(Display an integer reversed) Write a method with the following header 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 then displays its reversal.

Write a program that displays all the numbers from 100 to 1,000, ten per line, that are divisible by 5 and 6. Numbers are separated by exactly one space.

Write a function to compute the following series:

$$m(i)=\frac{1}{2}+\frac{2}{3}+\ldots+\frac{i}{i+1}$$

Write a test program that displays the following table:

i       m(i)
1       0.5000
2       1.1667
...
19      16.4023
20      17.3546

(Geometry: point position) Programming Exercise 3.32 shows how to test whether a point is on the left side of a directed line, on the right, or on the same line. Write the methods with the following headers:

/** Return true if point (x2, y2) is on the left side of the
* directed line from (x0, y0) to (x1, y1) */
public static boolean leftOfTheLine(double x0, double y0,
double x1, double y1, double x2, double y2)

/** Return true if point (x2, y2) is on the same
* line from (x0, y0) to (x1, y1) */
public static boolean onTheSameLine(double x0, double y0,
double x1, double y1, double x2, double y2)

/** Return true if point (x2, y2) is on the
* line segment from (x0, y0) to (x1, y1) */
public static boolean onTheLineSegment(double x0, double y0,
double x1, double y1, double x2, double y2)

Write a program that prompts the user to enter the three points for p0 , p1 , and p2 and displays whether p2 is on the left side of the line from p0 to p1 , right side, the same line, or on the line segment. Here are some sample runs:

Enter three points for p0, p1, and p2: 1 1 2 2 1.5 1.5
(1.5, 1.5) is on the line segment from (1.0, 1.0) to (2.0, 2.0)

Enter three points for p0, p1, and p2: 1 1 2 2 3 3
(3.0, 3.0) is on the same line from (1.0, 1.0) to (2.0, 2.0)

Enter three points for p0, p1, and p2: 1 1 2 2 1 1.5
(1.0, 1.5) is on the left side of the line
from (1.0, 1.0) to (2.0, 2.0)

Enter three points for p0, p1, and p2: 1 1 2 2 1 –1
(1.0, −1.0) is on the right side of the line
from (1.0, 1.0) to (2.0, 2.0)

Use the methods in the following program to print 100 uppercase letters and then 100 single digits, printing ten per line.

1   public class RandomCharacter {
2       /** Generate a random character between ch1 and ch2 */
3       public static char getRandomCharacter(char ch1, char ch2) {
4           return (char)(ch1 + Math.random() * (ch2 - ch1 + 1));
5       }
6
7       /** Generate a random lowercase letter */
8       public static char getRandomLowerCaseLetter() {
9           return getRandomCharacter('a', 'z');
10      }
11
12      /** Generate a random uppercase letter */
13      public static char getRandomUpperCaseLetter() {
14          return getRandomCharacter('A', 'Z');
15      }
16
17      /** Generate a random digit character */
18      public static char getRandomDigitCharacter() {
19          return getRandomCharacter('0', '9');
20      }
21
22      /** Generate a random character */
23      public static char getRandomCharacter() {
24          return getRandomCharacter('\u0000', '\uFFFF');
25      }
26  }

Write a method with the following header to format the integer with the specified width. public static String format(int number, int width) The method returns a string for the number with one or more prefix 0s. The size of the string is the width. For example, format(34, 4) returns 0034 and format(34, 5) returns 00034. If the number is longer than the width, the method returns the string representation for the number. For example, format(34, 1) returns 34. Write a test program that prompts the user to enter a number and its width and displays a string returned by invoking format(number, width).

A regular polygon is an n-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon is:

$$\text { Area }=\frac{n \times s^2}{4 \times \tan \left(\frac{\pi}{n}\right)}$$

Write a method that returns the area of a regular polygon using the following header:

public static double area(1nt $\mathrm{n}$, double side)

Write a main method that prompts the user to enter the number of sides and the side of a regular polygon and displays its area.

The area of a pentagon can be computed using the following formula:

$$\text { Area }=\frac{5 \times s^2}{4 \times \tan \left(\frac{\pi}{5}\right)}$$

Write a method that returns the area of a pentagon using the following header:

public static double area(double side)

Write a main method that prompts the user to enter the side of a pentagon and displays its area.

(Print calendar) Programming Exercise 3.21 uses Zeller’s congruence to calculate the day of the week. Simplify Listing 6.12, PrintCalendar.java, using Zeller’s algorithm to get the start day of the month.

(Current date and time) Invoking System.currentTimeMillis() returns the elapsed time in milliseconds since midnight of January 1, 1970. Write a program that displays the date and time. Here is a sample run:

Current date and time is May 16, 2012 10:34:23

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, ..., 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. Then, revise the program run it 10,000 times and display the number of winning games.

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. 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):

• 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.

(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, . . ., 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

(Palindrome integer) Write the methods with the following headers:

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

// Return true if number is a palindrome
public static boolean isPalindrome(int number)

Use the reverse method to implement isPalindrome . A number is a palin- drome 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.