CMPSC 201 - Ch. 4 Notes

Objective #1: Understand how decisions are made in programs.

• 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 (also called comparison 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

• You normally use relational operators in relational expressions that look like these examples
  
  (num > 5)        (0 <= price)     (menuChoice != 3)     (temp == 32)
  
  
• Relational expressions evaluate to true or false depending on the values stored in any variables used in the expression.

Objective #4: Use logical operators.

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

  &&        which means "and"
  ||            which means "or". You type the | symbol by holding down the shift key and pressing the backspace key on the keyboard.
  !            which means "not"

• Examples of Boolean expressions that involve relational expressions are:
  
  (num > 5 || num < 10)
  (0 <= price && price <= 10)         which cannot be typed as (0 <= price <= 10)
  (!(num > 10))                                 which is equivalent to (num <= 10)
  
  
• 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 order of operations:   
  
                  "not" operator (!), "and" operator (&&), "or" operator (||)
  
  
• 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
  
  
• 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) 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 #5: Use the if statement.

• Practically all computer languages have some sort of if statement. In C++, an if statement looks like this,

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

• All if statements use a control expression to determine if the code in the braces is to be executed. In the example above,
  (number == 3) is the control expression. Note the use of the relational operator, ==, not the assignment operator, =.
• Be sure to place the semicolon at the end of each statement within the body of the if statement (i.e. within the curly braces), which can contain many executable statements. However, do not place a semicolon immediately after the control expression as in:
  
  if (number == 4);
  {
       cout << "The value of number is 3";
  }
  
  The example above will not cause any syntax errors to occur and will display the statement "The value of number is 3" whether or not the variable is equal to 3 or not.

• Realize that you must use the AND operator (&&) to form a compound relational expression. The the following syntax is invalid:
  
  if (0 < number < 10)
  {
        cout << number << " is greater than 0 but less than 10." << endl;
  }
  
  Rather the following syntax must be used:
  
  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: Use the if/else statement.

• The if/else statement adds flexibility to the if decision structure. It is a two-way selection statement since either the block of code after the "if" part will be executed or the block of code after the "else" part will be executed.
• The "if" part is executed if the control expression is TRUE while the "else" part is executed if the "if" part is false, guaranteeing one part of the expression to be executed or the other.
• 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.
  
• C++ also allows the use of an if/else if statement as in:
  
  if (number > 89)
  {
       cout << "A";
  }
  else if (number > 79)
  {
       cout << "B";
  }
  else if (number > 69)
  {
       cout << "C";
  }
  else
  {
       cout << "D";
  }
  
  
• 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 #7: Use 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.