**Background**

We have discussed, in detail, the function of Stacks and Queues and how they are specifically implemented in Python. To get a better understanding of the utility of these data structures, we will be creating functions which use the data structures and comparing the functionality of each.

Other Resources

String object documentation in Python 3.

**Palindromes**

A palindrome is a string of characters that is the same both forwards and backwards. A full and robust definition of what a palindrome is can be found on Wikipedia. Colloquially, however, a palindrome is considered to be any string of data that is the same both forwards and backwards after all spaces and punctuation has been removed and capitalization is normalized. Consider, for example, the title of the 1971 book by David McCullough about the construction of the Panama Canal:

A Man, A Plan, A Canal: Panama!

This title is (hopefully obviously) not a palindrome if punctuation is left in as there is no exclamation point at the beginning of the sentence. However, with the punctuation and spaces removed and capitalization normalized, the title becomes:

AMANAPLANACANALPANAMA

The central C has been bolded and turned red to give you a point to focus on.

1. Download the files array_stack.py, exceptions.py, and palindrome.py. from this Moodle page. Use (and do not alter) the ArrayStack object in array_stack.py to implement the is_palindrome_stack function declared in palindrome.py. As mentioned in the associated comment, this function should take a string and use an ArrayStack in a non-trivial way in order to determine if the string, without spaces, without punctuation, and with normalized capitalization, is a palindrome. It should return True if it is a palindrome and False if it is not.

2. Download the file array_queue.py from this Moodle page. Use (and do not alter) the ArrayQueue object in array_queue.py to implement the is_palindrome_queue function declared in palindrome.py. As mentioned in the associated comment, this function should take a string and use an ArrayQueue in a non-trivial way in order to determine if the string, without spaces, without punctuation, and with normalized capitalization, is a palindrome. It should return True if it is a palindrome and False if it is not.

3. Examine both function implementations. Which of these functions is more efficient and why? (Note: You may use Big-O notation as part of your evidence but, even if you determine that they have the same Big-O functionality, you should be able to determine which of the two functions is nominally more efficient.)

**Postfix Notation**

Postfix notation, also sometimes called Reverse Polish Notation or RPN, is a type of mathematical notation that, by its very structure, is unambiguous without the need for parentheses for grouping. This notation was made famous by Hewlett Packard during the 1970’s and 1980’s when all handheld and desktop calculators (yes, such a thing used to exist) implemented postfix notation as their exclusive input method.

The algorithm for implementing postfix notation is fairly simple and famous:

//I) For each token in the expression

//A) If the token is a number

//1) Push the token on the stack

//B) Else, if the token is an operator

//1) Pop 2 tokens off the stack

//2) Perform the operation on those 2 tokens (second operator first)

//3) Push the resulting token back onto the stack

//II) Return the 1 token remaining on the stack

The above algorithm does not account for any errors that you could encounter in the processing of your string. These include unidentifiable tokens (such as alphabetical or non-mathematical operator characters), encountering a operator too soon (without two tokens on the stack) or having too many tokens.

Below are some examples of postfix notation and the resulting value:

3 4 + 7

5 6 + 3 * 33

5 + 6 * 3ERROR!

1 2 + 4 – 8 * -8

PassERROR!

3 4 + 5ERROR!

4. Download the file postfix.py from this Moodle page. Use (and do not alter) the ArrayStack object in array_stack.py to implement the postfix_calculator function declared in postfix.py. As mentioned in the associated comment, this function should take a string and use an ArrayStack to implement the postfix notation algorithm implemented above. If your implementation encounters any problems during execution, it should throw the RPNError declared and defined in postfix.py.

**Lab Requirements**

Download and alter palindrome.py and postfix.py as described above. You may add any additional helper methods as needed. Helper functions should be named with an underscore at the front as they are not designed to be publicly accessible If you add a helper function, be sure to comment it in the same style as the other, included functions.

Additionally, the “testing structure” of if __name__ == ‘__main__’ has been included at the bottom of each file. You should use that section for your test code. I may look at it for understanding of how you are approaching testing but you will not be explicitly graded on code included there.

Remember: These requirements may not be all encompassing. Use your brain, your knowledge of the system, and any descriptions within the code as sanity checks and reminders to make a complete system.

This assignment has been answered **3 times** in private sessions.

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