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%\usepackage{cs5114}
% macros useful for handouts and homeworks.
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\setcourse{CS 4104}
\setsem{Spring 2014}
\sethwnum{3}
\chead{\course (\sem): Homework \hwnum}
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\newcommand{\solution}[1]{\textbf{Solution:} #1}
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\begin{document}
\title{\vspace{-0.5in}\textbf{Homework \hwnum}}
\author{\course (\sem)}
\date{Assigned on Wednesday, February 26, 2014. \\Submit a PDF file
containing your solutions on Scholar by the beginning of class on
Wednesday, March 5, 2014.}
\maketitle
\paragraph{Instructions:}
\begin{itemize}
\item You can pair up with another student to solve the homework. You
are allowed to discuss possible algorithms and bounce ideas with your
team-mate. \textbf{Do not discuss proofs of correctness or running time in
detail with your team-mate.} Please form teams yourselves. Of course,
you can ask me for help if you cannot find a team-mate. You may choose
to work alone. \emph{Each of you must write down your solution
individually, and write down the name of the other member in your
team. If you do not have a team-mate, please say so.}
\item Apart from your team-mate, you are not allowed to consult any
sources other than your textbook, the slides on the course web page,
your own class notes, the TAs, 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] (20 points) Solve exercise 2 in Chapter 4 (page 189) of your
textbook. \emph{Note:} We will discuss minimum spanning trees in the
next class, but you can read the definition on page 142 of your textbook.
% \solution{
% }
\item[Problem 2] (35 points) Solve exercise 5 in Chapter 4 (pages 190-191) of
your textbook. Just in case the problem statement is not completely
clear, you can assume that the road is the $x$-axis,
that each house lies directly on the road, and that the position of
each house can be specified by its $x$-coordinate.
% \solution{
% }
\item[Problem 3] (45 points) Solve exercise 13 in Chapter 4 (pages 194-195) of your
textbook. \emph{Hint:} Try to use one of the techniques we
have seen for proving the correctness of greedy algorithms. Working
``backwards'' from what you need to prove might help you to discover
the algorithm.
% \solution{
% }
\end{description}
\end{document}