[20 Marks] You just won the lottery – but the prize is paid in a very peculiar w

Question

[20 Marks] You just won the lottery – but the prize is paid in a very peculiar way. For the first week, you will receive one cent. For week 2, you will receive 2 cents; 4 cents for week 3; 8 cents for week 4 – and the amount received keeps doubling every week until the end of the year. So at the end of week one, you will have been paid 1 cent; at the end of week two, 3cents(2+1cents);attheendofweekthree,thetotalwillbe7cents(4+3+1)andsoon. Write a program that implements two recursive methods: one that given the week number, it will report the amount to be received for that week (i.e. week 10 pays $5.12); and second method that reports the total amount received to date given the week number (i.e. by the end of week 8, $2.55 has received in total). The program should repeatedly ask the user to indicate the number of weeks and report the results of the two recursive methods. If the user enters 0 weeks, the program will terminate.

Explanation / Answer

/**The java program that prompts user to enter number
* of weeks and display the amount paid for each week
* and display total amount in dollars at end of weeks*/
//Lottery.java
import java.util.Scanner;
public class Lottery
{
   public static void main(String[] args)
   {
       int sentinal=0;
       double amount=0;
       //Scanner object to read input
       Scanner keyboard=new Scanner(System.in);
       System.out.println("Enter number of weeks : ");
      
       //read number of weeks
       int weeks=keyboard.nextInt();
       //continue loop until user enter 0 to stop
       while(weeks!=sentinal)
       {
          
           System.out.println("Lotter payment system ");
           System.out.printf("%-10s%-10s ","Week","Payment(in cents)");
           for (int index = 0; index < weeks; index++)
           {
               //call method1 to find the amount in cents for weeks
               amount=method1(index);          
               System.out.printf("%-10d%-10.2f ",(index+1),amount);                                          
           }
          
           //call method2 find total amount paid in total dollars
           amount=method2(weeks);
           System.out.println("By the end of week "+weeks+", $"+amount/100 +" has received in total.");
           //reset amount to zero
           amount=0;
          
           System.out.println("Enter number of weeks : ");
           //prompt for next value
           weeks=keyboard.nextInt();
       }

   }

  
  
   /**The method method2 takes the number of weeks and
   *calls the method1 to find the number of cents
   *for the week paid and adds the total cents added to the
   *pay*/
   private static double method2(int weeks)
   {
       double pay=0;

       for (int week = 0; week < weeks; week++)
       {
           pay+=method1(week);
       }

       return pay;

   }

   /**The method1 that takes the weeks and returns the number of cents
   * paid in that week*/
   private static double method1(int weeks)
   {      
       if(weeks==0)
           return 1;      
       else
           return 2*method1(weeks-1);

   }
}

--------------------------------------------------------------------------------------------------------------------------------

Sample Output:

Enter number of weeks :
8
Lotter payment system
Week      Payment(in cents)
1         1.00    
2         2.00    
3         4.00    
4         8.00    
5         16.00   
6         32.00   
7         64.00   
8         128.00  
By the end of week 8, $2.55 has received in total.
Enter number of weeks :
10
Lotter payment system
Week      Payment(in cents)
1         1.00    
2         2.00    
3         4.00    
4         8.00    
5         16.00   
6         32.00   
7         64.00   
8         128.00  
9         256.00  
10        512.00  
By the end of week 10, $10.23 has received in total.
Enter number of weeks :
0

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.