A skeleton version of the programs will appear when you run update21 in a terminal window. The program handin21 will only submit files in this directory.

You may work with a partner on this assignment. If you work with a partner, put your name and the name of your partner in the list of authors at the top of your program. Only one partner should run handin21 to submit the files for the group. Both partners will receive the same grade.

A palindrome is a sentence that contains the same sequence of letters reading it either forwards or backwards. A classic example is: "Able was I, ere I saw Elba." Another example is: "A man, a plan, a canal, Panama!"

In the file palindrome.py, write a recursive function called isPalindrome that returns True when a given string is a palindrome, and otherwise returns False. The basic idea is to check that the first and the last letters of the string are the same letter. If they are, then the entire string is potentially a palindrome, as long as everything between those letters is also a palindrome. There are a couple of special cases to check for. If either the first or last character of the string is not a letter, you can ignore that letter and check to see if the rest of the string is a palindrome. Also, when you compare letters, make sure that they are all the same case. The ideal solution will not require any additional helper functions other than the python string methods isalpha and lower.

Use your function in a main program that repeatedly prompts the user for a phrase and then reports whether or not it is a palindrome, as shown here:

This program will test if a series of phrases are palindromes.

Enter a phrase or 'quit' to end: wow
This is a palindrome!

Enter a phrase or 'quit' to end: mom
This is a palindrome!

Enter a phrase or 'quit' to end: wow mom
Sorry, this is not a palindrome.

Enter a phrase or 'quit' to end: wow, mom wow
This is a palindrome!

Enter a phrase or 'quit' to end: Able was I, ere I saw Elba.
This is a palindrome!

Enter a phrase or 'quit' to end: A man, a plan, a canal, panama.
This is a palindrome!

Enter a phrase or 'quit' to end: quit

Can you think of any other interesting palindromes? If so, add them as comments in your program.

In the file recursion.py, complete each of the following functions. You will write two versions of each function, one that is an iterative solution and one that is a recursive solution.

You should not use any of the list class methods (such as append, insert, remove, etc). You should only need to use slicing and concatenation.

• Write an iterative function called maximumIter that takes a list of numbers and returns the number in the list with the highest value. You may use the function max2, which is included in the file, as a helper. Write a recursive version of this function called maximumRecur.
  
  Below are some test cases for the functions you will write. You should add some more test cases. They need not be exhaustive, but they should check more than just a few basic test cases. In subsequent questions, you will write most or all of the test cases yourself. You should put your tests in a separate function called test which is started below. The assert statement checks to be sure that the statement is true, and if not, raises an AssertionError.

def test():
    """
    Tests the functions in this program.  Be sure to verify that the
    answer your are expecting is the answer you get by using the
    assert statement.  
    """
    result = maximumIter([9, 5, 3, 7])
    assert result == 9

    result = maximumIter([3, 5, 9, 7])
    assert result == 9

    result = maximumRecur([9, 5, 3, 7])
    assert result == 9

    result = maximumRecur([3, 5, 9, 7])
    assert result == 9

• Write an iterative function called isSortedIter that tests if a list is in ascending sorted order. If so it returns True, otherwise it returns False. Write a recursive version of this function called isSortedRecur.
• Write an iterative function called multiplyListIter that takes a list of numbers and returns the product of those numbers. If the list is empty it should return 0. If the list contains only one number, then the product should be that number. Write a recursive version of this function called multiplyListRecur.
• Write an iterative function called addOneIter that takes a list of numbers and returns a new list of numbers where each of the original numbers have been incremented by one. Write a recursive version of this function called addOneRecur.

Once you are satisfied with your programs, hand them in by typing handin21 in a terminal window.