1. Decisions, decisions, decisions
Chapter 5
Spring 2006
CS 101
Aaron Bloomfield

2. Background
Our problem-solving solutions so far have the straight-line property
They execute the same statements for every run of the program
public class DisplayForecast
// main(): application entry point
public static void main(String[] args) {
System.out.print("I think there is a world");
System.out.print(" market for maybe five ");
System.out.println("computers. “);
System.out.print(" Thomas Watson, IBM, “);
System.out.println("1943.“); }

3. Background For general problem solving we need more capabilities
The ability to control which statements are executed
The ability to control how often a statement is executed
We will concentrate first on controlling which statements are executed
Java provides the if and switch conditional constructs to control whether a statement list is executed
The if constructs use logical expressions to determine their course of action
We will start with logical expressions

4. Logical expressions

5. Logical expressions
The branch of mathematics dealing with logical expressions is Boolean algebra
Developed by the British mathematician George Boole

6. Logical expressions
A logical expression has either the value logical true or logical false
Some expressions whose values are logical true
The year 2004 is a leap year
A meter equals 100 centimeters
Some expressions whose values are logical false
A triangle has four sides
The area of square is always equal to twice its perimeter

7. Logical expressions
There are three primary logical operators for manipulating logical values
Logical and
Logical or
Logical not
The operators work as most of us would expect

8. Truth tables
We use truth tables to give formal specifications of the operators
“It works as most of us would expect” allows for ambiguity of interpretation
Jim is smiling or Patty is smiling
Can both Jim and Patty both be smiling?
Truth tables
Lists all combinations of operand values and the result of the operation for each combination
p q p and q
False False False
False True False
True False False
True True True

9. Or and not truth tables p q p or q False False False False True True
True False True
True True True
p not q
False True
True False

10. Boolean algebra
Can create complex logical expressions by combining simple logical expressions
not (p and q)
p q p and q not (p and q)
False False False True
False True False True
True False False True
True True True False

11. DeMorgan’s laws not (p and q) equals (not p) or (not q)
(not p) or p q p and q not (p and q) ( not p) (not q) (not q)
False False False True True True True
False True False True True False True
True False False True False True True
True True True False False False False

12. DeMorgan’s laws not (p or q) equals (not p) and (not q)
(not p) and p q p or q not (p or q) ( not p) (not q) (not q)
False False False True True True True
False True True False True False False
True False True False False True False
True True True False False False False

13. DeMorgan’s laws
If you remember nothing else about the Boolean operators, remember that:
not (a and b) == (not a) or (not b)
not (a or b) == (not a) and (not b)

14. Sidewalk chalk guy
Source:

15. Boolean expressions

16. A boolean type Java has the logical type boolean
Type boolean has two literal constants
true
false
Operators
The and operator is &&
Don’t use &
The or operator is ||
Don’t use |
The not operator is !

17. Defining boolean variables
Local boolean variables are uninitialized by default
boolean isWhitespace;
boolean receivedAcknowledgement;
boolean haveFoundMissingLink;

18. Defining boolean variables
Local boolean variables with initialization
boolean canProceed = true;
boolean preferCyan = false;
boolean completedSecretMission = true;

19. Assignment vs. comparison
= is the assignment operator
It copies the value on the right to the location on the left
Consider:
int x;
x = 5;
The value 5 is copied to the spot x in memory
== is the comparison operator
Returns a boolean (true or false) if the two sides are equal
int x = 5;
System.out.println (x == 5);
System.out.println (x == 6);
Prints out true, false

20. Other operators Equality operators == and != Operator ==
Returns true if the operands have the same value; otherwise, returns false
This is not the assignment operator!
Operator !=
Returns true if the operands have different values; otherwise, returns false
The operators work with all types of values

21. Evaluating boolean expressions
Suppose
boolean p = true;
boolean q = false;
boolean r = true;
boolean s = false;
What is the value of
p p && s
!s p == q
q q != r
p && r r == s
q || s q != s

22. Evaluating boolean expressions
Suppose
int i = 1;
int j = 2;
int k = 2;
char c = '#';
char d = '%';
char e = '#';
What is the value of
j == k i != k
i == j j != k
c == e d != e
c == d c != e

23. A bit of humor…

24. Translating English to logical expressions

25. Translating English to logical expressions
English doesn’t always translate cleanly into logical expressions
To see this, we need to examine the NOR operator
It doesn’t exist in Java, but we can fake it
p NOR q == NOT (p OR q)
NOR is represented by a downward arrow: 
In Java, given variables p and q
NOR is done by: !(p||q)
p q p or q not (p or q) p nor q
False False False True True
False True True False False
True False True False False
True True True False False

26. Translation Example
“I have neither given nor received help on this exam”
Rephrased: “I have not given nor received …”
Let p = “I have given help on this exam”
Let q = “I have received help on this exam”
Translation is: pq
Remember the precedence: NOT is done first! p q p
pq T F

27. Translation example, take 2
“I have neither given nor received help on this exam”
Rephrased: “I have not (given nor received …)”
Let p = “I have given help on this exam”
Let q = “I have received help on this exam”
Another translation is: (pq) = p || q p q
p || q T F

28. Translation example, rephrased
What is meant is “I have not given and I have not received help on this exam”
Or “I have not (given or received) help on this exam”
This is a DeMorgaization of the one above it
The problem:  has a higher precedence than  in Boolean logic, but not always in English
Also, “neither” is vague p q
pq
(p||q) T F

29. Disclaimer
The preceding example was showing that when English can be clear, it does not always translate clearly into Boolean logic
The English meaning is exact
The Boolean translation is not
This does not mean that you can cheat, and say that I said it was allowed by the honor code

30. Floating point comparison

31. Floating point precission
What gets printed?
class FloatTest {
public static void main (String args[]) {
double y = ;
System.out.println (y); }
There are ’s

32. Program demo
FloatTest.java

33. Take care with floating-point values
Consider
double a = 1;
double b =
double c = ;
Two true expressions!
c == b b != a
Two false expressions!
a == b b != c
Problem lies with the finite precision of the floating-point types
Instead with the ordering operators for closeness

34. How to solve this
Don’t compare floating-point values if you can help it!
Both doubles and floats
Need to test if the two doubles are “close” in value
final double EPSILON = ;
boolean foo = Math.abs (a-b) < EPSILON;

35. The 2002 Ig Nobel Prizes Biology Physics Interdisciplinary Chemistry
Mathematics
Literature
Peace
Hygiene
Economics
Medicine
“Courtship behavior of ostriches towards humans under
farming conditions in Britain”
“Demonstration of the exponential decay law using beer
froth”
A comprehensive study of human belly button lint
Creating a four-legged periodic table
“Estimation of the surface area of African elephants”
“The effects of pre-existing inappropriate highlighting on
reading comprehension”
For creating Bow-lingual, a computerized dog-to-human
translation device
For creating a washing machine for cats and dogs
Enron et. al. for applying imaginary numbers to the
business world
“(male) asymmetry in man in ancient sculpture”

36. More on evaluating expressions

37. Ordering operators
Java provides ordering operators for the primitive types
Four ordering operators, <, >, <=, and >=
They correspond to mathematical operators of <, >, ≤, and ≥
Together the equality and ordering operators are known as the relational operators
False is less than true

38. Evaluation boolean expressions
Suppose
int i = 1;
int j = 2;
int k = 2;
What is the value of
i < j
j < k
i <= k
j >= k
i >= k

39. Unicode values Character comparisons are based on their Unicode values
Characters ‘0’, ‘1’, … ‘9’ have expected order
Character ‘0’ has the encoding 48
Character ‘1’ has the encoding 49, and so on.
Upper case Latin letters ‘A’, ‘B’, … ‘Z’ have expected order
Character ‘A’ has the encoding 65, character ‘B’ has the encoding 66, and so on.
Lower case Latin letters ‘a’, ‘b’, … ‘z’ have expected order
Character ‘a’ has the encoding 97
Character ‘b’ has the encoding 98, and so on.

40. Evaluation boolean expressions
Suppose
char c = '2';
char d = '3';
char e = '2';
What is the value of
c < d
c < e
c <= e
d >= e
c >= e

41. Operator precedence revisited
Highest to lowest
Parentheses
Unary operators
Multiplicative operators
Additive operators
Relational ordering
Relational equality
Logical and
Logical or
Assignment

42. Expressions vs. statements
A statement is a single command for Java to do, and always ends in a semi-colon (for now, at least)
System.out.println (“hello world”);
int x = 4;
++x;
An expression returns a value, and does not have a semi-colon 5
circle.getRadius() x
Note the difference between the following:
++i is an expression
++i; is a statement

43. Sand Castles

44. if statement

45. Conditional constructs
Provide
Ability to control whether a statement list is executed
Two constructs
If statement if
if-else
if-else-if
Switch statement

46. Basic if statement Syntax if (Expression) Action
If the Expression is true then execute Action
Action is either a single statement or a group of statements within braces
For us, it will always be a group of statements within braces
Expression
Action
true
false

47. Example if (value < 0) { value = -value; } Is our number negative?
false
Value < 0
Value = -Value
true
If Value is less than
zero then we need
to update its value
to that of its additive
inverse
If Value is not
less than zero
then our number
is fine as is
Our number is now
definitely
nonnegative

48. Sorting two values What happens if the user enters 11 and 28?
System.out.print("Enter an integer number: ");
int value1 = stdin.nextInt();
System.out.print("Enter another integer number: ");
int value2 = stdin.nextInt();
// rearrange numbers if necessary
if (value2 < value1) {
// values are not in sorted order
int rememberValue1 = value1;
value1 = value2;
value2 = rememberValue1; }
// display values
System.out.println("The numbers in sorted order are "
+ value1 + " and then " + value2);
What happens if the user enters 11 and 28?
What happens if the user enters 11 and 4?

49. If semantics Are the numbers out of order Rearrange value1 and
value2 < value1
int
rememberValue1 = value1
value1 = value2
value2 = rememberValue1
true
false
Are the numbers out
of order
Rearrange value1 and
value2 to put their
values in the proper
order
The numbers were rearranged into
the proper order
The numbers
were
initially in
order
The numbers are in order

50. What an if statement executes
An if statement executes the next block of code
A block is either:
A single statement without curly brackets:
if (a == b)
System.out.println (“a==b!!!”);
A number of statements enclosed by curly brackets:
if (a == b) {
System.out.print (“a”);
System.out.print (“==”);
System.out.print (“b”);
System.out.println (“!!!”); }

51. Why we always use braces
What is the output?
int m = 5;
int n = 10;
if (m < n)
++m;
++n;
System.out.println(" m = " + m + " n = " n);

52. New 2005 demotivatiors!

53. if-else statement

54. The if-else statement Syntax if (Expression) Action1 else Action2
If Expression is true then execute Action1 otherwise execute Action2
The actions are either a single statement or a list of statements within braces
Expression
Action1
Action2
true
false

55. Finding the maximum of two values
System.out.print("Enter an integer number: ");
int value1 = stdin.nextInt();
System.out.print("Enter another integer number: ");
int value2 = stdin.nextInt();
int maximum;
if (value1 < value2) { // is value2 larger?
maximum = value2; // yes: value2 is larger }
else { // (value1 >= value2)
maximum = value1; // no: value2 is not larger
System.out.println("The maximum of " + value1
+ " and " + value2 + " is " + maximum);
But is it initialized?

56. Finding the maximum of two values
System.out.print("Enter an integer number: ");
int value1 = stdin.nextInt();
System.out.print("Enter another integer number: ");
int value2 = stdin.nextInt();
int maximum;
if (value1 < value2) { // is value2 larger?
maximum = value2; // yes: value2 is larger }
System.out.println("The maximum of " + value1
+ " and " + value2 + " is " + maximum);
But is it initialized?

57. Finding the maximum of two values
Is value2 larger than value1
Yes, it is . So value2 is
larger than value1. In
this case, maximum is
set to value2
value1 < value2
maximum = value2
maximum = value1
true
false
No, its not. So value1
is at least as large as
value2. In this case,
maximum is set to
value1
Either case, maximum is set
correctly

58. Why we use whitespace What does the following do?
System.out.print("Enter an integer number: ");
int value1 = stdin.nextInt();
System.out.print("Enter another integer number: ");
int value2 = stdin.nextInt();
if (value2 < value1) {
int rememberValue1 = value1;
value1 = value2;
value2 = rememberValue1; }
System.out.println("The numbers in sorted order are "
+ value1 + " and then " + value2);

59. How do you like your braces?
if (a == b) {
//...
} else }
if (a == b) {
//... }
else
if (a == b) {
//... }
else {
if (a == b) {
//... }
else {
if (a == b) {
//...
} else { }

60. If-then-else precedence
if (number != 0)
if (number > 0)
System.out.println("positive");
else
System.out.println("negative");
Which if does this
else refer to?

61. If-then-else precedence without whitespace
if (number != 0)
if (number > 0)
System.out.println("positive");
else
System.out.println("negative");
System.out.println("zero");

62. Program demo
ElsePrecedence.java

63. All your base are belong to us
Flash animation
Reference:

64. if-else-if statement

65. We can change the whitespace of the code These braces aren’t needed
If-else-if
Consider
We can change the whitespace of the code
if (number == 0) {
System.out.println("zero"); }
else {
These braces aren’t needed
if (number > 0) {
System.out.println("positive"); }
else {
System.out.println("negative");
Same results as previous segment – but this segment better expresses the meaning of what is going on }

66. Sorting three values
For sorting values n1, n2, and n3 there are six possible orderings
n1 £ n2 £ n3
n1 £ n3 £ n2
n2 £ n1 £ n3
n2 £ n3 £ n1
n3 £ n1 £ n2
n3 £ n2 £ n1
Suppose s1, s2, s3 are to be a sorted version of n1, n2, and n3

67. Sorting three values
if ((n1 <= n2) && (n2 <= n3)) { // n1 <= n2 <= n3
s1 = n1; s2 = n2; s3 = n3; }
else if ((n1 <= n3) && (n3 <= n2)) { // n1 <= n3 <= n2
s1 = n1; s2 = n3; s3 = n2;
else if ((n2 <= n1) && (n1 <= n3)) { // n2 <= n1 <= n3
s1 = n2; s2 = n1; s3 = n3;
else if ((n2 <= n3) && (n3 <= n1)) { // n2 <= n3 <= n1
s1 = n2; s2 = n3; s3 = n1;
else if ((n3 <= n1) && (n1 <= n2)) { // n3 <= n1 <= n2
s1 = n3; s2 = n1; s3 = n2;
else { // n3 <= n2 <= n1
s1 = n3; s2 = n2; s3 = n1;

68. ?: notation

69. Finding the minimum value
Consider:
// z is to hold the minimum of x and y
if ( x < y )
z = x;
else
z = y;
Another way to do this:
z = (x<y) ? x : y;
Notice no braces!

70. The ?: notation Only works when both “cases” return a value!
Meaning when both “cases” are expressions
Example: z = (x<y) ? x : y;
Thus, you can’t put a print statement in there!
Can be difficult to read
System.out.println ((number != 0) ? ((number > 0) ? "positive“ : "negative") : "zero“);
if (number != 0)
if (number > 0)
System.out.println("positive");
else
System.out.println("negative");
System.out.println("zero");

71. A bit of humor…

72. switch statement

73. Switch statement
Software engineers often confronted with programming tasks where required action depends on the values of integer expressions
The if-else-if construct can be used
Separately compare the desired expression to a particular value
If the expression and value are equal, then perform the appropriate action
Because such programming tasks occur frequently
Java includes a switch statement
The task is often more readable with the switch then with the if-else-if

74. A switch statement example
switch (a) {
case ‘0’:
System.out.println (“zero”);
break;
case ‘1’:
System.out.println (“one”);
case ‘2’:
System.out.println (“two”);
case ‘3’:
System.out.println (“three”);
case ‘4’:
System.out.println (“four”);
default:
System.out.println (“five+”); }
if (a == ‘0’)
System.out.println (“zero”);
else if (a == ‘1’)
System.out.println (“one”);
else if (a == ‘2’)
System.out.println (“two”);
else if (a == ‘3’)
System.out.println (“three”);
else if (a == ‘4’)
System.out.println (“four”);
else
System.out.println (“five+”);

75. Integral expression to
Switch statement
Integral expression to
be matched with a case
expression
switch (
SwitchExpression
) {
case
CaseExpression 1 :
Action ; 2
... n
default +1 }
Java
statements
Constant
integral
expression

76. Testing for vowel-ness
switch (ch) {
case 'a':
case 'A':
case 'e':
case 'E':
case 'i':
case 'I':
case 'o':
case 'O':
case 'u':
case 'U': System.out.println("vowel“);
break;
default: System.out.println("not a vowel“); }

77. Testing for vowel-ness
switch (ch) {
case 'a': case 'A':
case 'e': case 'E':
case 'i': case 'I':
case 'o': case 'O':
case 'u': case 'U': System.out.println("vowel“);
break;
default: System.out.println("not a vowel“); }
The break causes an exiting of the switch
Handles all of the other cases

78. A better way to format that switch statement
switch (ch) {
case 'a':
// FALL THRU
case 'A':
case 'e':
case 'E':
case 'i':
case 'I':
...

79. Processing a request System.out.print("Enter a number: ");
int n1 = stdin.nextInt();
System.out.print("Enter another number: ");
int n2 = stdin.nextInt();
System.out.print("Enter desired operator: ");
char operator = stdin.nextLine().charAt(0);
switch (operator) {
case '+' : System.out.println((n1 + n2)); break;
case '-' : System.out.println(n1 - n2); break;
case '*' : System.out.println(n1 * n2); break;
case '/' : System.out.println(n1 / n2); break;
default: System.out.println(“Illegal request“); }

80. Biggest software errors
Ariane 5 rocket explosion (1996)
Due to loss of precision converting 64-bit double to 16-bit int
Pentium division error (1994)
Due to incomplete look-up table (like an array)
Patriot-Scud missile error (1991)
Rounding error on the time
The missile did not intercept an incoming Scud missile, leaving 28 dead and 98 wounded
Mars Climate Orbiter (1999)
Onboard used metric units; ground computer used English units
AT&T long distance (1990)
Wrong break statement in C code
Therac-25, X-ray ( )
Badly designed software led to radiation overdose in chemotherapy patients
NE US power blackout (2003)
Flaw in GE software contributed to it
References:

81. Survey
How many people feel they understand the switch statement?

82. Object equality

83. Testing variables for equality
Consider
System.out.print("Enter an integer number: ");
int n1 = stdin.nextInt();
System.out.print("Enter another integer number: ");
int n2 = stdin.nextInt();
if (n1 == n2) {
System.out.println("Same"); }
else {
System.out.println(“Different");
What is the output if the user enters 88 and 3?
What is the output if the user enters 88 both times?

84. Program Demo
IntEquality

85. Testing objects for equality
Consider
String s1 = “pastel”;
String s2 = s1;
if (s1 == s2) {
System.out.println("Same"); }
else {
System.out.println("Different");

86. Testing objects for equality
Memory looks like
The comparison is between the references!
Thus, s1 and s2 are the same (they refer to the same object)
"pastel" s1 s2

87. Testing objects for equality
Consider
System.out.print("Enter a string: ");
String s1 = stdin.nextLine();
System.out.print("Enter another string: ");
String s2 = stdin.nextLine();
if (s1 == s2) {
System.out.println("Same"); }
else {
System.out.println("Different");
What is the output if the user enters "pastel" both times?

88. Program Demo
StringEquality

89. Testing objects for equality
When it is executed
System.out.print("Enter a string: ");
String s1 = stdin.nextLine();
System.out.print("Enter another string: ");
String s2 = stdin.nextLine();
Memory looks like
As a result no matter what is entered s1 and s2 are not the same
They refer to different objects
"
pastel s 1 2

90. Comparing strings for equality
Consider:
String s = "hello";
String t = "hello";
System.out.println (s == t);
What gets printed?
true
String u = new String("hello");
String v = new String("hello");
System.out.println (u == v);
false
Huh?
These aren’t the
exact same thing

91. Program Demo
StringEquality2

92. Testing operators for equality
Consider
System.out.print("Enter a string: ");
String s1 = stdin.nextLine();
System.out.print("Enter another string: ");
String s2 = stdin.nextLine();
if (s1.equals(s2)) {
System.out.println("Same"); }
else {
System.out.println("Different");
Tests whether s1 and s2 represent the same object
All classes have a method equals(). It compares the objects themselves, not the references.

93. Short-circuit evaluation

94. Short-circuit evaluation
The value of a logical expression can be known before all the operands have been considered
If left operand of && is false, then the value must be false
If left operand of || is true, then the value must be true
Java uses these properties to make logical operations efficient
Evaluates left operand before it evaluates right operand
If the operator value is determined from the left operand, then the right operand is not evaluated
The operation is short-circuited

95. Short-circuit evaluation
Short-circuit evaluation is useful when some property must be true for some other expression to be evaluated
Suppose you are interested in knowing whether scoreSum divided by nbrScores is greater than value
The condition can be evaluated only if nbrScores is nonzero
The following expression correctly represents the condition
(nbrScores != 0) && ((scoreSum / nbrScores) > value)

96. Short-circuit evaluation
Output
returnsFalse() called
returnsTrue() called
Assume we have a returnsFalse() method from a ‘foo’ object
It returns false
And it prints “returnsFalse() called”
And a returnsTrue() method
Consider:
if ( foo.returnsFalse() && foo.returnsTrue() ) { }
if ( foo.returnsTrue() && foo.returnsFalse() ) {
if ( foo.returnsFalse() || foo.returnsTrue() ) {
if ( foo.returnsTrue() || foo.returnsFalse() ) {

97. Quick survey
How comfortable do you feel with if’s and switches?

98. Becoming an IEEE author