Chapter 5

Decisions

Chapter Goals

To be able to implement decisions using if statements
To understand how to group statements into blocks
To learn how to compare integers, floating-point numbers, strings, and objects
To recognize the correct ordering of decisions in multiple branches
To program conditions using Boolean operators and variables

`if` Statement

if (amount <= balance)
   balance = balance - amount;

`if`/`else` Statement

if (amount <= balance)
   balance = balance - amount;
else
   balance = balance - OVERDRAFT_PENALTY;

Block Statement

if (amount <= balance)
{
   double newBalance = balance - amount;
   balance = newBalance;
}

Syntax 5.1. The `if` Statement

if(condition) statement if(condition) statement
else statement

Example:

if (amount <= balance)
   balance = balance - amount;

if (amount <= balance)
   balance = balance - amount;
else
   balance = balance - OVERDRAFT_PENALTY;

Purpose:

To execute a statement when a condition is true or false

Syntax 5.2. Block Statement

{ statement statement . . . }

Example:

{
      double newBalance = balance - amount;
   balance = newBalance;
}

Purpose:

To group several statements together to form a single statement

Statement Types

Simple statement
balance = balance - amount;
Compound statement
if (balance >= amount) balance = balance - amount;Also while, for, etc. (see chapter 6)
Block statement
{ double newBalance = balance - amount; balance = newBalance; }

Relational Operators

Java	Math Notation	Description
`>`	>	Greater than
`>=`	≥	Greater than or equal
`<`	<	Less than
`<=`	≤	Less than or equal
`==`	=	Equal
`!=`	≠	Not equal

Equality Testing vs. Assignment

The == operator tests for equality:
if (x == 0) . . // if x equals zero
The = operator assigns a value to a variable:

x = 0; // assign 0 to x
Don't confuse them.
Java == is the same as mathematical =

Comparing Floating-Point Numbers

Consider this code:

double r = Math.sqrt(2); 
double d = r * r -2; 
if (d == 0) 
   System.out.println(
      "sqrt(2)squared minus 2 is 0"); 
else 
   System.out.println(
      "sqrt(2)squared minus 2 is not 0 but " + d);

It prints:
sqrt(2)squared minus 2 is not 0 but 4.440892098500626E-16
Don't use == to compare floating-point numbers

Comparing Floating-Point Numbers

Two numbers are close to another if
|x - y| <= ε
ε is a small number such as 10^-14
Not good enough if x, y very large or very small. Then use
|x - y| / max(|x|, |y|) <= ε
But if one of the numbers is zero, don't divide by max(|x |, |y|)

String Comparison

Don't use == for strings!
if (input == "Y") // WRONG!!!
Use equals method:
if (input.equals("Y"))
== tests identity, equals tests equal contents
Case insensitive test ("Y" or "y")
if (input.equalsIgnoreCase("Y"))

Lexicographic Comparison

s.compareTo(t) < 0 means:
s comes before t in the dictionary
"car"comes before "cargo"
"cargo" comes before "cathode"
All uppercase letters come before lowercase:
"Hello" comes before "car"

Lexicographic Comparison

Object Comparison

== tests for identity, equals for identical content
Rectangle cerealBox = new Rectangle(5, 10, 20, 30); Rectangle oatmealBox = new Rectangle(5, 10, 20, 30); Rectangle r = cerealBox;
cerealBox != oatmealBox,
but cerealBox.equals(oatmealBox)
cerealBox == r
Caveat: equals must be defined for the class (see chapter 11)

Object Comparison

The `null` Reference

null reference refers to no object at all
Can be used in tests:
if (account == null) . . .
Use ==, not equals, to test for null
showInputDialog returns null if the user hit the cancel button:
String input = JOptionPane.showInputDialog("..."); if (input != null) { ... }
null is not the same as the empty string ""

Multiple Alternatives

if (condition1) statement1; else if (condition2) statement2; else if (condition3) statement3; else statement4;
The first matching condition is executed.
Order matters.

File Earthquake.java

1	/**
2	A class that describes the effects of an earthquake.
3	`*/`
4	public class Earthquake
5	{
6	/**
7	Constructs an Earthquake object.
8	@param magnitude the magnitude on the Richter scale
9	`*/`
10	public Earthquake(double magnitude)
11	{
12	richter = magnitude;
13	}
14
15	/**
16	Gets a description of the effect of the earthquake.
17	@return the description of the effect
18	`*/`
19	public String getDescription()
20	{
21	String r;
22	if (richter >= 8.0)
23	r = "Most structures fall";
24	else if (richter >= 7.0)
25	r = "Many buildings destroyed";
26	else if (richter >= 6.0)
27	r = "Many buildings considerably damaged, some collapse";
28	else if (richter >= 4.5)
29	r = "Damage to poorly constructed buildings";
30	else if (richter >= 3.5)
31	r = "Felt by many people, no destruction";
32	else if (richter >= 0)
33	r = "Generally not felt by people";
34	else
35	r = "Negative numbers are not valid";
36	return r;
37	}
38
39	private double richter;
40	}

File EarthquakeTest.java

1	import javax.swing.JOptionPane;
2
3	/**
4	A class to test the Earthquake class.
5	`*/`
6	public class EarthquakeTest
7	{
8	public static void main(String[] args)
9	{
10	String input = JOptionPane.showInputDialog(
11	"Enter a magnitude on the Richter scale:");
12	double magnitude = Double.parseDouble(input);
13	Earthquake quake = new Earthquake(magnitude);
14	System.out.println(quake.getDescription());
15	System.exit(0);
16	}
17	}

Multiple Alternatives

Order matters:
if (richter >= 0) // always passes r = "Generally not felt by people"; else if (richter >= 3.5) // not tested r = "Felt by many people, no destruction"; . . .
Don't omit else if (richter >= 8.0) r = "Most structures fall"; if (richter >= 7.0) // omitted else--ERROR r = "Many buildings destroyed

Nested Branches

Branch inside another branch

if (condition1)
{
   if (condition1a)
      statement1a;
   else
      statement1b;
}
else
   statement2;

Tax Return

If your filing status is Single

If the taxable income is over	But not over	The tax is	Of the amount over
$0	$21,450	15%	$0
$21,450	$51,900	$3,217.50 + 28%	$21,450
$51,900		$11,743.50 + 31%	$51,900

If your filing status is Married

If the taxable income is over	But not over	The tax is	Of the amount over
$0	$35,800	15%	$0
$35,800	$86,500	$5,370.00 + 28%	$35,800
$86,500		$19,566.00 + 31%	$86,500

Tax Return

File TaxReturn.java

1	/**
2	A tax return of a taxpayer in 1992.
3	`*/`
4	class TaxReturn
5	{
6	/**
7	Constructs a TaxReturn object for a given income and
8	marital status.
9	@param anIncome the taxpayer income
10	@param aStatus either SINGLE or MARRIED
11	`*/`
12	public TaxReturn(double anIncome, int aStatus)
13	{
14	income = anIncome;
15	status = aStatus;
16	}
17
18	public double getTax()
19	{
20	double tax = 0;
21
22	if (status == SINGLE)
23	{
24	if (income <= SINGLE_CUTOFF1)
25	tax = RATE1 * income;
26	else if (income <= SINGLE_CUTOFF2)
27	tax = SINGLE_BASE2
28	+ RATE2 * (income - SINGLE_CUTOFF1);
29	else
30	tax = SINGLE_BASE3
31	+ RATE3 * (income - SINGLE_CUTOFF2);
32	}
33	else
34	{
35	if (income <= MARRIED_CUTOFF1)
36	tax = RATE1 * income;
37	else if (income <= MARRIED_CUTOFF2)
38	tax = MARRIED_BASE2
39	+ RATE2 * (income - MARRIED_CUTOFF1);
40	else
41	tax = MARRIED_BASE3
42	+ RATE3 * (income - MARRIED_CUTOFF2);
43	}
44
45	return tax;
46	}
47
48	public static final int SINGLE = 1;
49	public static final int MARRIED = 2;
50
51	private static final double RATE1 = 0.15;
52	private static final double RATE2 = 0.28;
53	private static final double RATE3 = 0.31;
54
55	private static final double SINGLE_CUTOFF1 = 21450;
56	private static final double SINGLE_CUTOFF2 = 51900;
57
58	private static final double SINGLE_BASE2 = 3217.50;
59	private static final double SINGLE_BASE3 = 11743.50;
60	private static final double MARRIED_CUTOFF1 = 35800;
61	private static final double MARRIED_CUTOFF2 = 86500;
62
63	private static final double MARRIED_BASE2 = 5370;
64	private static final double MARRIED_BASE3 = 19566;
65
66	private double income;
67	private int status;
68	}

File TaxReturnTest.java

1	import javax.swing.JOptionPane;
2
3	/**
4	A class to test the TaxReturn class.
5	`*/`
6	public class TaxReturnTest
7	{
8	public static void main(String[] args)
9	{
10	String input = JOptionPane.showInputDialog(
11	"Please enter your income:");
12	double income = Double.parseDouble(input);
13
14	input = JOptionPane.showInputDialog(
15	"Please enter S (single) or M (married)");
16	int status = 0;
17
18	if (input.equalsIgnoreCase("S"))
19	status = TaxReturn.SINGLE;
20	else if (input.equalsIgnoreCase("M"))
21	status = TaxReturn.MARRIED;
22	else
23	{
24	System.out.println("Bad input.");
25	System.exit(0);
26	}
27
28	TaxReturn aTaxReturn = new TaxReturn(income, status);
29
30	System.out.println("The tax is "
31	+ aTaxReturn.getTax());
32
33	System.exit(0);
34	}
35	}

The `boolean` Type

George Boole (1815-1864): pioneer in the study of logic
value of expression amount < 1000 is true or false.
boolean type: one of these 2 truth values

Predicate Method

return type boolean
Example:
public boolean isOverdrawn() { return balance < 0; }
Use in conditions
if (harrysChecking.isOverdrawn()) ...
Useful predicate methods in Character class:
isDigit isLetter isUpperCase isLowerCase
if (Character.isUpperCase(ch)) ...

Boolean Operators

&& and
|| or
! not
if (0 < amount && amount < 1000) ...
if (input.equals("S") || input.equals("M")) ...

`&&` and `||` Operators

Truth Tables

A	B	A `&&` B
`true`	`true`	`true`
`true`	`false`	`false`
`false`	Any	`false`

A	B	A `\|\|` B
`true`	Any	`true`
`false`	`true`	`true`
`false`	`false`	`false`

A	`!` A
`true`	`false`
`false`	`true`

De Morgan's Law

Negating a complex condition can be confusing:
if (!(0 < amount && amount < 1000))
De Morgan's law states that
!(A && B) is the same as !A || !B!(A || B) is the same as !A && !B
Note that the && and || flip when moving the ! inwards
(!(0 < amount && amount < 1000)) is
!(0 < amount) || !(amount < 1000) , that is
0 >= amount || amount >= 1000
Note that the opposite of < is >=

Boolean Variables

private boolean married;
Set to truth value:
married = input.equals("M");
Use in conditions:
if (married) ... else ... if (!married) ...
Also called flag
Don't test Boolean variables against truth values--sign of cluelessness:
if (married == true) // DON'T if (married == false) // DON'T if (married != false) // NO!!!

Chapter 5

Decisions

Chapter Goals

if Statement

if/else Statement

Block Statement

Syntax 5.1. The if Statement

Example:

Purpose:

Syntax 5.2. Block Statement

Example:

Purpose:

Statement Types

Relational Operators

Equality Testing vs. Assignment

Comparing Floating-Point Numbers

Comparing Floating-Point Numbers

String Comparison

Lexicographic Comparison

Lexicographic Comparison

Object Comparison

Object Comparison

The null Reference

Multiple Alternatives

File Earthquake.java

File EarthquakeTest.java

Multiple Alternatives

Nested Branches

Tax Return

Tax Return

File TaxReturn.java

File TaxReturnTest.java

The boolean Type

Predicate Method

Boolean Operators

&& and || Operators

Truth Tables

De Morgan's Law

Boolean Variables

`if` Statement

`if`/`else` Statement

Syntax 5.1. The `if` Statement

The `null` Reference

The `boolean` Type

`&&` and `||` Operators