=========================
Practice problems: Week 6
=========================

This set of practice problems will allow you to test your
understanding of recursion.

To get started run ``git pull upstream master``, which will pick up a
directory named ``pp5``.  

As usual, the problems are broken up into two parts: a set of
"be-a-computer" warm-up exercises and a set of programming problems.
For the programming problems, we provide the code that handles the
input/output of the problem. Make sure you read the comments in the
provided code so you understand exactly what part of the code you need
to modify.

Warm-up exercise #1: What is the output of the following code?

.. literalinclude:: warmup.py
   :lines: 3-14

Warm-up exercise #2: What is the output of the following code?

.. literalinclude:: warmup.py
   :lines: 17-35


Some of the programming problems are taken from a placement exam; you can ignore
the warning about getting "zero points". As usual, these practice
problems are not graded.

Please remember you can find instructions on how to test and submit the Kattis problems in our
`Using Kattis
<https://www.classes.cs.uchicago.edu/archive/2015/fall/12100-1/kattis.html>`_ page.

We have included sample inputs and outputs for the Kattis programming
problems in the distribution to allow you test your code on the sample
data before trying it out on Kattis.  Here is an example use of a
sample input file for the first programming problem::

    python3 gcd.py < gcd-sample/gcd-001.in 

The corresponding output can be found in the file ``gcd-sample/gcd-001.ans``.

**We expect you to write recursive solutions for all of these problem.**

Programming problem #1: `Dijkstra's Other Algorithm <https://uchicago.kattis.com/problems/uchicago%3Ampcs%3Agcd>`_

Programming problem #2: `Don't Be Such a Square <https://uchicago.kattis.com/problems/uchicago%3Ampcs%3Asquare>`_

Programming problem #3: `Ninety-One <https://uchicago.kattis.com/problems/uchicago%3Ampcs%3Aninetyone>`_

Programming problem #4: `Line Them Up <https://open.kattis.com/problems/lineup>`_