5.11 Case Study: Generating Random Characters 175

Tip

You can view the complete documentation for the Math class online at http://java.sun.com/ javase/6/docs/api/index.html, as shown in Figure 5.7.

Note

Not all classes need a main method. The Math class and JOptionPane class do not have main methods. These classes contain methods for other classes to use.

5.11 Case Study: Generating Random Characters

Computer programs process numerical data and characters. You have seen many examples that involve numerical data. It is also important to understand characters and how to process them. This section presents an example for generating random characters.

As introduced in §2.13, every character has a unique Unicode between 0 and FFFF in hexadecimal (65535 in decimal). To generate a random character is to generate a random integer between 0 and 65535 using the following expression (note that since 0 <= Math.random() < 1.0, you have to add 1 to 65535):

(int)(Math.random() * (65535 + 1))

Now let us consider how to generate a random lowercase letter. The Unicodes for lowercase letters are consecutive integers starting from the Unicode for 'a', then that for 'b', 'c', Á , and 'z'. The Unicode for 'a' is

(int)'a'

So a random integer between (int)'a' and (int)'z' is

(int)((int)'a' + Math.random() * ((int)'z' - (int)'a' + 1)

As discussed in §2.13.3, all numeric operators can be applied to the char operands. The char operand is cast into a number if the other operand is a number or a character. Thus the preceding expression can be simplified as follows:

'a' + Math.random() * ('z' - 'a' + 1)

and a random lowercase letter is

(char)('a' + Math.random() * ('z' - 'a' + 1))

To generalize the foregoing discussion, a random character between any two characters ch1 and ch2 with ch1 < ch2 can be generated as follows:

(char)(ch1 + Math.random() * (ch2 – ch1 + 1))

This is a simple but useful discovery. Let us create a class named RandomCharacter in Listing 5.10 with five overloaded methods to get a certain type of character randomly. You can use these methods in your future projects.

LISTING 5.10 RandomCharacter.java

1 public class RandomCharacter {

2/** Generate a random character between ch1 and ch2 */

5}

178 Chapter 5 Methods

For this example, the problem is first broken into two subproblems: get input from the user, and print the calendar for the month. At this stage, you should be concerned with what the subproblems will achieve, not with how to get input and print the calendar for the month. You can draw a structure chart to help visualize the decomposition of the problem (see Figure 5.9(a)).

FIGURE 5.9 The structure chart shows that the printCalendar problem is divided into two subproblems, readInput and printMonth, and that printMonth is divided into two smaller subproblems, printMonthTitle and printMonthBody.

The problem of printing the calendar for a given month can be broken into two subproblems: print the month title, and print the month body, as shown in Figure 5.9(b). The month title consists of three lines: month and year, a dash line, and the names of the seven days of the week. You need to get the month name (e.g., January) from the numeric month (e.g., 1). This is accomplished in getMonthName (see Figure 5.10(a)).

printMonthBody

printMonthTitle

getMonthName getStartDay

FIGURE 5.10 (a) To printMonthTitle, you need getMonthName. (b) The printMonthBody problem is refined into several smaller problems.

In order to print the month body, you need to know which day of the week is the first day of the month (getStartDay) and how many days the month has (getNumberOfDaysInMonth), as shown in Figure 5.10(b). For example, December 2005 has 31 days, and December 1, 2005, is Thursday.

How would you get the start day for the first date in a month? There are several ways to do so. For now, we’ll use the following approach. Assume you know that the start day (startDay1800 = 3) for Jan 1, 1800, was Wednesday. You could compute the total number of

getStartDay getTotalNumberOfDays

getNumberOfDaysInMonth

getTotalNumberOfDays isLeapYear

FIGURE 5.11 (a) To getStartDay, you need getTotalNumberOfDays. (b) The getTotalNumberOfDays problem is refined into two smaller problems.

5.12 Method Abstraction and Stepwise Refinement 179

days (totalNumberOfDays) between Jan 1, 1800, and the first date of the calendar month. The start day for the calendar month is (totalNumberOfDays + startDay1800) % 7, since every week has seven days. So the getStartDay problem can be further refined as getTotalNumberOfDays, as shown in Figure 5.11(a).

To get the total number of days, you need to know whether the year is a leap year and the number of days in each month. So getTotalNumberOfDays is further refined into two subproblems: isLeapYear and getNumberOfDaysInMonth, as shown in Figure 5.11(b). The complete structure chart is shown in Figure 5.12.

printCalendar (main)

printMonthTitle printMonthBody

getMonthName getStartDay

getTotalNumberOfDays

getNumberOfDaysInMonth

isLeapYear

FIGURE 5.12 The structure chart shows the hierarchical relationship of the subproblems in the program.

5.12.2Top-Down or Bottom-Up Implementation

Now we turn our attention to implementation. In general, a subproblem corresponds to a method in the implementation, although some are so simple that this is unnecessary. You would need to decide which modules to implement as methods and which to combine in other methods. Decisions of this kind should be based on whether the overall program will be easier to read as a result of your choice. In this example, the subproblem readInput can be simply implemented in the main method.

You can use either a “top-down” or a “bottom-up” approach. The top-down approach imple- top-down approach ments one method in the structure chart at a time from the top to the bottom. Stubs can be used for

the methods waiting to be implemented. A stub is a simple but incomplete version of a method. stub The use of stubs enables you to quickly build the framework of the program. Implement the main method first, then use a stub for the printMonth method. For example, let printMonth display

the year and the month in the stub. Thus, your program may begin like this:

public class PrintCalendar { /** Main method */

public static void main(String[] args) { Scanner input = new Scanner(System.in);

// Prompt the user to enter year System.out.print("Enter full year (e.g., 2001): "); int year = input.nextInt();

182 Chapter 5 Methods

Key Terms 183

98total = total + 366;

99else

100total = total + 365;

102// Add days from Jan to the month prior to the calendar month

103for (int i = 1; i < month; i++)

104total = total + getNumberOfDaysInMonth(year, i);

106return total;

107}

109/** Get the number of days in a month */

115if (month == 4 || month == 6 || month == 9 || month == 11)

116return 30;

117

118 if (month == 2) return isLeapYear(year) ? 29 : 28; 119

120return 0; // If month is incorrect

121}

125return year % 400 == 0 || (year % 4 == 0 && year % 100 != 0);

126}

127}

The program does not validate user input. For instance, if the user enters either a month not in the range between 1 and 12 or a year before 1800, the program displays an erroneous calendar. To avoid this error, add an if statement to check the input before printing the calendar.

This program prints calendars for a month but could easily be modified to print calendars for a whole year. Although it can print months only after January 1800, it could be modified to trace the day of a month before 1800.

Note

Method abstraction modularizes programs in a neat, hierarchical manner. Programs written as collections of concise methods are easier to write, debug, maintain, and modify. This writing style also promotes method reusability.

When implementing a large program, use the top-down or bottom-up approach. Do not write the entire program at once. Using these approaches seems to take more development time (because you repeatedly compile and run the program), but it actually saves time and makes debugging easier.

KEY TERMS

Review Questions 185

12.Method abstraction is achieved by separating the use of a method from its implementation. The client can use a method without knowing how it is implemented. The details of the implementation are encapsulated in the method and hidden from the client who invokes the method. This is known as information hiding or encapsulation.

13.Method abstraction modularizes programs in a neat, hierarchical manner. Programs written as collections of concise methods are easier to write, debug, maintain, and modify than would otherwise be the case. This writing style also promotes method reusability.

14.When implementing a large program, use the top-down or bottom-up coding approach. Do not write the entire program at once. This approach seems to take more time for coding (because you are repeatedly compiling and running the program), but it actually saves time and makes debugging easier.

REVIEW QUESTIONS

Sections 5.2–5.4

5.1What are the benefits of using a method? How do you define a method? How do you invoke a method?

5.2What is the return type of a main method?

5.3Can you simplify the max method in Listing 5.1 using the conditional operator?

5.4True or false? A call to a method with a void return type is always a statement itself, but a call to a value-returning method is always a component of an expression.

5.5What would be wrong with not writing a return statement in a value-returning method? Can you have a return statement in a void method? Does the return statement in the following method cause syntax errors?

public static void xMethod(double x, double y) { System.out.println(x + y);

return x + y;

}

5.6Define the terms parameter, argument, and method signature.

5.7Write method headers for the following methods:

■Computing a sales commission, given the sales amount and the commission rate.

■Printing the calendar for a month, given the month and year.

■Computing a square root.

■Testing whether a number is even, and returning true if it is.

■Printing a message a specified number of times.

■Computing the monthly payment, given the loan amount, number of years, and annual interest rate.

■Finding the corresponding uppercase letter, given a lowercase letter.

5.12For (a) in the preceding question, show the contents of the stack just before the method max is invoked, just as max is entered, just before max is returned, and right after max is returned.

Section 5.8

5.13What is method overloading? Is it permissible to define two methods that have the same name but different parameter types? Is it permissible to define two methods in a class that have identical method names and parameter lists but different return value types or different modifiers?

5.14What is wrong in the following program?

public class Test {

public static void method(int x) {

}

public static int method(int y) { return y;

}

}

Section 5.9

5.15Identify and correct the errors in the following program:

1 public class Test {

2 public static void main(String[] args) {

3nPrintln("Welcome to Java!", 5);

188 Chapter 5 Methods

8for (int i = 0; i < n; i++)

9 System.out.println(message);

10}

11}

Section 5.10

5.16True or false? The argument for trigonometric methods represents an angle in radians.

5.17Write an expression that returns a random integer between 34 and 55. Write an expression that returns a random integer between 0 and 999. Write an expression that returns a random number between 5.5 and 55.5. Write an expression that returns a random lowercase letter.

5.18Evaluate the following method calls:

(a)Math.sqrt(4)

(b)Math.sin(2 * Math.PI)

(c)Math.cos(2 * Math.PI)

(d)Math.pow(2, 2)

(e)Math.log(Math.E)

(f)Math.exp(1)

(g)Math.max(2, Math.min(3, 4))

(h)Math.rint1- 2.52

(i)Math.ceil1- 2.52

(j)Math.floor1- 2.52

(k)Math.round1- 2.5F2

(l)Math.round1- 2.52

(m)Math.rint(2.5)

(n)Math.ceil(2.5)

(o)Math.floor(2.5)

(p)Math.round(2.5F)

(q)Math.round(2.5)

(r)Math.round(Math.abs1- 2.52)

5.1(Math: pentagonal numbers) A pentagonal number is defined as n13n - 12/2 for n = 1, 2, Á , and so on. So, the first few numbers are 1, 5, 12, 22, Á . Write the following method that returns a pentagonal number:

5.2*

Programming Exercises 189

5.3** (Palindrome integer) Write the following two methods

//Return the reversal of an integer, i.e. reverse(456) returns 654 public static int reverse(int number)

//Return true if number is palindrome

public static boolean isPalindrome(int number)

Use the reverse method to implement isPalindrome. A number is a palindrome if its reversal is the same as itself. Write a test program that prompts the user to enter an integer and reports whether the integer is a palindrome.

5.4* (Displaying an integer reversed) Write the following method to display an integer in reverse order:

public static void reverse(int number)

For example, reverse(3456) displays 6543. Write a test program that prompts the user to enter an integer and displays its reversal.

5.5* (Sorting three numbers) Write the following method to display three numbers in increasing order:

public static void displaySortedNumbers( double num1, double num2, double num3)

5.6* (Displaying patterns) Write a method to display a pattern as follows:

1

2 1

3 2 1

...

n n-1 ... 3 2 1

The method header is

public static void displayPattern(int n)

5.7* (Financial application: computing the future investment value) Write a method that computes future investment value at a given interest rate for a specified number of years. The future investment is determined using the formula in Exercise 2.13.

Use the following method header:

public static double futureInvestmentValue(

double investmentAmount, double monthlyInterestRate, int years)

For example, futureInvestmentValue(10000, 0.05/12, 5) returns 12833.59. Write a test program that prompts the user to enter the investment amount (e.g., 1000) and the interest rate (e.g., 9%) and prints a table that displays future value

for the years from 1 to 30, as shown below:

The amount invested: 1000

Annual interest rate: 9%

Years Future Value

11093.80

2913467.25

3014730.57

192 Chapter 5 Methods

5.16* (Number of days in a year) Write a method that returns the number of days in a year using the following header:

public static int numberOfDaysInAYear(int year)

Write a test program that displays the number of days in year from 2000 to 2010.

Sections 5.10–5.11

5.17* (Displaying matrix of 0s and 1s) Write a method that displays an n-by-n matrix using the following header:

public static void printMatrix(int n)

Each element is 0 or 1, which is generated randomly. Write a test program that prints a 3-by-3 matrix that may look like this:

0 1 0

0 0 0

1 1 1

5.18(Using the Math.sqrt method) Write a program that prints the following table using the sqrt method in the Math class.

5.19* (The MyTriangle class) Create a class named MyTriangle that contains the following two methods:

/** Returns true if the sum of any two sides is * greater than the third side. */

public static boolean isValid(

double side1, double side2, double side3)

/** Returns the area of the triangle. */ public static double area(

double side1, double side2, double side3)

Write a test program that reads three sides for a triangle and computes the area if the input is valid. Otherwise, it displays that the input is invalid. The formula for computing the area of a triangle is given in Exercise 2.21.

5.20(Using trigonometric methods) Print the following table to display the sin value and cos value of degrees from 0 to 360 with increments of 10 degrees. Round the value to keep four digits after the decimal point.

Programming Exercises 193

5.21** (Statistics: computing mean and standard deviation) In business applications, you are often asked to compute the mean and standard deviation of data. The mean is simply the average of the numbers. The standard deviation is a statistic that tells you how tightly all the various data are clustered around the mean in a set of data. For example, what is the average age of the students in a class? How close are the ages? If all the students are the same age, the deviation is 0. Write a program that prompts the user to enter ten numbers, and displays the mean and standard deviations of these numbers using the following formula:

The standard deviation is 2.99794

5.22** (Math: approximating the square root) Implement the sqrt method. The square root of a number, num, can be approximated by repeatedly performing a calculation using the following formula:

nextGuess = (lastGuess + (num / lastGuess)) / 2

When nextGuess and lastGuess are almost identical, nextGuess is the approximated square root.

The initial guess can be any positive value (e.g., 1). This value will be the starting value for lastGuess. If the difference between nextGuess and lastGuess is less than a very small number, such as 0.0001, you can claim that nextGuess is the approximated square root of num. If not, nextGuess becomes lastGuess and the approximation process continues.

Sections 5.10–5.11

5.23* (Generating random characters) Use the methods in RandomCharacter in Listing 5.10 to print 100 uppercase letters and then 100 single digits, printing ten per line.

5.24** (Displaying current date and time) Listing 2.9, ShowCurrentTime.java, displays the current time. Improve this example to display the current date and time. The calendar example in Listing 5.12, PrintCalendar.java, should give you some ideas on how to find year, month, and day.

5.25** (Converting milliseconds to hours, minutes, and seconds) Write a method that converts milliseconds to hours, minutes, and seconds using the following header:

public static String convertMillis(long millis)

The method returns a string as hours:minutes:seconds. For example, convertMillis(5500) returns a string 0:0:5, convertMillis(100000) returns a string 0:1:40, and convertMillis(555550000) returns a string 154:19:10.

194 Chapter 5 Methods

Comprehensive

5.26** (Palindromic prime) A palindromic prime is a prime number and also palindromic. For example, 131 is a prime and also a palindromic prime. So are 313 and 757. Write a program that displays the first 100 palindromic prime numbers. Display 10 numbers per line and align the numbers properly, as follows:

5.27** (Emirp) An emirp (prime spelled backward) is a nonpalindromic prime number whose reversal is also a prime. For example, 17 is a prime and 71 is a prime. So, 17 and 71 are emirps. Write a program that displays the first 100 emirps. Display 10 numbers per line and align the numbers properly, as follows:

5.28** (Mersenne prime) A prime number is called a Mersenne prime if it can be written in the form 2p - 1 for some positive integer p. Write a program that finds all Mersenne primes with p … 31 and displays the output as follows:

p2^p - 1

23

37

531

...

5.29** (Game: craps) Craps is a popular dice game played in casinos. Write a program to play a variation of the game, as follows:

Roll two dice. Each die has six faces representing values 1, 2, Á , and 6, respectively. Check the sum of the two dice. If the sum is 2, 3, or 12 (called craps), you lose; if the sum is 7 or 11 (called natural), you win; if the sum is another value (i.e., 4, 5, 6, 8, 9, or 10), a point is established. Continue to roll the dice until either a 7 or the same point value is rolled. If 7 is rolled, you lose. Otherwise, you win.

Your program acts as a single player. Here are some sample runs.

You rolled 5 + 6 = 11

You win

You rolled 1 + 2 = 3

You lose

You rolled 4 + 4 = 8 point is 8

You rolled 6 + 2 = 8 You win

You rolled 3 + 2 = 5 point is 5

You rolled 2 + 5 = 7 You lose

Programming Exercises 195

5.30** (Twin primes) Twin primes are a pair of prime numbers that differ by 2. For example, 3 and 5 are twin primes, 5 and 7 are twin primes, and 11 and 13 are twin primes. Write a program to find all twin primes less than 1000. Display the output as follows:

(3, 5)

(5, 7)

...

5.31** (Financial: credit card number validation) Credit card numbers follow certain patterns. A credit card number must have between 13 and 16 digits. It must start with:

■4 for Visa cards

■5 for Master cards

■37 for American Express cards

■6 for Discover cards

In 1954, Hans Luhn of IBM proposed an algorithm for validating credit card numbers. The algorithm is useful to determine whether a card number is entered correctly or whether a credit card is scanned correctly by a scanner. All credit card numbers are generated following this validity check, commonly known as the Luhn check or the Mod 10 check, which can be described as follows (for illustration, consider the card number 4388576018402626):

1.Double every second digit from right to left. If doubling of a digit results in a two-digit number, add up the two digits to get a single-digit number.

2 * 2 = 4

2 * 2 = 4

4 * 2 = 8

1 * 2 = 2 6 * 2 = 12 (1 + 2 = 3)

5 * 2 = 10 (1 + 0 = 1) 8 * 2 = 16 (1 + 6 = 7) 4 * 2 = 8

2.Now add all single-digit numbers from Step 1. 4 + 4 + 8 + 2 + 3 + 1 + 7 + 8 = 37

3.Add all digits in the odd places from right to left in the card number. 6 + 6 + 0 + 8 + 0 + 7 + 8 + 3 = 38

4.Sum the results from Step 2 and Step 3. 37 + 38 = 75

5.If the result from Step 4 is divisible by 10, the card number is valid; otherwise, it is invalid. For example, the number 4388576018402626 is invalid, but the number 4388576018410707 is valid.

Write a program that prompts the user to enter a credit card number as a long integer. Display whether the number is valid or invalid. Design your program to use the following methods:

/** Return true if the card number is valid */ public static boolean isValid(long number)

/** Get the result from Step 2 */

public static int sumOfDoubleEvenPlace(long number)

CHAPTER 6

SINGLE-DIMENSIONAL ARRAYS

Objectives

■To describe why arrays are necessary in programming (§6.1).

■To declare array reference variables and create arrays (§§6.2.1–6.2.2).

■To initialize the values in an array (§6.2.3).

■To access array elements using indexed variables (§6.2.4).

■To declare, create, and initialize an array using an array initializer (§6.2.5).

■To program common array operations (displaying arrays, summing all elements, finding min and max elements, random shuffling, shifting elements) (§6.2.6).

■To simplify programming using the for-each loops (§6.2.7).

■To apply arrays in the LottoNumbers and DeckOfCards problems (§§6.3–6.4).

■To copy contents from one array to another (§6.5).

■To develop and invoke methods with array arguments and return value (§6.6–6.7).

■To define a method with variable-length argument list (§6.8).

■To search elements using the linear (§6.9.1) or binary (§6.9.2) search algorithm.

■To sort an array using the selection sort (§6.10.1)

■To sort an array using the insertion sort (§6.10.2).

■To use the methods in the Arrays class (§6.11).