CS414 Fall 2017: Assignment #1

Due Thursday, February 9, 2017, before midnight

Late penalty: Fri 5%, Sat 10%, Sun 100%

Before You Begin:

• Create a folder on your computer where your files will be kept.
• Download the following files, and save them into the folder you just created. You should modify them.
  1. temp_table.py
  2. sphere.py
  3. monotonic.py
  4. payroll.py
  5. collatz.py
• If you are holding a paper copy of this assignment, the links won't work ;-) . Go to the course webpage, and find this assignment on that page: cs.unh.edu/~cs414 .

Questions:

1. Loops and float-to-int conversion:

   Write a program temp_table.py that prints a temperature conversion table. It should look something like this:

           Celsius Fahrenheit
           -40 -40
           -35 -31
           ...
           35 95
           40 104
         

   The Celsius temperatures should range from -40 to +40 (inclusive), in steps of 5 degrees.

   The Fahrenheit temperatures should be rounded to the nearest integer.

2. Geometry:

   Write a program sphere.py that prompts the user for the radius of a sphere (a float), and prints the sphere's circumference, surface area, and volume.

   In case you forgot all the geometry you learned in high school, here are the formulas:
   Circumference = 2πr
   Area = 4πr²
   Volume = (4/3)πr³

   Some gotchas to be aware of:

   • 4 / 3 == 1 because python 2.7 does integer division. Use floats instead.
   • In math, ab does multiplication, but in python a b is an error.

3. Booleans:

   Write a program monotonic.py that gets three ints x, y, and z from the user, checks if they form a monotonic sequence, and prints either monotonic or non-monotonic. This means they for an increasing sequence, or a decreasing sequence:
   x ≤ y ≤ z or
   x ≥ y ≥ z.
   Examples:

           x is 1, y is 2, z is 3: is a monotonic sequence
           x is 1, y is 1, z is 3: is a monotonic sequence
           x is 2, y is 1, z is 3: is a non-monotonic sequence
           x is 3, y is 2, z is 1: is a monotonic sequence
         

   Gotcha: You can't type x <= y <= z. That's a syntax error.

4. Payroll:

   Write a program payroll.py that prompts the user for two numbers relating to an employee's work week: the hours worked, and the hourly pay rate.

   It then computes the employee's gross pay, and prints it. Any hours worked beyond 40 are paid as overtime, at a rate 1.5 times the usual hourly rate ('time and a half').

5. (Bonus 10%):

   Consider this rule for transforming a positive integer n:

   • if n is even, divide it by 2
   • if not, multiply it by 3 and add 1

   The Collatz conjecture says that, no matter what integer you start with, applying this transformation over and over will eventually reach the value 1.

   Write a program collatz.py that prompts the user for a starting value n, applies the above transformation repeatedly, until n is 1. The program should simply count the number of transformations it took to reach 1, and print that count.

   Examples:

   • n == 1: 0 transformations
   • n == 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1: 16 transformations.

Turn in your work