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\handout{lec7-sup}{The Aymptotic Cheat Sheet}{September 29, 1998}

\section{Notation}

Asymptotic notation consists of six funny symbols used to describe
relative growth rate of functions.  These symbols are defined in the
table below.

\begin{tabular}{cllll}
f(n) = O(g(n))	&  $f$ grows no faster than $g$
		&  \parbox{1.5in}{Frequently used to give an upper bound on the
		   running time or memory requirement of a program.}
		&  \parbox{1.5in}{``True, your algorithm has run time
		   $O(n \log n)$, and my algorithm is only $O(n^2)$, but
		   because I'm a hacker and you are a theoretician, my program
		   still runs faster for $n < 1000000$.''}
		&  \parbox{1.5in}{These exists an $n_0$ and a constant $c > 0$
		   such that for all $n \geq n_0$, $f(n) \leq c g(n)$.}
\end{tabular}

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