Objective #1: Understand how true and false is represented in C++.

• When decisions are made in a computer program, they are simply the result of a computation in which the final result is either true or false. Computer programs do not have intuition or "gut feelings"; they simply make thousands of yes-or-no-like decisions at blinding speeds. The computer programmer must set up these decisions within the algorithm of a computer program to achieve the desired results.
  
  
• The value zero (0) is considered to be false by C++. Any positive or negative value is considered to be true. Many people assume that only positive one is considered to be true but technically C++ evaluates any non-zero value to be true.
  
  
• Boolean expressions are used in certain kinds of C++ statements. A Boolean expression evaluates to either true or false. A simple example of a Boolean expression is (price < 10.00) where price is a variable. If price is equal to the value 8.34, then the Boolean expression as a whole would be considered to be true since 8.34 is indeed less than 10.00.

Objective #2: Use relational operators.

• Relational operators provide the tools with which programs make decisions with true and false evaluations.
  
  Relational operators:
  

==      equal to     NOTE: this is two equals symbols next to each other, not to be confused with the assignment operator, =
>        greater than
<        less than
>=      greater than or equal to
<=      less than or equal to
!=       not equal to

Objective #3: Use logical operators.

• When complex decisions must be coded into an algorithm, it may be necessary to "chain together" a few Boolean expressions (that use relational operators).   This is done with logical operators (also called Boolean operators.)
  
  Logical operators:
  

  &&        is the logical AND             operator
  ||            is the logical OR             operator
  !            is the logical NOT            operator
  

• Use this truth table to determine the results of the logical operators. In this table, 1 represents true and 0 represents false.
  
  

  AND				OR				NOT
  A	B	A && B		A	B	A || B		A	!A
  0	0	0		0	0	0		0	1
  0	1	0		0	1	1		1	0
  1	0	0		1	0	1
  1	1	1		1	1	1

  
  
• Logical operators may be mixed within evaluation statements but you must abide by their precedence rules (aka order of operations):   
  
                  NOT operator (!), AND operator (&&), OR operator (||)
  
  You must remember that the && operation is always performed before the || operation because && is similar to multiplication in normal arithmetic while || is similar to addition.
  
  
• Short-circuit evaluation in C++ allows the compiler to quickly evaluate a logical expression in some cases without having to completely evaluate each part of the expression.

Example:    inRange = ( i > 0 && i < 11);     if i is not greater than zero, the program doesn't even worry about checking whether i < 11 or not (since the whole right-hand expression can never be true if i <= 0 ).


• The following control expressions (as we will use within if statements below) have the resulting value of true assuming that the integer variables a, b, & c have the values a = 1, b = 2, & c = 3.
  
  (a < 2)
  (a + 1 == b)
  (a <= b && b < c)
  (b < a || b < c)
  (0 > b || b > 0 && b > 1)
  (a > 0)
  (a)
  (-a)
  (a = 3)
  
  Note that in the control expression (a = 3) where the assignment operator is sometimes accidentally used instead of the "double equals" relational operator, C++ evaluates the control expression as true even if the variable a is previously assigned some other value.
  
  
• The control expression (a) where the variable a was previously assigned the value 1 is true since C++ considers any control expression that evaluates to a nonzero value to be true. Even if the variable a was assigned the value -3, the control expression (a) would evaluate to true.
  
  The following control expressions evaluate to true where a = 1, b = 2, and c = 3:
  
  (b)
  (c + a)
  (2 * b)
  (c - 2 * -30)
  (0 + b)
  (c - a + b)
  
  While the following control expressions evaluate to false where a = 1, b = 2, and c = 3:
  
  (a - 1)
  (!(a))
  (0 * c)
  (c - a - b)
  
  Note that the ! symbol (the logical NOT operator) changes a true to a false.
  
  The following control expressions have the resulting value of false assuming that the integer variables a, b, & c have the values a = 1, b = 2, & c = 3.
  
  (a > 1)
  (b == 1)
  (a > 0 && a < -9)
  (c % 3)
  (a > 0 + 4)
  
  
• The complete order of operations including all of the arithmetic, relational, and logical operators including all of the basic arithmetic, relational, & logical operators is:
  
  *, /, %
  +, -
  <, >, <=, >=, ==, !=
  !
  &&
  ||
  

Objective #4: Be able to use the if statement.

• In C++, an if statement is a one-way selection structure. Example:

  if (number == 3)
  {
          cout << "The value of number is 3"; 
  }

• An if statement contains a control expression which evaluates to true or false.
  
  In the example above,     (number == 3)      is the control expression. Note the use of the "double equals" relational operator == rather than the assignment operator =.
  
  If the control expression is true, then the code inside the body of the if statement (which is usually surrounded by curly braces) is executed. If the control expression is false, then the body of the if statement is not executed.
  
  
• Note that the following control expression causes a compile error:
  
  if (0 < number < 10)
  {
        cout << number << " is greater than 0 but less than 10." << endl;
  }
  
  Rather, the control expression must be typed with && operator:
  
  if (0 < number && number < 10)
  {
        cout << number << " is greater than 0 but less than 10." << endl;
  }
  
  
• According to our Coding Standards, you must use curly braces around the body of an if statement even if there is only one statement. If you use the following statement in a program assignment for this class, you will lose points for not including curly braces even though the statement would not cause compile errors.
  
  if (num > 10)
     cout << num << " is greater than 10";
  
  This is stressed so that beginner programmers develop safe habits and good style. In the following code segment

  if (num > 0)
      cout << "num is positive" << endl;
      cout << "num is not zero" << endl;

  the body of the if statement is only considered to be the first cout statement according to the C++ compiler. The second statement would execute even if num is equal to zero. The indentation of the second statement has no effect on the way the compiler interprets this code.

• According to our Coding Standards, you must not write one line if statements. If you use the following statement in a program assignment for this class, you will lose points for not breaking it up over multiple lines even though it would not cause compile errors.
  
  if (num > 10) cout << num << " is greater than 10";
  
  
• Avoid the following common mistakes that are made with if statements:

  Always use the "double equals" symbol (i.e. comparison operator) rather than the assignment operator in control expressions:

  int num = 0:

  if (num == 5)
  {
     cout << "hello world" << endl;
  }

  which would not display "hello world" rather than:

  int num = 0;

  if (num = 5)
  {
     cout << "hello world" << endl;
  }

  which would assign the value 5 to the variable num and then display "hello world"

  Avoid using an unnecessary semicolon after a control expression:

  if (num > 0);
  {
     cout << "num is positive" << endl;
  } 

  which would cause the phrase "num is positive" to be displayed even if num is negative.
  

• An interesting use of the mod operator ( % ) is to determine whether a variable is even or odd. Since any even number leaves a remainder of 0 when divided by two and any odd number leaves a remainder of 1 when divided by two, we can use the following if statement
  
  if (num % 2 == 0)
  {
     cout << num << " is an even number" << endl;
  }
  else if (num % 2 == 1)
  {
     cout << num << " is an odd number" << endl;
  }
  

Objective #6: Be able to use the if else statement.

• The if else statement adds flexibility since it is a two-way selection statement. If the control expression is true then the body of the "if" part will execute. But if the control expression is false, then the body of the "else" part will execute.
  
  
• Example:

  if (number < 0)
  {
          cout << "The number is negative.";
  }
  else
  {
          cout << "The number is zero or positive.";
  }

• Don't forget to include boundary cases when you code control expressions. That is, be sure to use <= or >= instead of < or >, respectively, when necessary.
  
• For good style, you should always surround each part of an if else statement with curly braces. If you do not, you risk making an error such as the following
  
  if (number < 0 && number > -5)
     cout << "number is less than zero" << endl;
     cout << "number is greater than negative five" << endl;
  else
     cout << "number is not between -5 and 0" << endl;
  
  The code above would cause a compile error because curly braces are required if there are two or more statements in the body of the if clause.
  
  Similarly the following example leads to a logic error:
  
  if (number <= -5 || number >= 0)
     cout << "number not between -5 and 0" << endl;
  else
     cout << "number is less than zero" << endl;
     cout << "number is greater than negative five" << endl;
  
  In this latter example, the phrase "number is greater than negative five" displays in every situation whether the control expression is true or false. Remember, indentation means nothing to the compiler so the last cout statement is NOT considered to be part of the else clause.
  
  

Objective #7: Be able to use the if else if statement.

• You can use an if else if statement as well. The else clause is optional just as it is with an if statement. Example:
  
  if (number > 10)
  {
          cout << number << " is greater than 10." << endl;
  }
  else if (number <= 9 && number >= 6)
  {
          cout << number << " is greater than 5 and less than 10." << endl;
  }
  else
  {
          cout << number << "must be less than 6." << endl;
  }
  
  

• According to our Coding Standards, you must include one blank line above an if or an if else statement and one blank line below it for good style and readability.
  
  In this example, the if statement "stands out" and is easy to read.
  
  int num = 5;
  
  if (num > 0)
  {
     cout << num << " is greater than 0" << endl;
  }
  
  return 0;
  
  In this example, the code "runs together" and isn't very easy to read. You will lost points if you submit assignments that do not include blank lines around if statements or other structures such as loops, functions, and switch statements.
  
  int num = 5;
  if (num > 0)
  {
     cout << num << " is greater than 0" << endl;
  }
  return 0;

Objective #8: Be able to trace and write nested if statements.

• if statements and if else statements can be nested within one another in order to model complex decision structures. Be sure to use the braces and semicolons properly when coding such structures. Also, be sure to rigorously check the logic of your algorithm since it is quite easy to overlook possible errors.
  
  
• Example:
  
  The if statement that tests for divisibility by 5 is located inside of the if statement that tests for divisibility by 3 therefore it is considered to be a nested if statement.
  
  if (number % 3 == 0)
  {
          cout << number << " is divisible by 3." << endl;
  
          if (number % 5 == 0)
          {
                 cout << number << " is divisible by 3 and 5." << endl;
          }
  
  }
  
  Notice the blank lines around the inner if statement for good style.