SOLUTION TEMPLATE INSTRUCTIONS

We have prepared a template for you in writeup/ps2_sol.tex. Please modify it to
include all your answers, except for the Python source code, and then upload it
to Stellar.

To fill in the answer to a problem, e.g. Problem 2(c), search the document for
the answer start / end markers, which look like this:
    %%% PROBLEM 2(c) ANSWER START %%%
    %%% PROBLEM 2(c) ANSWER END %%%

You should then write your answer between the ANSWER START and ANSWER END
marker lines. Do NOT edit the marker lines.

Your homework will be automatically graded, and any changes to the marker lines 
or to the surrounding document may cause you to lose points. For additional
peace of mind, we recommend copying the original template to ps2_orig.tex, and
using a diff tool to compare your version to the original.
    Linux / MacOS:   diff ps2_sol.tex ps2_orig.tex
    Windows:         fc ps2_sol.tex ps2_orig.tex

MULTIPLE CHOICE QUESTIONS

The answer for multiple choice questions should be the number to the left of
your answer. For example, if Problem 1(a) has the answers:
    1. log n
    2. n
    3. 3n
    4. 4n

and you wish to answer "log n" (answer 1), your solution template should look
as follows:
    %%% PROBLEM 2(c) ANSWER START %%%
    1
    %%% PROBLEM 2(c) ANSWER END %%%


PYTHON IDENTIFIER QUESTION

When answering questions that want the name of a Python variable, method or
class name, write the method name between the answer markers. Don't add any
fancy formatting, such as a \verbatim block. 
    %%% PROBLEM 2(c) ANSWER START %%%
    method_name
    %%% PROBLEM 2(c) ANSWER END %%%

You may use \_ instead of _, so that you can compile your solutions without
errors. Our grading tool will recognize the variation below as "method_name".
    %%% PROBLEM 2(c) ANSWER START %%%
    method\_name
    %%% PROBLEM 2(c) ANSWER END %%%


PROOF QUESTION

Write your LaTeX proof between the answer markers. The LaTeX that you learned
for the PS 1 proof should be sufficient for PS 2.


COLLABORATORS

Remember to list the full names of your collaborators, separated by commas,
between the answer markers.
    %%% COLLABORATORS START %%%
    John Doe, Jane Doe
    %%% COLLABORATORS END %%%