Chapter 3 Selection Statements

§3.1 The Boolean Type and Operators§3.2 The if-else Statements§3.3 Case Studies§3.4 Logical Operators§3.5 Switch Statements§3.6 Operator Precedence and Associativity

• Boolean （布尔） type– The data type with two possible values “true” or “false” bool lighton = true;

• Internal representation– “1” -> “true”; “0” -> “false”cout<<lighton;– Any non-zero value is treated as truebool lighton = -1;cout<<lighton;

§3.1 The Boolean Type and Operators

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Relational Operators(关系运算符 )• Also named “Comparison” (比较 )operators• To compare two values• The result is a Boolean value

Operator Name Example Result < less than 1 < 2 true

<= less than or equal to 1 <= 2 true

> greater than 1 > 2 false

>= greater than or equal to 1 >= 2 false

== equal to 1 == 2 false

!= not equal to 1 != 2 true

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bool lighton = (1>2);

• “?”: – the result value depends on the truth value of a Boolean

expression.– Boolean expression: expression with a Boolean value

(booleanExp) ? exp1 : exp2

y = (x > 0) ? 1 : -1;

If x>0, y is assigned to be 1;Otherwise, y is assigned to be -1;

Conditional (条件 ) Operator

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• Statement (语句 ) is the minimal executable entity

• Three types of statements– Simple, composite, and empty statement

§3.2 The if-else Statements

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• Sequence：顺序• Selection (branching)：选择• Loop (Iteration)：循环

Three control structures

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• if• if-else• switch

Selection Statements

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if (BooleanExpression) { statement(s);}

Simple if Statements

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if (radius >= 0) { area = radius * radius * PI; cout << "The area for the circle of "

<< " radius " << radius << " is " << area;

}

Boolean Expression

true

Statement(s)

false (radius >= 0)

true

area = radius * radius * PI; cout << "The area for the circle of " << " radius " << radius << " is " << area;

false

(a) (b)

Note

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Example: Even or Odd?

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Listing 3.1 -- a program that checks whether a number is even or odd.

-- prompts the user to enter an integer (line 9) -- displays “number is even” if it is even (lines 11-12) and “number is odd” if it is odd (lines 14-15).

TestBoolean

A common mistake: Adding a semicolon at the end of an if clause.

Caution

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This mistake is hard to find: Not a compilation error; Not a runtime error; A logic error!

if (radius >= 0); { area = radius * radius * PI; cout << "The area " << " is " << area; } (a)

Equivalent

Logic Error

if (radius >= 0) { }; { area = radius * radius * PI; cout << "The area " << " is " << area; } (b)

Empty Body

if (booleanExpression){ statement(s)-for-the-true-case;}else{ statement(s)-for-the-false-case;}

The if...else Statement

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Boolean Expression

false true

Statement(s) for the false case Statement(s) for the true case

if (i > k) { if (j > k) cout << "i and j are greater than k";}else cout << "i is less than or equal to k";

Nested(嵌套 ) if Statements

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Multiple Alternative if Statements

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if (score >= 90.0) grade = 'A'; else if (score >= 80.0) grade = 'B'; else if (score >= 70.0) grade = 'C'; else if (score >= 60.0) grade = 'D'; else grade = 'F';

Equivalent

if (score >= 90.0) grade = 'A'; else if (score >= 80.0) grade = 'B'; else if (score >= 70.0) grade = 'C'; else if (score >= 60.0) grade = 'D'; else grade = 'F';

Trace if-else statement

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if (score >= 90.0) grade = 'A';else if (score >= 80.0) grade = 'B';else if (score >= 70.0) grade = 'C';else if (score >= 60.0) grade = 'D';else grade = 'F';

Suppose score is 70.0 Exit the if statementThe condition is falseThe condition is falseThe condition is truegrade is C

The else clause matches the most recent if clause in the same block.

Dangling (垂悬 ) “else”

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Use braces to make the matching clear!

}

{

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Dangling elseNothing is printed from the preceding statement. To force the else clause to match the first if clause, you must add a pair of braces:

int i = 1; int j = 2; int k = 3;

if (i > j) { if (i > k) cout << "A";}else cout << "B";

This statement prints B.

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Tips

if (number % 2 == 0) even = true; else even = false;

(a)

Equivalent bool even = number % 2 == 0;

(b)

This is better

if (even == true) cout <<"It is even.";

(a)

Equivalent if (even) cout << "It is even.";

(b) This is better

• Error 1: Forgetting Necessary Braces

• Error 2: Wrong Semicolon at the if Line

Common Errors in Selection

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if (radius >= 0) area = radius * radius * PI; cout << "The area " << " is " << area; (a) Wrong

if (radius >= 0) { area = radius * radius * PI; cout << "The area " << " is " << area; }

(b) Correct

if (radius >= 0); { area = radius * radius * PI; cout << "The area " << " is " << area; }

Equivalent

Logic Error if (radius >= 0) { }; { area = radius * radius * PI; cout << "The area " << " is " << area; }

Empty Body

• Error 3: Mistakenly Using = for ==

Common Errors in Selection

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if (count = 1) cout << "count is 1" << endl;else cout << "count is not 1" << endl;

• The Problem of Body Mass Index (BMI)– BMI is a measure of health on weight. – The interpretation of BMI for people 16 years or

older is as follows:

§3.3 Case Studies

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BMI Interpretation below 16 serious underweight

16-18 underweight 18-24 normal weight 24-29 overweight 29-35 seriously overweight above 35 gravely overweight

ComputeBMI

The US federal personal income tax is calculated based on the filing status and taxable income.The tax rates for 2002 are shown in Table 3.6.

Example: Computing Taxes

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if (status == 0) { // Compute tax for single filers}else if (status == 1) { // Compute tax for married file jointly}else if (status == 2) { // Compute tax for married file separately}else if (status == 3) { // Compute tax for head of household}else { // Display wrong status}

Example: Computing Taxes, cont.

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ComputeTax

• A program for a first grader to practice subtractions. – Randomly generates two single-digit integers number1 and

number2 with number1 >= number2,– displays a question such as “What is 9 – 2?”– The student types the answer,– The program displays a message to indicate whether the

answer is correct.

Example: A Simple Math Learning Tool

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SubtractionQuiz

• Show the output of the following code, with the variable values on the right, respectively.

Review Questions

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if(x>2) if(y>2){ int z = x+ y;

cout<< "z is "<< z << endl; }else

cout<<" x is "<< x << endl;

x = 2, y = 3;

x = 3, y = 2;

• Also known as “Boolean” operators• To operate on Boolean values to get a new

one

§3.4 Logical (逻辑 ) Operators

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Operator Name! not&& and|| or

Truth Table

p1 p2 p1 && p2

false false false

false true false

true false false

true true true

Example

(3 > 2) && (5 >= 5) is true, because (3 > 2) and (5 >= 5) are both true.

(3 > 2) && (5 > 5) is false, because (5 > 5) is false.

p1 p2 p1 || p2

false false false

false true true

true false true

true true true

Example

(2 > 3) || (5 > 5) is false, because (2 > 3) and (5 > 5) are both false.

(3 > 2) || (5 > 5) is true, because (3 > 2) is true.

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p !p

true false

false true

Example

!(1 > 2) is true, because (1 > 2) is false.

!(1 > 0) is false, because (1 > 0) is true.

• Listing 3.3

Example

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int number;

cout << "Enter an integer: "; cin >> number;

cout<< (number % 2 == 0 && number % 3 == 0);cout<< (number % 2 == 0 || number % 3 == 0) ;cout<< ((number % 2 == 0 || number % 3 == 0) && !(number % 2 == 0 && number % 3 == 0)) ;

TestBooleanOperators

• &&: conditional or short-circuit AND operator p1 && p2– C++ first evaluates p1,– if p1 is true, then evaluates p2; – if p1 is false, it does not evaluate p2.

• ||: conditional or short-circuit OR operatorp1 || p2– C++ first evaluates p1, – if p1 is false then evaluates p2; – if p1 is true, it does not evaluate p2.

Short-Circuit (短路 )Operator

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• A program to justify whether a given year it is a leap year.– The number is input by user

Example: Leap year

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LeapYear

(year % 4 == 0 && year % 100 != 0) || (year % 400 == 0)

• A lottery game– A two-digit number by computer randomly– A two-digit number by user– If the two numbers are equal, user wins $10,000– If the two digits match, user wins $3,000– If one of the two digits matches, user wins $1,000

Example: Lottery

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Lottery

switch (status) { case 0: compute taxes for single filers; break; case 1: compute taxes for married file jointly; break; case 2: compute taxes for married file separately; break; case 3: compute taxes for head of household; break; default:

cout<<"Errors: invalid status";}

§3.5 Switch Statements

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switch Statement Flow Chart

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status is 0 Compute tax for single filers break

Compute tax for married file jointly break status is 1

Compute tax for married file separatly break status is 2

Compute tax for head of household break status is 3

Default actions default

Next Statement

switch Statement Rules

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switch (switch-expression) { case value1: statement(s)1; break; case value2: statement(s)2; break; … case valueN: statement(s)N; break; default: statement(s)-for-default;}

a value of integerenclosed in parentheses.

The case branch is executed when the value in the case statement matches the value of the switch-expression.

value1, ..., and valueN are different constant expressions

they cannot contain variables in the expression, such as 1 + x

switch Statement Rules

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The default case is optionalIt can be used to perform actions when none of the specified cases matches

The order of the cases (including the default case) does not matter.

The keyword break is optionalIt should be used at the end of each

case to terminate the remainder of the switch statement.

If the break statement is not present, the next case statement will be executed.

switch (switch-expression) { case value1: statement(s)1; break; case value2: statement(s)2; break; … case valueN: statement(s)N; break; default: statement(s)-for-default;}

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Trace switch statement

switch (day) { case 1: // Fall to through to the next case case 2: // Fall to through to the next case case 3: // Fall to through to the next case case 4: // Fall to through to the next case case 5: cout << "Weekday"; break; case 0: // Fall to through to the next case case 6: cout << "Weekend"; }

Suppose day is 3:

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Trace switch statement

switch (day) { case 1: // Fall to through to the next case case 2: // Fall to through to the next case case 3: // Fall to through to the next case case 4: // Fall to through to the next case case 5: cout << "Weekday"; break; case 0: // Fall to through to the next case case 6: cout << "Weekend"; }

Suppose day is 3:

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Trace switch statement

switch (day) { case 1: // Fall to through to the next case case 2: // Fall to through to the next case case 3: // Fall to through to the next case case 4: // Fall to through to the next case case 5: cout << "Weekday"; break; case 0: // Fall to through to the next case case 6: cout << "Weekend"; }

Suppose day is 3:

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Trace switch statement

switch (day) { case 1: // Fall to through to the next case case 2: // Fall to through to the next case case 3: // Fall to through to the next case case 4: // Fall to through to the next case case 5: cout << "Weekday"; break; case 0: // Fall to through to the next case case 6: cout << "Weekend"; }

Suppose day is 3:

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Trace switch statement

switch (day) { case 1: // Fall to through to the next case case 2: // Fall to through to the next case case 3: // Fall to through to the next case case 4: // Fall to through to the next case case 5: cout << "Weekday"; break; case 0: // Fall to through to the next case case 6: cout << "Weekend"; }

Suppose day is 3:

Trace switch Statement w/o “break”

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cin>>ch;switch (ch) { case 'a': cout << ch; case 'b': cout << ch; case 'c': cout << ch;}

Next statement;

Suppose ch is 'a': ch is 'a': Execute this lineExecute this lineExecute this lineExecute next statement

Trace switch statement

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switch (ch) { case 'a': cout << ch; break; case 'b': cout << ch; break; case 'c': cout << ch;}

Next statement;

Execute next statementSuppose ch is 'a': ch is 'a': Execute this lineExecute this line

• Get the year from user,, and display the animal.

Example: Chinese Zodiac

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ChineseZodiac

• What’s the value of y after the following code?

Review Questions

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x = 0;y = 1;switch (x+1){

case 0: y +=1;case 1: y +=2;default: y +=x;

}

How to evaluate 3 + 4 * 4 > 5 * (4 + 3) – 1?

• Precedence– The precedence that the operators are “operated”

• Associativity– The order that adjacent operators with the same

precedence are “operated”

§3.6 Operator Precedence and Associativity

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Operator Precedencevar++, var-- , static_cast()+, - (plus and minus), ++var,--var (type) Casting ! (Not) *, /, % +, - (addition and subtraction) <, <=, >, >===, !=; && (AND)|| (OR)=, +=, -=, *=, /=, %= (Assignment

operator) 46

• Left-associative– Evaluate the “left” side first

• Right-associative– Evaluate the “right” side first

Operator Associativity

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All binary operators except “=“

“=“

Example3 + 4 * 4 > 5 * 7 – 1

3 + 16 > 5 * 7 – 1

3 + 16 > 35 – 1

19 > 35 – 1

19 > 34

FALSE

3 + 4 * 4 || 5 * (4 + 3) – 1

3 + 16 || 5 * (4 + 3) – 1

19 || 5 * (4 + 3) – 1

TRUE

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• Rational operators• Logical operators• if-else• switch• Operator precedence and associativity

Summary

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1. Fill in the blanks to make the two code blocks equivalent.

2. Switch statements can always be converted equivalently to if-else ones, right? And vice versa? Why?

3. Assume that int a = 2 and double d = 1.1. Show the result of each expression below. The expressions are independent.

Homework Questions

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if___________min=a;else if _____________min = b;else min = c;

min =a;if____________min = b;if____________min = c;

d += 1.5*3 +(++d);d -= 1.5*3 + d++;

a = (a =3) + a;a = a + (a =3);a += a + (a=3);a = 1 + 5 * 2 % a--;a = 2 + 4 * 5 % (++a + 1);