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"/home/never/Documents/InNa/26_SoSe/AGT/übung_1/ads_übung_1.tex" "ads_übung_1.pdf" "ads_übung_1" 1776429129.32904 0 +["lualatex"] 1776444596.07125 "/home/never/Documents/InNa/26_SoSe/AGT/agt_exercise/übung_1/ads_übung_1.tex" "ads_übung_1.pdf" "ads_übung_1" 1776444597.83098 0 "/home/never/.texlive2025/texmf-var/luatex-cache/generic/fonts/otl/euler-math.luc" 1770519352.28514 417132 89f085d929a7f52a226e499fed2b660f "" "/home/never/.texlive2025/texmf-var/luatex-cache/generic/fonts/otl/lmroman10-bold.luc" 1770519351.28214 128405 86240d2e88c12243734a13e4bf6704ec "" "/home/never/.texlive2025/texmf-var/luatex-cache/generic/fonts/otl/lmroman10-regular.luc" 1770519350.86413 127322 64667bb671c8def3fa5d85c341ebd817 "" @@ -15,9 +15,9 @@ "/home/never/.texlive2025/texmf-var/luatex-cache/generic/fonts/otl/texgyrepagella-bolditalic.luc" 1770519351.48314 287795 ed687cb1567d94bda5cbe1fed2b3c16f "" "/home/never/.texlive2025/texmf-var/luatex-cache/generic/fonts/otl/texgyrepagella-italic.luc" 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1802 7595c33e7cfa7c377b26012654f0dae1 "" "/home/never/texmf/tex/latex/ngutils/ngutils.sty" 1776422986.52973 2546 cdbbac1864d91b223f5034978567f395 "" "/usr/local/texlive/2025/texmf-dist/fonts/opentype/public/euler-math/Euler-Math.otf" 1761682777 433104 26cb5ed06a913ce89a33ff41234f5c7a "" @@ -166,8 +166,8 @@ "/usr/local/texlive/2025/texmf-var/fonts/map/pdftex/updmap/pdftex.map" 1770517628 5541377 824b1e5beafd2ebda40585373b35bb6b "" "/usr/local/texlive/2025/texmf-var/tex/generic/config/language.dat" 1770517624.99251 6800 99336720d16c8191172704bea65615e7 "" "/usr/local/texlive/2025/texmf-var/web2c/luahbtex/lualatex.fmt" 1770517696 5655839 756767735d369e65a483b47207bff649 "" - "ads_übung_1.aux" 1776429129.10996 2560 e7016168588901a60d123ae63e7648b5 "lualatex" - "ads_übung_1.tex" 1776429124.47193 1643 ce89290d4b850fa5a506bbb049e9ca6e "" + "ads_übung_1.aux" 1776444597.60105 2664 ee5f5228ebef91457d56f27531fb2310 "lualatex" + "ads_übung_1.tex" 1776444595.14003 3051 c9f0cea3acbf5485f64aa9520ca7bf9f "" "msb.eps" 1776424417.18606 5913 81dafb89427e3a448260b7481993e119 "" (generated) "ads_übung_1.aux" diff --git a/übung_1/ads_übung_1.fls b/übung_1/ads_übung_1.fls index cc48d97..6b52e33 100644 --- a/übung_1/ads_übung_1.fls +++ b/übung_1/ads_übung_1.fls @@ -1,6 +1,6 @@ -PWD /home/never/Documents/InNa/26_SoSe/AGT/übung_1 +PWD /home/never/Documents/InNa/26_SoSe/AGT/agt_exercise/übung_1 INPUT /usr/local/texlive/2025/texmf-var/web2c/luahbtex/lualatex.fmt -INPUT /home/never/Documents/InNa/26_SoSe/AGT/übung_1/ads_übung_1.tex +INPUT /home/never/Documents/InNa/26_SoSe/AGT/agt_exercise/übung_1/ads_übung_1.tex OUTPUT ads_übung_1.log INPUT /usr/local/texlive/2025/texmf-dist/tex/latex/tex-ini-files/lualatexquotejobname.lua INPUT /usr/local/texlive/2025/texmf-dist/tex/latex/base/ltluatex.lua diff --git a/übung_1/ads_übung_1.log b/übung_1/ads_übung_1.log index 650f304..b4a2251 100644 --- a/übung_1/ads_übung_1.log +++ b/übung_1/ads_übung_1.log @@ -1,7 +1,8 @@ -This is LuaHBTeX, Version 1.22.0 (TeX Live 2025) (format=lualatex 2026.2.8) 17 APR 2026 14:32 +This is LuaHBTeX, Version 1.22.0 (TeX Live 2025) (format=lualatex 2026.2.8) 17 APR 2026 18:49 restricted system commands enabled. -**/home/never/Documents/InNa/26_SoSe/AGT/übung_1/ads_übung_1.tex -(/home/never/Documents/InNa/26_SoSe/AGT/übung_1/ads_übung_1.tex +**/home/never/Documents/InNa/26_SoSe/AGT/agt_exercise/übung_1/ads_übung_1.tex + +(/home/never/Documents/InNa/26_SoSe/AGT/agt_exercise/übung_1/ads_übung_1.tex LaTeX2e <2025-11-01> L3 programming layer <2026-01-19> Lua module: luaotfload 2024-12-03 v3.29 Lua based OpenType font support @@ -1277,7 +1278,7 @@ File: bkm-pdftex.def 2023-12-10 v1.31 bookmark driver for pdfTeX and luaTeX (HO )) (./ads_übung_1.aux Package babel Info: 'ngerman' activates 'german' shorthands. -(babel) Reported on input line 14. +(babel) Reported on input line 12. ) \openout1 = ads_übung_1.aux @@ -1334,12 +1335,12 @@ Package epstopdf Info: Source file: (epstopdf) size: 3745 bytes (epstopdf) Command: -(epstopdf) \includegraphics on input line 32. +(epstopdf) \includegraphics on input line 33. Package epstopdf Info: Output file is already uptodate. File: msb-eps-converted-to.pdf Graphic file (type pdf) -Package luatex.def Info: msb-eps-converted-to.pdf used on input line 32. +Package luatex.def Info: msb-eps-converted-to.pdf used on input line 33. (luatex.def) Requested size: 71.69984pt x 74.25963pt. [1 @@ -1354,27 +1355,28 @@ L3 programming layer <2026-01-19> ) Here is how much of LuaTeX's memory you used: - 21548 strings out of 476076 + 21557 strings out of 476076 100000,1144653 words of node,token memory allocated - 1185 words of node memory still in use: - 19 hlist, 12 vlist, 10 rule, 2 local_par, 22 glue, 10 kern, 2 penalty, 6 glyp -h, 59 attribute, 61 glue_spec, 30 attribute_list, 1 write nodes - avail lists: 2:660,3:274,4:3,5:209,6:49,7:3862,8:13,9:401,10:3,11:317 - 43688 multiletter control sequences out of 65536+600000 - 116 fonts using 28210383 bytes - 122i,8n,114p,11284b,508s stack positions out of 10000i,1000n,20000p,200000b,200000s - -Output written on ads_übung_1.pdf (2 pages, 28941 bytes). + 1757 words of node memory still in use: + 31 hlist, 20 vlist, 18 rule, 4 local_par, 38 glue, 16 kern, 4 penalty, 10 gly +ph, 103 attribute, 61 glue_spec, 52 attribute_list, 1 write nodes + avail lists: 1:1,2:745,3:291,4:4,5:253,6:55,7:4025,8:13,9:524,10:4,11:314 + 43696 multiletter control sequences out of 65536+600000 + 117 fonts using 28458551 bytes + 122i,8n,114p,11297b,516s stack positions out of 10000i,1000n,20000p,200000b,200000s + +Output written on ads_übung_1.pdf (2 pages, 37194 bytes). -PDF statistics: 97 PDF objects out of 1000 (max. 8388607) - 69 compressed objects within 1 object stream - 11 named destinations out of 1000 (max. 131072) +PDF statistics: 105 PDF objects out of 1000 (max. 8388607) + 74 compressed objects within 1 object stream + 12 named destinations out of 1000 (max. 131072) 33 words of extra memory for PDF output out of 10000 (max. 100000000) diff --git a/übung_1/ads_übung_1.pdf b/übung_1/ads_übung_1.pdf index efa3bdb..5cc8bf0 100644 Binary files a/übung_1/ads_übung_1.pdf and b/übung_1/ads_übung_1.pdf differ diff --git a/übung_1/ads_übung_1.synctex.gz b/übung_1/ads_übung_1.synctex.gz index cb313e0..55871b8 100644 Binary files a/übung_1/ads_übung_1.synctex.gz and b/übung_1/ads_übung_1.synctex.gz differ diff --git a/übung_1/ads_übung_1.tex b/übung_1/ads_übung_1.tex index a53e7cc..eab69a3 100644 --- a/übung_1/ads_übung_1.tex +++ b/übung_1/ads_übung_1.tex @@ -3,7 +3,7 @@ \title{1. Übungsblatt} \subject{Algorithmische Graphentheorie} -\author{Jasper Gude} +\author{Jasper Gude \and Pia Rötgers} \begin{document} \maketitle @@ -27,6 +27,7 @@ und $s \in V \deg$ ein ausgezeichneter Knoten. von $G$ ein Breitensuchbaum mit Quelle $s$. \end{quote} Falsch, siehe \autoref{fig:msb}. + \points{2} \begin{figure}[h] \centering \includegraphics[width=0.2\textwidth]{msb.eps} @@ -41,9 +42,42 @@ und $s \in V \deg$ ein ausgezeichneter Knoten. Sei $w(e) = 1$ für alle $e \in E$ so gilt das Gegenbeispiel von oben. Also ist die Aussage falsch. + \points{2} \end{enumerate} \section{Kreissuche} +\begin{enumerate} + \item + Wähle Startknoten $s$ und füge ihn in eine neue Queue $Q$ ein. + + Nimm den vordersten Knoten aus $Q$ und füge seine noch nicht verbrauchten + Nachbarn ein. Markiere diesen Knoten anschließend als verbraucht ($black$). + Wiederhole den Schritt solange bis $Q$ leer ist. Merke dir dabei die zwei + letzten entnommenen Knoten. Sind sie gleich, hat der Graph einen + einfachen Kreis. + + \begin{algorithmic} + \alg{EinfacherKreis}(Graph $G$, Vertex $s$) \+ \\ + \alg{Initialize}($G$, $s$) \\ + $Q \gets$ new \alg{Queue}() \\ + $Q.$\alg{Enqueue}($s$) \\ + $t_1 \gets nil$ \\ + $t_2 \gets s$ \\ + while $Q \neq \emptyset$ do \+ \\ + $u \gets Q.$\alg{Dequeue}() \\ + $t_1 \gets t_2$ \\ + $t_2 \gets u$ \\ + foreach $v \in Adj[u]$ do \+ \\ + if $v.color = white$ then \+ \\ + $Q.$\alg{Enqueue}($v$) \-\- \\ + $u.color \gets black$ \- \\ + if $t_1 = t_2$ then \+ \\ + return $true$ \- \\ + else \+ \\ + return $false$ + + \end{algorithmic} +\end{enumerate} \section{Eulerwege}