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

The `if` Statement

The if statement lets a program carry out different actions depending on a condition
```
if (amount <= balance)
   balance = balance - amount;
```

The `if`/`else` Statement

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

Statement Types

Simple statement
balance = balance - amount;
Compound statement
if (balance >= amount) balance = balance - amount;Also while, for, etc. (loop statements–Chapter 7)
Block statement
{ double newBalance = balance - amount; balance = newBalance; }

Syntax 6.1: The `if` Statement

if(condition) statement if(condition) statement₁
else statement₂

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 6.2: Block Statement

{ statement₁ statement₂ . . . }

Example:

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

Purpose:

To group several statements together to form a single statement

Self Check

Why did we use the condition amount <= balance and not amount < balance in the example for the if/else statement?

What is logically wrong with the statement

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

and how do you fix it?

Answers

If the withdrawal amount equals the balance, the result should be a zero balance and no penalty
Only the first assignment statement is part of the if statement. Use braces to group both assignment statements into a block statement

Comparing Values: Relational Operators

Relational operators compare values

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

The == denotes equality testing

a = 5; // Assign 5 to a
if (a == 5) . . . // Test whether a equals 5

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

Comparing Floating-Point Numbers

To avoid roundoff errors, don't use == to compare floating-point numbers

To compare floating-point numbers test whether they are close enough: |x - y| ≤ ε

final double EPSILON = 1E-14;
if (Math.abs(x - y) <= EPSILON)
   // x is approximately equal to y

ε is a small number such as 10^-14

Comparing Strings

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

Lexicographic Comparison

Comparing Objects

== tests for identity, equals for identical content
Rectangle box1 = new Rectangle(5, 10, 20, 30); Rectangle box2 = box1; Rectangle box3 = new Rectangle(5, 10, 20, 30);
box1 != box3,
but box1.equals(box3)
box1 == box2
Caveat: equals must be defined for the class

Object Comparison

Testing for `null`

null reference refers to no object

String middleInitial = null; // Not set
if ( . . . )
   middleInitial = middleName.substring(0, 1);

Can be used in tests:

if (middleInitial == null)
   System.out.println(firstName + " " + lastName);
else
   System.out.println(firstName + " " + middleInitial + ". " + lastName);

Use ==, not equals, to test for null
null is not the same as the empty string ""

Self Check

What is the value of s.length() if s is
1. the empty string ""?
2. the string " " containing a space?
3. null?
Which of the following comparisons are syntactically incorrect? Which of them are syntactically correct, but logically questionable?
```
String a = "1";
String b = "one";
double x = 1;
double y = 3 * (1.0 / 3);
```
1. a == "1"
2. a == null
3. a.equals("")
4. a == b
5. a == x
6. x == y
7. x - y == null
8. x.equals(y)

Answers

(a) 0; (b) 1; (c) an exception is thrown
Syntactically incorrect: e, g, h. Logically questionable: a, d, f

Multiple Alternatives: Sequences of Comparisons

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

File Earthquake.java

File EarthquakeTester.java

Output

   Enter a magnitude on the Richter scale: 7.1
   Many buildings destroyed

Multiple Alternatives: Nested Branches

Branch inside another branch

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

Tax Schedule

If your filing status is Single		If your filing status is Married
Tax Bracket	Percentage	Tax Bracket	Percentage
$0 . . . $21,450	15%	0 . . . $35,800	15%
Amount over $21,450, up to $51,900	28%	Amount over $35,800, up to $86,500	28%
Amount over $51,900	31%	Amount over $86,500	31%

Nested Branches

Compute taxes due, given filing status and income figure: (1) branch on the filing status, (2) for each filing status, branch on income level
The two-level decision process is reflected in two levels of if statements
We say that the income test is nested inside the test for filing status

File TaxReturn.java

File TaxReturnTester.java

Output

   Please enter your income: 50000
   Please enter S (single) or M (married): S
   The tax is 11211.5

Self Check

The if/else/else statement for the earthquake strength first tested for higher values, then descended to lower values. Can you reverse that order?
Some people object to higher tax rates for higher incomes, claiming that you might end up with less money after taxes when you get a raise for working hard. What is the flaw in this argument?

Answers

Yes, if you also reverse the comparisons:

if (richter < 3.5)
   r = "Generally not felt by people";
else if (richter < 4.5)
   r = "Felt by many people, no destruction";
else if (richter < 6.0)
   r = "Damage to poorly constructed buildings";
. . .

The higher tax rate is only applied on the income in the higher bracket. Suppose you are single and make $51,800. Should you try to get a $200 raise? Absolutely–you get to keep 72% of the first $100 and 69% of the next $100

Using Boolean Expressions: 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

Using Boolean Expressions: Predicate Method

A predicate method returns a boolean value
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)) . . .
Useful predicate methods in Scanner class: hasNextInt() and hasNextDouble()
if (in.hasNextInt()) n = in.nextInt();

Using Boolean Expressions: The 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`

Using Boolean Variables

private boolean married;
Set to truth value:
married = input.equals("M");
Use in conditions:
if (married) . . . else . . . if (!married) . . .
Also called flag
It is considered gauche to write a test such as
if (married == true) . . . // Don't
Just use the simpler test
if (married) . . .

Self Check

When does the statement
system.out.println (x > 0 || x < 0);
print false?
Rewrite the following expression, avoiding the comparison with false:
if (Character.isDigit(ch) == false) . . .

Answers

When x is zero
if (!Character.isDigit(ch)) . . .

Chapter 5

Decisions

Chapter Goals

The if Statement

The if/else Statement

Statement Types

Syntax 6.1: The if Statement

Example:

Purpose:

Syntax 6.2: Block Statement

Example:

Purpose:

Self Check

Answers

Comparing Values: Relational Operators

Comparing Floating-Point Numbers

Comparing Floating-Point Numbers

Comparing Strings

Lexicographic Comparison

Comparing Objects

Object Comparison

Testing for null

Self Check

Answers

Multiple Alternatives: Sequences of Comparisons

File Earthquake.java

File EarthquakeTester.java

Output

Multiple Alternatives: Nested Branches

Tax Schedule

Nested Branches

File TaxReturn.java

File TaxReturnTester.java

Output

Self Check

Answers

Using Boolean Expressions: The boolean Type

Using Boolean Expressions: Predicate Method

Using Boolean Expressions: The Boolean Operators

&& and || Operators

Truth Tables

Using Boolean Variables

Self Check

Answers

The `if` Statement

The `if`/`else` Statement

Syntax 6.1: The `if` Statement

Testing for `null`

Using Boolean Expressions: The `boolean` Type

`&&` and `||` Operators