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MATH2-Inf-10: Aufgabe 1 bearbeitet.

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Jim Martens 2014-01-06 12:01:41 +01:00
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optimierung/Uebungsblatt10.tex
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@ -37,7 +37,101 @@ Stephan Niendorf (6242417)}
\title{Hausaufgaben zum 6. Januar}
\maketitle
\section{} %1
\begin{tikzpicture}[node distance=2cm]
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\node (a) [above right=of s] {a};
\node (b) [right=of s] {b};
\node (c) [below right=of s] {c};
\node (d) [right=of c] {d};
\node (e) [right=of b] {e};
\node (t) [right=of e] {t};
\node (sCap) [below=0.1 of s] {(-, $\infty$)};
\node (aCap) [above=0.1 of a] {(s, +, 3)};
\node (bCap) [above=0.1 of b] {(s, +, 5)};
\node (cCap) [below=0.1 of c] {(s, +, 6)};
\node (tCap) [above=0.1 of t] {(a, +, 3)};
\path[->] (s) edge[line width=2pt] node [above left] {0(3)} (a)
(s) edge node [below] {0(5)} (b)
(s) edge node [below left] {0(6)} (c)
(a) edge[line width=2pt] node [above right] {0(5)} (t)
(b) edge node [below] {0(2)} (e)
(b) edge node [below left] {0(6)} (d)
(c) edge node [below] {0(4)} (d)
(d) edge node [below right] {0(5)} (t)
(e) edge node [below] {0(3)} (t);
\end{tikzpicture}
\begin{tikzpicture}[node distance=2cm]
\node (s) {s};
\node (a) [above right=of s] {a};
\node (b) [right=of s] {b};
\node (c) [below right=of s] {c};
\node (d) [right=of c] {d};
\node (e) [right=of b] {e};
\node (t) [right=of e] {t};
\node (sCap) [below=0.1 of s] {(-, $\infty$)};
\node (bCap) [above=0.1 of b] {(s, +, 5)};
\node (cCap) [below=0.1 of c] {(s, +, 6)};
\node (dCap) [below=0.1 of d] {(b, +, 6)};
\node (tCap) [above=0.1 of t] {(d, +, 5)};
\path[->] (s) edge node [above left] {3(3)} (a)
(s) edge[line width=2pt] node [below] {0(5)} (b)
(s) edge node [below left] {0(6)} (c)
(a) edge node [above right] {3(5)} (t)
(b) edge node [below] {0(2)} (e)
(b) edge[line width=2pt] node [below left] {0(6)} (d)
(c) edge node [below] {0(4)} (d)
(d) edge[line width=2pt] node [below right] {0(5)} (t)
(e) edge node [below] {0(3)} (t);
\end{tikzpicture}
\begin{tikzpicture}[node distance=2cm]
\node (s) {s};
\node (a) [above right=of s] {a};
\node (b) [right=of s] {b};
\node (c) [below right=of s] {c};
\node (d) [right=of c] {d};
\node (e) [right=of b] {e};
\node (t) [right=of e] {t};
\node (sCap) [below=0.1 of s] {(-, $\infty$)};
\node (eCap) [below=0.1 of e] {(b, +, 2)};
\node (cCap) [below=0.1 of c] {(s, +, 6)};
\node (dCap) [below=0.1 of d] {(c, +, 4)};
\node (tCap) [above=0.1 of t] {(e, +, 2)};
\node (bCap) [above=0.1 of b] {(d, -, 5)};
\path[->] (s) edge node [above left] {3(3)} (a)
(s) edge node [below] {5(5)} (b)
(s) edge[line width=2pt] node [below left] {0(6)} (c)
(a) edge node [above right] {3(5)} (t)
(b) edge[line width=2pt] node [below] {0(2)} (e)
(b) edge[line width=2pt] node [below left] {5(6)} (d)
(c) edge[line width=2pt] node [below] {0(4)} (d)
(d) edge node [below right] {5(5)} (t)
(e) edge[line width=2pt] node [below] {0(3)} (t);
\end{tikzpicture}
\begin{tikzpicture}[node distance=2cm]
\node (s) {s};
\node (a) [above right=of s] {a};
\node (b) [right=of s] {b};
\node (c) [below right=of s] {c};
\node (d) [right=of c] {d};
\node (e) [right=of b] {e};
\node (t) [right=of e] {t};
\node (sCap) [below=0.1 of s] {(-, $\infty$)};
\node (cCap) [below=0.1 of c] {(s, +, 4)};
\node (dCap) [below=0.1 of d] {(c, +, 2)};
\node (bCap) [above=0.1 of b] {(d, -, 3)};
\path[->] (s) edge node [above left] {3(3)} (a)
(s) edge node [below] {5(5)} (b)
(s) edge node [below left] {2(6)} (c)
(a) edge node [above right] {3(5)} (t)
(b) edge node [below] {2(2)} (e)
(b) edge node [below left] {3(6)} (d)
(c) edge node [below] {2(4)} (d)
(d) edge node [below right] {5(5)} (t)
(e) edge node [below] {2(3)} (t);
\end{tikzpicture}
\section{} %2
\subsection{} %a
\begin{alignat*}{9}