Question

Recursion Intro Assignment. YOU HAVE TO DO IT USING "HELPER METHOD" AND NO IMPORTS ARE ALLOWED. You may not use for or while. Any looping must be accomplished using recursion. You may not declare static or non-static member fields – only local or parameter variables allowed. Thanks!

Implement the method public static int fibby (int n). fibby is mathematically defined for nonnegative values in the following way: fibby(0)1 fibby(n) - fibby(ln/4]) fibby(13n/4]) where n > 0 and x means the floor of x (round down) HINT: recall Java's integer division behavior. Table of examples: 4 7 10 20 100 Part 2b. Sparse table generation (20 pts) Notice that for many values i, fibby(i) - fibby(i+1). Implement the method public static void printsparsetable(int start, int end). Output using System.out.println all consecutive values of n and fibby(n) (just the two numeric values separated by a space) where n 2 start andn s end However, skip a line of output if the previous row printed has the same fibby value

Answer 1

//This method returns the value fibby(n) for n >= 0 using recursion

//It returns -1 for n < 0

public static int fibby(int n)

{

       //Return -1 if n is negative

       if(n < 0)

             return -1;

       //Return 1 for fibby(0)

       if(n == 0)

             return 1;

       //Otherwise return fibby(n / 4) + fibby(3n / 4) with

       //floor values of n / 4 and 3n / 4

       return fibby((int)(n / 4)) + fibby((int)(3 * n / 4));

}

//This method is a helper method for printsparsetable() method

//It prints the pairs n, fibby(n) which are unique except the very first pair

//from start to end

//Example, it prints 6, 8; 8, 11 for printsparsetable(5, 10)

//5, 6 is printed by printsparsetable()

public static void printremainingsparsetable(int start, int end)

{

       //Stop the recursion if start crossed end

       if(start <= end)

       {

             //Print the n, fibby(n) pair if fibby(n) == fibby(n - 1)

             if(fibby(start) != fibby(start - 1))

                    System.out.println(start + " " + fibby(start));

             //Again call printremainingsparsetable() for range start + 1 to end

             printremainingsparsetable(start + 1, end);

       }

}

//This method prints the first n, fibby(n) pair

//and then calls printremainingsparsetable() for range start + 1 to end

//Example, it prints 5, 6 for printsparsetable(5, 10)

public static void printsparsetable(int start, int end)

{

       //Proceed only if start and end values are valid

       if(start <= end)

       {

             //Print the first pair

             System.out.println(start + " " + fibby(start));

             //Call printremainingsparsetable() for the remaining pairs

             printremainingsparsetable(start + 1, end);

       }

}

The ouputs of the sample data given in the question are verified and the functions are functioning without any errors.

public static void main(String[] args)

{

       for(int i = 1; i <= 10; i++)

             System.out.println(i + " " + fibby(i));

       System.out.println("20 " + fibby(20));

       System.out.println("100 " + fibby(100));

}

Output:

1 2
2 3
3 4
4 6
5 6
6 8
7 8
8 11
9 11
10 11
20 24
100 111

public static void main(String[] args)

{

       printsparsetable(5, 10);

}

Output:

5 6
6 8
8 11

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