From 564dbc9790bcb93cdbc7624ba7e78ffa61719b2b Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Tue, 25 Mar 2014 16:05:28 +0100 Subject: [PATCH] =?UTF-8?q?Polnische=20Notation=20/=20Infix,=20Pr=C3=A4-?= =?UTF-8?q?=20und=20Postfixnotation?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../Programmierparadigmen/Java-Bytecode.tex | 50 +++++++++++++++++- .../Programmierparadigmen.pdf | Bin 844797 -> 849459 bytes 2 files changed, 48 insertions(+), 2 deletions(-) diff --git a/documents/Programmierparadigmen/Java-Bytecode.tex b/documents/Programmierparadigmen/Java-Bytecode.tex index 4f3775f..abdc0b8 100644 --- a/documents/Programmierparadigmen/Java-Bytecode.tex +++ b/documents/Programmierparadigmen/Java-Bytecode.tex @@ -13,8 +13,6 @@ Bytecode ist unabhängig von realer Hardware. und in beliebiger Reihenfolge wieder freigegeben werden können. \end{definition} - - \textit{Activation Record} ist ein \textit{Stackframe}.\index{Activation Record|see{Stackframe}} \section{Instruktionen} \begin{table}[h] @@ -29,8 +27,56 @@ Bytecode ist unabhängig von realer Hardware. \end{tabular} \end{table} +\section{Polnische Notation} +\begin{definition}[Schreibweise von Rechenoperationen] + Sei $f: A \times B \rightarrow C$ eine Funktion, $a \in A$ und $b \in B$. + + \begin{defenum} + \item Die Schreibweise $a\ f\ b$ heißt \textbf{Infix-Notation}\xindex{Infix-Notation}. + \item Die Schreibweise $f\ a\ b$ heißt \textbf{Präfixnotation}\xindex{Präfixnotation} + \item Die Schreibweise $a\ b\ f$ heißt \textbf{Postfixnotation}\xindex{Postfixnotation}. + \end{defenum} +\end{definition} + +\textit{Polnische Notation}\index{Notation!polnische|see{Präfixnotation}} ist ein Synonym für die Präfixnotation. + +\textit{Umgekehrte polnische Notation}\index{Notation!umgekehrte polnische|see{Postfixnotation}} ist ein Synonym für die Postfixnotation. + +\begin{beispiel}[Schreibweise von Rechenoperationen] + \begin{bspenum} + \item $1 + 2$ nutzt die Infix-Notation. + \item $f\ a\ b$ nutzt die polnische Notation. + \item Wir der Ausdruck $1 + 2 \cdot 3$ in Infix-Notation ohne Operatoren-Präzedenz + ausgewertet, so gilt: + \[1 + 2 \cdot 3 = 9\] + Wird er mit Operatoren-Präzendenz ausgewertet, so gilt: + \[1 + 2 \cdot 3 = 7\] + \item Der Ausdruck + \[1 + 2 \cdot 3 = 7\] + entspricht + \[+\ 1\ \cdot\ 2\ 3\] + in der polnischen Notation und + \[1\ 2\ 3\ \cdot\ +\] + in der umgekehrten polnischen Notation. + \end{bspenum} +\end{beispiel} + +\begin{bemerkung}[Eigenschaften der Prä- und Postfixnotation] + \begin{bemenum} + \item Die Reihenfolge der Operanden kann beibehalten und gleichzeitig + auf Klammern verzichtet werden, ohne dass sich das Ergebnis + verändert. + \item Die Infix-Notation kann in einer Worst-Case Laufzeit von $\mathcal{O}(n)$, + wobei $n$ die Anzahl der Tokens ist mittels des + \textit{Shunting-yard-Algorithmus}\xindex{Shunting-yard-Algorithmus} in + die umgekehrte Polnische Notation überführt werden. + \end{bemenum} +\end{bemerkung} + \section{Weitere Informationen} \begin{itemize} \item \url{http://cs.au.dk/~mis/dOvs/jvmspec/ref-Java.html} + \item \href{http://scanftree.com/Data_Structure/prefix-postfix-infix-online-converter}{scanftree.com}: + Infix $\leftrightarrow$ Postfix Konverter \end{itemize} \index{Java Bytecode|)} \ No newline at end of file diff --git a/documents/Programmierparadigmen/Programmierparadigmen.pdf b/documents/Programmierparadigmen/Programmierparadigmen.pdf index e906034f1d3e768763a7eded9b29a550e4a7af38..b9017042a0db2e1768ee63c67c80206c5a967ab2 100644 GIT binary patch delta 171383 zcmZsi1yEbvyRQlE4#nL)xVt;W-JRlY!M!*Q#jUu95-9HO#kII=fdVbue*f>>bIzT) zGkf;DS(BOUWUtA7*7JMUpAjC&IZvZ1Dl8utL>-k800zVX@WEj;aOwa)@Qo@Q0ptSh z93CJ54mX3tgIr)s!DY_g5Sl9APie(tK$%HfBG9(yJu-@R;9r%fcwv4hET$js#QbbTJMY?N4IsR(88 zQ=Tq9@yGJaS;2XK?@vlzlB7xsCmJ@Hj7R9i6^zq{+!XS8j2To%u!a|-O*Dz(BROoK z0XC6lob3a{K1_wte(^oSp9kQL!2p%ogH1eUa1au;WEza9wE0qAuTh_alQ- 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