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% !TEX program = xelatex
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\documentclass[dvipsnames,14pt,t,xelatex]{beamer}
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\usepackage{../slides}
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\usepackage{../graphics}
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\usepackage{../langs}
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%%\usepackage{../data}
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\usetikzlibrary{shapes}
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%\setmonofont[Scale=.88]{Consolas}
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%\newfontfamily{\consolas}{Consolas}
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\lstset{language=Scala,
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style=mystyle,
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numbersep=0pt,
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numbers=none,
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xleftmargin=0mm}
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\newcommand{\LEFTarrow}[3]{%
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\begin{textblock}{0}(#2,#3)%
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\onslide<#1>{%
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\begin{tikzpicture}%
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\node at (0,0) [single arrow, shape border rotate=180, fill=red,text=red]{a};%
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\end{tikzpicture}}%
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\end{textblock}}
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\newcommand{\DOWNarrow}[3]{%
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\begin{textblock}{0}(#2,#3)%
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\onslide<#1>{%
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\begin{tikzpicture}%
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\node at (0,0) [single arrow, shape border rotate=270, fill=red,text=red]{a};%
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\end{tikzpicture}}%
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\end{textblock}}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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% beamer stuff
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\renewcommand{\slidecaption}{PEP (Scala) 04, King's College London}
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\begin{filecontents}{re3a.data}
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1 0.00003
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500001 0.22527
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1000001 0.62752
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1500001 0.88485
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2000001 1.39815
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2500001 1.68619
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3000001 1.94957
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3500001 2.15878
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4000001 2.59918
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4500001 5.90679
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5000001 13.11295
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5500001 19.15376
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6000001 40.16373
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\end{filecontents}
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\begin{filecontents}{re-python2.data}
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1 0.033
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5 0.036
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10 0.034
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15 0.036
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18 0.059
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19 0.084
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20 0.141
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21 0.248
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22 0.485
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23 0.878
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24 1.71
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25 3.40
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26 7.08
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27 14.12
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28 26.69
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\end{filecontents}
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\begin{filecontents}{re-js.data}
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5 0.061
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10 0.061
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15 0.061
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20 0.070
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23 0.131
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25 0.308
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26 0.564
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28 1.994
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30 7.648
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31 15.881
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32 32.190
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\end{filecontents}
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\begin{filecontents}{re-java.data}
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5 0.00298
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10 0.00418
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15 0.00996
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16 0.01710
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17 0.03492
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18 0.03303
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19 0.05084
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20 0.10177
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21 0.19960
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22 0.41159
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23 0.82234
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24 1.70251
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25 3.36112
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26 6.63998
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27 13.35120
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28 29.81185
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\end{filecontents}
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\begin{filecontents}{re-java9.data}
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1000 0.01410
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2000 0.04882
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3000 0.10609
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4000 0.17456
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5000 0.27530
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6000 0.41116
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7000 0.53741
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8000 0.70261
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9000 0.93981
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10000 0.97419
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11000 1.28697
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12000 1.51387
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14000 2.07079
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16000 2.69846
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20000 4.41823
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24000 6.46077
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26000 7.64373
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30000 9.99446
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34000 12.966885
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38000 16.281621
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42000 19.180228
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46000 21.984721
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50000 26.950203
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60000 43.0327746
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\end{filecontents}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\[5mm]
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\huge PEP Scala (4)
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\end{tabular}}
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\normalsize
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\begin{center}
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\begin{tabular}{ll}
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Email: & christian.urban at kcl.ac.uk\\
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Office: & N\liningnums{7.07} (North Wing, Bush House)\bigskip\\
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Slides \& Code: & KEATS\\
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& \onslide<2>{\alert{A Crash-Course in Scala}}\bigskip\\
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Office Hours: & Thursdays 12:00 -- 14:00\\
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Additionally: & (for Scala) Tuesdays 10:45 -- 11:45\\
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\end{tabular}
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\end{center}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c]
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\frametitle{Hints in CW}
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\begin{center}
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\includegraphics[scale=0.4]{../pics/hints.png}
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\end{center}
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\small
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\begin{itemize}
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\item Scala Library, e.g.~\texttt{span} in \\
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\url{https://www.scala-lang.org/api/current/scala/collection/immutable/List.html}
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c]
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\frametitle{Preliminary 7}
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Raw marks (261 submissions):\bigskip
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\begin{itemize}
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\item 4\%: \hspace{4mm}236
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\item 3\%: \hspace{4mm}10
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\item 2\%: \hspace{4mm}1
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\item 1\%: \hspace{4mm}0
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\item 0\%: \hspace{4mm}15
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\end{itemize}\bigskip\bigskip
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\footnotesize
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(interviews ongoing!)
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\small
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\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=1mm]
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def is_legal(dim: Int, p: Path, x: Pos) = {
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if (...some_really_long_condition...) false
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else true
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}
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\end{lstlisting}
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\pause
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\bigskip
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\rule{11cm}{0.3mm}
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\bigskip
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\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=1mm]
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def is_legal(dim: Int, p: Path, x: Pos) =
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!(...some_really_long_condition...)
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\end{lstlisting}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\small
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\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=1mm]
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def foobar(...) = {
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val cs = for (c <- str) yield c.toLowerCase
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...
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}
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\end{lstlisting}
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\pause
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\bigskip
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\rule{11cm}{0.3mm}
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\bigskip
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\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=1mm]
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def foobar(...) = {
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val cs = str.map(_.toLowerCase)
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...
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}
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\end{lstlisting}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\small
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\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=-7mm]
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def RomanNumeral2Int(rs: RomanNumeral): Int =
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rs match {
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case Nil => 0
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case M::r => 1000 + RomanNumeral2Int(r)
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case C::M::r => 900 + RomanNumeral2Int(r)
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case D::r => 500 + RomanNumeral2Int(r)
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case C::D::r => 400 + RomanNumeral2Int(r)
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case C::r => 100 + RomanNumeral2Int(r)
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case X::C::r => 90 + RomanNumeral2Int(r)
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case L::r => 50 + RomanNumeral2Int(r)
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case X::L::r => 40 + RomanNumeral2Int(r)
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case X::r => 10 + RomanNumeral2Int(r)
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case I::X::r => 9 + RomanNumeral2Int(r)
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case V::r => 5 + RomanNumeral2Int(r)
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case I::V::r => 4 + RomanNumeral2Int(r)
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case I::r => 1 + RomanNumeral2Int(r)
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}
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\end{lstlisting}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\frametitle{Last Week: Pattern Matching}
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\small
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\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=3mm]
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def fizz_buzz(n: Int) : String =
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(n % 3, n % 5) match {
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case (0, 0) => "fizz buzz"
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case (0, _) => "fizz"
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case (_, 0) => "buzz"
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case _ => n.toString
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}
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\end{lstlisting}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\frametitle{Reverse Polish Notation}
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{\Large\bl{$(3 + 1) * (2 + 9)$}}\bigskip
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{\Large$\Rightarrow$}\bigskip
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{\;\;\Large\bl{$3\;\;1\;+\;2\;\;9\;+\;*$}}
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\begin{textblock}{3}(11,4)
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\begin{onlyenv}<2>
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\begin{lstlisting}[language=JVMIS]
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ldc 3
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ldc 1
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iadd
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ldc 2
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ldc 9
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iadd
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imul
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\end{lstlisting}
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\end{onlyenv}
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\end{textblock}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\frametitle{Sudoku}
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A very simple-minded version on 110 problems:\bigskip
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\begin{itemize}
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\item 1 core: 800 secs
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\item 2 cores: 400 secs
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\item 8 cores: 290 secs
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\item 18 cores: 142 secs
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c]
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\frametitle{DFAs}
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\begin{center}
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\begin{tikzpicture}[>=stealth',very thick,auto,
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every state/.style={minimum size=0pt,inner sep=2pt,
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draw=blue!50,very thick,fill=blue!20},]
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\only<1,3->{\node[state,initial] (Q_0) {$\mbox{Q}_0$};}
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\only<2>{\node[state,initial,fill=red] (Q_0) {$\mbox{Q}_0$};}
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\only<1,2,4->{\node[state] (Q_1) [right=of Q_0] {$\mbox{Q}_1$};}
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\only<3>{\node[state,fill=red] (Q_1) [right=of Q_0] {$\mbox{Q}_1$};}
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\only<-3,5->{\node[state] (Q_2) [below right=of Q_0] {$\mbox{Q}_2$};}
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\only<4>{\node[state,fill=red] (Q_2) [below right=of Q_0] {$\mbox{Q}_2$};}
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\only<-4,6->{\node[state] (Q_3) [right=of Q_2] {$\mbox{Q}_3$};}
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\only<5>{\node[state,fill=red] (Q_3) [right=of Q_2] {$\mbox{Q}_3$};}
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\only<-5>{\node[state, accepting] (Q_4) [right=of Q_1] {$\mbox{Q}_4$};}
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\only<6->{\node[state, accepting,fill=red] (Q_4) [right=of Q_1] {$\mbox{Q}_4$};}
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\path[->] (Q_0) edge node [above] {\alert{$a$}} (Q_1);
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\path[->] (Q_1) edge node [above] {\alert{$a$}} (Q_4);
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\path[->] (Q_4) edge [loop right] node {\alert{$a, b$}} ();
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\path[->] (Q_3) edge node [right] {\alert{$a$}} (Q_4);
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\path[->] (Q_2) edge node [above] {\alert{$a$}} (Q_3);
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\path[->] (Q_1) edge node [right] {\alert{$b$}} (Q_2);
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\path[->] (Q_0) edge node [above] {\alert{$b$}} (Q_2);
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\path[->] (Q_2) edge [loop left] node {\alert{$b$}} ();
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\path[->] (Q_3) edge [bend left=95, looseness=1.3] node [below] {\alert{$b$}} (Q_0);
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\end{tikzpicture}
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\end{center}
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\begin{textblock}{9}(4,12)
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\LARGE{}
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\only<3->{\boldmath\alert{$a$}}%
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\only<4->{\boldmath\alert{$b$}}%
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\only<5->{\boldmath\alert{$a$}}%
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\only<6->{\boldmath\alert{$a$}}%
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\only<7->{\boldmath\alert{$a\quad\Rightarrow \textbf{yes}$}}%
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\end{textblock}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{DFAs}
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A \alert{\bf deterministic finite automaton}, DFA, consists of
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5 things:
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391 |
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\begin{itemize}
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\item an alphabet \bl{$\varSigma$}
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\item a set of states \bl{$\mbox{Qs}$}
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\item one of these states is the start state \bl{$\mbox{Q}_0$}
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\item some states are accepting states \bl{$F$}, and
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\item there is transition function \bl{$\delta$}\bigskip
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398 |
|
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|
399 |
\small
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400 |
which takes a state and a character as arguments and produces a
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new state; this function might not be everywhere defined
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402 |
\end{itemize}
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403 |
|
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\begin{center}
|
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|
405 |
\bl{$A(\varSigma, \mbox{Qs}, \mbox{Q}_0, F, \delta)$}
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\end{center}
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67
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407 |
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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410 |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c]
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413 |
\frametitle{NFAs}
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67
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414 |
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222
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415 |
\begin{center}
|
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|
416 |
\begin{tikzpicture}[>=stealth',very thick, auto,
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every state/.style={minimum size=0pt,inner sep=3pt,
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draw=blue!50,very thick,fill=blue!20},scale=2]
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\node[state,initial] (Q_0) {$\mbox{Q}_0$};
|
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|
420 |
\node[state] (Q_1) [right=of Q_0] {$\mbox{Q}_1$};
|
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|
421 |
\node[state, accepting] (Q_2) [right=of Q_1] {$\mbox{Q}_2$};
|
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|
422 |
\path[->] (Q_0) edge [loop above] node {\alert{$b$}} ();
|
|
|
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\path[<-] (Q_0) edge node [below] {\alert{$b$}} (Q_1);
|
|
|
424 |
\path[->] (Q_0) edge [bend left] node [above] {\alert{$a$}} (Q_1);
|
|
|
425 |
\path[->] (Q_0) edge [bend right=45,looseness=1.3] node [below] {\alert{$a$}} (Q_2);
|
|
|
426 |
\path[->] (Q_1) edge [loop above] node {\alert{$a,b$}} ();
|
|
|
427 |
\path[->] (Q_1) edge node [above] {\alert{$a$}} (Q_2);
|
|
|
428 |
\end{tikzpicture}
|
|
|
429 |
\end{center}
|
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|
430 |
|
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|
431 |
\end{frame}
|
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|
432 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
68
|
433 |
|
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155
|
434 |
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325
|
435 |
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436 |
\begin{frame}[t]
|
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437 |
|
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|
438 |
\begin{center}
|
|
|
439 |
\includegraphics[scale=0.3]{../pics/blow.png}
|
|
|
440 |
\end{center}
|
|
|
441 |
|
|
|
442 |
\begin{textblock}{14}(2,11.4)
|
|
|
443 |
\large\bf{}Mind-Blowing Regular Expressions:\\
|
|
|
444 |
\centering in Python, JavaScript, Java
|
|
|
445 |
\end{textblock}
|
|
|
446 |
\end{frame}
|
|
67
|
447 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
325
|
448 |
|
|
|
449 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
450 |
\begin{frame}[c,fragile]
|
|
|
451 |
\frametitle{Regular Expressions}
|
|
|
452 |
|
|
|
453 |
Suppose you have a regular expression
|
|
|
454 |
\only<1-3>{\alert{\texttt{(a*)b}}}%
|
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|
455 |
\only<4->{\alert{\texttt{(a*)*b}}} :\bigskip
|
|
|
456 |
|
|
|
457 |
\begin{center}
|
|
|
458 |
\only<1>{\code{"aaaaaaaaaaaaaaab"}}
|
|
|
459 |
\only<2>{\code{"aaaaa...........aaaaaaaaaaaaaaaaaaaab"}}
|
|
|
460 |
\only<3>{\code{"aaaaa...........aaaaaaaaaaaaaaaaaaaa"}}
|
|
|
461 |
\only<4>{\code{"aaaaa...........aaaaaaaaaaaaaaaaaaaab"}}
|
|
|
462 |
\only<5->{\code{"aaaaa...........aaaaaaaaaaaaaaaaaaaa"}}
|
|
|
463 |
\end{center}
|
|
|
464 |
|
|
|
465 |
\only<6>{
|
|
|
466 |
\begin{textblock}{13}(5,12)
|
|
|
467 |
How long does Python need to find out?
|
|
|
468 |
\end{textblock}}
|
|
|
469 |
|
|
|
470 |
\end{frame}
|
|
|
471 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
472 |
|
|
|
473 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
474 |
\begin{frame}<1>[c]
|
|
|
475 |
\frametitle{CW 9: Regexes}
|
|
68
|
476 |
|
|
|
477 |
\begin{center}
|
|
325
|
478 |
Graphs: \alert{\texttt{(a*)*b}} and strings $\underbrace{\;\texttt{a}\ldots \texttt{a}\;}_{n}$\bigskip
|
|
68
|
479 |
|
|
|
480 |
\begin{tabular}[t]{@{\hspace{-8mm}}c@{\hspace{-4mm}}c@{}}
|
|
222
|
481 |
\only<1>{\raisebox{6mm}{\begin{tikzpicture}
|
|
68
|
482 |
\begin{axis}[
|
|
|
483 |
xlabel={$n$},
|
|
|
484 |
x label style={at={(1.05,0.0)}},
|
|
|
485 |
ylabel={time in secs},
|
|
|
486 |
enlargelimits=false,
|
|
|
487 |
xtick={0,5,...,30},
|
|
|
488 |
xmax=33,
|
|
|
489 |
ymax=35,
|
|
|
490 |
ytick={0,5,...,30},
|
|
|
491 |
scaled ticks=false,
|
|
|
492 |
axis lines=left,
|
|
|
493 |
width=5.5cm,
|
|
|
494 |
height=5cm,
|
|
222
|
495 |
legend entries={\small{}Python, \small{}Java 8, \small{}JavaScript},
|
|
68
|
496 |
legend pos=north west,
|
|
|
497 |
legend cell align=left]
|
|
|
498 |
\addplot[blue,mark=*, mark options={fill=white}] table {re-python2.data};
|
|
|
499 |
\addplot[cyan,mark=*, mark options={fill=white}] table {re-java.data};
|
|
222
|
500 |
\addplot[red,mark=*, mark options={fill=white}] table {re-js.data};
|
|
68
|
501 |
\end{axis}
|
|
222
|
502 |
\end{tikzpicture}}}%
|
|
|
503 |
\only<2>{\raisebox{0mm}{\begin{tikzpicture}
|
|
|
504 |
\begin{axis}[
|
|
|
505 |
xlabel={$n$},
|
|
|
506 |
x label style={at={(1.05,0.0)}},
|
|
|
507 |
ylabel={time in secs},
|
|
|
508 |
%y label style={at={(0.06,0.5)}},
|
|
|
509 |
enlargelimits=false,
|
|
|
510 |
%xtick={0,30000,...,60000},
|
|
|
511 |
xmax=65000,
|
|
|
512 |
ymax=35,
|
|
|
513 |
ytick={0,5,...,30},
|
|
|
514 |
scaled ticks=true,
|
|
|
515 |
axis lines=left,
|
|
|
516 |
width=5.5cm,
|
|
|
517 |
height=5cm,
|
|
|
518 |
legend entries={\small{}Java 9},
|
|
|
519 |
legend pos=north west]
|
|
|
520 |
\addplot[cyan,mark=*, mark options={fill=white}] table {re-java9.data};
|
|
|
521 |
\end{axis}
|
|
|
522 |
\end{tikzpicture}}}
|
|
68
|
523 |
&
|
|
222
|
524 |
\onslide<1-2>{\begin{tikzpicture}
|
|
68
|
525 |
\begin{axis}[
|
|
|
526 |
xlabel={$n$},
|
|
|
527 |
x label style={at={(1.05,0.0)}},
|
|
|
528 |
ylabel={time in secs},
|
|
|
529 |
enlargelimits=false,
|
|
|
530 |
ymax=35,
|
|
|
531 |
ytick={0,5,...,30},
|
|
|
532 |
axis lines=left,
|
|
|
533 |
%%scaled ticks=false,
|
|
|
534 |
width=5.5cm,
|
|
|
535 |
height=5cm]
|
|
|
536 |
%%\addplot[green,mark=square*,mark options={fill=white}] table {re2a.data};
|
|
222
|
537 |
\addplot[magenta,mark=square*,mark options={fill=white}] table {re3a.data};
|
|
68
|
538 |
\end{axis}
|
|
70
|
539 |
\end{tikzpicture}}
|
|
68
|
540 |
\end{tabular}
|
|
|
541 |
\end{center}
|
|
66
|
542 |
|
|
68
|
543 |
\hfill\small\url{https://vimeo.com/112065252}
|
|
66
|
544 |
\end{frame}
|
|
325
|
545 |
|
|
|
546 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
67
|
547 |
|
|
325
|
548 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
68
|
549 |
\begin{frame}[c]
|
|
67
|
550 |
|
|
222
|
551 |
\begin{center}
|
|
325
|
552 |
\includegraphics[angle=90,scale=0.35]{/Users/cu/vote.pdf}
|
|
222
|
553 |
\end{center}
|
|
67
|
554 |
|
|
|
555 |
\end{frame}
|
|
325
|
556 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
67
|
557 |
|
|
325
|
558 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
559 |
\begin{frame}[c]
|
|
|
560 |
|
|
|
561 |
\begin{center}
|
|
|
562 |
\includegraphics[scale=0.25]{/Users/cu/dresden.png}
|
|
|
563 |
\end{center}
|
|
67
|
564 |
|
|
325
|
565 |
\begin{textblock}{13}(2,12)
|
|
|
566 |
\includegraphics[scale=0.08]{/Users/cu/kiss.jpg}
|
|
|
567 |
\end{textblock}
|
|
|
568 |
|
|
|
569 |
\begin{textblock}{13}(6.8,12)
|
|
|
570 |
\includegraphics[scale=0.079]{/Users/cu/pioniere.jpg}
|
|
|
571 |
\end{textblock}
|
|
|
572 |
|
|
|
573 |
\begin{textblock}{13}(11,12)
|
|
|
574 |
\includegraphics[scale=0.20]{/Users/cu/iron.jpg}
|
|
|
575 |
\end{textblock}
|
|
|
576 |
|
|
|
577 |
\DOWNarrow{1}{11}{8.6}
|
|
66
|
578 |
|
|
|
579 |
\end{frame}
|
|
325
|
580 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
581 |
|
|
70
|
582 |
|
|
66
|
583 |
|
|
|
584 |
|
|
|
585 |
\end{document}
|
|
|
586 |
|
|
|
587 |
%%% Local Variables:
|
|
|
588 |
%%% mode: latex
|
|
|
589 |
%%% TeX-master: t
|
|
|
590 |
%%% End:
|
|
|
591 |
|