Java, Java, Java

In this section we consider several numeric programming examples. They are carefully chosen to illustrate different issues and concepts associated with processing numeric data.

Example: Rounding to Two Decimal Places

As an example of how to use Math class methods, let’s consider the prob- lem of rounding numbers. When dealing with applications that involve monetary values—dollars and cents—it is often necessary to round a cal- culated result to two decimal places. For example, suppose a program computes the value of a certificate of deposit (CD) to be 75.19999. Be- fore we output this result, we would want to round it to two decimal

places—to 75.20. The following algorithm can be used to accomplish this: Algorithm design

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Step 3 of this algorithm can be done using the Math.floor(R) method, which rounds its real argument, R, to the largest integer not less than R (from Table 5.11). If the number to be rounded is stored in the double variable R, then the following expression will round R to two decimal places:

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Alternatively, we could use the Math.round() method (Table 5.11). This method rounds a floating-point value to the nearest integer. For exam- ple, Math.round(65.3333) rounds to 65 and Math.round(65.6666) rounds to 66. The following expression uses it to round to two decimal places:

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What objects do we need?

 

 

Figure5.3:Interactingob- jects:The user interacts with

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Note that it is important here to divide by 100.0 and not by 100. Other- wise, the division will give an integer result and we’ll lose the two decimal places.

 

Example: Converting Fahrenheit to Celsius

To illustrate some of the issues that arise in using numeric data, let’s de- sign a program that performs temperature conversions from Fahrenheit to Celsius and vice versa.

 

Problem Decomposition

This problem requires two classes, a Temperature class and a TemperatureUI class. The Temperature class will perform the temper- ature conversions, and TemperatureUI will serve as the user interface (Fig. 5.3).

 

1: Convert 100C to F

 

the user interface (Tempera- tureUI), which interacts with the Temperature object.

3: result=212

2: result=celsToFahr(100)

 

 

 

 

 

 

 

What data do we need?

Class Design: Temperature

The purpose of the Temperature class is to perform the temperature con- versions. To convert a Celsius temperature to Fahrenheit or vice versa, it is not necessary to store the temperature value. Rather, a conversion method could take the Celsius (or Fahrenheit) temperature as a parameter, per- form the conversion, and return the result. Therefore, the Temperature

 

class does not need any instance variables. Note that in this respect the Temperature class resembles the Math class. Unlike OneRowNim, which stores the game’s state—the number of sticks remaining and whose turn it is—the Math and Temperature classes are stateless.

Thus, following the design of the Math class, the Temperature class What methods do we need?

will have two public static methods: one to convert from Fahrenheit to Celsius and one to convert from Celsius to Fahrenheit. Recall that static methods are associated with the class rather than with its instances. There- fore, we needn’t instantiate a Temperature object to use these methods. Instead, we can invoke the methods through the class itself.

The methods will use the standard conversion formulas: F = ⁹C + 32 and C = ⁵ (F 32). Each of these methods should have a single parameter to store the temperature value that is being converted.

Because we want to be able to handle temperatures such as 98.6, we should use real-number data for the methods’ parameters. Generally speaking, because Java represents real literals such as 98.6 as doubles, the double type is more widely used than float. Because doubles are more widely used in Java, using double wherever a floating point value is needed will cut down on the number of implicit data conversions that a program would have to perform. Therefore, each of our conversion meth- ods should take a double parameter and return a double result. These considerations lead

 

 

 

 

 

 

Implementation: Temperature

The implementation of the Temperature class is shown in Figure 5.5. Note that because celsToFahr() uses the double value temp in its cal- culation, it uses floating-point literals (9.0, 5.0, and 32.0) in its conversion expression. This helps to reduce the reliance on Java’s built-in promo- tion rules, which can lead to subtle errors. For example, to the design

shown in Figure 5.4, suppose we had written what looks like an equivalent

expression using integer literals:

, ,Figure 5.4: The Temperature

class. Note that static elements are

Junderlined in UML. (NEEDS RE-

 

Because 9 divided by 5 gives the integer result 1, this expression is always equivalent to temp + 32, which is not the correct conversion formula.

VISION)

 

This kind of subtle semantic error can be avoided if you avoid mixingSemantic error

 

types wherever possible.

 

 

 

 

 

 

 

 

Testing strategy

 

Designing test data

Testing and Debugging

The next question to be addressed is how should this program be tested? As always, you should test the program in a stepwise fashion. As each method is coded, you should test it both in isolation and in combination with the other methods, if possible.

Also, you should develop appropriate test data. It is not enough to just plug in any values. The values you use should test for certain potential problems. For this program, the following tests are appropriate:

 

Test converting 0 degrees C to 32 degrees F.

Test converting 100 degrees C to 212 degrees F.

Test converting 212 degrees F to 100 degrees C.

Test converting 32 degrees F to 0 degrees C.

 

The first two tests use the celsToFahr() method to test the freezing point and boiling point temperatures, two boundary values for this prob- lem. A boundary value is a value at the beginning or end of the range of values that a variable or calculation is meant to represent. The second pair of tests performs similar checks with the fahrToCels() method. One

 

 

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Figure 5.5: The Temperature class.

 

advantage of using these particular values is that we know what results the methods should return.

 

 

 

 

The TemperatureUI Class

The purpose of the TemperatureUI class is to serve as a user interface— that is, as an interface between the user and a Temperature object. It will accept a Fahrenheit or Celsius temperature from the user, pass it to one of the public methods of the Temperature object for conversion, and display the result that is returned.

As we discussed in Chapter 4, the user interface can take various forms, ranging from a command-line interface to a graphical interface. Figure 5.6 shows a design for the user interface based on the command-line interface developed in Chapter 4. The TemperatureUI uses a KeyboardReader to handle interaction with the user and uses static methods in the Temperature class to perform the temperature conversions.

 

 

SELF-STUDY EXERCISES

 

 

 

 

 

 

 

 

 

 

Figure 5.6: A command-line user interface.

 

EXERCISE 5.1 Following the design in Figure 5.6, implement the TemperatureUI class and use it to test the methods in Temperature class. The run() method should use an input-process-output algorithm: Prompt the user for input, perform the necessary processing, and output the result. Note that because Temperature’s conversion methods are class methods, you do not need to instantiate a Temperature object in this project. You can invoke the conversion methods directly through the Temperature class:

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Labels

AppletButtons Input Temperature >>

 

45

C to FF to C Conversion Result:

 

 

 

 

 

 

 

 

 

TextFields

EXERCISE 5.2 Following the design for the GUI developed in Chap- ter 4, implement a GUI to use for testing the Temperature class. The GUI should have the layout shown in Figure 5.7.

Example: Using Class Constants

As we noted in Chapter 0, in addition to instance variables, which are associated with instances (objects) of a class, Java also allows class vari- ables, which are associated with the class itself. One of the most common uses of such variables is to define named constants to replace literal val- ues. A named constant is a variable that cannot be changed once it has

 

been given an initial value. In this section, we use our running example,

OneRowNim, to illustrate using class constants.

 

Figure 5.7: Layout design of a GUI that performs temperature con- versions.

Recall that methods and variables that are associated with a class must be declared with the static modifier. If a variable is declared static, there is exactly one copy of that variable created no matter how many times its class is instantiated. To turn a variable into a constant, it must be declared with the final modifier. Thus, the following would be exam- ples of a class constants, constant values that are associated with the class rather than with its instances:

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The final modifier indicates that the value of a variable cannot be changed. When final is used in a variable declaration, the variable must be assigned an initial value. After a final variable is properly declared, it is a syntax error to attempt to try to change its value. For example, given the preceding declarations, the following assignment statement would cause a compiler error:

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Note how we use uppercase letters and underscore characters ( ) in the names of constants. This is a convention that professional Java program- mers follow, and its purpose is to make it easy to distinguish the constants

 

from the variables in a program. This makes the program easier to read and understand.

 

 

 

 

 

 

Another way that named constants improve the readability of a pro- gram is by replacing the reliance on literal values. For example, for the OneRowNim class, compare the following two if conditions:

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Clearly, the second condition is easier to read and understand. In the first condition, we have no good idea what the literal value 3 represents. In the second, we know that MAX PICKUP represents the most sticks a player can pick up.

Thus, to make OneRowNim more readable, we should replace all occur- rences of the literal value 3 with the constant MAX PICKUP. This same principle would apply to some of the other literal values in the program.

Thus, instead of using 1 and 2 to represent the two players, we could useReadability

PLAYER ONE and PLAYER TWO to make methods such as the following easier to read and understand:

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Another advantage of named constants (over literals) is that their use makes the program easier to modify and maintain. For example, suppose

that we decide to change OneRowNim so that the maximum number ofMaintainability

sticks that can be picked up is 4 instead of 3. If we used literal values, we would have to change all occurrences of 4 that were used to represent the

 

maximum pick up. If we used a named constant, we need only change its declaration to:

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So far, all of the examples we have presented show why named con- stants (but not necessarily class constants) are useful. Not all constants are class constants. That is, not all constants are declared static. How- ever, the idea of associating constants with a class makes good sense. In addition to saving memory resources, by creating just a single copy of the constant, constants such as MAX STICKS and PLAYER ONE make more conceptual sense to associate with the class itself rather than with any particular OneRowNim instance.

Class constants are used extensively in the Java class library. For ex-

ample, as we saw in Chapter 2, Java’s various built-in colors are rep- resented as constants of the java.awt.Color class—Color.blue and Color.red. Similarly, java.awt.Label uses int constants to specify how a label’s text should be aligned: Label.CENTER.

Another advantage of class constants is that they can be used before

instances of the class exist. For example, a class constant (as opposed to an instance constant) may be used during object instantiation:

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Note how we use the name of the class to refer to the class constant. Of course, MAX STICKS has to be a public variable in order to be accessible outside the class. To use MAX STICKS as a constructor argument it has to be a class constant because at this point in the program there are no instances of OneRowNim. A new version of OneRowNim that uses class constants is shown in Figure 5.8.

It is important to note that Java also allows class constants to be referenced through an instance of the class. Thus, once we have instantiated game, we can refer to MAX STICKS with either OneRowNim.MAX STICKS or game.MAX STICKS.

SELF-STUDY EXERCISE

EXERCISE 5.3 Implement a command-line interface class named KBTestOneRowNim, that uses our new version of OneRowNim. Make use of the MAX STICKS and MAX PICKUP in the user interface.

OBJECT-ORIENTED DESIGN: Information Hiding

The fact that our new versions of OneRowNim—we’ve developed two new versions in this chapter—are backward compatible with the previous version

 

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public c l a s s OneRowNim

public s t a t i c f i n a l in t PLAYER ONE = 1 ; public s t a t i c f i n a l in t PLAYER TWO = 2 ; public s t a t i c f i n a l in t MAX PICKUP = 3 ; public s t a t i c f i n a l in t MAX STICKS = 1 1 ;

public s t a t i c f i n a l boolean GAME OVER = fa l s e ;

 

private in t n S t i c ks = MAX STICKS ;

private boolean onePlaysNext = t rue ;

 

public OneRowNim( )

{

// One Row Nim ( ) c o n s t r u c t o r 1

public OneRowNim( in t s t i c k s )

{n S t i c ks = s t i c k s ;

// One Row Nim ( ) c o n s t r u c t o r 2

public OneRowNim( in t s t i c k s , in t s t a r t e r ) n S t i c ks = s t i c k s ;

onePlaysNext = ( s t a r t e r == PLAYER ONE ) ;

// One Row Nim ( ) c o n s t r u c t o r 3

public boolean t a k e S t i c k s ( in t num)

i f (num < 1num > MAX PICKUPnum > n S t i c ks )

return fa l s e ;// E r r o r

e ls e// V a l i d move

n St i c ks = n St i c ksnum;

onePlaysNext = ! onePlaysNext ;

return t rue ;

} // e l s e

// t a k e S t i c k s ( )

public in t g e t S t i c k s ( )

{return n St i c ks ;

// g e t S t i c k s ( )

public in t get Player ( )

i f ( onePlaysNext )

return PLAYER ONE;

e ls e return PLAYER TWO;

// g e t P l a y e r ( )

public boolean gameOver ( )

{return ( n St i c ks <= 0 ) ;

// g a m e O v e r ( )

public in t getWinner ( )

i f ( n St i c ks < 1 )

return get Player ( ) ;

e ls e return 0 ;// Game i s n o t o v e r

// g e t W i n n e r ( )

public S t r i n g report ( )

{return ( ”Number of s t i c k s l e f t : ” + g e t S t i c k s ( )

+ ”\ nNext turn by player ” + get Player ( ) + ”\n” ) ;

}// r e p o r t ( )

// One Row Nim c l a s s

\J

Figure 5.8: This version of OneRowNim uses named constants.

 

Preserving the public interface

 

 

 

 

Information hiding

is due in large part to the way we have divided up its public and private elements. Because the new versions still present the same public interface, programs that use the OneRowNim class, such as the OneRowNimApp from Chapter 4 (Fig. 4.24), can continue to use the class without changing a single line of their own code. To confirm this, see the Self-Study Exercise at the end of this section.

Although we have made significant changes to the underlying rep- resentation of OneRowNim, the implementation details—its data and algorithms—are hidden from other objects. As long as OneRowNim’s pub- lic interface remains compatible with the old version, changes to its pri- vate elements won’t cause any inconvenience to those objects that were dependent on the old version. This ability to change the underlying im- plementation without affecting the outward functionality of a class is one of the great benefits of the information hiding principle.

 

 

 

 

 

The lesson to be learned here is that the public parts of a class should be restricted to just those parts that must be accessible to other objects. Everything else should be private. Things work better, in Java program- ming and in the real world, when objects are designed with the principle of information hiding in mind.

 

SELF-STUDY EXERCISE

EXERCISE 5.4 To confirm that our new version of OneRowNim still works correctly with the user interfaces we developed in Chapter 4, com- pile and run it with OneRowNimApp (Fig. 4.24).

Example: A Winning Algorithm for One Row Nim

Now that we have access to numeric data types and operators, lets de- velop an algorithm that can win the One Row Nim game. Recall that in Chapter 4 we left things such that when the computer moves, it al- ways takes 1 stick. Let’s replace that strategy with a more sophisticated approach.

If you have played One Row Nim, you have probably noticed that in a game with 21 sticks, you can always win the game if you leave your opponent with 1, 5, 9, 13, 17, or 21 sticks. This is obvious for the case of 1 stick. For the case where you leave your opponent 5 sticks, no matter what the opponent does, you can make a move that leaves the other player with 1 stick. For example, if your opponent takes 1 stick, you can take 3; if your opponent takes 2, you can take 2; and, if your opponent takes 3, you can take 1. In any case, you can win the game by making the right move, if you have left your opponent with 5 sticks. The same arguments apply for the other values: 9, 13, 17, and 21.

 

What relationship is common to the numbers in this set? Notice that if you take the remainder after dividing each of these numbers by 4 you always get 1:

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Thus, we can base our winning strategy on the goal of leaving the oppo- nent with a number of sticks, N, such that N % 4 equals 1.

To determine how many sticks to take in order to leave the opponent with N, we need to use a little algebra. Let’s suppose that sticksLeft represents the number of sticks left before our turn. The first thing we have to acknowledge is that if sticksLeft % 4 == 1, then we have been left with 1, 5, 9, 13, and so on, sticks, so we cannot force a win. In that case, it doesn’t matter how many sticks we pick up. Our opponent should win the game.

So, let’s suppose that sticksLeft % 4 != 1, and let M be the number of sticks to pickup in order to leave our opponent with N, such that N % 4 ==

1. Then we have the following two equations:

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We can combine these into a single equation, which can be simplified as follows:

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If sticksLeft - M leaves a remainder of 1 when divided by 4, that means that

sticksLeft - M is equal some integer quotient, Q times 4 plus 1:

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By adding M to both sides and subtracting 1 from both sides of this equa- tion, we get:

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This equation is saying that (sticksLeft - 1) % 4 == M. That is, that when you divide sticksLeft-1 by 4, you will get a remainder of M, which is the number of sticks you should pick up. Thus, to decide how many sticks to take, we want to compute:

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To verify this, let’s look at some examples:

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The examples in this table show that when we use (sticksLeft-1 % 4) to calculate our move, we always leave our opponent with a losing situation. Note that when sticksLeft equals 9 or 5, we can’t apply this strategy because it would lead to an illegal move.

Let’s now convert this algorithm into Java code. In addition to incor- porating our winning strategy, this move() method makes use of two important Math class methods:

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The move() method will return an int representing the best move pos- sible. It begins by getting the number of sticks left from the OneRowNim object, which is referred to as nim in this case. It then checks whether it can win by computing (sticksLeft-1) % 4. However, note that rather than use the literal value 4, we use the named constant MAX PICKUP, which is accessible through the nim object. This is an especially good use for the class constant because it makes our algorithm completely general – that is, our winning strategy will continue to work even if the game is changed so that the maximum pickup is 5 or 6. The then clause computes and re- turns (sticksLeft-1) % nim.MAX PICKUP+1, but here again it uses the class constant.

The else clause would be used when it is not possible to make a winning move. In this case we want to choose a random number of sticks between 1 and some maximum number. The maximum number depends on how many sticks are left. If there are more than 3 sticks left, then the most we can pick up is 3, so we want a random number between 1 and 3. However, if there are 2 sticks left, then the most we can pick up is 2 and we want a random number between 1 and 2. Note how we use the Math.min() method to decide the maximum number of sticks that can be picked up:

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SECTION 5.6 • From the Java Libraryjava.text.NumberFormat 229

The min() method returns the minimum value between its two argu- ments.

Finally, note how we use the Math.random() method to calculate a random number between 1 and the maximum:

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The random() method returns a real number between 0 and 0.999999 – that is, a real number between 0 and 1 but not including 1:

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If we multiply Math.random() times 2, the result would be a value be- tween 0 and 1.9999999. Similarly, if we multiplied it by 3, the result would be a value between 0 and 2.9999999. In order to use the random value, we have to convert it into an integer, which is done by using the (int) cast operator:

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Recall that when a double is cast into an int, Java just throws away the fractional part. Therefore, this expression will give us a value between 0 and maxPickup-1. If maxPickup is 3, this will give a value between 0 and 2, whereas we want a random value between 1 and 3. To achieve this desired value, we merely add 1 to the result. Thus, using the expression

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gives us a random number between 1 and maxPickup, where maxPickup is either 1, 2, or 3, depending on the situation of the game at that point.

SELF-STUDY EXERCISE

EXERCISE 5.5 Implement a class named NimPlayer that incorporates the move() method designed in this section. The class should implement the design shown in Figure 5.9. That is, in addition to the move() method, it should have an instance variable, nim, which will serve as a reference to the OneRowNim game. Its constructor method should take a OneRowNim parameter, allowing the NimPlayer to be given a reference when it is instantiated.

EXERCISE 5.6 Modify OneRowNim’s command-line interface to play One Row Nim between the user and the computer, where the NimPlayer implemented in the previous exercise represents the computer.