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1) The greatest common divisor of integers x and y is the largest integer that e

ID: 3573372 • Letter: 1

Question

1) The greatest common divisor of integers x and y is the largest integer that evenly divides both x and y. Write a recursive function gcd that returns the greatest common divisor of x and y. The gcd of x and y is defined recursively as follows. If y is 0 the answer is x; otherwise gcd(x, y) is gcd(y, x%y). 2) Write a recursive program that finds out if n is a Fibonacci number or not. The Fibonacci numbers are 0 1 1 2 3 5 8 13 21 … Your program should have the following interface: Enter a number (enter a negative number to quit): 14 !!!!! Sorry14 is not a Fibonacci number Enter a number (enter a negative number to quit): 13 Yes, you got it, 13 is a Fibonacci number Enter a number (enter a negative number to quit): 22 !!!!! Sorry 22 is not a Fibonacci number Enter a number (enter a negative number to quit): 23 !!!!! Sorry 23 is not a Fibonacci number Enter a number (enter a negative number to quit): 21 Yes, you got it, 21 is a Fibonacci number Enter a number (enter a negative number to quit): -1 (*Thanks – Have a good Day*)

Explanation / Answer

Q1)import java.util.*;
public class gcd {
   public static void main(String[] args) {
       // TODO Auto-generated method stub
       Scanner sc=new Scanner(System.in);
       System.out.println("enter fistvalue:");
       int first=sc.nextInt();
       System.out.println("enter second:");
       int second=sc.nextInt();
      
gcd g=new gcd();
System.out.println(g.gcd1(first, second));
   }
public int   gcd1(int first,int second){
       int first1=first;
       int second1=second;
       if(second1==0)
           return first1;
       else if(second1>first1)
           return gcd1(second1,first1);
       else
           return gcd1(second1,first1%second1);
      
          
   }
}

output:

enter fistvalue:
81
enter second:
153
9

2Q0)

import java.util.*;
public class fibnoic_number {
   public static void main(String[] args) {
       Scanner sc=new Scanner(System.in);
       while(true){
       System.out.println("enter a number to check it is febnoic or not:");
       System.out.println("febnoic numbers are 0 1 1 2 3 5 8 13 21 ");
       System.out.println("enter negitive number to quit:");
       int n=sc.nextInt();
       if(n<0)
           System.exit(0);
      
       else {
           int val=fibnocy(n);
           System.out.println(val+" ");
           if(n==0||n==1||n==2||n==3||n==5||n==8||n==13||n==21)
               System.out.println("yes you got is "+n+" is fibnoci");
           else
               System.out.println("sorry"+n +"is not febonic");
          
       }
       }
   }
   public static int fibnocy(int n){
       if(n == 1 || n == 2){
           return 1;
           }
       return fibnocy(n-1) + fibnocy(n -2);
       }
  

  

}

enter a number to check it is febnoic or not:
febnoic numbers are 0 1 1 2 3 5 8 13 21
enter negitive number to quit:
5
5
yes you got is 5 is fibnoci
enter a number to check it is febnoic or not:
febnoic numbers are 0 1 1 2 3 5 8 13 21
enter negitive number to quit:
13
233
yes you got is 13 is fibnoci
enter a number to check it is febnoic or not:
febnoic numbers are 0 1 1 2 3 5 8 13 21
enter negitive number to quit:
21
10946
yes you got is 21 is fibnoci
enter a number to check it is febnoic or not:
febnoic numbers are 0 1 1 2 3 5 8 13 21
enter negitive number to quit:
34
5702887
sorry34is not febonic
enter a number to check it is febnoic or not:
febnoic numbers are 0 1 1 2 3 5 8 13 21
enter negitive number to quit: