Question

1. In Java a function can call itself(we may explore more about this later in the course).  This is called a “recursive function”. In order for this to work there must be a situation where the function finally stopscalling itself and simply returns a value (or just returns). We can use a Java ifstatement to make a recursive function return as required to make it work properly. This special case where the function finally returns is called the recursive function base case.
   
   Here is a simple example: a function to calculate the factorial of an integer number
   n>= 1. Remember that the factorial of n, n!, is n•(n-1)•(n-2)•…•1 if nis greater than or equal to 1. Factorial’s base caseoccurswhen n is 1èthe function should then return1; otherwise the function returns n•(n-1)!àby definition, n! isn•(n-1)! if n> 1.
   
   Here’s a Java recursive factorial function implementation, assuming nis at least 1:
   
      public static long factorial(int n)

   // header line: long return value since factorials grow rapidly!
   {
        if (n == 1) // this tests to see if nis 1, the base case
             return 1; // if so, the function returns 1
         
        return n*factorial(n-1); // assumes n >= 1

        // otherwise a recursive call – factorial calls itself!
        // this second returnexecutes if the ifcondition is false
   }

Your job for this part of the Lab is to create and testa similar recursive function that calculates and returns an integer power pof some integer number n; nand pare the parameters to the function, with header line staticlong power(int n, int p). You can assume that pis at least 0.Modify the above factorial function as follows:

Update the headerline for the function as above and then make these changes:

The base caseforthe powerfunction occurs when pis 0, at which point the function returns the value 1(by definition, any number raised to the 0 power is 1). To test for 0, the base case, replace the ifcondition with this one: if (p == 0).  

If pis not0 then the function should return n*power(n, p-1)àn^pisn•n^(p-1)
if pis greater than 0. Use that information to change the second returnstatement.  

Now test to make sure powerworks by having maincall it with some known values and print out the results. For example, power(3, 2) should return 3²=9,
power(-2, 7) should return (-2)⁷=-128, and power(8, 0) should return 1.

Derive Power.java from Factorial.java, and modify mainto test power.

Answer 1

If you have any doubts, please give me comment...

public class Power {

    public static long power(int n, int p) {

        if (p == 0)

            return 1;

        else

            return n * power(n, p - 1);

    }

    public static void main(String[] args) {

        System.out.println("power(3,2) = "+power(3, 2));

        System.out.println("power(-2,7) = "+power(-2, 7));

        System.out.println("power(8,0) = "+power(8, 0));

    }

}