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% macros useful for handouts and homeworks.
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\setcourse{CS 5114}
\setsem{Spring 2013}
\sethwnum{7}
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\chead{\course (\sem): Homework \hwnum}
\begin{document}
\title{\vspace{-0.5in}\textbf{Homework \hwnum}}
\author{\course (\sem)}
\date{Assigned on April 25, 2013. \\Submit PDF solutions by
email to the TA\\
beginning of class on May 2, 2013.}
\maketitle
\paragraph{Instructions:}
\begin{itemize}
\item You are not allowed to consult any sources other than your
textbook, the slides on the course web page, your own class notes, the
TA, and the instructor. In particular, do not use a search engine.
\item Do not forget to typeset your solutions. \emph{Every mathematical
expression must be typeset as a mathematical expression, e.g., the
square of $n$ must appear as $n^2$ and not as ``n\^{}2''.} Students
can use the \LaTeX\ version of the
homework problems to start entering their solutions.
\item Describe your algorithms as clearly as possible. The style used in
the book is fine, as long as your description is not
ambiguous. Explain your algorithm in words. A step-wise description is
fine. \emph{However, if you submit detailed pseudo-code without an
explanation, we will not grade your solutions.}
\item Do not make any assumptions not stated in the problem. If you do
make any assumptions, state them clearly, and explain why the
assumption does not decrease the generality of your solution.
\item Do not describe your algorithms only for a specific example you
may have worked out.
\item You must also provide a clear proof that your solution is correct
(or a counter-example, where applicable). Type out all the statements you
need to complete your proof. \emph{You must convince us that you can
write out the complete proof. You will lose points if you work out
some details of the proof in your head but do not type them out in
your solution.}
\item Describe an analysis of your algorithm and state and prove the
running time. You will only
get partial credit if your analysis is not tight, i.e., if the bound
you prove for your algorithm is not the best upper bound possible.
\end{itemize}
\begin{description}
\item[Problem 1] (10 points) Solve exercise 6 in Chapter 8 (page 507) of
your textbook.
% \solution{
% }
\item[Problem 2] (30 = 15 + 15 points) Solve exercise 10 in Chapter 8 (pages
508-509) of your textbook.
% \solution{
% }
\item[Problem 3] (30 = 15 + 15 points) Solve exercise 19 in Chapter 8 (pages
514-515) of your textbook.
% \solution{
% }
\item[Problem 4] (30 points) Solve exercise 37 in Chapter 8 (pages
526-527) of your textbook.
% \solution{
% }
\end{description}
\end{document}