improve adjacency matrix slides

1 files changed, 93 insertions, 36 deletions

diff --git a/Info/11/NTG/1/Adjazenzmatrix/slides.md b/Info/11/NTG/1/Adjazenzmatrix/slides.md
index 040e3311..3a5c849e 100644
--- a/Info/11/NTG/1/Adjazenzmatrix/slides.md
+++ b/Info/11/NTG/1/Adjazenzmatrix/slides.md
@@ -84,14 +84,43 @@ digraph {
 ```
 `\end{center}`{=latex}
 
+## \faIcon{hands-helping} / \faIcon{chalkboard} Arbeitsauftrag: Wege durch Graphen \hfill{} 2/5
+
+### Diskutiert folgende Aussage:
+
+\vspace{0.2cm}
+> Ein Graph heißt \boldred{vollständig}, wenn jeder Knoten mit jedem anderen Knoten mit einer Kante verbunden ist.
+> Ein derartiger Graph hat immer $\frac{(n^2-n)}{2}$ Kanten, wenn n die Anzahl der Knoten ist.
+
+`\begin{center}`{=latex}
+```{.graphviz dpi=150 height=5cm}
+graph {
+  bgcolor=transparent
+  node [shape=circle]
+  layout=circo
+  A -- B
+  A -- C
+  A -- D
+  A -- E
+  B -- C
+  B -- D
+  B -- E
+  C -- D
+  C -- E
+  D -- E
+}
+```
+`\end{center}`{=latex}
+
 ## \faIcon{hands-helping} / \faIcon{chalkboard} Arbeitsauftrag: Wege durch Graphen \hfill{} 3/5
 
 ### Diskutiert folgende Aussage:
 
-\vspace{1cm}
+\vspace{0.5cm}
 > Der \boldred{Pfad} `A/B/D` ist kürzer als der Pfad `A/B/C/D`, weil er [weniger]{.underline} Knoten enthält.
 
-```{.graphviz dpi=150}
+`\begin{center}`{=latex}
+```{.graphviz dpi=150 height=3cm}
 digraph {
   bgcolor=transparent
   rankdir=LR
@@ -102,6 +131,21 @@ digraph {
   C -> D [label=1]
 }
 ```
+`\end{center}`{=latex}
+
+\pause
+
+Die Länge eines Pfades in einem [gewichteten]{.underline} Graphen ist die **Summe der Kantengewichte**.
+
+::: {.columns}
+:::: {.column width=50%}
+* Laenge(`A/B/D`) = 5
+::::
+
+:::: {.column width=50%}
+* Laenge(`A/B/C/D`) = \boldred{4}
+::::
+:::
 
 ## \faIcon{hands-helping} / \faIcon{chalkboard} Arbeitsauftrag: Arrays initialisieren \hfill{} 4/5
 
@@ -110,14 +154,16 @@ digraph {
 ```java
 int[] zahlen;
 zahlen = new zahlen[10];
-verwende(zahlen);
+verwende(zahlen[2]);
 
 Knoten[] knoten = new Knoten[42];
-verwende(knoten);
+verwende(knoten[4]);
 ```
-\vspace{1cm}
+\vspace{0.7cm}
 > Um die Werte eines Array verwenden zu können, reicht es aus das Array zu deklarieren und dieses anschließend zu initialisieren.
 
+\pause
+Die **einzelnen** Einträge müssen ebenfalls initialisiert werden.
 
 ## \faIcon{hands-helping} / \faIcon{chalkboard} Arbeitsauftrag: Graphendarstellung \hfill{} 5/5
 
@@ -128,8 +174,13 @@ verwende(knoten);
 
 ![](img/Copyrighted/Cornelsen_S11_A6.png){.center}
 
+\pause
+
+\boldred{iii} ist mit den anderen nicht identisch, da beispielsweise \textbf{A} keine Kante zu \textbf{E} hat.
+
 ##
 
+\vspace{0.4cm}
 ![](../Intro/img/bike.png)
 
 ## \faIcon{pencil-alt} Arbeitsauftrag: Abitur 2021 Burning Man - 10min
@@ -196,47 +247,50 @@ verwende(knoten);
 ::::
 
 :::: {.column width=50%}
+\begin{center}
 \begin{tabular}{c | c | c | c | c | c}
-\rowcolor{gray!30}  & v1 & v2 & v3 & v4 & v5 \\
+\rowcolor{gray!30}\cellcolor{gray} & v1 & v2 & v3 & v4 & v5 \\
 \hline
-\cellcolor{gray!30} v1 & \only<3>{0} & \only<2->{\textbf 1} & \only<3>{0} & \only<3>{0} & \only<2->{\textbf 1} \\
+\cellcolor{gray!30} v1 & \only<3>{\cellcolor{gray!30}0} & \only<2->{\textbf 1} & \only<3>{0} & \only<3>{0} & \only<2->{\textbf 1} \\
 \hline
-\cellcolor{gray!30} v2 & \only<2->{\textbf 1} & \only<3>{0} & \only<2->{\textbf 1} & \only<3>{0} & \only<2->{\textbf 1} \\
+\cellcolor{gray!30} v2 & \only<2->{\textbf 1} & \only<3>{\cellcolor{gray!30}0} & \only<2->{\textbf 1} & \only<3>{0} & \only<2->{\textbf 1} \\
 \hline
-\cellcolor{gray!30} v3 & \only<3>{0} & \only<2->{\textbf 1} & \only<3>{0} & \only<2->{\textbf 1} & \only<2->{\textbf 1} \\
+\cellcolor{gray!30} v3 & \only<3>{0} & \only<2->{\textbf 1} & \only<3>{\cellcolor{gray!30}0} & \only<2->{\textbf 1} & \only<2->{\textbf 1} \\
 \hline
-\cellcolor{gray!30} v4 & \only<3>{0} & \only<3>{0} & \only<2->{\textbf 1} & \only<3>{0} & \only<2->{\textbf 1} \\
+\cellcolor{gray!30} v4 & \only<3>{0} & \only<3>{0} & \only<2->{\textbf 1} & \only<3>{\cellcolor{gray!30}0} & \only<2->{\textbf 1} \\
 \hline
-\cellcolor{gray!30} v5 & \only<2->{\textbf 1} & \only<2->{\textbf 1} & \only<2->{\textbf1} & \only<2->{\textbf 1} & \only<3>{0} \\
+\cellcolor{gray!30} v5 & \only<2->{\textbf 1} & \only<2->{\textbf 1} & \only<2->{\textbf1} & \only<2->{\textbf 1} & \only<3>{\cellcolor{gray!30}0} \\
 \end{tabular}
+\end{center}
 ::::
 :::
 
 ## Adjazenzmatrix - gerichtet
 
 ::: {.columns align=center}
-:::: {.column width=50%}
+:::: {.column width=45%}
 \resizebox{0.9\textwidth}{!}{
   \tikzstyle{edge} = [thick, -Triangle]
   \input{graph.tikz}
 }
 ::::
 
-:::: {.column width=50%}
+:::: {.column width=55%}
+\begin{center}
 \begin{tikzpicture}
 \node {
 \begin{tabular}{c | c | c | c | c | c}
 \cellcolor{gray} & \only<-2>{\cellcolor{gray!30}} \only<3>{\cellcolor{teal!30}}v1 & \only<-2>{\cellcolor{gray!30}} \only<3>{\cellcolor{teal!30}}v2 & \only<-2>{\cellcolor{gray!30}} \only<3>{\cellcolor{teal!30}}v3 & \only<-2>{\cellcolor{gray!30}} \only<3>{\cellcolor{teal!30}}v4 & \only<-2>{\cellcolor{gray!30}} \only<3>{\cellcolor{teal!30}}v5 \\
 \hline
-\only<-2>{\cellcolor{gray!30}}\only<3>{\cellcolor{yellow!30}} v1 & \only<2->{0} & \only<2->{\textbf 1} & \only<2->{0} & \only<2->{0} & \only<2->{\textbf 1} \\
+\only<-2>{\cellcolor{gray!30}}\only<3>{\cellcolor{yellow!30}} v1 & \only<2->{\cellcolor{gray!30}0} & \only<2->{\textbf 1} & \only<2->{0} & \only<2->{0} & \only<2->{\textbf 1} \\
 \hline
-\only<-2>{\cellcolor{gray!30}}\only<3>{\cellcolor{yellow!30}} v2 & \only<2->{0} & \only<2->{0} & \only<2->{\textbf 1} & \only<2->{0} & \only<2->{\textbf 1} \\
+\only<-2>{\cellcolor{gray!30}}\only<3>{\cellcolor{yellow!30}} v2 & \only<2->{0} & \only<2->{\cellcolor{gray!30}0} & \only<2->{\textbf 1} & \only<2->{0} & \only<2->{\textbf 1} \\
 \hline
-\only<-2>{\cellcolor{gray!30}}\only<3>{\cellcolor{yellow!30}} v3 & \only<2->{0} & \only<2->{0} & \only<2->{0} & \only<2->{\textbf 1} & \only<2->{\textbf 1} \\
+\only<-2>{\cellcolor{gray!30}}\only<3>{\cellcolor{yellow!30}} v3 & \only<2->{0} & \only<2->{0} & \only<2->{\cellcolor{gray!30}0} & \only<2->{\textbf 1} & \only<2->{\textbf 1} \\
 \hline
-\only<-2>{\cellcolor{gray!30}}\only<3>{\cellcolor{yellow!30}} v4 & \only<2->{0} & \only<2->{0} & \only<2->{0} & \only<2->{0} & \only<2->{\textbf 1} \\
+\only<-2>{\cellcolor{gray!30}}\only<3>{\cellcolor{yellow!30}} v4 & \only<2->{0} & \only<2->{0} & \only<2->{0} & \only<2->{\cellcolor{gray!30}0} & \only<2->{\textbf 1} \\
 \hline
-\only<-2>{\cellcolor{gray!30}}\only<3>{\cellcolor{yellow!30}} v5 & \only<2->{0} & \only<2->{0} & \only<2->{0} & \only<2->{0} & \only<2->{0} \\
+\only<-2>{\cellcolor{gray!30}}\only<3>{\cellcolor{yellow!30}} v5 & \only<2->{0} & \only<2->{0} & \only<2->{0} & \only<2->{0} & \only<2->{\cellcolor{gray!30}0} \\
 \end{tabular}
 };
 \only<-2> {
@@ -248,6 +302,7 @@ verwende(knoten);
   \node[fill=teal!30] at (1, 2.1) {Zielknoten};
 }
 \end{tikzpicture}
+\end{center}
 ::::
 :::
 
@@ -261,19 +316,21 @@ verwende(knoten);
 ::::
 
 :::: {.column width=50%}
+\begin{center}
 \begin{tabular}{c | c | c | c | c | c}
-\rowcolor{gray!30}  & v1 & v2 & v3 & v4 & v5 \\
+\rowcolor{gray!30} \cellcolor{gray} & v1 & v2 & v3 & v4 & v5 \\
 \hline
-\cellcolor{gray!30} v1 & \only<2->{\boldred{-1}} & \only<2->{\textbf{10}} & \only<2->{\boldred{-1}} & \only<2->{\boldred{-1}} & \only<2->{\textbf{30}} \\
+\cellcolor{gray!30} v1 & \cellcolor{gray!30} \only<2->{\boldred{-1}} & \only<2->{\textbf{10}} & \only<2->{\boldred{-1}} & \only<2->{\boldred{-1}} & \only<2->{\textbf{30}} \\
 \hline
-\cellcolor{gray!30} v2 & \only<2->{\textbf{10}} & \only<2->{\boldred{-1}} & \only<2->{\textbf{40}} & \only<2->{\boldred{-1}} & \only<2->{\textbf{50}} \\
+\cellcolor{gray!30} v2 & \only<2->{\textbf{10}} & \cellcolor{gray!30}\only<2->{\boldred{-1}} & \only<2->{\textbf{40}} & \only<2->{\boldred{-1}} & \only<2->{\textbf{50}} \\
 \hline
-\cellcolor{gray!30} v3 & \only<2->{\boldred{-1}} & \only<2->{\textbf{40}} & \only<2->{\boldred{-1}} & \only<2->{\textbf{10}} & \only<2->{\textbf{30}} \\
+\cellcolor{gray!30} v3 & \only<2->{\boldred{-1}} & \only<2->{\textbf{40}} & \cellcolor{gray!30}\only<2->{\boldred{-1}} & \only<2->{\textbf{10}} & \only<2->{\textbf{30}} \\
 \hline
-\cellcolor{gray!30} v4 & \only<2->{\boldred{-1}} & \only<2->{\boldred{-1}} & \only<2->{\textbf{10}} & \only<2->{\boldred{-1}} & \only<2->{\textbf{20}} \\
+\cellcolor{gray!30} v4 & \only<2->{\boldred{-1}} & \only<2->{\boldred{-1}} & \only<2->{\textbf{10}} & \cellcolor{gray!30}\only<2->{\boldred{-1}} & \only<2->{\textbf{20}} \\
 \hline
-\cellcolor{gray!30} v5 & \only<2->{\textbf{30}} & \only<2->{\textbf{50}} & \only<2->{\textbf{30}} & \only<2->{\textbf{20}} & \only<2->{\boldred{-1}} \\
+\cellcolor{gray!30} v5 & \only<2->{\textbf{30}} & \only<2->{\textbf{50}} & \only<2->{\textbf{30}} & \only<2->{\textbf{20}} & \cellcolor{gray!30}\only<2->{\boldred{-1}} \\
 \end{tabular}
+\end{center}
 
 
 \vspace{0.5cm}
@@ -322,13 +379,13 @@ graph {
 \begin{tabular}{c|c|c|c|c}
 \rowcolor{gray!30}\cellcolor{gray} & v1 & v2 & v3 & v4 \\
 \hline
-\cellcolor{gray!30} v1 & 0 & 1 & 0 & 1 \\
+\cellcolor{gray!30} v1 & \cellcolor{gray!30}0 & 1 & 0 & 1 \\
 \hline
-\cellcolor{gray!30} v2 & 1 & 0 & 1 & 0 \\
+\cellcolor{gray!30} v2 & 1 & \cellcolor{gray!30}0 & 1 & 0 \\
 \hline
-\cellcolor{gray!30} v3 & 0 & 1 & 0 & 1 \\
+\cellcolor{gray!30} v3 & 0 & 1 & \cellcolor{gray!30}0 & 1 \\
 \hline
-\cellcolor{gray!30} v4 & 1 & 0 & 1 & 0 \\
+\cellcolor{gray!30} v4 & 1 & 0 & 1 & \cellcolor{gray!30}0 \\
 \end{tabular}
 \end{center}
 ::::
@@ -381,13 +438,13 @@ graph {
 \begin{tabular}{c|c|c|c|c}
 \rowcolor{gray!30}\cellcolor{gray} & v1 & v2 & v3 & v4 \\
 \hline
-\cellcolor{gray!30} v1 & 0 & 1 & 0 & 1 \\
+\cellcolor{gray!30} v1 & \cellcolor{gray!30}0 & 1 & 0 & 1 \\
 \hline
-\cellcolor{gray!30} v2 & 1 & 0 & 1 & 0 \\
+\cellcolor{gray!30} v2 & 1 & \cellcolor{gray!30}0 & 1 & 0 \\
 \hline
-\cellcolor{gray!30} v3 & 0 & 1 & 0 & 1 \\
+\cellcolor{gray!30} v3 & 0 & 1 & \cellcolor{gray!30}0 & 1 \\
 \hline
-\cellcolor{gray!30} v4 & 1 & 0 & 1 & 0 \\
+\cellcolor{gray!30} v4 & 1 & 0 & 1 & \cellcolor{gray!30}0 \\
 \end{tabular}
 \end{center}
 ::::
@@ -447,13 +504,13 @@ graph {
 \begin{tabular}{c|c|c|c|c}
 \rowcolor{gray!30}\cellcolor{gray} & v1 & \cellcolor{teal!30} v2 & v3 & v4 \\
 \hline
-\cellcolor{gray!30} v1 & 0 & 1 & 0 & 1 \\
+\cellcolor{gray!30} v1 & \cellcolor{gray!30} 0 & 1 & 0 & 1 \\
 \hline
-\cellcolor{gray!30} v2 & 1 & 0 & 1 & 0 \\
+\cellcolor{gray!30} v2 & 1 & \cellcolor{gray!30} 0 & 1 & 0 \\
 \hline
-\cellcolor{yellow!30} v3 & 0 & \boldred{1} & 0 & 1 \\
+\cellcolor{yellow!30} v3 & 0 & \boldred{1} & \cellcolor{gray!30} 0 & 1 \\
 \hline
-\cellcolor{gray!30} v4 & 1 & 0 & 1 & 0 \\
+\cellcolor{gray!30} v4 & 1 & 0 & 1 & \cellcolor{gray!30} 0 \\
 \end{tabular}
 \end{center}
 ::::