Question

Using java programming.

Question 1. Write a recursive function fibo(n) that returns the nth Fibonacci number which is defined as follows:

fibo(0) = 0 fibo(1) = 1 fibo(n) = fibo(n-1) + fibo(n-2) for n >= 2

Question 2. Write a recursive function that calculates the sum of quintics: 1power of5 + 2power of5 + 3power of5 + … + n5

Question 3. Write a program to find a route from one given position to another given position for the knight that takes a given number of moves. It works as in the following examples:

Example 1: Enter the start position: d2

Enter the end position: b8

Enter number of moves: 2

No route found.

Example 2: Enter the start position: d2

Enter the end position: b8

Enter number of moves: 4

Route found: d2, c4, b6, d7, b8.

Answer 1

1.

int fibo(int n)
   {
       if(n==0)
       return 0;
       if(n==1)
       return 1;
       else
       {
           return fibo(n-1)+fibo(n-2);
       }
   }

1 2 3 import java.io.BufferedReader; import java.io.*; class fibonacci in public static void main (String[] args) throws IOException BufferedReader x=new BufferedReader(new InputStreamReader(System.in)); System.out.println("enter the index of fibonnaci number:"); int n=Integer.parseInt(x.readLine()); fibonacci a=new fibonacci; System.out.println(n+"th fibonacci number is:"+a.fibo(n)); 11 static int fibo(int n) 14- if(n==0) return 0; if(n==1) return 1; else return fibo(n-1)+fibo(n-2); 22 23 24 } input Output 5

1 2 3 import java.io.BufferedReader; import java.io.*; class fibonacci in public static void main (String[] args) throws IOException BufferedReader x=new BufferedReader(new InputStreamReader(System.in)); System.out.println("enter the index of fibonnaci number:"); int n=Integer.parseInt(x.readLine()); fibonacci a=new fibonacci; System.out.println(n+"th fibonacci number is:"+a.fibo(n)); 11 static int fibo(int n) 14- if(n==0) return 0; if(n==1) return 1; else return fibo(n-1)+fibo(n-2); 22 23 24 } input Output Success #stdin #stdout 0.15s 36200KB enter the index of fibonnaci number: 5th fibonacci number is:5