1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
|
%
% graph.tex
%
% (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil
%
\begin{frame}[fragile]
\frametitle{Problem: Kürzeste Wege}
\begin{center}
\begin{tikzpicture}[>=latex]
\def\blob#1#2#3{
\fill[color=#3] #1 circle[radius=0.2];
\draw[line width=0.7pt] #1 circle[radius=0.2];
\node at #1 {{\tiny #2}};
}
\def\kante#1#2{
\draw[line width=0.7pt,shorten >= 0.2,shorten >= 0.2] #1 -- #2 ;
}
\def\a{72}
\def\r{1.0}
\def\R{2.0}
\def\RR{3.5}
\coordinate (A1) at ({\r*cos(0*\a)},{\r*sin(0*\a)});
\coordinate (B1) at ({\r*cos(1*\a)},{\r*sin(1*\a)});
\coordinate (C1) at ({\r*cos(2*\a)},{\r*sin(2*\a)});
\coordinate (D1) at ({\r*cos(3*\a)},{\r*sin(3*\a)});
\coordinate (E1) at ({\r*cos(4*\a)},{\r*sin(4*\a)});
\coordinate (F1) at ({\R*cos(0*\a)},{\R*sin(0*\a)});
\coordinate (G1) at ({\R*cos(1*\a)},{\R*sin(1*\a)});
\coordinate (H1) at ({\R*cos(2*\a)},{\R*sin(2*\a)});
\coordinate (I1) at ({\R*cos(3*\a)},{\R*sin(3*\a)});
\coordinate (J1) at ({\R*cos(4*\a)},{\R*sin(4*\a)});
\coordinate (K1) at ({\RR*cos(0.5*\a)},{\RR*sin(0.5*\a)});
\coordinate (L1) at ({\RR*cos(1.5*\a)},{\RR*sin(1.5*\a)});
\coordinate (M1) at ({\RR*cos(2.5*\a)},{\RR*sin(2.5*\a)});
\coordinate (N1) at ({\RR*cos(3.5*\a)},{\RR*sin(3.5*\a)});
\coordinate (O1) at ({\RR*cos(4.5*\a)},{\RR*sin(4.5*\a)});
\kante{(A1)}{(C1)}
\kante{(C1)}{(E1)}
\kante{(E1)}{(B1)}
\kante{(B1)}{(D1)}
\kante{(D1)}{(A1)}
\kante{(F1)}{(G1)}
\kante{(G1)}{(H1)}
\kante{(H1)}{(I1)}
\kante{(I1)}{(J1)}
\kante{(J1)}{(F1)}
\kante{(A1)}{(F1)}
\kante{(B1)}{(G1)}
\kante{(C1)}{(H1)}
\kante{(D1)}{(I1)}
\kante{(E1)}{(J1)}
\kante{(K1)}{(L1)}
\kante{(L1)}{(M1)}
\kante{(M1)}{(N1)}
\kante{(N1)}{(O1)}
\kante{(O1)}{(K1)}
\kante{(F1)}{(K1)}
\kante{(G1)}{(L1)}
\kante{(H1)}{(M1)}
\kante{(I1)}{(N1)}
\kante{(J1)}{(O1)}
\kante{(F1)}{(O1)}
\kante{(G1)}{(K1)}
\kante{(H1)}{(L1)}
\kante{(I1)}{(M1)}
\kante{(J1)}{(N1)}
\uncover<2>{
\draw[line width=2pt,color=red] (M1)--(H1)--(G1)--(B1);
}
\uncover<3>{
\draw[line width=2pt,color=red] (M1)--(L1)--(G1)--(B1);
}
\uncover<4>{
\draw[line width=2pt,color=red] (M1)--(I1)--(D1)--(B1);
}
\uncover<5>{
\draw[line width=2pt,color=red] (M1)--(I1)--(D1)--(A1)--(F1);
}
\uncover<6->{
\draw[line width=2pt,color=red] (M1)--(I1)--(J1)--(F1);
}
\uncover<2-4>{
\blob{(B1)}{1}{red!20}
\blob{(M1)}{12}{red!20}
}
\uncover<5-8>{
\blob{(M1)}{1}{red!20}
\blob{(F1)}{12}{red!20}
}
\blob{(A1)}{0}{white}
\uncover<1>{
\blob{(B1)}{1}{white}
}
\uncover<5-8>{
\blob{(B1)}{12}{white}
}
\blob{(C1)}{2}{white}
\blob{(D1)}{3}{white}
\blob{(E1)}{4}{white}
\uncover<1-4>{
\blob{(F1)}{5}{white}
}
\blob{(G1)}{6}{white}
\blob{(H1)}{7}{white}
\blob{(I1)}{8}{white}
\blob{(J1)}{9}{white}
\blob{(K1)}{10}{white}
\blob{(L1)}{11}{white}
\uncover<1>{
\blob{(M1)}{12}{white}
}
\blob{(N1)}{13}{white}
\blob{(O1)}{14}{white}
\node at (6,0) {\begin{minipage}{5cm}
\begin{itemize}
\item<3-> Nicht eindeutig
\item<5-> geradeste Wege sind nicht unbedingt die kürzesten
\item<7-> Gewichtung der Kanten
($\text{Schnellstrassen}\ne\text{Feldwege}$)
\item<8-> Orientierung der Kanten?
\end{itemize}
\end{minipage}};
\end{tikzpicture}
\end{center}
\end{frame}
|
