Question

Write a recursive methodcalledpermutationthataccepts two integersnandras parameters and returns the number of unique permutations ofritems from a group ofnitems. For given values ofnandr, this valuepermutation(n,r)can be computed as follows:

permutation(n,r)= n!/ (n-r)!

hint: permutation(6, 4)should return360. It may be helpful to note thatpermut(5, 3)returns60, or 360/6.

Answer 1

The recursive function to find permutation can be defined as follows:

int permutation(int n, int r)
{
    if(r == 1) 
           return n; //stops recursion
    return n*permutation(n-1, r-1);//recursive call
}

The required program and the corresponding output are as follows:

import java.io.*;
import java.lang.*;

class Testing{  
   
        static int permutation(int n, int r)
        {
                if(r == 1) 
                   return n; //stops recursion
                return n*permutation(n-1, r-1);//recursive call
        }    
  
    public static void main(String args[]){  
         
                int nv,rv,p; 
                try{
                DataInputStream dis = new DataInputStream(System.in);
                System.out.println("Enter value for n : ");
                nv=Integer.parseInt(dis.readLine());//reading n value
                System.out.println("Enter value for r : ");
                rv=Integer.parseInt(dis.readLine());//reading r value
                p=permutation(nv,rv);//function call
                System.out.println("Nunber of unique permutations : " +p);
        }
     catch(Exception e){        System.out.println("Error : " +e);      }
  
   }  
}

Output: