diff options
| -rw-r--r-- | graph/edmondsKarp.cpp (renamed from maxFlow/edmondsKarp.cpp) | 4 | ||||
| -rw-r--r-- | graph/graph.tex | 7 | ||||
| -rw-r--r-- | graph/scc.cpp | 54 | ||||
| -rw-r--r-- | maxFlow/maxFlow.tex | 4 | ||||
| -rw-r--r-- | maxFlow/q.log | 25 | ||||
| -rw-r--r-- | sonstiges/.2sat.cpp.kate-swp | bin | 0 -> 325 bytes | |||
| -rw-r--r-- | sonstiges/2sat.cpp | 63 | ||||
| -rw-r--r-- | sonstiges/sonstiges.tex | 7 | ||||
| -rw-r--r-- | tcr.pdf | bin | 81835 -> 111986 bytes | |||
| -rw-r--r-- | tcr.tex | 2 |
10 files changed, 70 insertions, 96 deletions
diff --git a/maxFlow/edmondsKarp.cpp b/graph/edmondsKarp.cpp index ccfb1d2..26c5b0d 100644 --- a/maxFlow/edmondsKarp.cpp +++ b/graph/edmondsKarp.cpp @@ -10,7 +10,7 @@ void augment(int v, int minEdge) { res[p[v]][v] -= f; res[v][p[v]] += f; }} -nt maxFlow() { //first inititalize res, adjList, s and t +int maxFlow() { //first inititalize res, adjList, s and t int mf = 0; while (true) { f = 0; @@ -30,5 +30,5 @@ nt maxFlow() { //first inititalize res, adjList, s and t if (f == 0) break; mf += f; } - return maxFlow; + return mf; }
\ No newline at end of file diff --git a/graph/graph.tex b/graph/graph.tex new file mode 100644 index 0000000..1c37bc7 --- /dev/null +++ b/graph/graph.tex @@ -0,0 +1,7 @@ +\section{Graph} + +\subsection{Strongly Connected Components (\textsc{Tarjans}-Algorithmus)} +\lstinputlisting{graph/scc.cpp} + +\subsection{Max-Flow (\textsc{Edmonds-Karp}-Algorithmus)} +\lstinputlisting{graph/edmondsKarp.cpp}
\ No newline at end of file diff --git a/graph/scc.cpp b/graph/scc.cpp new file mode 100644 index 0000000..b33616b --- /dev/null +++ b/graph/scc.cpp @@ -0,0 +1,54 @@ +int counter, sccCounter, n; //n == number of vertices +vector<bool> visited, inStack; +vector< vector<int> > adjlist; +vector<int> d, low, sccs; +stack<int> s; + +void visit(int v) { + visited[v] = true; + d[v] = counter; + low[v] = counter; + counter++; + inStack[v] = true; + s.push(v); + + for (int i = 0; i < (int)adjlist[v].size(); i++) { + int u = adjlist[v][i]; + if (!visited[u]) { + visit(u); + low[v] = min(low[v], low[u]); + } else if (inStack[u]) { + low[v] = min(low[v], low[u]); + } + } + + if (d[v] == low[v]) { + int u; + do { + u = s.top(); + s.pop(); + inStack[u] = false; + sccs[u] = sccCounter; + } while(u != v); + sccCounter++; + } +} + +void scc() { + //read adjlist + + visited.clear(); visited.assign(n, false); + d.clear(); d.resize(n); + low.clear(); low.resize(n); + inStack.clear(); inStack.assign(n, false); + sccs.clear(); sccs.resize(n); + + counter = 0; + sccCounter = 0; + for (i = 0; i < n; i++) { + if (!visited[i]) { + visit(i); + } + } + //sccs has the component for each vertex +}
\ No newline at end of file diff --git a/maxFlow/maxFlow.tex b/maxFlow/maxFlow.tex deleted file mode 100644 index a88e5ff..0000000 --- a/maxFlow/maxFlow.tex +++ /dev/null @@ -1,4 +0,0 @@ -\section{Max Flows} -\subsection{\textsc{Edmonds-Karp}-Algorithmus} - -\lstinputlisting{maxFlow/edmondsKarp.cpp}
\ No newline at end of file diff --git a/maxFlow/q.log b/maxFlow/q.log deleted file mode 100644 index 2a742c3..0000000 --- a/maxFlow/q.log +++ /dev/null @@ -1,25 +0,0 @@ -This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2014.5.4) 25 OCT 2014 13:42 -entering extended mode - restricted \write18 enabled. - %&-line parsing enabled. -**tcr.tex -(/usr/share/texlive/texmf-dist/tex/latex/tools/q.tex -LaTeX2e <2011/06/27> -Babel <3.9h> and hyphenation patterns for 7 languages loaded. -File ignored -) -! Emergency stop. -<*> tcr.tex - -*** (job aborted, no legal \end found) - - -Here is how much of TeX's memory you used: - 7 strings out of 494976 - 248 string characters out of 6179138 - 46219 words of memory out of 5000000 - 3331 multiletter control sequences out of 15000+600000 - 3640 words of font info for 14 fonts, out of 8000000 for 9000 - 14 hyphenation exceptions out of 8191 - 5i,0n,1p,87b,8s stack positions out of 5000i,500n,10000p,200000b,80000s -! ==> Fatal error occurred, no output PDF file produced! diff --git a/sonstiges/.2sat.cpp.kate-swp b/sonstiges/.2sat.cpp.kate-swp Binary files differnew file mode 100644 index 0000000..b688b2e --- /dev/null +++ b/sonstiges/.2sat.cpp.kate-swp diff --git a/sonstiges/2sat.cpp b/sonstiges/2sat.cpp deleted file mode 100644 index 627e484..0000000 --- a/sonstiges/2sat.cpp +++ /dev/null @@ -1,63 +0,0 @@ -vector< vector<int> > adjlist; //adjazenzliste -vector<int> sccs; //speichert die gefundenen SCCs -vector<bool> visited; //welcher Knoten ist schon besucht worden (in der DFS) -vector<bool> inStack; //ist Knoten gerade im Stack -vector<int> d; //discovery time -vector<int> low; //wie weit hoch geht's im Tiefensuchbaum -int counter; //Zaehler fuer discovery time -stack<int> st; //der Stack -int sccCounter; //Zaehler fuer SCCs - -//Tiefensuche, die starke Zusammenhangskomponenten findet -void visit(int v) { - visited[v] = true; - d[v] = counter; - low[v] = counter; - counter++; - st.push(v); - inStack[v] = true; - - for (int i = 0; i < (int)adjlist[v].size(); i++) { - int w = adjlist[v][i]; - - if (!visited[w]) { - visit(w); - low[v] = min(low[v], low[w]); - } else if (inStack[w]) { - low[v] = min(low[v], low[w]); - } - } - - if (low[v] == d[v]) { - int next; - do { - next = st.top(); - st.pop(); - sccs[next] = sccCounter; - inStack[next] = false; - } while (next != v); - - sccCounter++; - } -} - -void solve() { - //adjlist initialisieren - //(a || b) wird zu (!a => b) und (!b => a) - - visited.clear(); visited.assign(adjlist.size(), false); - inStack.clear(); inStack.assign(adjlist.size(), false); - d.clear(); d.assign(adjlist.size(), false); - low.clear(); low.assign(adjlist.size(), false); - sccs.clear(); sccs.resize(adjlist.size()); - - counter = 0; - sccCounter = 0; - for (i = 0; i < (int)adjlist.size(); i++) { - if (!visited[i]) { - visit(i); - sccCounter++; - } - } - // genau dann loesbar, wenn keine Variable in gleicher SCC wie Negation ist -}
\ No newline at end of file diff --git a/sonstiges/sonstiges.tex b/sonstiges/sonstiges.tex index 0befff3..09ea14c 100644 --- a/sonstiges/sonstiges.tex +++ b/sonstiges/sonstiges.tex @@ -1,4 +1,9 @@ \section{Sonstiges} \subsection{2-SAT} -\lstinputlisting{sonstiges/2sat.cpp}
\ No newline at end of file +\begin{enumerate} + \item Bedingungen in 2-CNF formulieren. + \item Implikationsgraph bauen, $\left(a \vee b\right)$ wird zu $\neg a \Rightarrow b$ und $\neg b \Rightarrow a$. + \item Finde die starken Zusammenhangskomponenten. + \item Genau dann lösbar, wenn keine Variable mit ihrer Negation in einer SCC liegt. +\end{enumerate}
\ No newline at end of file Binary files differ@@ -47,7 +47,7 @@ \tableofcontents \newpage -\input{maxFlow/maxFlow} +\input{graph/graph} \input{geometry/geometry} \input{sonstiges/sonstiges} |