Finished compression handout

Advanced/Compression/main.tex

@@ -8,12 +8,15 @@
 
 \input{tikzset.tex}
 \usepackage{units}
+\usepackage{pdfpages}
 
 \uptitlel{Advanced 2}
 \uptitler{\smallurl{}}
 \title{Compression}
 \subtitle{Prepared by Mark on \today{}}
 
+% TODO: add a section on info theory,
+% shannon entropy. etc.
 
 \begin{document}
 
@@ -23,5 +26,6 @@
 	\input{parts/1 runlength.tex}
 	\input{parts/2 lzss.tex}
 	\input{parts/3 huffman.tex}
+	\input{parts/4 bonus.tex}
 
 \end{document}

Advanced/Compression/parts/1 runlength.tex

@@ -35,7 +35,7 @@
 
 
 \problem{}<runlenone>
-Using a na\"ive coding scheme, encode \texttt{AAAA$\cdot$AAAA$\cdot$BCD$\cdot$AAAA$\cdot$AAAA} in binary. \par
+Using the na\"ive coding scheme, encode \texttt{AAAA$\cdot$AAAA$\cdot$BCD$\cdot$AAAA$\cdot$AAAA} in binary. \par
 \note[Note]{
 	We're still using the four-symbol alphabet $\{\texttt{A}, \texttt{B}, \texttt{C}, \texttt{D}\}$. \par
 	Dots ($\cdot$) in the string are drawn for readability. Ignore them.
@@ -44,6 +44,11 @@ Using a na\"ive coding scheme, encode \texttt{AAAA$\cdot$AAAA$\cdot$BCD$\cdot$AA
 \begin{solution}
 	There are eight \texttt{A}s on each end of that string. Mapping symbols as before, \par
 	we get \texttt{[00 00 00 00 00 00 00 00 01 10 11 00 00 00 00 00 00 00 00]}
+
+	\begin{instructornote}
+		In this handout, all encoded binary is written in square brackets. \par
+		Spaces, dashes, dots, and etc are added for readability, and should be ignored.
+	\end{instructornote}
 \end{solution}
 
 

Advanced/Compression/parts/3 huffman.tex

@@ -3,7 +3,7 @@
 
 \example{}
 Now consider the alphabet $\{\texttt{A}, \texttt{B}, \texttt{C}, \texttt{D}, \texttt{E}\}$. \par
-With a na\"ive coding scheme, we can encode a length $n$ string with $3n$ bits, by mapping...
+With the na\"ive coding scheme, we can encode a length $n$ string with $3n$ bits, by mapping...
 \begin{itemize}
 	\item $\texttt{A}$ to $\texttt{000}$
 	\item $\texttt{B}$ to $\texttt{001}$
@@ -12,8 +12,7 @@ With a na\"ive coding scheme, we can encode a length $n$ string with $3n$ bits,
 	\item $\texttt{E}$ to $\texttt{100}$
 \end{itemize}
 For example, this encodes \texttt{ADEBCE} as \texttt{[000 011 100 001 010 100]}. \par
-To encode strings over $\{\texttt{A}, \texttt{B}, \texttt{C}, \texttt{D}, \texttt{E}\}$ with this scheme, we
+It is easy to see that this scheme uses an average of three bits per symbol.
-need an average of three bits per symbol.
 
 \vspace{2mm}
 

Advanced/Compression/parts/4 bonus.tex

@@ -0,0 +1,40 @@
+\section{Bonus problems}
+
+
+\problem{}
+Make sense of the document on the next page. \par
+What does it describe, and how does it work?
+
+
+\problem{}
+Given a table with a marked point, $O$, and with $2013$ properly working watches put down on the table, prove that there exists a moment in time when the sum of the distances from $O$ to the watches' centers is less than the sum of the distances from $O$ to the tips of the watches' minute hands.
+
+\vfill
+
+
+\problem{A Minor Inconvenience}
+A group of eight friends goes out to dinner. Each drives his own car, checking it in with valet upon arrival.
+Unfortunately, the valet attendant forgot to tag the friends' keys. Thus, when the group leaves the restaurant,
+each friend is handed a random key.
+\begin{itemize}
+	\item What is the probability that everyone gets the correct set of keys?
+	\item What is the probability that each friend gets the wrong set?
+\end{itemize}
+
+\vfill
+
+
+\problem{Bimmer Parking}
+A parking lot has a row of 16 spaces, of which a random 12 are taken. \par
+Ivan drives a BMW, and thus needs two adjacent spaces to park. \par
+What is the probability he'll find a spot?
+
+\vfill
+\pagebreak
+
+\includepdf[
+	pages=1,
+	fitpaper=true
+]{parts/qoi-specification.pdf}
+
+\pagebreak