Decisions, decisions, decisions

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

9
Or and not truth tables
10
Boolean algebra

• Can create complex logical expressions by
  combining simple logical expressions
• not (p and q)

11
DeMorgans laws

• not (p and q) equals (not p) or (not q)

12
DeMorgans laws

• not (p or q) equals (not p) and (not q)

13
DeMorgans 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 http//www.gprime.net/images/sidewalkchalk
  guy/

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
• Dont use
• The or operator is
• Dont 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
• Consider
• 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 doesnt always translate cleanly into
  logical expressions
• To see this, we need to examine the NOR operator
• It doesnt 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 !(pq)

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 T F F
T F F T
F T T F
F F 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 T T
T F T
F T T
F F 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 ?(pq)
T T F F
T F F F
F T F F
F F T T
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
End of lecture on Wed, 8 February 2006

• But rushed through the last 5 slides, so I want
  to do them again

31
Floating point comparison
32
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 0.1s
33
Program demo

• FloatTest.java

34
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

35
How to solve this

• Dont 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) lt EPSILON

36
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 Demonstrati
on 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
37
More on evaluating expressions
38
Ordering operators

• Java provides ordering operators for the
  primitive types
• Four ordering operators, lt, gt, lt, and gt
• They correspond to mathematical operators of lt,
  gt, , and
• Together the equality and ordering operators are
  known as the relational operators
• False is less than true

39
Evaluation boolean expressions

• Suppose
• int i 1
• int j 2
• int k 2
• What is the value of
• i lt j
• j lt k
• i lt k
• j gt k
• i gt k

40
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.

41
Evaluation boolean expressions

• Suppose
• char c '2'
• char d '3'
• char e '2'
• What is the value of
• c lt d
• c lt e
• c lt e
• d gt e
• c gt e

42
Operator precedence revisited

• Highest to lowest
• Parentheses
• Unary operators
• Multiplicative operators
• Additive operators
• Relational ordering
• Relational equality
• Logical and
• Logical or
• Assignment

43
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

44
Sand Castles
45
if statement
46
Conditional constructs

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

47
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

48
Example

• if (value lt 0)
• value -value

49
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 lt 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?
50
If semantics
51
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 (ab!!!)
• 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 (!!!)

52
Why we always use braces

• What is the output?
• int m 5
• int n 10
• if (m lt n)
• m
• n
• System.out.println(" m " m " n " n)

53
New 2005 demotivatiors!
54
if-else statement
55
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

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 lt value2) // is value2 larger?
• maximum value2 // yes value2 is larger
• else // (value1 gt value2)
• maximum value1 // no value2 is not
  larger
• System.out.println("The maximum of " value1
• " and " value2 " is " maximum)

But is it initialized?
57
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 lt 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?
58
Finding the maximum of two values
59
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 lt value1)
• int rememberValue1 value1
• value1 value2
• value2 rememberValue1
• System.out.println("The numbers in sorted order
  are "
• value1 " and then " value2)

60
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 //...
61
If-then-else precedence

• if (number ! 0)
• if (number gt 0)
• System.out.println("positive")
• else
• System.out.println("negative")

Which if does this else refer to?
62
If-then-else precedence without whitespace

• if (number ! 0)
• if (number gt 0)
• System.out.println("positive")
• else
• System.out.println("negative")
• else
• System.out.println("zero")

63
Program demo

• ElsePrecedence.java

64
All your base are belong to us

• Flash animation
• Reference http//en.wikipedia.org/wiki/All_your_b
  ase_are_belong_to_us

65
if-else-if statement
66
If-else-if

• Consider

We can change the whitespace of the code
if (number 0) System.out.println("zero")
else

These braces arent needed
if (number gt 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

67
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

68
Sorting three values

• if ((n1 lt n2) (n2 lt n3)) // n1 lt n2
  lt n3
• s1 n1 s2 n2 s3 n3
• else if ((n1 lt n3) (n3 lt n2)) // n1 lt n3
  lt n2
• s1 n1 s2 n3 s3 n2
• else if ((n2 lt n1) (n1 lt n3)) // n2 lt n1
  lt n3
• s1 n2 s2 n1 s3 n3
• else if ((n2 lt n3) (n3 lt n1)) // n2 lt n3
  lt n1
• s1 n2 s2 n3 s3 n1
• else if ((n3 lt n1) (n1 lt n2)) // n3 lt n1
  lt n2
• s1 n3 s2 n1 s3 n2
• else // n3 lt n2 lt n1
• s1 n3 s2 n2 s3 n1

69
? notation
70
Finding the minimum value

• Consider
• // z is to hold the minimum of x and y
• if ( x lt y )
• z x
• else
• z y
• Another way to do this
• z (xlty) ? x y

Notice no braces!
71
The ? notation

• Only works when both cases return a value!
• Meaning when both cases are expressions
• Example z (xlty) ? x y
• Thus, you cant put a print statement in there!
• Can be difficult to read
• System.out.println ((number ! 0) ? ((number gt 0)
  ? "positive "negative") "zero)
• if (number ! 0)
• if (number gt 0)
• System.out.println("positive")
• else
• System.out.println("negative")
• else
• System.out.println("zero")

72
A bit of humor
73
switch statement
74
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

75
A switch statement example
switch (a) case 0 System.out.println
(zero) break case 1 System.out.println
(one) break case 2 System.out.println
(two) break case 3 System.out.println
(three) break case 4 System.out.print
ln (four) break default System.out.print
ln (five) break

• 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)

76
Switch statement
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)

78
End of lecture on 13 February 2006

• But want to start up again at the beginning of
  this section

79
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
80
A better way to format that switch statement

• switch (ch)
• case 'a'
• // FALL THRU
• case 'A'
• // FALL THRU
• case 'e'
• // FALL THRU
• case 'E'
• // FALL THRU
• case 'i'
• // FALL THRU
• case 'I'
• // FALL THRU
• ...

81
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)

82
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
• ATT 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.ht
  ml, http//en.wikipedia.org/wiki/Computer_bug,
  http//www.cs.tau.ac.il/nachumd/verify/horror.htm
  l

83
Survey

• How many people feel they understand the switch
  statement?

84
Object equality
85
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?
86
Program Demo

• IntEquality

87
Testing objects for equality

• Consider
• String s1 pastel
• String s2 s1
• if (s1 s2)
• System.out.println("Same")
• else
• System.out.println("Different")

88
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)

89
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?
90
Program Demo

• StringEquality

91
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

92
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?

93
Program Demo

• StringEquality2

94
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.
95
Short-circuit evaluation
96
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

97
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) gt
  value)

98
Short-circuit evaluation
Output
returnsFalse() called returnsTrue()
called returnsFalse() called returnsFalse()
called returnsTrue() 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() )

99
Quick survey

• How comfortable do you feel with ifs and
  switches?

100
Becoming an IEEE author