Question

Give a recursive implementation of sumNumbers. A method signature is given below.

//TODO: implement recursive sum implementation.  

public class RecursiveSum {

      public static int sumNumbers(int n) {

Would you consider the fantastic four approach helpful? Why or why not? Could you apply this method to any recursive problem? 

Answer 1

The recursive implementation of sumNumbers using the method given in the question is as follows:

public class RecursiveSum

{

      public static int sumNumbers(int n)

     {

            if (n == 1)

                return 1

            else

                return n + sumNumbers(n-1)

       }

}

The fantastic four approach is helpful in writing the above recursive problem as the fantastic four approach consists of the following steps:

1. Formulation of size-n problem: The size-n problem is computed as follows:

static int sumNumbers(int n)

In the above declaration, the size n is given as parameter and the return type of the function is given as int. The return value of the problem is the value that is required to be computed by the function.

2. Base condition: The base condition is also known as the stopping condition. If the base condition is true, the function returns the value and exits. If the base condition is not true, the function call itself.

In the above function, the base condition is:

if (n ==1)

       return 1

3. Formulating the size-m problem: The size m problem can be formulated by replacing n by m. If the size of the problem is reduced by 1, m is n-1, so size-(n-1) problem is formulated. The return value of size-(n-1) sumNumbers is sumNumbers(n-1).
4. Construction of size-n problem: Finally, the solution for size-m or size-(n-1) problem is constructed. So, the solution of the above problem is n + sumNumbers(n-1)

The fantastic four approach can also be used to solve the problem of finding factorial of a number through recursive approach.