3

Max. 9 points

Download hw_3.tar.gz and extract it. This archive contains a grader which works for all current versions of Python 3 and expects the solution files to be placed in the same directory. It has to be executed from this directory via

python hw3_grader.py

Add your solutions in the directory contained in the archive. Right after the shebang, each of your files must contain your name using the following template

"""
.. moduleauthor:: Your Name <your.name@example.com>
"""

We did not discuss every detail required to solve the following tasks. Use your favorite search engine and some common sense to solve the tasks.

This homework is to be prepared in teams of two students. Ask the lecturer to announce the teams to know who you'll be working with.

1. Equation solver
   Write a function quadratic(a, b, c) that solves quadratic equations. If you have trouble solving this task, have a look at the Python functions video tutorial on youtube. In addition to what is shown in the video, the function must be able to deal with input leading to complex numbers as results.
   Name the program file: equations.py
2. Sum
   Write a function sum_to(num) that takes an integer num >= 0 as sole argument. The function should return the sum of all positive integers <= num. In the function, assert that the input is ≥ 0 by using assert.
   Name the program file: addition.py
3. Conversion between Celsius and Fahrenheit
   Based on the formulas and your code of the second homework, write a function celsius2fahrenheit(.) that converts from Celsius to Fahrenheit and fahrenheit2celsius(.) for the other way around.
   Name the program file: conversion.py
4. Geometry functions
   Implement the following functions calculating the perimeters, areas, surfaces or volumes of common geometric shapes:
   

   perimeter_right_triangle(c1, c2)
   area_right_triangle(c1, c2)
   perimeter_circle(r)
   area_circle(r)
   surface_sphere(r)
   volume_sphere(r)
   surface_cylinder(r, h)
   volume_cylinder(r, h)
   surface_cone(r, h)
   volume_cone(r, h)

   Name the program file: geometry.py
5. Business functions
   Implement a function that returns the terminal value of investing money: terminal_value(capital, rate, years=1, tax=0). If a positive tax value is entered, every year's interest is to be reduced by the tax. The rate and tax parameters must be between 0 (0%) and 1 (100%). The number of years is integral. Use the formulas $$\text{capital}\ast (1+\text{rate}\ast (1-\text{tax}){)}^{\text{years}}$$
   Implement a second function interest(capital, rate, years=1, tax=0) that returns the profit (compound interest) of investing money.
   Name the program file: business.py
6. ROT13
   Building on your solution to the ROT13 task in the last homework, write a function encode(.) that takes a string and returns the given string rotated by 13 places. For symmetry, also provide a corresponding decode(.) function. Convert the input to upper case before performing the rotation.
   
   1. Arire gehfg n cebtenz lbh qba'g unir fbheprf sbe.
   Name the program file: rot13.py
7. VRPTW instances
   Write a function read_string_list(.) that opens a VRPTW data file given as filename argument. The argument must be optional and default to "r101"). If the argument doesn't contain a filename extension (".txt"), this extension must be added before opening the file. Your function should return a list of strings - one for each entry. The headers should not be included in that list.
   A sample execution of this function:

   >>> read_string_list('r101.txt')
   ['  1    35.00    35.00     0.00     0.00   230.00     0.00\n',
    '  2    41.00    49.00    10.00   161.00   171.00    10.00\n',
   ...
    '100    20.00    26.00     9.00    83.00    93.00    10.00\n',
    '101    18.00    18.00    17.00   185.00   195.00    10.00\n']

   Name the program file: vrptw_reader.py
8. More on VRPTW instances
   Expand the file of the last task to include more functions. The second function get_demand(.) takes two arguments. The first argument should be a list of strings (one for each entry) and the second should be a customer number (CUST_NO.). The function has to return that customer's demand as floating point number. The last function, calc_distance(.), should take three parameters – a list of strings and two customer numbers. It should return the euclidean distance between the two customers.
   Name the program file: vrptw_reader.py
9. Main function
   Write a single module that imports all the other modules you wrote for this homework. In the module implement a main function that uses all the functions you created. This main function is a first attempt of testing your code in the other modules. For each of the other tasks, create valid input data and deduce the functions output. Print these values, followed by the actual values the function produces for these inputs. Here's an example line this function could contain:

   def main():
       # ...
       print('prime_addition.prime_sum_to(9); expected: 17, actual:',
             prime_addition.prime_sum_to(9))
       # ...

   The main function must be called itself using the ifmain pattern. If all went well, the main function must return 0 to inform the calling process of the successful termination. Name the program file: main.py