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Practice Recursion
1. Implement a recursive method palindrome that takes a string as a parameter and returns true if the
string is a palindrome and false otherwise.
2. Implement a recursive method fib that takes an integer num as a parameter and returns the nth Fibonacci
number. Fib sequence is 1, 2, 3, 5, 8, 13, …
3. Implement a recursive method reversal that takes an integer num as a parameter and prints its digits in
reverse order on one line. Try to see if you can also print it one digit per line.
4. Implement a recursive method mult that takes two integer parameters, x and y and returns their product.
(note: remember that multiplication is really multiple additions)
5. Implement a recursive method repete that takes as parameters a String s and an integer i and returns a
String that has s repeated i times. For example, if the given string is "CS113" and the integer is 3 then
the return value would be "CS113 CS113 CS113 ".
Note that if the integer is 0, then the empty string "" should be returned.
6. Write a recursive method chain (that takes an integer parameter x. The method prints x asterisks,
followed by x exclamation points. If x = 5 we get as output: *****!!!!!
7. Write a method show with one positive int parameter called n. The method will write 2 n-1 integers.
Here are the patterns of output for various values of n:
n=1: Output is: 1
n=2: Output is: 1 2 1
n=3: Output is: 1 2 1 3 1 2 1
n=4: Output is: 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
And so on. Note that the output for n always consists of the output for n-1, followed by n itself, followed
by a second copy of the output for n-1
8. Write a recursive method converts that takes a decimal integer and a base integer as parameters. It
converts the decimal format into the new base representation. Example: if the decimal is 28 and the base
is 2 the output would be: 1 1 1 0 0 (the binary equivalent)
Try problems 4, 5, and 3 first. Then do any of the others.