# 3rd Homework

Download hw_3.tar.gz and extract it. Then add your homework solutions to the files contained in the directory. Rename the directory according to the rules in the syllabus before submitting it as compressed archive. Starting from this homework, the grader uses so-called unit tests, but can be executed as any other Python 3 program.
This homework is the first homework to be solved in teams of two using pair programming. Find your partner for this homework on moodle.uni-graz.at. Each team has to submit only one archive containing all team members' names.

1. Polynomial evalution
Write a function eval_polynomial(coefficients, x) that evaluates the polynomial given by the coefficients. Note that coefficients[i] is the coefficient of x^i.
Name the program file: polynomials.py
2. Prime Sum
Write a function prime_sum_to(num) that takes an integer num >= 0 as sole argument. The function should return the sum of all prime numbers <= num. In the function, assert that the input is ≥ 0 by using assert.
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 gemoetric 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
Implement a function interest(capital, rate, years=1, tax=0) that returns the profit (compound interest) of investing money. 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.
Using the above function, implement a second function that returns the terminal value of investing money: terminal_value(capital, rate, years=1, tax=0).
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']

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.
def main():