第五章

決定

5.1 `if` 敘述

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

`if`/`else` 敘述

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

Block 敘述

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

Syntax 5.1. `if` 敘述

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

例題:

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

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

用途:

To execute a statement when a condition is true or false

Syntax 5.2. Block 敘述

{ statement statement . . . }

例題:

{

   double newBalance = balance - amount;
   balance = newBalance;

}

用途:

To group several statements together to form a single statement

敘述型式

簡單敘述
balance = balance - amount;
複雜敘述
if (balance >= amount) balance = balance - amount;Also while, for, etc. (see chapter 6)
Block 敘述
{ double newBalance = balance - amount; balance = newBalance; }

5.2 數值的比較

關係運算子

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

相等和指定

== 測試是否相等:
if (x == 0) . . // if x equals zero
= 指定一數值給一變數:
x = 0; // assign 0 to x
注意不要用錯

浮點數比較

由於精確度有限，浮點數的計算可能產生捨入誤差(roundoff error)，如下列程式碼:

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);

執行後的結果為:
sqrt(2)squared minus 2 is not 0 but 4.440892098500626E-16
因此，不要用 == 比較浮點數

浮點數比較

兩數幾乎相等, 假如

|x - y| <= ε
ε 是一很小的數, 如 10^-14
假如 x, y 很大或很小, 不足以判斷, 就必須用

|x - y| / max(|x|, |y|) <= ε
但是But if one of the numbers is zero, don't divide by max(|x |, |y|)

字串比較

不要用 == 比較字串!
if (input == "Y") // WRONG!!!
用 equals 方法:
if (input.equals("Y"))
== 測試身份, equals 測試內容是否相同
大小寫不拘時 (如 "Y" or "y") 用 equalsIgnoreCase()
if (input.equalsIgnoreCase("Y"))

依字典的次序比較(Lexicographic Comparison)

Java 所用的次序，數字在前，接著大寫字母，再接著小寫字母。

s.compareTo(t) < 0 表示:
在字典中 s 是在 t 之前
"car" 在 "cargo" 之前
"cargo" 在 "cathode" 之前
所有大寫字母都在小寫字母之前, 如:
"Hello" 在 "car" 之前

依字典的次序比較

物件比較

== 測試身份, equals 測試內容是否相同
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)

物件比較

The `null` Reference

null reference refers to no object at all
可用於測試:
if (account == null) . . .
用 ==, 不是用 equals, 測試 null
假如用者按下取消鍵 showInputDialog 傳回 null:
String input = JOptionPane.showInputDialog("..."); if (input != null) { ... }
null 不是空字串 ""

5.3 多重選擇(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


/**
   A class that describes the effects of an earthquake.
*/
public class Earthquake
{
   /**
      Constructs an Earthquake object.
      @param magnitude the magnitude on the Richter scale
   */
   public Earthquake(double magnitude)
   {
      richter = magnitude;
   }

   /**
      Gets a description of the effect of the earthquake.
      @return the description of the effect
   */
   public String getDescription()
   {
      String r;
      if (richter >= 8.0)
         r = "Most structures fall";
      else if (richter >= 7.0)
         r = "Many buildings destroyed";
      else if (richter >= 6.0)
         r = "Many buildings considerably damaged, some collapse";
      else if (richter >= 4.5)
         r = "Damage to poorly constructed buildings";
      else if (richter >= 3.5)
         r = "Felt by many people, no destruction";
      else if (richter >= 0)
         r = "Generally not felt by people";
      else
         r = "Negative numbers are not valid";
      return r;
   }

   private double richter;
}

File EarthquakeTest.java


import javax.swing.JOptionPane;

/**
   A class to test the Earthquake class.
*/
public class EarthquakeTest
{
   public static void main(String[] args)
   {
      String input = JOptionPane.showInputDialog(
         "Enter a magnitude on the Richter scale:");
      double magnitude = Double.parseDouble(input);
      Earthquake quake = new Earthquake(magnitude);
      System.out.println(quake.getDescription());
      System.exit(0);
   }
}

多重選擇

測試的先後次序會影儁結果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"; . . .
不要漏了 else if (richter >= 8.0) r = "Most structures fall"; if (richter >= 7.0) // omitted else--ERROR r = "Many buildings destroyed

多層分支(Nested Branches)

分支內的分支

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

所得稅申報

假如婚姻狀況是單身

所得總額超過	但未超過	稅額為	總額超過
$0	$21,450	15%	$0
$21,450	$51,900	$3,217.50 + 28%	$21,450
$51,900		$11,743.50 + 31%	$51,900

假如婚姻狀況是已婚

所得總額超過	但未超過	稅額為	總額超過
$0	$35,800	15%	$0
$35,800	$86,500	$5,370.00 + 28%	$35,800
$86,500		$19,566.00 + 31%	$86,500

所得稅申報流程圖

File TaxReturn.java


/**
   A tax return of a taxpayer in 1992.
*/
class TaxReturn
{
   /**
      Constructs a TaxReturn object for a given income and
      marital status.
      @param anIncome the taxpayer income
      @param aStatus either SINGLE or MARRIED
   */
   public TaxReturn(double anIncome, int aStatus)
   {
      income = anIncome;
      status = aStatus;
   }

   public double getTax()
   {
      double tax = 0;

      if (status == SINGLE)
      {
         if (income <= SINGLE_CUTOFF1)
            tax = RATE1 * income;
         else if (income <= SINGLE_CUTOFF2)
            tax = SINGLE_BASE2
               + RATE2 * (income - SINGLE_CUTOFF1);
         else
            tax = SINGLE_BASE3
               + RATE3 * (income - SINGLE_CUTOFF2);
      }
      else
      {
         if (income <= MARRIED_CUTOFF1)
            tax = RATE1 * income;
         else if (income <= MARRIED_CUTOFF2)
            tax = MARRIED_BASE2
               + RATE2 * (income - MARRIED_CUTOFF1);
         else
            tax = MARRIED_BASE3
               + RATE3 * (income - MARRIED_CUTOFF2);
      }

      return tax;
   }

   public static final int SINGLE = 1;
   public static final int MARRIED = 2;

   private static final double RATE1 = 0.15;
   private static final double RATE2 = 0.28;
   private static final double RATE3 = 0.31;

   private static final double SINGLE_CUTOFF1 = 21450;
   private static final double SINGLE_CUTOFF2 = 51900;

   private static final double SINGLE_BASE2 = 3217.50;
   private static final double SINGLE_BASE3 = 11743.50;
   private static final double MARRIED_CUTOFF1 = 35800;
   private static final double MARRIED_CUTOFF2 = 86500;

   private static final double MARRIED_BASE2 = 5370;
   private static final double MARRIED_BASE3 = 19566;

   private double income;
   private int status;
}

File TaxReturnTest.java


/**
   A tax return of a taxpayer in 1992.
*/
class TaxReturn
{
   /**
      Constructs a TaxReturn object for a given income and
      marital status.
      @param anIncome the taxpayer income
      @param aStatus either SINGLE or MARRIED
   */
   public TaxReturn(double anIncome, int aStatus)
   {
      income = anIncome;
      status = aStatus;
   }

   public double getTax()
   {
      double tax = 0;

      if (status == SINGLE)
      {
         if (income <= SINGLE_CUTOFF1)
            tax = RATE1 * income;
         else if (income <= SINGLE_CUTOFF2)
            tax = SINGLE_BASE2
               + RATE2 * (income - SINGLE_CUTOFF1);
         else
            tax = SINGLE_BASE3
               + RATE3 * (income - SINGLE_CUTOFF2);
      }
      else
      {
         if (income <= MARRIED_CUTOFF1)
            tax = RATE1 * income;
         else if (income <= MARRIED_CUTOFF2)
            tax = MARRIED_BASE2
               + RATE2 * (income - MARRIED_CUTOFF1);
         else
            tax = MARRIED_BASE3
               + RATE3 * (income - MARRIED_CUTOFF2);
      }

      return tax;
   }

   public static final int SINGLE = 1;
   public static final int MARRIED = 2;

   private static final double RATE1 = 0.15;
   private static final double RATE2 = 0.28;
   private static final double RATE3 = 0.31;

   private static final double SINGLE_CUTOFF1 = 21450;
   private static final double SINGLE_CUTOFF2 = 51900;

   private static final double SINGLE_BASE2 = 3217.50;
   private static final double SINGLE_BASE3 = 11743.50;
   private static final double MARRIED_CUTOFF1 = 35800;
   private static final double MARRIED_CUTOFF2 = 86500;

   private static final double MARRIED_BASE2 = 5370;
   private static final double MARRIED_BASE3 = 19566;

   private double income;
   private int status;
}

使用布林(boolean)式

`boolean` 型式

George Boole (1815-1864): 邏輯研究的先驅者
式子值 amount < 1000 是 true 或 false.
boolean 型式: true 或 false

斷定性方法(Predicate Method)

回值的型式為 boolean
例子:
public boolean isOverdrawn() { return balance < 0; }
用於測試條件中
if (harrysChecking.isOverdrawn()) ...
Character 類別中, 有用的斷定性方法有:
isDigit isLetter isUpperCase isLowerCase
if (Character.isUpperCase(ch)) ...

布林運算子

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

`&&` 和 `||` 運算子

真實表(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 定律

否定一複雜條件容易引起混淆:
if (!(0 < amount && amount < 1000))
De Morgan's 定律說明
!(A && B) 和 !A || !B 相同!(A || B) 和 !A && !B 相同
注意 ! 移入括弧內 && 和 || 對調
(!(0 < amount && amount < 1000)) 即
!(0 < amount) || !(amount < 1000) , 即
0 >= amount || amount >= 1000
注意 < 的相反是 >=

布林變數

private boolean married;
設定的是真實值:
married = input.equals("M");
在條件中使用:
if (married) ... else ... if (!married) ...
不要測試布林變數是否等(或不等)於真實值之一, 如:
if (married == true) // DON'T if (married == false) // DON'T if (married != false) // NO!!!

第 五 章

決定

5.1 if 敘述

if/else 敘述

Block 敘述

Syntax 5.1. if 敘述

例題:

用途:

Syntax 5.2. Block 敘述

例題:

用途:

敘述型式

5.2 數值的比較

關係運算子

相等和指定

浮點數比較

浮點數比較

字串比較

依字典的次序比較(Lexicographic Comparison)

依字典的次序比較

物件比較

物件比較

The null Reference

5.3 多重選擇(Multiple Alternatives)

File Earthquake.java

File EarthquakeTest.java

多重選擇

多層分支(Nested Branches)

所得稅申報

所得稅申報流程圖

File TaxReturn.java

File TaxReturnTest.java

使用布林(boolean)式

boolean 型式

斷定性方法(Predicate Method)

布林運算子

&& 和 || 運算子

真實表(Truth Tables)

De Morgan's 定律

布林變數

第五章

5.1 `if` 敘述

`if`/`else` 敘述

Syntax 5.1. `if` 敘述

The `null` Reference

`boolean` 型式

`&&` 和 `||` 運算子