/*
  Author  : Michael Robinson
  Program : recursion.java
  Purpose : To implement recursion functions
            In this example we want to find the factorial of 7
            The mathematical representation is 7! = 5040 
            which means  7 * 6 * 5 * 4 * 3 * 2 * 1
            
            We can find the factorial of any number by passing its
            value to the method factorial( int n ) 
 
            7! = 7*6! = 7*720 = 5040
            6! = 6*5! = 6*120 =  720
            5! = 5*4! = 5*24  =  120  
            4! = 4*3! = 4*6   =   24 
            3! = 3*2! = 3*2   =    6  
            2! = 2*1! = 2*1   =    2
            1! = 1    = 1     =    1  //base case
             
            note 0! = 1 always
           
  Updated : January 13, 2099
*/


class recursion
{
    public static long factorial( int n )
    {
        System.out.printf( "Processing factorial( %d )\n\n",  n );
       
        if( n <= 1 ) //base case
        {
            System.out.printf( "Reached base case, returning %d\n\n", n);
              
            System.out.printf( "Now returning the accumulated " + 
                               "values from RAM\n" );    	 
            return 1; 
        }
        else
        {
            System.out.printf( "Doing recursion by calling" + 
                               "factorial( %d-1 )\n",  n );
            
            //doing recursion by calling factorial(n - 1)
            long counter = n * factorial(n - 1); 
            
            System.out.printf( "Receiving results of " +
                               "factorial( %d ) =  %d * %d! =" +
                               " %d\n",  n, n, (n-1), counter );
                    
            return counter;
        }
             
    }//end public static long fact(long n)
                   
        	
    public static void main(String args[])
    {
        System.out.println( "\nRecursion Program" );	
        System.out.println( "=================" );	
        
        System.out.println( "\nThe factorial of 7 = " + 
                            factorial( 7 ) );
    }//end public static void main(String args[])
    
}//end class recursion