Question

Exercise 2 - More iterative vs. recursive methods .

1. Create a new class called Abo.java.
2. Consider a mathematical series, Abo, defined as:
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
3. In the Abo class, create a method called rabo(int n) that uses recursion to calculate the value of Abo(n) for a given integer n.
4. Add a main() method and print out the first 20 Abo numbers in the series, i.e. Abo(0) through Abo(19). Note: the results should be: 0, 1, 2, 4, 3, 6, 5, 5, 4, 8, 7, 7, 6, 7, 6, 6, 5, 10, 9, 9
5. Create a method called i abo(int n) and try to calculate the series iteratively.
6. It is not impossible to do, but it is much more complex than the recursive method. Why is this algorithm difficult to design using the iterative approach?

Answer 1

The algorithm is difficult to design using the iterative approach because it requires keeping track of multiple variables and conditions.

Step-by-step explanation:

This algorithm is difficult to design using the iterative approach because it requires keeping track of multiple variables and conditions. With recursion, we can break down the problem into smaller subproblems and solve them easily.

For example, when calculating Abo(n/2), we can simply call the Abo() method again with n/2 as the argument. However, with iteration, we need to manually keep track of the values and conditions, which can make the code more complex and error-prone.