CSCI 150 HW: recursion

To receive full credit, for each exercise you should do the following:

1. Design: First, write a Python function as requested in the exercise.

2. Check: Run the provided test code. Does your actual output agree with the given correct output?

3. Evaluate: If the actual output does not match the expected output, keep experimenting, consult the textbook or Python documentation, ask a friend or TA or professor, etc. until you can fix your class definition and explain what your misunderstanding(s) were. (You do not need to do anything for step 3 if the outputs already agree exactly.)

You should consider the code in each exercise separately from the other exercises.

1. Consider the function logarithm(b,n) given below, which counts how many times n has to be divided by b before falling below b:

    def logarithm(b: float, n: float) -> int:
        count = 0
        while n >= b:
            count += 1
            n /= b
        return count
   

   Write a new version of logarithm which uses recursion instead of a while loop.

   To test your function, you can type in the following tests:

    def main():
        print(logarithm(2, 128) == 7)
        print(logarithm(2, 35)  == 5)
        print(logarithm(5, 125) == 3)
        print(logarithm(2, 1)   == 0)
        print(logarithm(2, 3)   == 1)
        print(logarithm(10, 19740983) == 7)
   

   If you have implemented logarithm correctly, main() should print True six times.

2. Write a recursive function is_palindrome which takes a string as a parameter and returns a boolean indicating whether the string is a palindrome (a palindrome is a string which is equal to its reversal).

   You can test your function with this main2(), which should print all True:

    def main2():
        print(is_palindrome('kayak'))
        print(is_palindrome('kayyak'))
        print(is_palindrome(''))
        print(is_palindrome('a'))
        print(is_palindrome('aa'))
        print(not is_palindrome('ab'))
        print(not is_palindrome('bbbbbbcbbb'))
        print(not is_palindrome('myhelicopterisfullofeels'))
        print(is_palindrome('amanaplanacanalpanama'))