Used when you must nest a series of decisions about a single variable

• Questions from last class?
• Questions about labs or upcoming homework?

^ top

Learning from the Midterm

^ top

Post Midterm Review

• Has anyone NOT completed the midterm yet?
• Post midterm data
• If you had problems with a topic I suggest reviewing the notes, homeworks and labs
• We will have another midterm before the final
• Grading policies, including midterm weighting, are listed in the syllabus

^ top

Post Midterm Survey

^ top

Making the Grade

• Oftentimes students who got less than an "A" on the midterm wonder if they can still get an "A" in the course
• Since this is the first midterm, the answer is "Yes" unless:
  • You have not completed most of the homework
  • You failed the midterm with < 50%
• Even with the above, you can still pass the course and even get a "B"
• However, you will need to start doing more homework and study for the tests

^ top

Exercise: Midterm Self-Reflection

In this exercise we reflect on our progress in this course.

You Can Learn Anything: from the Khan Academy

Specifications (5m)

1. Please take out a piece of paper and something to write with.

   There is no need to tear the paper out of a notebook. If you need paper or a writing tool, ask a classmate or the instructor for one.

2. Reflect on the following questions and write down an answer for yourself:
   1. What do you want to get from this course?
   2. Are you achieving your goals for this course?
   3. What ways can you think of to improve your performance in achieving your goal?
   4. What actions are you going to take to better meet your goals?

^ top

More About Selections

^ top

Multiple Alternatives

• By using collections of if-else statements, a program can distinguish between multiple alternatives
• For example, consider the following example where a user enters the name of a coin, and the program displays the value

Program For an Arcade Love Tester 

Choosing Between Alternatives

• This program has four alternatives to choose from:
  1. Please hold my hand.
  2. Just friends.
  3. In love.
  4. Ouch!!
• Note that the order that the alternatives are checked is important
• We can follow the alternatives in the flowchart shown below

Flowchart of Multiple Alternative for Love Tester

1. In the above program, what happens if the pressure sensor reads 423?
2. True or false? An elegant way to choose among multiple alternatives is to nest if statements in an else clause.
3. If score = 85, what is output by the following code fragment?
   

4. In the above sequence of if-statements, the test condition of the first if-statement must be ________before the second if-statement executes.

^ top

4.2.2: When Order Matters

• In some cases, the order of the tests is not important
• IF all the tests used == then they can be done in any order
• Note that in the love tester the order of the tests is important to ensure that the right results are printed

Order Is Important

• If we rearranged the order of the if-else statements, we would get the wrong results
• For example, if we reversed the order of the tests:

  if (pressure < 800) { Serial.println("In love."); }else if (pressure < 500) { Serial.println("Just friends."); }else if (pressure < 100) { Serial.println("Please hold my hand.");

  }else{ Serial.println("Ouch!!"); }

• This does not work because all "Just Friends" values also meet the "In love" criteria
• Some tests will never be attempted

Importance of Using if-else-if Structure

• Note that we cannot remove the else portion of the structure like shown below: if (pressure < 100) { Serial.println("Please hold my hand.");
  } if (pressure < 500) { Serial.println("Just friends."); } if (pressure < 800) { Serial.println("In love."); }
• The conditions must be exclusive and we need the else-if conditions to ensure exclusivity
• Independent if statements may cause a single input to print several messages

Check Yourself

1. True or false? Order never matters in a sequence of if and else statements.
2. Suppose the sensor read -1 into the love tester program. What is printed?
3. How can the following code be simplified? if (price > 100) { discount = price - 20; } else if (price <= 100) { discount = price - 10; }

^ top

4.2.3: switch Statements

• The switch statement provides an alternative to an if-else-if chain
• Executes a section of code depending on the value of a single number
• The general syntax is: switch (integerExpression) { case label1: statements break; case label2: statements break; ... case labeln: statements break; default: statements }
• Where:
  • integerExpression: an arithmetic expression that resolves to an integer number
  • labelx: an integer constant
  • statements: the statements to execute when the condition is met
• Any number of case labels can be placed in any order
• When run, the integerExpression tries to match one of the case labels
• If a label matches then the statements after the case label start executing
• Any value that does not match starts executing with the statement after default
• Execution continues until the end of the switch statement or encountering a break statement
• The break statement causes an immediate exit from the switch statement
• Just as case identifies possible starting points, break determines end points

Example Program Using a switch Statement

When to Use switch Statements

• Switch statements can only be used when
• The are integers or chars 
• You are looking for exact matches
• Thus, switch statements are inherently less useful than if-else statements
• Also, the syntax is no clearer than if-else statements
• There is a reason for the limitations of the switch statement
• The compiler can generate faster code for switch statements
• Though you shouldn't count on it...
• However, modern compilers are quite capable of optimizing if-else statements 
• Be careful when using a switch statement
• Every branch of the switch statement must be terminated by a break statement
• If the break statement is missing, the program falls through and executes the next case without testing
• There are rare uses for this fall through behavior, such as printing the words for the song, The Twelve Days of Christmas
• However, according to a study by Peter van der Linden, reported in his book, Expert C Programming, p. 38, the falling through behavior is needed less than 3% of the time
• Thus, the default behavior is wrong 97% of the time
• Forgetting to type the break statement is a very common error and the source of many bugs
• So one has to ask oneself, "Why use an inferior programming statement that causes more problems than it solves?"

Check Yourself

1. True or false: C++ switch statements allow testing for inequalities like < and >.
2. True or false: the default behavior of a switch statement, to continue executing past the next label, is usually correct.
3. True or false: programmers never forget to include a break statement when needed inside a switchstatement.

^ top

4.2.4: Nested Branches

• Nested if-else statements can be used when there are two (or more) levels of decision making.
• For example, consider the following two tax tables from 1992
• There is a different table for each marital status (decision 1)
• Once you have found the right table, you are taxed differently according to your income (decision 2)

Tax Table if Single

If your status is Single and if the taxable income is over	but not over	the tax is	of the amount over
$0	$21,450	15%	$0
$21,450	$51,900	$3,217.50 + 28%	$21,450
$51,900		$11,743 + 31%	$51,900

Tax Table if Married

If your status is Married and if the taxable income is over	but not over	the tax is	of the amount over
$0	$35,800	15%	$0
$35,800	$86,500	$5,370.00 + 28%	$35,800
$86,500		$19,566.00+ 31%	$86,500

Programming Two-Level Decisions

• When we program this two-level decision process, we often use two levels of if statements
• We say the income test is nested inside the test for filing status
• We can see this two-level decision in the flowchart shown below
• Also, we can examine and run the program from the code shown below
• Note that more complicated decisions may require deeper levels of nesting

Flowchart of Two-level Tax Decision Process

Program Computing Single and Married Tax Rates

Try It: Using Nested if-statements (8m)

We want to write a program to calculate a student's letter grade according to the following table:

Numerical Grade	Letter Grade
greater than or equal to 90	A
less than 90 but greater than or equal to 80	B
less than 80 but greater than or equal to 70	C
less than 70 but greater than or equal to 60	D
less than 60	F

1. Copy the following program into the Arduino IDE editor and then compile and run the starter program to make sure you copied it correctly. void setup() { Serial.begin(9600); Serial.setTimeout(-1); } void loop() { }
2. Add code to get user input into a variable named score of type double. When you run the program after adding this code, the output should look like: Enter a score: 95.7

   Make sure you declare the variable with a compatible data type. Note that the underlined numbers above shows what the user enters and is not part of your code. For more information see section 2.4.7: Input and Output.

3. First we will look at a series of if statements and see that if statements alone are not enough to solve this problem. Copy the following into your program after the input statements: String grade; if (score >= 90) { grade = "A"; } if (score >= 80) { grade = "B"; } if (score >= 70) { grade = "C"; } if (score >= 60) { grade = "D"; } if (score < 60) { grade = "F"; } Serial.println(grade);

   Compile and run your modified program. There is a logic problem with this code. Each test condition needs to work over a range of values rather than with a single value.

4. One way to correct the problem is to nest an if statement inside of another if statement. To see how this works, modify your code to add nested if statements as shown below:
   

5. To test the range, the outer if statement tests the lower condition and the inner if statement tests the upper condition.

6. Compile and run your modified program to make sure you made the changes correctly. When you run the program, the output should look like: Enter a score: 80 B

   Run your program a few times with different score to verify that any score displays the correct letter grade.

7. Save your grader.ino file to submit as part of the next exercise.
8. Be prepared to answer the following Check Yourself questions when called upon.

Check Yourself

1. True or false? You can nest if statements within another if statement.
2. If you are single and your taxable income is $21,450, your tax is ________.
3. If you get a $1000 per year raise and now make $22,450, you now pay taxes of ________.
4. Some people object to higher taxes for higher incomes, claiming that you might end up with less money after taxes when you get a raise for working hard. The flaw in this argument is ________.

^ top

4.2.5: Boolean Variables

• Sometime we need to evaluate a logical condition in one part of a program and use it elsewhere
• To store a condition that can only be true or false, we use a Boolean variable
• Boolean variables are named after George Boole (1815-1864), a pioneer in the study of logic
• We specify a Boolean variable using the bool type, which can hold just one of two values: true orfalse bool isCool = true; bool lies = false;
• Question: What type of tests does George Boole give? (answer)
• Question: How does George Boole order lunch? (see here)

Test Conditions and Boolean Values

• Remember that test conditions always evaluate to true or false if (num > 0)
• Thus we can use a boolean variable as a test condition bool isPositive = (num >= 0); if (isPositive)
• Note that we do not need to add a relational expression to a boolean variable, like: if (isPositive == true) // avoid!
• Since the boolean variable already evaluates to true or false, adding the == true is redundant
• Likewise, we do not need to use: if (isPositive != false) // avoid!
• If we want to reverse the test condition, we can use the not (!) operator if (!isPositive)
• We can see the use of a Boolean variable in the following example

Example Application Using a Boolean Variable

Check Yourself

1. True or false: the number of values that can be stored in a Boolean data type are 3: true, false and null.
2. True or false: the Boolean data type is spelled boolean (with a lower case "b") in C++.
3. True or false: a test condition always evaluates to a Boolean value.
4. True or false: a Boolean variable can substitute for a test condition in an if-statement.

^ top

4.2.6: Logical Operators

• Sometimes we need to test for multiple conditions in our programs
• For example, we want to test if an age is between 18 and 25
• We need to test both that age >= 18 and age <= 25
• One way to make the tests is with nested if statements int age = 0; Serial.println("Enter your age:"); age = Serial.parseInt(); if (age >= 18) { if (age <= 25) { Serial.println("Correct age!"); } else { Serial.println("Wrong age!"); } } else { Serial.println("Wrong age!"); }
• If the age entered is correct, like 19, we get the message, "Correct age!"
• If the age entered is not correct, like 15, we get the message, "Wrong age!"
• While this works, it is cumbersome to code and read
• A better approach is to combine test conditions with logical operators

Combining Test Conditions with Logical Operators

• A logical operator, or Boolean operator, is an operator that treats operands as Boolean values (true orfalse)
• C++ has several logical operators, but we only need to use three to create any possible test condition
• These three operators are and, or and not, which are discussed below
• These logical operators are traditionally written as && (and), || (or) and ! (not)
• Both variants are legal under ANSI C++
• The words are easier to read but many C++ programmers still use the older form

Truth Tables for and, or and not

and (&&) Operator Truth Table

If expr1 is...	And expr2 is...	Then expr1 and expr2 is...	Example	Result
true	true	true	5 < 10 and 5 > 2	true
true	false	false	5 < 10 and 5 < 2	false
false	true	false	5 > 10 and 5 > 2	false
false	false	false	5 > 10 and 5 < 2	false

or (||) Operator Truth Table

If expr1 is...	|| expr2 is...	Then expr1 or expr2 is...	Example	Result
true	true	true	5 < 10 or 5 > 2	true
true	false	true	5 < 10 or 5 < 2	true
false	true	true	5 > 10 or 5 > 2	true
false	false	false	5 > 10 or 5 < 2	false

not (!) Operator Truth Table

If expr is...	Then ! expr is...	Example	Result
true	false	!true	false
false	true	!(5 < 2)	true

Example Using Logical Operators

• We could rewrite our age test using an and (&&) operator like this: int age = 0; Serial.println("Enter your age:"); age = Serial.parseInt(); if (age >= 18 && age <= 25) { cout << "Correct age!\n"; } else { cout << "Wrong age!\n"; }
• Notice that the code is shorter and it is easier to follow the logic
• Another way to use logical operators to test the age is: int age = 0; Serial.println("Enter your age:"); age = Serial.parseInt(); if (age < 18 || age > 25) { cout << "Correct age!\n"; } else { cout << "Wrong age!\n"; }
• Many people confuse && and || conditions, especially when learning about logical operators
• A value lies between 0 and 100 if the value is at least 0 and at most 100
• A value is outside that range if it is less than 0 or greater than 100
• There is no golden rule; we have to think carefully and test our conditions

Another Look at Truth Tables

• Note that most computers store true as 1 and false as 0
• If we substitute 1 for true and 0 for false, we have these truth tables:

• With this substitution we see that the AND operation is the minimum of the operands
• Conversely, the OR operation is the maximum of the operands
• The NOT operator simply reverses its operand

Parenthesis

• Remember that a Boolean expression in an if statement must be enclosed in parenthesis
• Thus, an if statement with && might look like: if ((guess != GUESS1) && (guess != GUESS2))
• However, relational operators have a higher precedence than logical operators
• Thus, we can remove the inner parenthesis without affecting the meaning: if (guess != GUESS1 && guess != GUESS2)
• However, if using parenthesis is easier to understand then use the extra parenthesis

Example Program with Logical Operators

Try It: Using Logical Operators (5m)

We previously used a nested if-statement to test multiple conditions. Often, a better approach is to use Boolean operators like && and ||.

1. Modify your grader.ino code from the last Try It to remove nested if statements and replace them with logical operators.
2. Compile and run your modified program to make sure you made the changes correctly. When you run the program, the output should look like: Enter a score: 80 B

   Run your program a few times with different score to verify that any score displays the correct letter grade.

3. Save your grader.ino file to submit as part of the next exercise.
4. Be prepared to answer the following Check Yourself questions when called upon.

More Information

Check Yourself

1. Of the following groups ________ is larger.
   1. Students wearing denim
   2. Students wearing denim AND corrective lenses
2. Of the following groups ________ is larger.
   1. Students wearing denim
   2. Students wearing denim OR corrective lenses
3. Of the following groups ________ is larger.
   1. Students wearing denim
   2. Students wearing denim AND NOT corrective lenses
4. For the following code, the test condition evaluates to ________. bool denim = true; bool lenses = false; Serial.println(denim && lenses);
5. For the following code, the test condition evaluates to ________. int age = 21; Serial.println(age >= 18 && age <= 25);
6. Of the following logical expressions, the test to see if x is between 1 and 10 (including 1 and 10) is________.
   1. (x >= 1 && x <= 10)
   2. (1 <= x and x <= 10)
   3. (x >= 1 || x <= 10)
   4. (1 <= x or x <= 10)

^ top

Exercise 4.2 (5m)

In this exercise we test multiple alternatives in a program. As an example, we will calculate a student's letter grade according to the following table:

Numerical Grade	Letter Grade
greater than or equal to 90	A
less than 90 but greater than or equal to 80	B
less than 80 but greater than or equal to 70	C
less than 70 but greater than or equal to 60	D
less than 60	F

Specifications

1. Complete the Try It: Using Nested if-statements.
2. In addition, complete the Try It: Using Logical Operators.
3. Perhaps the most elegant solution is to nest an if statement in the else clause of the preceding if. Modify the series of if statements in grader.ino to include an else clause.

   We are nesting if statements in the else clause. Nesting in the else clause makes each test condition of the if statement exclusive of the others because each test condition eliminates all the preceding conditions. Thus, in this scenario the order is important. For more information see section 4.2.2: When Order Matters.

4. Compile and run your modified program to make sure you made the changes correctly. When you run the program, the output should look like: Enter a score: 80 B

   Run your program a few times with different scores to verify that any score displays the correct letter grade.

5. Submit your final program source code to Canvas as part of lab 6.

As time permits, read the following sections and be prepared to answer the Check Yourself questions in the section: 4.2.8: Summary.

^ top

4.2.7: Conditional Pitfalls

• Unfortunately, you can write many things in C++ that should be incorrect but end up working for some obscure reason
• This means that you can code something that should create an error message but does not
• Thus, a program may compile and run with no error messages but still be wrong
• Since you may not realize that it is wrong, it can be hard to find and correct these types of errors

Using = Instead of ==

• One common mistake is to use = when you meant to use ==
• For example, look at the test condition in the following code: if (guess = 7) { Serial.println("*** Correct! ***"); } else { Serial.println("Sorry, that is not correct."); }
• Notice that the condition is really an assignment statement and not a test
• You would think that it would fail to compile -- but it does not
• However, it will not work as you might expect
• A way to prevent this type of problem is to reverse the order of your test condition: if (7 = guess) {
• Now the compiler will give you an error message and your code will not compile: guess.ino: In function `void loop()": guess:10: error: non-lvalue in assignment
• However, if you correctly use == then your code will compile if (7 == guess) {

Strings of Inequalities

• Do NOT use a string of inequalities like the following: int a = 5, b = 1, c = 10; if (a < b < c) { Serial.println ("b is between a and c"); } else { Serial.println ("b is NOT between a and c"); }
• Your code may compile and run but give incorrect results
• The test condition is evaluated by the computer from left to right
• The first condition is a < b which evaluates to 0 (false)
• The second condition is then 0 < c which evaluates to 1 (true)
• Since the whole test condition evaluates to true you get an incorrect result
• Instead, the correct way is to use && as follows: int a = 5, b = 1, c = 10; if (a < b && b < c) { Serial.println("b is between a and c"); } else { Serial.println("b is NOT between a and c"); }

Strings of Logical Operators

• Logical expressions often read like "normal" English.
• However, C++ requires more exactness than English
• For example, the following code will compile and run but give wrong results: int guess; Serial.println("Enter a guess:"); guess = Serial.parseInt(); if (guess == 7 || 8) { Serial.println("*** Correct! ***"); } else { Serial.println("Sorry, that is not correct."); }
• The test condition is evaluated by the computer from left to right
• The left hand side is (guess == 7) which can evaluate to either true or false
• The right hand side is 8, which is interpreted as true by C++
• Since (something or true) is always true, then the test condition always evaluates to true
• Instead, the correct way is to use || as follows: int guess; Serial.println("Enter a guess:"); guess = Serial.parseInt();
  if (guess == 7 || guess == 8) { Serial.println("*** Correct! ***"); } else { Serial.println("Sorry, that is not correct."); }

Check Yourself

1. Can you spot the error in the following code fragment? if (person = terrorist) { punish_severely(); } else { return 0; }

   Answer and credit for the idea.

2. What is wrong with the following string of inequalities and how do you correct the code? int a = 5, b = 1, c = 10; if (a < b < c) { Serial.println("b is between a and c"); } else { Serial.println("b is NOT between a and c"); }
3. What is wrong with the following string of logical operators and how do you correct the code? int guess; Serial.println("Enter a guess:");
   guess = Serial.parseInt(); if (guess == 7 || 8) { Serial.println("*** Correct! ***"); } else { Serial.println("Sorry, that is not correct."); }

^ top

Summary

• By using collections of if-else statements, a program can distinguish between multiple alternatives
• Sometimes the order of statements is important for our program to work correctly
• We must think carefully and test our conditions rigorously
• Nested if-else statements can be used when there are two (or more) levels of decision making.
• We looked at an example of tax tables, filing as single or married
• To create conditions with multiple cases, we looked at using logical operators: &&, || and !
• We looked at some examples including: ((guess != GUESS1) && (guess != GUESS2)) ((GUESS1 == guess) || (GUESS2 == guess)) !((GUESS1 == guess) || (GUESS2 == guess))
• Unfortunately, you can write things in C++ that should be incorrect but end up working for some obscure reason
• These types of errors are often very difficult to find
• One common mistake is to use = when you mean to use == if (guess = 7)
• Which should be written as: if (guess == 7)
• Another common problem is trying to use a string of inequalities without a logical operator separating each condition, like: if (a < b < c)
• Which should be written as: if (a < b && b < c)
• Another common error is trying to use logical operators without enough operands: if (guess == 7 || 8)
• Which should be written as: if (guess == 7 || guess == 8)

Check Yourself

Answer these questions to check your understanding. You can find more information by following the links after the question.

1. True or false? An elegant way to choose among multiple alternatives is to nest if statements in an else clause. (4.2.1)
2. If score = 85, what is output by the following code fragment? (4.2.1) 
   

3. True or false? Order never matters in a sequence of if and else statements. (4.2.2)
4. In a game program, the scores of player A and B are stored in variables scoreA and scoreB. Assuming that the player with a larger score wins, write a sequence of conditional statements that prints our "A won", "B won" or "Game tied". (4.2.2)
5. What is the difference between if-else if-else and nested if statements? (4.2.2 vs. 4.2.4, answer)
6. True or false? A switch statement is a more powerful solution to multiple if-else if-else statements (4.2.3)
7. True or false? You can nest if statements within another if statement. (4.2.4)
8. What date type stores only the values true or false? (4.2.5)
9. When does an AND (&&) of two or more conditions evaluate to true? (4.2.6)
10. When does an OR (||) of two or more conditions evaluate to false? (4.2.6)
11. What is the effect of the NOT (!) operator? (4.2.5)
12. True or false? A && B is the same as B && A for any Boolean conditions A and B. (4.2.6)
13. If score = 85, what is output by the following code fragment? (4.2.6)
    

14. How many errors can you spot in the following code fragment? (4.2.7) if (person = terrorist) { punish_severely(); } else { return 0; }

    Answerand credit for the idea.

15. What is wrong with the following string of inequalities and how do you correct the code? (4.2.7) int a = 5, b = 1, c = 10; if (a < b < c) { Serial.println("b is between a and c"); } else { Serial.println("b is NOT between a and c"; }
16. What is wrong with the following string of logical operators and how do you correct the code? (4.2.7) int guess; Serial.println("Enter a guess:"); guess = Serial.parseInt(); if (guess == 7 || 8) { cout << "*** Correct! ***\n"; } else { cout << "Sorry, that is not correct.\n"; }

^ top

Wrap Up and Reminders

• For the next homework, see the schedule
• When class is over, please shut down your computer.
• Complete unfinished exercises from today before the next class meeting

^ top