Decisions, decisions, decisions
Chapter 5
Fall 2006
CS 101
Aaron Bloomfield
1
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.“);
}
}
2
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
3
Logical expressions
4
Logical expressions
 The branch of mathematics dealing with logical expressions
is Boolean algebra
 Developed by the British mathematician George Boole
5
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
6
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
7
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
True
True
False
True
False
True
False
False
False
True
8
Or and not truth tables
p
q
False
False
True
True
False
True
False
True
p or q
False
True
True
True
p
False
True
not p
True
False
9
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
True
True
False
True
False
True
False
False
False
True
True
True
True
False
10
DeMorgan’s laws
 not (p and q) equals (not p) or (not q)
p
False
False
True
True
q
False
True
False
True
p and q
False
False
False
True
(not p) or
not (p and q) ( not p) (not q)
(not q)
True
True
True
False
True
True
True
False
False True
False False
True
True
True
False
11
DeMorgan’s laws
 not (p or q) equals (not p) and (not q)
p
False
False
True
True
q
False
True
False
True
p or q
False
True
True
True
not (p or q)
True
False
False
False
(not p) and
( not p) (not q)
(not q)
True
True
True
False
False True
False False
True
False
False
False
12
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)
13
Sidewalk chalk guy

Source:
http://www.gprime.net/images/sidewalkchalkguy/
14
Boolean expressions
15
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 !
16
Defining boolean variables

Local boolean variables are uninitialized by default
boolean isWhitespace;
boolean receivedAcknowledgement;
boolean haveFoundMissingLink;
isWhitespace
-
receivedAcknowledgement
-
haveFoundMissingLink
-
17
Defining boolean variables

Local boolean variables with initialization
boolean canProceed = true;
boolean preferCyan = false;
boolean completedSecretMission = true;
canProceed
true
preferCyan
false
completedSecretMission
true
18
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
 Consider:
int x = 5;
System.out.println (x == 5);
System.out.println (x == 6);
19
 Prints out true, false
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
20
Evaluating boolean expressions


Suppose
boolean
boolean
boolean
boolean
p = true;
q = false;
r = true;
s = false;
What is the value of
p
!s
q
p && r
q || s
p && s
p == q
q != r
r == s
q != s
21
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 == j
c == e
c == d
i != k
j != k
d != e
c != e
22
A bit of humor…
23
Translating English to logical
expressions
24
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: 
p
False
False
True
True

q
False
True
False
True
p or q
False
True
True
True
not (p or q)
True
False
False
False
In Java, given variables p and q
 NOR is done by: !(p||q)
p nor q
True
False
False
False
25
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
T
F
F
T
F
F
T
F
T
T
F
F
F
T
F
26
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
T
T
T
F
T
F
T
T
F
F
F
27
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
p
q
pq
(p||q)
T
T
F
F
T
F
F
F
F
T
F
F
F
F
T
T
The problem:  has a higher precedence than  in Boolean logic,
but not always in English
Also, “neither” is vague
28
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
29
Floating point comparison
31
Floating point precission
 What gets printed?
class FloatTest {
public static void main (String args[]) {
double y = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 +
0.1 + 0.1 + 0.1 + 0.1 + 0.1;
System.out.println (y);
}
}
There are 10 0.1’s
32
Program demo

FloatTest.java
33
Take care with floating-point values
 Consider
double a = 1;
double b = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1
+ 0.1 + 0.1 + 0.1 + 0.1
double c = .9999999999999999;
 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 = 0.000001;
boolean foo = Math.abs (a-b) < EPSILON;
35
More on evaluating expressions
36
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
37
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
38
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.
39
Evaluation boolean expressions
 Suppose
char c = '2';
char d = '3';
char e = '2';
 What
c
c
c
d
c
is the value of
< d
< e
<= e
>= e
>= e
40
Operator precedence revisited
 Highest to lowest
 Parentheses
 Unary operators
 Multiplicative operators
 Additive operators
 Relational ordering
 Relational equality
 Logical and
 Logical or
 Assignment
41
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 semicolon
 5
 circle.getRadius()
 x
 Note the difference between the following:
 ++i
is an expression
 ++i;
is a statement
42
Sand Castles
43
if statement
44
Conditional constructs
 Provide
 Ability to control whether a statement list is executed
 Two constructs
 If statement
if
if-else
if-else-if
 Switch statement
45
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
Expression
true
false
Action
 For us, it will always be a group
of statements within braces
46
Example
if (value < 0) {
value = -value;
}
Is our number
negative?
If Value is less than
zero then we need
to update its value
to that of its additive
inverse
Value < 0
true
Value = -Value
Our number is now
definitely
nonnegative
false
If Value is not
less than zero
then our number
is fine as is
47
Sorting two values
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
What happens if the
user enters 11 and
28?
What happens if the
user enters 11 and
4?
System.out.println("The numbers in sorted order are "
+ value1 + " and then " + value2);
48
Are the numbers out
of order
If semantics
Rearrange value1 and
value2 to put their
values in the proper
order
value2 < value1
true
false
int rememberValue1 = value1
value1 = value2
value2 = rememberValue1
The numbers were rearranged into
the proper order
The numbers were initially in
order
The numbers are in order
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 (“!!!”);
}
50
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);
51
Warn your grandparents!

Historically, this class has been lethal to
grandparents of students in the class
– More often grandmothers

This happens most around test time
– Although occasionally around the times a big
assignment is due

See
http://www.cis.gsu.edu/~dstraub/Courses/Grandma.htm52
if-else statement
53
The if-else statement
 Syntax
if (Expression)
Action1
else
Action2
 If Expression is
execute
Action1
execute Action2
Expression
true then
otherwise
 The actions are either a single
statement
or
a
list
of
statements within braces
true
false
Action1
Action2
54
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();
But is it initialized?
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);
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) {
maximum = value2;
}
But is it initialized?
// is value2 larger?
// yes: value2 is larger
System.out.println("The maximum of " + value1
+ " and " + value2 + " is " + maximum);
56
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
true
maximum = value2
Either case, maximum is set
correctly
No, its not. So value1
is at least as large as
value2. In this case,
maximum is set to
value1
false
maximum = value1
57
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);
58
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
{
//...
}
59
If-then-else precedence
if (number != 0)
if (number > 0)
System.out.println("positive");
Which if does this
else
else refer to?
System.out.println("negative");
60
If-then-else precedence without
whitespace
if (number != 0)
if (number > 0)
System.out.println("positive");
else
System.out.println("negative");
else
System.out.println("zero");
61
Program demo

ElsePrecedence.java
62
if-else-if statement
64
If-else-if
 Consider
if (number == 0) {
System.out.println("zero");
}
else {
if (number > 0) {
We can change
the whitespace
of the code
These braces
aren’t needed
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 65
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
66
Sorting three values
if ((n1 <= n2) && (n2 <= n3))
s1 = n1;
s2 = n2;
s3 =
}
else if ((n1 <= n3) && (n3 <=
s1 = n1;
s2 = n3;
s3 =
}
else if ((n2 <= n1) && (n1 <=
s1 = n2;
s2 = n1;
s3 =
}
else if ((n2 <= n3) && (n3 <=
s1 = n2;
s2 = n3;
s3 =
}
else if ((n3 <= n1) && (n1 <=
s1 = n3;
s2 = n1;
s3 =
}
else { // n3 <= n2 <= n1
s1 = n3;
s2 = n2;
s3 =
}
{
n3;
// n1 <= n2 <= n3
n2)) { // n1 <= n3 <= n2
n2;
n3)) { // n2 <= n1 <= n3
n3;
n1)) { // n2 <= n3 <= n1
n1;
n2)) { // n3 <= n1 <= n2
n2;
n1;
67
?: notation
68
Finding the minimum value
 Consider:
// z is to hold the minimum of x and y
if ( x < y )
z = x;
Notice no braces!
else
z = y;
 Another way to do this:
z = (x<y) ? x : y;
69
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");
else
System.out.println("zero");
70
A bit of humor…
71
switch statement
72
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
73
A switch statement example
if (a == ‘0’)
System.out.println
else if (a == ‘1’)
System.out.println
else if (a == ‘2’)
System.out.println
else if (a == ‘3’)
System.out.println
else if (a == ‘4’)
System.out.println
else
System.out.println
(“zero”);
(“one”);
(“two”);
(“three”);
(“four”);
(“five+”);
switch (a) {
case ‘0’:
System.out.println
break;
case ‘1’:
System.out.println
break;
case ‘2’:
System.out.println
break;
case ‘3’:
System.out.println
break;
case ‘4’:
System.out.println
break;
default:
System.out.println
break;
(“zero”);
(“one”);
(“two”);
(“three”);
(“four”);
(“five+”);
74
Switch statement
Integral expression to
be matched with a case
expression
switch ( SwitchExpression )
case CaseExpression1 :
Action1 ;
case CaseExpression2 :
Action2 ;
Java
statements
{
Constant
integral
expression
...
case CaseExpressionn :
Actionn ;
default :
}
Actionn+1 ;
76
Testing for vowel-ness
switch
case
case
case
case
case
case
case
case
case
case
}
(ch) {
'a':
'A':
'e':
'E':
'i':
'I':
'o':
'O':
'u':
'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;
The break causes an exiting of the switch
default:
System.out.println("not a vowel“);
}
Handles all of the other cases
78
A better way to format that switch
statement
switch (ch) {
case 'a':
// FALL
case 'A':
// FALL
case 'e':
// FALL
case 'E':
// FALL
case 'i':
// FALL
case 'I':
// FALL
...
THRU
THRU
THRU
THRU
THRU
THRU
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
Survey

How many people feel they understand the
switch statement?
81
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 (1975-1987)
– Badly designed software led to radiation overdose in chemotherapy patients

NE US power blackout (2003)
– Flaw in GE software contributed to it

References: http://www5.in.tum.de/~huckle/bugse.html,
http://en.wikipedia.org/wiki/Computer_bug,
http://www.cs.tau.ac.il/~nachumd/verify/horror.html
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
s1
"pastel"
s2
 The comparison is between the references!
 Thus, s1 and s2 are the same (they refer to the same
object)
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
s1
"pastel"
s2
"pastel"
 As a result no matter what is entered s1 and s2 are not the
same
90
 They refer to different objects
Comparing strings for equality
 Consider:
String s = "hello";
String t = "hello";
System.out.println (s == t);
 What gets printed?
 true
 Consider:
String u = new String("hello");
String v = new String("hello");
System.out.println (u == v);
 What gets printed?
 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();
Tests whether s1 and s2
represent the same object
if (s1.equals(s2)) {
System.out.println("Same");
}
else {
System.out.println("Different");
}
Most classes have a method equals(). It compares the
objects themselves, not the references.
93
All your base are belong to us
94
Short-circuit evaluation
95
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
96
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)
97
Short-circuit evaluation
Output
returnsFalse() 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
}
if
}
if
}
if
}
returnsTrue() called
returnsFalse() called
returnsFalse() called
returnsTrue() called
returnsTrue() called
( foo.returnsFalse() && foo.returnsTrue() ) {
( foo.returnsTrue() && foo.returnsFalse() ) {
( foo.returnsFalse() || foo.returnsTrue() ) {
( foo.returnsTrue() || foo.returnsFalse() ) {
98
Quick survey

How comfortable do you feel with if ’s and
switches?
99
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”
100