Question

The Abo series is the following: 0, 1, 2, 4, 3, 6, 5, 5, 4, 8, 7, 7, 6, 7, 6, 6, 5, 10... This series is defined in the following manner:

• Abo(n) = 0 for n <= 0
• Abo(1) = 1
• Abo(n) = 1 + Abo(n/2) if n > 1 is even
• Abo(n) = 2 + Abo((n+1)/2) if n > 1 is odd

Write a recursive method that computes Abo(n). Write a program that prints the first 20 Abo numbers: Abo(0), Abo(1), Abo(2), ..., Abo(19).

Try to write an iterative method that computes Abo(n). Explain why this algorithm is difficult to design. Write your answer in AnswersLab10.

Language is java btw

Answer 1

The recursive code for the given problem will be in Java as follows for ABo number for first 20 numbers:-

1. class Abo{  
2. static int abc(int n){    
3.   if (n <= 0)    
4.     return 0;   
5. if(n==1)
6. return 1;
7. else
8. {
   1. if(n%2==0)
      1. return(1+abc(n/2));
   2. else
      1. return(2+abc((n+1)/2)
9. }   
10. }    
11. public static void main(String args[ ])
12. {  
13.   int i,ab=1;  
14.   int number=20;//It is the number to calculate Abo number(given)    
15. for(i=0;i<number;i++)
16. {
17. ab = Abo(i);
18.   System.out.println("Abo( "+i+")"+ab);    
19. }  
20. }
21. }  

The iterative method for computing Abo series will be as follows:-

1. class IterAbo{  
2. public static void main(String args[ ]){  
3.   int i,ab=1;  
4.   int number=20;//It is the number to calculate abo (given)
5. if (number <= 0)    
6. return 0;
7. if(number ==1)
8. return 1;
9.   for(i=1;i<=number;i++){    
   1. if(i%2==0)
      1. System.out.println(ab=1+((i/2)+(i%2))); //
   2. else
      1. System.out.println(ab=2+((i+1)/2)); //
10.   }    
11. }  
12. }  
13. This above program is very difficult to design and this solution can be wrong also. But this solution will give you a basic idea about the correct solution.