Exercise 1: Write a static method that computes 1*2*3*...*n = n! by using recursion. Here is a template for the exercise:

import java.io.*;

class Factorial {
   public static void main(String[] args) {
      // get integer value of n as a command line parameter
      int n = (args.length==0)?20:Integer.parseInt(args[0]);
      System.out.println(n+"!="+factorial(n));
      return;
   }
	
   public static long factorial(int n) {
      // code the body of this method
      return 0L;  // a stub
   }
}
	

Exercise 2: Here's an exercise illustrating a situation where recursion is not efficient: the computation of Fibonacci numbers. The Fibonacci sequence is a sequence of integers whose first two elements are 0 and 1, and whose subsequent elements are found by adding the two previous terms. That is, f_n=f_n-1+f_n-2 for n > 1 with the starting values f₀=0 and f₁=1.. This infinite sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
Implement a method FibonacciByRecursion(int n) that uses recursion to compute the n-th Fibonacci number. A main routine that calls your method and a method that does the same computation iteratively are provided below. You should detect a dramatic difference in the speeds of these two computations.

import java.io.*;

public class Fibonacci {

   public static void main (String argv[]) {
 
      System.out.println("First 12 Fibonacci numbers computed using iteration:");
      for (int i=0; i<12; i++) { 
         System.out.print(FibonacciByIteration(i)+", ");
      } 
      System.out.println();
 
      System.out.println("First 12 Fibonacci numbers computed using recursion:");
      for (int i=0; i<12; i++) { 
         System.out.print(FibonacciByRecursion(i)+", ");
      }
      System.out.println();
 
      System.out.println("The 39th Fibonacci number is "+FibonacciByIteration(39));
      System.out.println("The 40th Fibonacci number is "+FibonacciByRecursion(40));
      System.out.println("The 41st Fibonacci number is "+FibonacciByIteration(41));
      System.out.println("The 42nd Fibonacci number is "+FibonacciByRecursion(42));
   } 

      
   public static long FibonacciByIteration(int n) {    // compute nth Fibonacci number using iteration
      long fnMinus2=0;
      long fnMinus1=1;
      long fn=0;
      if(n==0) {
         fn=0;
      }
      else if (n==1) {
         fn = 1;
      }
      else {
         int i=1;  // so far, we've only computed as far as f1
         while (i < n) {  // exit when i=n
            // compute next term
            fn = fnMinus1 + fnMinus2;
            i++;
            // update terms to add to get the next value in the sequence
            fnMinus2 = fnMinus1;
            fnMinus1 = fn;
         }
      }
      return fn;
   }
  
   public static long FibonacciByRecursion(int n) {     // compute nth Fibonacci number using recursion
      return 0L;  // a stub
   }

}