x0 = 1 xy = x*xy-1 for all y > 1File Power.java contains a main program that reads in integers base and exp and calls method power to compute baseexp. Fill in the code for power to make it a recursive method to do the power computation.
fib(0) = 0 fib(1) = 1 fib(n) = fib(n-1) + fib(n-2) n>1For example, the first eight elements of the sequence are 0,1,1,2,3,5,8,13.
Because the Fibonacci sequence is defined recursively, it is natural to write a recursive method to determine the nth number in the sequence. File Fib.java contains the skeleton for a program that reads an integer n from and computes and prints the nth Fibonacci number. Save this file to your directory. Following the specification above, fill in the code for method fib so that it recursively computes and returns the nth number in the sequence.
If s contains any characters (i.e., is not the empty string)
File Backwards.java contains a program that prompts the user for a string, then calls method printBackwards to print the string backwards. Save this file to your directory and fill in the code for printBackwards using the recursive strategy outlined above. Recall that for a String s in Java,
Write a program that prompts for and reads in a string, then prints a message saying whether it is a palindrome. Your main method should read the string and call a recursive (static) method palindrome that takes a string and returns true if the string is a palindrome, false otherwise.
Here is an example for converting 3010 to base 4:
quotient remainder -------- --------- 30/4 = 7 2 7/4 = 1 3 1/4 = 0 1The answer is read bottom to top in the remainder column, so 3010 = 1324.
Think about how this is recursive in nature: If you want to convert x (30 in our example) to base b (4 in our example), the rightmost digit is the remainder x % b. To get the rest of the digits, you perform the same process on what is left; that is, you convert the quotient x / b to base b. If x / b is 0, there is no rest; x is a single base b digit and that digit is x % b (which also is just x).
The file BaseConversion.java contains the shell of a method convert to do the base conversion and a main method to test the conversion. Note that the convert method returns a string representing the base b number. This means that in the base case, when the remainder is what is to be returned, it must be converted to a String object by concatenating it with a null string. Similarly, in the recursive case the result of the recursive call will be concatenated with the remainder.
Fill in the code for convert and the call in the main method. Here is some data to test your program on: