Lab 4

Programming exercises.

1. A Caesar Cipher is a way of sending secret messages. It uses an integer between 1 and 26 as a key. Each letter in a message is moved forward by that many letters (with letters at the end of the alphabet going to the start). For example, if the word is "yellow" and the key 3 then the message becomes "bhoorz". Write a script which when run first asks the user for an integer between 1 and 26 (the key). It should allow the user to either encode a message or decode a message. It should allow the user to try unlimited messages until they type exit.

   Modify "cgilogon.py" in Lab 2 to make use of the Cipher function in checking user password.

2. In Python we calculate powers using the symbol **. In this question we consider how the Python interpretor may have implemented this: do not use ** in your solution. The mathematical definition of taking a power is n^p = n*n^{p - 1} for positive integer p. Use this to create a recursive function power(n,p) which calculates n^p.

3. A palindrome is a word (or any other sequence of symbols) which reads the same forward and backward, for example ada,abba,level, etc. Write a recursive function isPalindrome(S) which returns a Boolean determining whether the string S is a palindrome. You should make use of argument in main() to test your function.

4. A Sierpinski Triangle of order 0 is just an equilateral triangle (all sides the same length). An order 1 Sierpinski Triangle is created by 3 smaller triangles coming together so their edges form the single larger one. An order 2 Sierpinski Triangle repeats this process within the 3 smaller triangles. Examples of level 1, 3, and 5 Sierpinski Triangle are shown below.

   Level	Output
   1
   3
   5

   Write Python code to draw the Sierpinski Triangle for a specified order.

5. Add Point class to the shape package in Lab1 tutorial folder, use Point to rewrite question 4 above.

6. Write a Python class called Client.

   Each instance of the class should have the attributes name, address and balance. The instantiation method should have input determining the customer name and address. It should also set the balance to zero. In addition to constructor and __str__ method for output, each instance should have access to methods debit and credit to change the balance.

   Test the class by rewriting SBapp program using a list to store and process Client objects with the following features required:

   • Make the balance a private attribute so that a user can only change it by going through the methods. Add an accessor method getBalance which a user can use to check their balance.
   • Ensure that the debit method does not allow a user to pay back more money than their balance.
   • Add an attribute number which keeps count of how many accounts have been created.

   Make sure your class and program includes a meaningful docstring.

7. A rational number is any number that can be expressed as the quotient or fraction n/d of two integers.

   Write a Python class called Rational. Every Rational object consists of two attributes n and d representing the numerator and denominator.

   • Note that n and d should both be integers. Ensure this by having the instantiation method throw an appropriate exception otherwise.
   • Further, d could not be zero and should always be positive. Extend the instantiation method so that if d is zero an exception is thrown; while if d is negative the equivalent object is created with attributes -n, -d.
   • Write a __str__ method that converts a Rational instance to the string "n/d".
   • Use names in Python arithmetic methods to implement the appropriate arithmetic special methods for the class Rational.

     Recall the following rules for arithmetic with fractions.

     

   • Note that different Rational objects can be mathematically equal. For example, 2/4 = 1/2. In general n1/d1 = n2/d2 if and only if n1*d2 = n2*d1. Write a method that takes two Fraction objects; and returns True is they are mathematically equal and False otherwise. Give it the appropriate special method name so that Python will use it when checking equality of two Rational objects with ==.
   • You could write similar methods for checking whether one fraction is bigger or smaller than another.
   • All equivalent mathematical fractions can be simplifed to a unique form by cancelling common factors in the numerator and detonator. Write a function to reduce the rational to its lowest form. Make this a method of the class and run it as part of the instantiation of any Rational object.

   Include doc string comment in Rational class. After testing, use pydoc to generate class documentation in HTML format.