Day 4

• Day 4
• Expressions and Statements
• Statements
• Whitespace
• Blocks and Compound Statements
• Expressions
• Listing 4.1. Evaluating complex expressions.
• Operators
• Assignment Operator
• Mathematical Operators
• Listing 4.2. A demonstration of subtraction and integer overflow.
• Integer Division and Modulus
• Combining the Assignment and Mathematical Operators
• Increment and Decrement
• Prefix and Postfix
• Listing 4.3. A demonstration of prefix and postfix operators.
• Precedence
• Nesting Parentheses
• The Nature of Truth
• Relational Operators
• The if Statement
• Listing 4.4. A demonstration of branching based on relational operators.
• Indentation Styles
• else
• Listing 4.5. Demonstrating the else keyword.
• The if Statement
• Advanced if Statements
• Listing 4.6. A complex, nested if statement.
• Using Braces in Nested if Statements
• Listing 4.7. A demonstration of why
• braces help clarify which else statement goes with which if statement.
• Listing 4.8. A demonstration of the proper use of braces with an if statement.
• Logical Operators
• Logical AND
• Logical OR
• Logical NOT
• Relational Precedence
• More About Truth and Falsehood
• Conditional (Ternary) Operator
• Listing 4.9. A demonstration of the conditional operator.
• Summary
• Q&A
• Workshop
• Quiz
• Exercises

• What statements are.
• What blocks are.
• What expressions are.
• How to branch your code based on conditions.
• What truth is, and how to act on it.

x = a + b;

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New Term: A null statement is a statement that does nothing. 

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x=a+b;

x                       =a

+           b          ;

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New Term: Whitespace characters (spaces, tabs, and newlines) cannot be seen. If these characters are printed, you see only the white of the paper. 

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{
     temp = a;
     a = b;
     b = temp;
}

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DO use a closing brace any time you have an opening brace. DO end your statements with a semicolon. DO use whitespace judiciously to make your code clearer. 

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The myriad pieces of code that qualify as expressions might surprise you. Here are three examples:

3.2                       // returns the value 3.2
PI                        // float const that returns the value 3.14
SecondsPerMinute          // int const that returns 60

The complicated expression

x = a + b;

y = x = a + b;

Assign the result of the expression a + b to x.

Assign the result of the assignment expression x = a + b to y.

If a, b, x, and y are all integers, and if a has the value 2 and b has the value 5, both x and y will be assigned the value 7.

Listing 4.1. Evaluating complex expressions.

1:    #include <iostream.h>
2:    int main()
3:    {
4:        int a=0, b=0, x=0, y=35;
5:        cout << "a: " << a << " b: " << b;
6:        cout << " x: " << x << " y: " << y << endl;
7:        a = 9;
8:        b = 7;
9:        y = x = a+b;
10:       cout << "a: " << a << " b: " << b;
11:       cout << " x: " << x << " y: " << y << endl;
12:          return 0;
13: }
Output: a: 0 b: 0 x: 0 y: 35
a: 9 b: 7 x: 16 y: 16

• Assignment operators.
• Mathematical operators.

x = a + b;

An operand that legally can be on the left side of an assignment operator is called an lvalue. That which can be on the right side is called (you guessed it) an rvalue.

Constants are r-values. They cannot be l-values. Thus, you can write

x = 35;          // ok

35 = x;          // error, not an lvalue!

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New Term: An lvalue is an operand that can be on the left side of an expression. An rvalue is an operand that can be on the right side of an expression. Note that all l-values are r-values, but not all r-values are l-values. An example of an rvalue that is not an lvalue is a literal. Thus, you can write x = 5;, but you cannot write 5 = x;. 

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Addition and subtraction work as you would expect, although subtraction with unsigned integers can lead to surprising results, if the result is a negative number. You saw something much like this yesterday, when variable overflow was described. Listing 4.2 shows what happens when you subtract a large unsigned number from a small unsigned number.

Listing 4.2. A demonstration of subtraction and integer overflow.

1: // Listing 4.2 - demonstrates subtraction and
2: // integer overflow
3: #include <iostream.h>
4:
5: int main()
6: {
7:    unsigned int difference;
8:    unsigned int bigNumber = 100;
9:    unsigned int smallNumber = 50;
10:   difference = bigNumber - smallNumber;
11:   cout << "Difference is: " << difference;
12:   difference = smallNumber - bigNumber;
13:   cout << "\nNow difference is: " << difference <<endl;
14:       return 0;
15: }
Output: Difference is: 50
Now difference is: 4294967246

Finding the modulus can be very useful. For example, you might want to print a statement on every 10th action. Any number whose value is 0 when you modulus 10 with that number is an exact multiple of 10. Thus 1 % 10 is 1, 2 % 10 is 2, and so forth, until 10 % 10, whose result is 0. 11 % 10 is back to 1, and this pattern continues until the next multiple of 10, which is 20. We'll use this technique when looping is discussed on Day 7, "More Program Flow."

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WARNING: Many novice C++ programmers inadvertently put a semicolon after their if statements:

if(SomeValue < 10);
SomeValue = 10;

What was intended here was to test whether SomeValue is less than 10, and if so, to set it to 10, making 10 the minimum value for SomeValue. Running this code snippet will show that SomeValue is always set to 10! Why? The if statement terminates with the semicolon (the do-nothing operator). Remember that indentation has no meaning to the compiler. This snippet could more accurately have been written as:

if (SomeValue < 10)  // test
;  // do nothing
SomeValue = 10;  // assign

Removing the semicolon will make the final line part of the if statement and will make this code do what was intended. 

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int myAge = 5;
int temp;
temp = myAge + 2;  // add 5 + 2 and put it in temp
myAge = temp;             // put it back in myAge

myAge = myAge + 2;

Even simpler to write, but perhaps a bit harder to read is

myAge += 2;

There are self-assigned subtraction (-=), division (/=), multiplication (*=), and modulus (%=) operators as well.

The increment operator (++) increases the value of the variable by 1, and the decrement operator (--) decreases it by 1. Thus, if you have a variable, C, and you want to increment it, you would use this statement:

C++;               // Start with C and increment it.

C = C + 1;

C += 1;

In a simple statement, it doesn't much matter which you use, but in a complex statement, when you are incrementing (or decrementing) a variable and then assigning the result to another variable, it matters very much. The prefix operator is evaluated before the assignment, the postfix is evaluated after.

The semantics of prefix is this: Increment the value and then fetch it. The semantics of postfix is different: Fetch the value and then increment the original.

This can be confusing at first, but if x is an integer whose value is 5 and you write

int a = ++x;

If, after doing this, you write

int b = x++;

Listing 4.3. A demonstration of prefix and postfix operators.

1:  // Listing 4.3 - demonstrates use of
2:  // prefix and postfix increment and
3:  // decrement operators
4:  #include <iostream.h>
5:  int main()
6:  {
7:      int myAge = 39;      // initialize two integers
8:      int yourAge = 39;
9:      cout << "I am: " << myAge << " years old.\n";
10:     cout << "You are: " << yourAge << " years old\n";
11:     myAge++;         // postfix increment
12:     ++yourAge;       // prefix increment
13:     cout << "One year passes...\n";
14:     cout << "I am: " << myAge << " years old.\n";
15:     cout << "You are: " << yourAge << " years old\n";
16:     cout << "Another year passes\n";
17:     cout << "I am: " << myAge++ << " years old.\n";
18:     cout << "You are: " << ++yourAge << " years old\n";
19:     cout << "Let's print it again.\n";
20:     cout << "I am: " << myAge << " years old.\n";
21:     cout << "You are: " << yourAge << " years old\n";
22:       return 0;
23: }
Output: I am      39 years old
You are   39 years old
One year passes
I am      40 years old
You are   40 years old
Another year passes
I am      40 years old
You are   41 years old
Let's print it again
I am      41 years old
You are   41 years old

On line 17, myAge is incremented as part of the printing statement, using the postfix increment operator. Because it is postfix, the increment happens after the print, and so the value 40 is printed again. In contrast, on line 18, yourAge is incremented using the prefix increment operator. Thus, it is incremented before being printed, and the value displays as 41.

Finally, on lines 20 and 21, the values are printed again. Because the increment statement has completed, the value in myAge is now 41, as is the value in yourAge.

x = 5 + 3 * 8;

Every operator has a precedence value, and the complete list is shown in Appendix A, "Operator Precedence." Multiplication has higher precedence than addition, and thus the value of the expression is 29.

When two mathematical operators have the same precedence, they are performed in left-to-right order. Thus

x = 5 + 3 + 8 * 9 + 6 * 4;

x = 5 + 3 + 72 + 24;

Be careful with this. Some operators, such as assignment, are evaluated in right-to-left order! In any case, what if the precedence order doesn't meet your needs? Consider the expression

TotalSeconds = NumMinutesToThink + NumMinutesToType * 60

In this case, you use parentheses to change the precedence order. Items in parentheses are evaluated at a higher precedence than any of the mathematical operators. Thus

TotalSeconds = (NumMinutesToThink + NumMinutesToType) * 60

TotalPersonSeconds = ( ( (NumMinutesToThink + NumMinutesToType) * 60) *  ?(PeopleInTheOffice + PeopleOnVacation) )

This example raises an important related issue. This expression is easy for a computer to understand, but very difficult for a human to read, understand, or modify. Here is the same expression rewritten, using some temporary integer variables:

TotalMinutes = NumMinutesToThink + NumMinutesToType;
TotalSeconds = TotalMinutes * 60;
TotalPeople = PeopleInTheOffice + PeopleOnVacation;
TotalPersonSeconds = TotalPeople * TotalSeconds;

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DO remember that expressions have a value. DO use the prefix operator (++variable) to increment or decrement the variable before it is used in the expression. DO use the postfix operator (variable++) to increment or decrement the variable after it is used. DO use parentheses to change the order of precedence. DON'T nest too deeply, because the expression becomes hard to understand and maintain. 

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If the integer variable myAge has the value 39, and the integer variable yourAge has the value 40, you can determine whether they are equal by using the relational "equals" operator:

myAge == yourAge;  // is the value in myAge the same as in yourAge?

myAge > yourAge;  // is myAge greater than yourAge?

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WARNING: Many novice C++ programmers confuse the assignment operator (=) with the equals operator (==). This can create a nasty bug in your program. 

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Table 4.1. The Relational Operators.

Name	Operator	Sample	Evaluates
Equals	==	100 == 50;	false
		50 == 50;	true
Not Equals	!=	100 != 50;	true
		50 != 50;	false
Greater Than	>	100 > 50;	true
		50 > 50;	false
Greater Than	>=	100 >= 50;	true
or Equals		50 >= 50;	true
Less Than	<	100 < 50;	false
		50 < 50;	false
Less Than	<=	100 <= 50;	false
or Equals		50 <= 50;	true

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DO remember that relational operators return the value 1 (true) or 0 (false). DON'T confuse the assignment operator (=) with the equals relational operator (==). This is one of the most common C++ programming mistakes--be on guard for it. 

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The simplest form of an if statement is this:

if (expression)
     statement;

if (bigNumber > smallNumber)
     bigNumber = smallNumber;

Because a block of statements surrounded by braces is exactly equivalent to a single statement, the following type of branch can be quite large and powerful:

if (expression)
{
     statement1;
     statement2;
     statement3;
}

if (bigNumber > smallNumber)
{
     bigNumber = smallNumber;
     cout << "bigNumber: " << bigNumber << "\n";
     cout << "smallNumber: " << smallNumber << "\n";
}

Listing 4.4. A demonstration of branching based on relational operators.

1:  // Listing 4.4 - demonstrates if statement
2:  // used with relational operators
3:  #include <iostream.h>
4:  int main()
5:  {
6:        int RedSoxScore, YankeesScore;
7:        cout << "Enter the score for the Red Sox: ";
8:        cin >> RedSoxScore;
9:
10:       cout << "\nEnter the score for the Yankees: ";
11:       cin >> YankeesScore;
12:
13:       cout << "\n";
14:
15:       if (RedSoxScore > YankeesScore)
16:            cout << "Go Sox!\n";
17:
18:       if (RedSoxScore < YankeesScore)
19:       {
20:            cout << "Go Yankees!\n";
21:            cout << "Happy days in New York!\n";
22:       }
23:
24:       if (RedSoxScore == YankeesScore)
25:       {
26:            cout << "A tie? Naah, can't be.\n";
27:            cout << "Give me the real score for the Yanks: ";
28:            cin >> YankeesScore;
29:
30:            if (RedSoxScore > YankeesScore)
31:                 cout << "Knew it! Go Sox!";
32:
33:            if (YankeesScore > RedSoxScore)
34:                 cout << "Knew it! Go Yanks!";
35:
36:            if (YankeesScore == RedSoxScore)
37:                 cout << "Wow, it really was a tie!";
38:       }
39:
40:       cout << "\nThanks for telling me.\n";
41:        return 0;
42: }
Output: Enter the score for the Red Sox: 10

Enter the score for the Yankees: 10

A tie? Naah, can't be
Give me the real score for the Yanks: 8
Knew it! Go Sox!
Thanks for telling me.

Note that if the initial Yankees score was higher than the Red Sox score, the if statement on line 15 would evaluate as FALSE, and line 16 would not be invoked. The test on line 18 would evaluate as true, and the statements on lines 20 and 21 would be invoked. Then the if statement on line 24 would be tested, and this would be false (if line 18 was true). Thus, the program would skip the entire block, falling through to line 39.

In this example, getting a true result in one if statement does not stop other if statements from being tested.

• Putting the initial brace after the condition and aligning the closing brace under the if to close the statement block.

if (expression){
     statements
}

• Aligning the braces under the if and indenting the statements.

if (expression)
{
    statements
}

• Indenting the braces and statements.

if (expression)
   {
   statements
   }

The method shown so far, testing first one condition and then the other, works fine but is a bit cumbersome. The keyword else can make for far more readable code:

if (expression)
     statement;
else
     statement;

Listing 4.5. Demonstrating the else keyword.

1:   // Listing 4.5 - demonstrates if statement
2:   // with else clause
3:   #include <iostream.h>
4:   int main()
5:   {
6:      int firstNumber, secondNumber;
7:      cout << "Please enter a big number: ";
8:      cin >> firstNumber;
9:      cout << "\nPlease enter a smaller number: ";
10:     cin >> secondNumber;
11:     if (firstNumber > secondNumber)
12:          cout << "\nThanks!\n";
13:     else
14:          cout << "\nOops. The second is bigger!";
15:
16:        return 0;
17: }

Output: Please enter a big number: 10

Please enter a smaller number: 12

Oops. The second is bigger!

if (expression)
    statement;
next statement;

if (expression)
    statement1;
else
    statement2;
next statement;

Example
if (SomeValue < 10)
  cout << "SomeValue is less than 10");
else
  cout << "SomeValue is not less than 10!");
cout << "Done." << endl;

if (expression1)
{
    if (expression2)
        statement1;
    else
    {
        if (expression3)
            statement2;
        else
            statement3;
    }
}
else
    statement4;

Listing 4.6 gives an example of such a complex if statement.

Listing 4.6. A complex, nested if statement.

1:  // Listing 4.5 - a complex nested
2:  // if statement
3:  #include <iostream.h>
4:  int main()
5:  {
6:      // Ask for two numbers
7:      // Assign the numbers to bigNumber and littleNumber
8:      // If bigNumber is bigger than littleNumber,
9:      // see if they are evenly divisible
10:     // If they are, see if they are the same number
11:
12:     int firstNumber, secondNumber;
13:     cout << "Enter two numbers.\nFirst: ";
14:     cin >> firstNumber;
15:     cout << "\nSecond: ";
16:     cin >> secondNumber;
17:     cout << "\n\n";
18:
19:     if (firstNumber >= secondNumber)
20:     {
21:       if ( (firstNumber % secondNumber) == 0) // evenly divisible?
22:       {
23:            if (firstNumber == secondNumber)
24:                 cout << "They are the same!\n";
25:            else
26:                 cout << "They are evenly divisible!\n";
27:       }
28:       else
29:            cout << "They are not evenly divisible!\n";
30:     }
31:     else
32:       cout << "Hey! The second one is larger!\n";
33:        return 0;
34: }

Output: Enter two numbers.
First: 10

Second: 2

They are evenly divisible!

If the if statement on line 21 fails, the else statement on line 28 is executed.

if (x > y)              // if x is bigger than y
    if (x < z)          // and if x is smaller than z
        x = y;         // then set x to the value in z

Listing 4.7. A demonstration of why braces help clarify which else statement goes with which if statement.

1:   // Listing 4.7 - demonstrates why braces
2:   // are important in nested if statements
3:   #include <iostream.h>
4:   int main()
5:   {
6:     int x;
7:     cout << "Enter a number less than 10 or greater than 100: ";
8:     cin >> x;
9:     cout << "\n";
10:
11:     if (x > 10)
12:        if (x > 100)
13:             cout << "More than 100, Thanks!\n";
14:     else                            // not the else intended!
15:        cout << "Less than 10, Thanks!\n";
16:
17:         return 0; 
18: }

Output: Enter a number less than 10 or greater than 100: 20

Less than 10, Thanks!

If the number entered is less than or equal to 10, the if statement on line 10 evaluates to FALSE. Program control goes to the next line following the if statement, in this case line 16. If you enter a number less than 10, the output is as follows:

Enter a number less than 10 or greater than 100: 9

It is a subtle bug because the compiler will not complain. This is a legal C++ program, but it just doesn't do what was intended. Further, most of the times the programmer tests this program, it will appear to work. As long as a number that is greater than 100 is entered, the program will seem to work just fine.

Listing 4.8 fixes the problem by putting in the necessary braces.

Listing 4.8. A demonstration of the proper use of braces with an if statement

1:    // Listing 4.8 - demonstrates proper use of braces
2:    // in nested if statements
3:    #include <iostream.h>
4:    int main()
5:    {
6:      int x;
7:      cout << "Enter a number less than 10 or greater than 100: ";
8:      cin >> x;
9:      cout << "\n";
10:
11:     if (x > 10)
12:     {
13:        if (x > 100)
14:             cout << "More than 100, Thanks!\n";
15:     }
16:     else                            // not the else intended!
17:        cout << "Less than 10, Thanks!\n";
18:         return 0;
19: }
Output: Enter a number less than 10 or greater than 100: 20

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NOTE: The programs shown in this book are written to demonstrate the particular issues being discussed. They are kept intentionally simple; there is no attempt to "bulletproof" the code to protect against user error. In professional-quality code, every possible user error is anticipated and handled gracefully. 

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Imagine a sophisticated alarm system that has this logic: "If the door alarm sounds AND it is after six p.m. AND it is NOT a holiday, OR if it is a weekend, then call the police." C++'s three logical operators are used to make this kind of evaluation. These operators are listed in Table 4.2.

Table 4.2. The Logical Operators.

Operator	Symbol	Example
AND	&&	expression1 && expression2
OR	||	expression1 || expression2
NOT	!	!expression

if ( (x == 5) && (y == 5) )

Note that the logical AND is two && symbols. A single & symbol is a different operator, discussed on Day 21, "What's Next."

if ( (x == 5) || (y == 5) )

Note that the logical OR is two || symbols. A single | symbol is a different operator, discussed on Day 21.

if ( !(x == 5) )

if (x != 5)

if ( x > 5 &&  y > 5  || z > 5)

If x is 3, and y and z are both 10, the first interpretation will be true (z is greater than 5, so ignore x and y), but the second will be false (it isn't true that both x and y are greater than 5 nor is it true that z is greater than 5).

Although precedence will determine which relation is evaluated first, parentheses can both change the order and make the statement clearer:

if (  (x > 5)  && (y > 5 ||  z > 5) )

---

NOTE: It is often a good idea to use extra parentheses to clarify what you want to group. Remember, the goal is to write programs that work and that are easy to read and understand. 

---

if (x)           // if x is true (nonzero)
    x = 0;

if (x != 0)      // if x is nonzero
    x = 0;

These two statements also are equivalent:

if (!x)           // if x is false (zero)
if (x == 0)       // if x is zero

---

DO put parentheses around your logical tests to make them clearer and to make the precedence explicit. DO use braces in nested if statements to make the else statements clearer and to avoid bugs. DON'T use if(x) as a synonym for if(x != 0); the latter is clearer. DON'T use if(!x) as a synonym for if(x == 0); the latter is clearer. 

---

---

NOTE: It is common to define your own enumerated Boolean (logical) type with enum Bool {FALSE, TRUE};. This serves to set FALSE to 0 and TRUE to 1. 

---

The conditional operator takes three expressions and returns a value:

(expression1) ? (expression2) : (expression3)

Listing 4.9 shows an if statement rewritten using the conditional operator.

Listing 4.9. A demonstration of the conditional operator.

1:   // Listing 4.9 - demonstrates the conditional operator
2:   //
3:   #include <iostream.h>
4:   int main()
5:   {
6:      int x, y, z;
7:      cout << "Enter two numbers.\n";
8:      cout << "First: ";
9:      cin >> x;
10:     cout << "\nSecond: ";
11:     cin >> y;
12:     cout << "\n";
13:
14:     if (x > y)
15:       z = x;
16:     else
17:       z = y;
18:
19:     cout << "z: " << z;
20:     cout << "\n";
21:
22:     z =  (x > y) ? x : y;
23:
24:     cout << "z: " << z;
25:     cout << "\n";
26:        return 0;
27: }
Output: Enter two numbers.
First: 5

Second: 8

z: 8
z: 8

You have seen that a block of statements enclosed by a pair of braces can be used anywhere a single statement can be used.

You have learned that every expression evaluates to a value, and that value can be tested in an if statement or by using the conditional operator. You've also seen how to evaluate multiple statements using the logical operator, how to compare values using the relational operators, and how to assign values using the assignment operator.

You have explored operator precedence. And you have seen how parentheses can be used to change the precedence and to make precedence explicit and thus easier to manage.

Q. Why use unnecessary parentheses when precedence will determine which operators are acted on first?

A. Although it is true that the compiler will know the precedence and that a programmer can look up the precedence order, code that is easy to understand is easier to maintain.

Q. If the relational operators always return 1 or 0, why are other values considered true?

A. The relational operators return 1 or 0, but every expression returns a value, and those values can also be evaluated in an if statement. Here's an example:

if ( (x = a + b) == 35 )

This is a perfectly legal C++ statement. It evaluates to a value even if the sum of a and b is not equal to 35. Also note that x is assigned the value that is the sum of a and b in any case.

Q. What effect do tabs, spaces, and new lines have on the program?

A. Tabs, spaces, and new lines (known as whitespace) have no effect on the program, although judicious use of whitespace can make the program easier to read.

Q. Are negative numbers true or false?

A. All nonzero numbers, positive and negative, are true.

1. What is an expression?

2. Is x = 5 + 7 an expression? What is its value?

3. What is the value of 201 / 4?

4. What is the value of 201 % 4?

5. If myAge, a, and b are all int variables, what are their values after:

myAge = 39;
a = myAge++;
b = ++myAge;

6. What is the value of 8+2*3?

7. What is the difference between x = 3 and x == 3?

8. Do the following values evaluate to TRUE or FALSE?

a. 0

b. 1

c. -1

d. x = 0

e. x == 0 // assume that x has the value of 0

1. Write a single if statement that examines two integer variables and changes the larger to the smaller, using only one else clause.

2. Examine the following program. Imagine entering three numbers, and write what output you expect.

1: #include <iostream.h>
2: int main()
3: { 4: int a, b, c;
5: cout << "Please enter three numbers\n";
6: cout << "a: ";
7: cin >> a;
8: cout << "\nb: ";
9: cin >> b;
10: cout << "\nc: ";
11: cin >> c;
12:
13: if (c = (a-b))
14: {cout << "a: ";
15: cout << a;
16: cout << "minus b: ";
17: cout << b;
18: cout << "equals c: ";
19: cout << c << endl;}
20: else
21: cout << "a-b does not equal c: " << endl;
22: return 0;
23: }

3. Enter the program from Exercise 2; compile, link, and run it. Enter the numbers 20, 10, and 50. Did you get the output you expected? Why not?

4. Examine this program and anticipate the output:

1: #include <iostream.h>
2: int main()
3: {
4: int a = 1, b = 1, c;
5: if (c = (a-b))
6: cout << "The value of c is: " << c;
7: return 0;
8: }

5. Enter, compile, link, and run the program from Exercise 4. What was the output? Why?