\documentstyle[oneside,hmwk,11pt]{handout}
\hmwknumber{1}
\topic{Asymptotics and Sorting}
\duedate{Tuesday, 2 July 1996}
\begin{document}
\maketitle

\vspace{-0.4in}

\section*{Reading}
\vspace{-0.1in}
Read carefully Ch. 1 and Ch. 2 of CLR.


\section*{Practice}
\vspace{-0.1in}
Recall, these exercises are purely for your own practice.  You need
only turn in the official problems.
\begin{itemize}
\item Do CLR 1.2-3.

\item Do CLR 1.2-6.

\item Do CLR 1.4-1.

\item Do CLR 2.1-2, 2.1-3.

\item Do CLR 2.2-4. [can you do this {\em without} Stirling's approximation?]

\end{itemize}


\section*{Problems}
\vspace{-0.1in}
\begin{enumerate}
\item Do CLR 1-2.

\item Do CLR 1.3-6.

\item Do CLR 2-4.  [Your proofs must be formal]

\item
Rank the following functions by order of growth, {\em i.e.},
find an arrangement $g_1, g_2, \ldots, g_{25}$ of the functions
satisfying $g_1=\Omega(g_2), g_2=\Omega(g_3), \ldots,
\break g_{24}=\Omega(g_{25})$.  Partition your list into equivalence classes
such that $f(n)$ and $g(n)$ are in the same class iff
$f(n)=\Theta(g(n))$.

[Note: We do not require proof for this problem, simply the ordering
and the equivalence classes.]

\begin{displaymath}
\begin{array}{ccccc}
(3/2)^n & (\sqrt{2})^{\lg n} & \lg^* n & n^2 &  (\lg n)!\\
 n^3 & \lg^2 n & \lg(n!) & 2^{2^n} & n^{1/\lg n}\\
\lg\lg n  & n\cdot 2^n & n^{\lg\lg n} & \ln n &  2^n \\
2^{\lg n} & (\lg n)^{\lg n} &  4^{\lg n} & (n+1)! & \sqrt{\lg n}\\
 n! & 2^{\sqrt{2\lg n}} & n  & n\lg n & 1
\end{array}
\end{displaymath}


\end{enumerate}


\section*{Extra Credit}
\vspace{-0.1in}
Do CLR 1.3-7.


\end{document}