Chapter 4 : Conditionals

1
Chapter 4 Conditionals
2
Objectives

• After studying this chapter you should understand
  the following
• the notions of preconditions, postconditions, and
  invariants
• the purpose of a conditional statement
• the function of boolean expressions
• the purpose of a compound statement.
• Also, you should be able to
• write and evaluate boolean expressions
• write conditional statements of various forms
• implementation methods that use conditional
  statements
• implement a class tester which automatically
  verifies test results.

3
Postconditions and invariants

• Method currentCount in Counter is specified as

/ The number of items counted. / public
int currentCount ()

• Specification stipulates invoking method returns
  a value of type int.

4
Postconditions and invariants

• Can be more precise in specifying result
  integer result is non- negative.

/ The number of items counted. _at_ensure
this.currentCount() gt 0 / public int
currentCount ()

• Postcondition condition that implementor
  promises will be satisfied when method completes
  execution.
• Implementor must make sure that the method
  satisfies the postcondition.

5
Postconditions and invariants

• Need to make sure instance variable used to store
  current count will never contain a negative
  value.
• Document this via a class invariant

private int count // current count //
invariant count gt 0

• A class invariant will always be true of all
  instances of the class.

6
Postconditions and invariants

• If we add decrementCount to Counter

public void decrementCount () Decrement positive
count by 1 zero count remains zero.

• In implementation, need to add guard to be sure
  not to decrement when count 0

7
The if-then statement

• if (condition)
• statement

B
E
G
I
N
true
condition
false
statement
E
N
D
8
Implemeting decrementCount

• /
• Decrement positive count by 1
• zero count remains zero
• /
• public void decrementCount ()
• if (count gt 0)
• count count - 1

9
Explorer invariants and guards

• Restrict Explorers tolerance to be a
  non-negative integer.

private int tolerance // current
tolerance // invariant tolerance gt 0 /
Damage (hit points) required to defeat this
Explorer. _at_ensure tolerance gt 0 / public
int tolerance () return tolerance

• Need to insure value assigned in each case is not
  negative.

10
Explorer invariants and guards

• Consider method takeThat.
• Need to guard the two statements

if (hitStrength lt tolerance) tolerance
tolerance - hitStrength if (hitStrength gt
tolerance) tolerance 0

• But, only one of those should execute when
  invoking takeThat.

11
if-then-else statement

• if (condition)
• statement1
• else
• statement2

B
E
G
I
N
true
false
condition
statement
statement
1
2
E
N
D
12
Implementing method takeThat

• public void takeThat (int hitStrength)
• if (hitStrength lt tolerance)
• tolerance tolerance - hitStrength
• else
• tolerance 0

13
Implementing constructor

• public Explorer (String name, Room
  location, int strength, int tolerance)
• if (tolerance gt 0)
• this.tolerance tolerance
• else
• this.tolerance 0

14
Compound statements

• if (condition)
• statement1
• statementN

• if (condition)
• statement11
• statement1N
• else
• statement21
• statement2M

15
Conditions boolean expressions

• Boolean expressions
• Produce boolean values when evaluated
• Evaluate to true or false.
• Can declare boolean variables, and assign values

private boolean tooBig

• And can assign values to it

• tooBig true
• Or
• tooBig size gt 10

16
Handling multiple cases

• A conditional statement divides problem into two
  cases to be considered independently.
• In many problems, there are more than two cases,
  or cases need to be further divided into
  subcases.
• Use nesting conditional statements.

17
Handling multiple cases

• Assume class Date with properties day,
  month,year.
• Implement a Dates query that will tell whether
  or not a date occurs in a leap year.

public boolean isLeapYear () This Date occurs in
a leap year.
18
Handling multiple cases
isLeapYear
19
Handling multiple cases
// This Date occurs in a leap year. public
boolean isLeapYear () boolean aLeapYear if
(year 4 0) if (year 100 0) // if
divisible by 100, // must also be divisible by
400 aLeapYear (year 400 0) else //
divisible by 4, not by 100 aLeapYear true
else // not divisible by 4 aLeapYear false
return aLeapYear
20
Cascading conditionals

• When problem splits into more than two cases
• cascade if-then-else statements.

if (case1) handleCase1 else if
(case2) handleCase2 else if (penultimateCase)
handlePenultimateCase else handleLastCase
21
TrafficLights change() method
22
TrafficLights change() method
public void change () if (light
GREEN) light YELLOW else if (light
YELLOW) light RED else // light
RED light GREEN
23
Dangling else

• There is an ambiguity as to whether the structure

if (condition1) if (condition2) statement1 else
statement2

• Is it an if-then nested in an if-then-else, or an
  if-then-else nested in an if-then?

24
Dangling else
25
Dangling else equivalent statements

• if (condition1)
• if (condition2)
• statement1
• else
• statement2

• if (condition1)
• if (condition2)
• statement1
• else
• statement2

26
Example combination lock

• Responsibilities
• Know
• The combination
• whether unlocked or locked
• Do
• lock
• unlock

27
CombinationLock class

• Class CombinationLock
• Queries
• is open
• Commands
• lock
• unlock

28
Class CombinationLock specifications

• public class CombinationLock
• Contructor
• public CombinationLock (int combination)
• Queries
• public boolean isOpen()
• Commands
• public void close ()
• public void open(int combination)

29
Class CombinationLock implementation

• Component variables

private int combination private boolean isOpen
30
Structure for a simple test

• public class CombinationLock
• private int combination
• private boolean isOpen
• public CombinationLock (int combination)
• public boolean isOpen ()
• return true
• public void close ()
• public void open (int combinationToTry)

31
Structure for a simple test

• class CombinationLockTest
• private CombinationLock lock
• public CombinationLockTest ()
• public void runTest ()

public class TestCombinationLock public
static void main (String argv) (new
CombinationLockTest()).runTest()
32
Precondition

• A condition client of a method must make sure
  holds when method is invoked.
• Requires Constructor and method enter have
  requirements that clients must meet for them to
  execute properly.

33
Constructor specifications

• /
• Create a lock with the specified combination.
• _at_require
• 0 lt combination combination lt 999
• _at_ensure
• this.isOpen()
• /
• public CombinationLock (int combination)

34
Testing locks

• Need method to create and test lock with given
  combination

private void testLock (int combination) Test a
lock with the specified combination.

• Invoke this method in runTest for each lock to
  test.

public void runTest () testLock(0) testLock(1
23) testLock(999)
35
Automating checking of test results

• private void verify (boolean test, String
  message)
• if (!test)
• System.out.println(
• "Verification failed " message)

36
testLock method

• testLock method must create lock and run initial
  state test

private void testLock (int combination) lock
new CombinationLock(combination) testInitialStat
e()
37
testLock method

• Initial state test should make sure that lock is
  open.
• So, instead of writing the test method

private void testInitialState()
System.out.println("Initial state "
lock.isOpen())

• Write

private void testInitialState()
verify(lock.isOpen(), "initial state")
38
Class CombinationLock implementation

• The straightforward implementations

• public CombinationLock (int combination)
• this.combination combination
• this.isOpen true
• public boolean isOpen ()
• return isOpen

39
Class CombinationLock implementation

• In constructor, there are two variables with same
  name.
• Component variable and
• local variable combination.
• this.combination refers to component variable.
• If variable does not include object reference
  this in front of it, it is a reference to local
  variable.

40
Class CombinationLock implementation
41
Method to test close

• write method to test close, and invoke it from
  testLock

private void testClose() lock.close() verify(
!lock.isOpen(), "close open lock") lock.close()
verify(!lock.isOpen(), "close closed
lock") private void testLock (int
combination) lock new CombinationLock(combina
tion) testInitialState() testClose()
42
Implementing close in Lock

• Command close is also easy to implement

public void close () isOpen false
43
Method to test open

• Test for the method open four cases to test
• closed lock, correct combination lock opens
• open lock, correct combination lock remains
  open
• closed lock, incorrect combination lock remains
  closed.
• open lock, incorrect combination lock remains
  open
• Test depends on combination, so pass correct
  combination as argument
• private void testOpen (int combination)

44
testOpen method

• private void testOpen (int combination)
• int badCombination (combination 1) 1000
• // test with correct combination
• lock.close()
• lock.open(combination) // open closed lock
• verify(lock.isOpen(), "open closed lock")
• lock.open(combination) // open opened lock
• verify(lock.isOpen(), "open opened lock")
• // test with incorrect combination
• lock.open(badCombination) // try opened lock
• verify(lock.isOpen(), "bad comb, opened lock")
• lock.close()
• lock.open(badCombination) // try closed lock
• verify(!lock.isOpen(), "bad comb, closed lock")

45
testOpen method

• Add an invocation of this method to testLock

private void testLock (int combination) lock
new CombinationLock(combination) testInitialStat
e() testClose() testOpen(combination)
46
Method open implementation

• The following implementation of open fails the
  tests.

public void open (int combination) isOpen
(this.combination combination)

• test will produce the following output
• Verification failed bad comb, opened lock
• Verification failed bad comb, opened lock
• Verification failed bad comb, opened lock
• Root of problem attempt to open an already
  opened lock with incorrect combination should not
  close it.

47
Method open implementation

• Correct implementation of method uses a
  conditional statement that opens the lock if the
  combination is correct, and does nothing if the
  combination is not correct

public void open (int combinationToTry) if
(this.combination combinationToTry) isOpen
true
48
Digit by digit lock

• This lock has a 3 digit combination.
• To open the lock, client provides the digits one
  at a time.
• If client enters three digits of combination in
  order, lock opens.
• It doesnt matter how many digits client
  provides, as long as combination is given.

49
Digit by digit lock combination 123

• Digit Entered
• 4
• 1
• 2
• 4
• 3
• 1
• 2
• 3
• Digit Entered
• 1
• 2
• 3
• 4
• 7

Lock Status closed closed closed closed closed clo
sed closed open Lock Status closed closed open op
en open
50
Digit by digit lock combination 123

• if client gives command close when combination
  has been partly entered,
• Client Command Lock Status
• enter 1 closed
• enter 2 closed
• close closed
• enter 3 ?
• Client Command Lock Status
• open
• enter 1 open
• enter 2 open
• close closed
• enter 3 ?
• command close resets lock, entire combination
  must be entered.

51
Digit by digit lock

• If combination is 123 and digits 1-2-2 are
  entered, we need three digits to open the lock
• Digit Entered Lock Status
• 1 closed (need 2-3 to open)
• 2 closed (need 3 to open)
• 2 closed (need 1-2-3 to open)
• If combination is 223 and the digits 2-2-2 are
  entered, a 3 will still open the lock
• Digit Entered Lock Status
• 2 closed (need 2-3 to open)
• 2 closed (need 3 to open)
• 2 closed (still need 3 to open)

52
Class CombinationLock

• Constructor
• public CombinationLock (int combination)
• require combination gt 0 combination lt999
• Queries
• public boolean isOpen ()
• Commands
• public void close ()
• public void enter (int digit)
• require digit gt0 digit lt9

53
CombinationLock responsibilities

• Know
• the 3-digit combination.
• whether locked or unlocked.
• the last three digits entered.
• Do
• lock.
• unlock, when given the proper combination.
• accept a digit.

54
Getting digits from integers.

• Using and / operators, can extract each digit.
• Suppose combination 123.
• 123 10 -gt 3
• 123 / 10 -gt 12
• 12 10 -gt 2
• 12 / 10 -gt 1
• 10 gets last digit
• / 10 gets remaining digits.

55
CombinationLock implementation

• private boolean isOpen // lock is unlocked
• private int digit1 // 1st combination digit
• private int digit2 // 2nd combination digit
• private int digit3 // 3rd combination digit
• // invariant
• // digit1 gt 0 digit1 lt 9
• // digit2 gt 0 digit2 lt 9
• // digit3 gt 0 digit3 lt 9

56
CombinationLock implementation

• // last, secondToLast, thirdToLast are the last
  three
• // digits entered, with last the most recent.
• // a value of -1 indicates digit has not been
  entered.
• private int last
• private int secondToLast
• private int thirdToLast
• // invariant
• // -1 lt last lt 9
• // -1 lt secondToLast lt 9
• // -1 lt thirdToLast lt 9

57

• Combination is 223, and digits 2-2 have been
  entered to a closed lock

58
Implementing constructor

• public CombinationLock (int combination)
• digit3 combination 10
• combination combination / 10
• digit2 combination 10
• digit1 combination / 10
• isOpen true
• last -1
• secondToLast -1
• thirdToLast -1

59
Implementing methods

• Query isOpen is the same as before.

public boolean isOpen () return isOpen

• Command close must resets lock.

public void close () open false last
-1 secondToLast -1 thirdToLast -1
60
Implementing method enter

• public void enter (int digit)
• thirdToLast secondToLast
• secondToLast last
• last digit
• if (thirdToLast digit1
• secondToLast digit2 last digit3)
• isOpen true

61
Relational operators

• lt less than or equal
• gt greater than
• gt greater than or equal
• equal (A single denotes assignment.)
• ! not equal
• A relational expression consists of two
  expressions joined with a relational operator.

62
Relational expressions

• Let i110, i2-20, i330.
• i1 lt 12 ? true
• i1 lt 10 ? true
• i3 i1 ? false
• i1 ! 2 ? true
• i1 lt 10 ? false
• i2 gt 0 ? false
• 2i1 i240 ? true
• i2(-1) ! i1i1 ? false

63
Relational expressions

• An expression like altbltc is illegal.
• int values are converted to double, in mixed type
  comparisons
• 10 gt 2.5 ? 10.0 gt 2.5 ? false

64
Relational expressions

• floating point values are approximations for real
  numbers, avoid using equality or inequality
  operators with them.
• (1.0/6.0 1.0/6.0 1.0/6.0
• 1.0/6.0 1.0/6.0 1.0/6.0) 1.0 ? false

65
Reference equality and object equality

• Operators and ! can be used to compare values
  of any type.
• Comparing reference values must be of same type.

Counter counter1 Counter counter2 Explorer
myHero counter1 counter2 // legal counter1
myHero // compilation error
66
Reference equality and object equality

• Two reference values are equal if they refer to
  same object.
• How to check if two different objects are equal?
• if string1, string2, and string3 are String
  variables,

string1 "c" string2 "ab" string1 string3
"a" "bc"

• string2 and string3 will reference two distinct
  objects.

string2 string3 ? false

• use String method equals,

string2.equals(string3) ? true
67
Boolean operators

• ! not
• and
• or
• Use

! booleanExpression booleanExpression
booleanExpression booleanExpression
booleanExpression

• A boolean expression evaluates to true or false

68
The ! (not) operator

• Not reverses boolean values.
• !true ? false
• !false ? true
• Given i110
• !( i1 gt 9) ? !(true) ? false
• Beware Not has high precedence.
• ! i1 gt 9 ? (!i1) gt 9 ? illegal

69
, (and then, or else) operators

• Given i110
• (i1gt10)(i110) ? false true ? true
• (i1gt10)(i1lt0) ? false false ? false
• (i1gt0)(i1lt5) ? true false ? false
• (i1gt0)(i1lt20) ? true true ? true

70
, (and then, or else) operators

• and have lower precedence than the
  relational operators.
• Parentheses are still useful as they enhance
  readability.
• i1 lt i2 i1 lt i3 means
• (i1 lt i2) (i1 lt i3)
• Using the and then operator, can express the
  condition that value of i1 is between 0 and 20
• (0 lt i1) (i1 lt 20)

71
The and are lazy operators

• They evaluate only the left operand only when
  that suffices.
• Given i110
• (i1 lt 10) (i1 gt 0) ? false (i1 gt 0)? false
• (i1 lt 11) (i1 gt 100)? true (i1 gt 100)?
  true
• Right operands, (i1 gt 0) and (i1 gt 100), are not
  evaluated.
• Useful when considering expressions like
• (x 0) (y/x lt 10)
• If left operand is true, x is 0, evaluating right
  operand will result in an attempt to divide by 0
  and a run-time error.

72
Operator precedence

• High
• unary , unary -, !
• , /,
• , -
• lt, lt, gt, gt
• , !
• Low

73
DeMorgans Laws

• Useful for simplifying expressions.
• !(b1 b2) ? !b1 !b2
• !(b1 b2) ? !b1 !b2
• !(i1gt5 i1lt8) ? !(i1gt5) !(i1lt8)

74
Summary

• Introduced boolean expressions and conditional
  statements.
• Conditional statements allow us to specify
  alternative computations and the circumstances
  under which each is to be performed.
• The particular action to be done is determined by
  the processor at execution time, depending on the
  current data values.

75
Summary

• The two forms of conditional statement weve seen
  are if-then and if-then-else.

if (condition) statement

• With an if-then-else, we specify two possible
  actions, one of which will be done

if (condition) statement1 else statement2
76
Summary

• Syntax of the Java language permits only a single
  statement as a conditional alternative.
• Need a way to package a number of statements into
  one.
• Compound statement put braces around a sequence
  of statements

statement1 statement2 statementn
77
Summary

• Boolean expression an expression that evaluates
  to a boolean value, true or false.
• Several kinds of operators useful for
  constructing boolean expressions
• relational operators lt, lt, gt, and gt,
• equality operators and !,
• boolean operators , , and !.

78
Summary

• introduced preconditions, postconditions, and
  invariants.
• Important in the specification and correctness
  verification of our designs.
• Not part of the language per se, we include them
  in comments.

79
Summary

• Client of a method responsible for making sure
  that all method preconditions are satisfied
  before invoking method.
• Method will work correctly only if preconditions
  are satisfied.
• Preconditions are documented in a require clause
  of method specification.

80
Summary

• Method implementor is responsible for making sure
  that all postconditions are satisfied when method
  completes.
• Postconditions documented in an ensure clause
  of method specification.

81
Summary

• Invariants are conditions that always hold.
• Class invariants are conditions that are always
  true of all instances of a class.
• A class instance is a consistent and coherent
  model of whatever entity the class represents if
  class invariants hold.