise

% compute real roots

% Display the results

% Otherwiseelse

% Print error messagedisp(‘error: a invalid’)

end56

% Collect the inputs from the usera = input(‘Enter coefficient a: ’);b = input(‘Enter coefficient b: ’);c = input(‘Enter coefficient c: ’);

% If no error conditionif a~=0 %means a not equal to zero, could have done (a<0 || a>0)

% Compute the discriminant (b2-4ac)discriminant = b^2-4*a*c;

% If discriminant < 0if discriminant<0

% display ‘Imaginary roots’

% Otherwiseelse

% compute real roots

% Display the results

end% Otherwiseelse

% Print error messagedisp(‘error: a invalid’)

end57

% Collect the inputs from the usera = input(‘Enter coefficient a: ’);b = input(‘Enter coefficient b: ’);c = input(‘Enter coefficient c: ’);

% If no error conditionif a~=0 %means a not equal to zero, could have done (a<0 || a>0)

% Compute the discriminant (b2-4ac)discriminant = b^2-4*a*c;

% If discriminant < 0if discriminant<0

% display ‘Imaginary roots’disp(‘Imaginary Roots’)

% Otherwiseelse

% compute real roots

% Display the results

end% Otherwiseelse

% Print error messagedisp(‘error: a invalid’)

end58

% Collect the inputs from the usera = input(‘Enter coefficient a: ’);b = input(‘Enter coefficient b: ’);c = input(‘Enter coefficient c: ’);

% If no error conditionif a~=0 %means a not equal to zero, could have done (a<0 || a>0)

% Compute the discriminant (b2-4ac)discriminant = b^2-4*a*c;

% If discriminant < 0if discriminant<0

% display ‘Imaginary roots’disp(‘Imaginary Roots’)

% Otherwiseelse

% compute real rootsx1 = (-b + sqrt(discriminant)) / (2*a);x2 = (-b - sqrt(discriminant)) / (2*a);% Display the resultsfprintf(‘x1 = %.2f and x2 = %.2f\n’,x1,x2)

end% Otherwiseelse

% Print error messagedisp(‘error: a invalid’)

end59

Wrapping Up What are the 5 steps?

1. State the problem Do research if the problem is not clear enough

2. Identify the Inputs/Outputs (Givens/Results) Create an I/O diagram Which devices are used for each side?

3. Manually solve the problem 4. Computerize the solution

4.1 Set up the algorithm 4.2 Code

5. test, Test, TEST!!!

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