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B*?<55 diff --git a/documents/Programmierparadigmen/Programmierparadigmen.tex b/documents/Programmierparadigmen/Programmierparadigmen.tex index 6ead892..b5f0fe8 100644 --- a/documents/Programmierparadigmen/Programmierparadigmen.tex +++ b/documents/Programmierparadigmen/Programmierparadigmen.tex @@ -53,6 +53,17 @@ \usepackage{wasysym} \usepackage[binary-units = true]{siunitx} % this package is for units! \sisetup{locale=DE} + +%%% Pseudocode settings +\usepackage{algorithm,algpseudocode} +\algtext*{EndIf} % Remove "end if" text +\algtext*{EndWhile} % Remove "end while" text +\algtext*{EndFunction} % Remove "end while" text +\algnewcommand\Global{\textbf{global }} +\makeatletter +\addto\captionsngerman{\renewcommand{\ALG@name}{Algorithmus}} +\makeatother +%%% End of Pseudocode settings \usepackage{shortcuts} \usepackage{fancyhdr} diff --git a/documents/Programmierparadigmen/Programmiersprachen.tex b/documents/Programmierparadigmen/Programmiersprachen.tex index 10ef06f..935c245 100644 --- a/documents/Programmierparadigmen/Programmiersprachen.tex +++ b/documents/Programmierparadigmen/Programmiersprachen.tex @@ -181,4 +181,39 @@ Manchmal werden Seiteneffekte auch als Nebeneffekt oder Wirkung bezeichnet. \end{beispiel} \footnotetext{Folie 268 von Prof. Snelting} +\begin{algorithm}[h] + \begin{algorithmic} + \Function{unify}{Gleichungsmenge $C$} + \If{$C == \emptyset$} + \State \Return $[]$ + \Else + \State Es sei $\Set{\theta_l = \theta_r} \cup C' == C$ + + \If{$\theta_l == \theta_r$} + \State \Call{unify}{$C'$} + \ElsIf{$\theta_l == Y$ and $Y \notin FV(\theta_r)$} + \State \Call{unify}{$[Y \text{\pointer} \theta_r] C'$} $\circ [Y \text{\pointer} \theta_r]$ + \ElsIf{$\theta_r == Y$ and $Y \notin FV(\theta_l)$} + \State \Call{unify}{$[Y \text{\pointer} \theta_l] C'$} $\circ [Y \text{\pointer} \theta_l]$ + \ElsIf{$\theta_l == f(\theta_l^1, \dots, \theta_l^n)$ and $\theta_r == f(\theta_r^1, \dots, \theta_r^n$} + \State \Call{unify}{$C' \cup \Set{\theta_l^1 = \theta_r^1, \dots \theta_l^n = \theta_r^n}$} + \Else + \State fail + \EndIf + \EndIf + \EndFunction + \end{algorithmic} +\caption{Klassischer Unifikationsalgorithmus} +\label{alg:klassischer-unifikationsalgorithmus} +\end{algorithm} + +Dieser klassische Algorithmus hat eine Laufzeit von $\mathcal{O}(2^n)$ für folgendes +Beispiel: + +\[f(X_1, X_2, \dots, X_n) = f(g(X_0, X_0), g(X_1, X_1), \dots, g(X_{n-1}, X_{n-1}) )\] + +Der \textit{Paterson-Wegman-Unifikationsalgorithmus}\xindex{Paterson-Wegman-Unifikationsalgorithmus} ist deutlich effizienter. +Er basiert auf dem \textit{Union-Find-Algorithmus}\xindex{Union-Find-Algorithmus}. + + \footnotetext{\url{https://de.wikipedia.org/w/index.php?title=Unifikation\_(Logik)&oldid=116848554\#Beispiel}} \ No newline at end of file