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diff --git a/Master/texmf-dist/source/latex/algorithms/algorithms.dtx b/Master/texmf-dist/source/latex/algorithms/algorithms.dtx new file mode 100644 index 00000000000..f90ef4799dc --- /dev/null +++ b/Master/texmf-dist/source/latex/algorithms/algorithms.dtx @@ -0,0 +1,1272 @@ +% \iffalse meta-comment +% +% Copyright (C) 1994-2004 Peter Williams <pwil3058@bigpond.net.au> +% Copyright (C) 2005-2009 Rogério Brito <rbrito@ime.usp.br> +% +% This document file is free software; you can redistribute it and/or +% modify it under the terms of the GNU Lesser General Public License as +% published by the Free Software Foundation; either version 2 of the +% License, or (at your option) any later version. +% +% This document file is distributed in the hope that it will be useful, but +% WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser +% General Public License for more details. +% +% You should have received a copy of the GNU Lesser General Public License +% along with this document file; if not, write to the Free Software +% Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 +% USA. +% +% \fi +% +% \iffalse +%<algorithm>\NeedsTeXFormat{LaTeX2e}[1999/12/01] +%<algorithm>\ProvidesPackage{algorithm} +%<algorithm> [2009/08/24 v0.1 Document Style `algorithm' - floating environment] +% +%<algorithmic>\NeedsTeXFormat{LaTeX2e}[1999/12/01] +%<algorithmic>\ProvidesPackage{algorithmic} +%<algorithmic> [2009/08/24 v0.1 Document Style `algorithmic'] +% +% +%<*driver> +\documentclass{ltxdoc} +\usepackage[latin1]{inputenc} +\usepackage[T1]{fontenc} +\usepackage[sc]{mathpazo} +\usepackage[pdfstartview={FitH}]{hyperref} +\usepackage{algorithm} +\usepackage{algorithmic} +\usepackage{multicol} +\EnableCrossrefs +\CodelineIndex +\RecordChanges +\begin{document} + \DocInput{algorithms.dtx} +\end{document} +%</driver> +% \fi +% +%\CheckSum{0} +% \CharacterTable +% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z +% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z +% Digits \0\1\2\3\4\5\6\7\8\9 +% Exclamation \! Double quote \" Hash (number) \# +% Dollar \$ Percent \% Ampersand \& +% Acute accent \' Left paren \( Right paren \) +% Asterisk \* Plus \+ Comma \, +% Minus \- Point \. Solidus \/ +% Colon \: Semicolon \; Less than \< +% Equals \= Greater than \> Question mark \? +% Commercial at \@ Left bracket \[ Backslash \\ +% Right bracket \] Circumflex \^ Underscore \_ +% Grave accent \` Left brace \{ Vertical bar \| +% Right brace \} Tilde \~} +% +% \changes{v0.1}{2009/08/24}{Migrated the package to .ins and .dtx format} +% +% \GetFileInfo{algorithm.sty} +% \GetFileInfo{algorithmic.sty} +% \DoNotIndex{\#,\$,\%,\&,\@,\\,\{,\},\^,\_,\~,\ } +% \DoNotIndex{\@ne} +% \DoNotIndex{\advance,\begingroup,\catcode,\closein} +% \DoNotIndex{\closeout,\day,\def,\edef,\else,\empty,\endgroup} +% +% \title{The \textsf{algorithms} bundle\thanks{This document +% corresponds to \textsf{algorithms}~\fileversion, +% dated~\filedate.}} +% \author{Rogério Brito\\ \href{mailto:rbrito@ime.usp.br}{\texttt{rbrito@ime.usp.br}}} +% +% \newcommand{\keyword}[1]{\texttt{#1}} +% \newcommand{\nameoffile}[1]{\texttt{#1}} +% +% \setcounter{tocdepth}{2} +% +% \addtocontents{toc}{\protect\begin{multicols}{2}} +% \maketitle +% \tableofcontents +% \listofalgorithms +% +% % \newtheorem{warning}{Warning} +% \renewcommand{\thewarning}{} +% +% \section{Introduction} +% +% This package provides two environments, \keyword{algorithmic} and +% \keyword{algorithm}, which are designed to be used together but may, +% depending on the necessities of the user, be used separately. +% +% The \keyword{algorithmic} environment provides an environment for +% describing algorithms and the \keyword{algorithm} environment provides +% a ``float'' wrapper for algorithms (implemented using +% \keyword{algorithmic} or some other method at the users's option). +% The reason for two environments being provided is to allow the user +% maximum flexibility. +% +% This work may be distributed and/or modified under the conditions of +% the GNU Lesser General Public License, either version 2 of the +% License, or (at your option) any later version, as published by the +% Free Software Foundation. See the file \nameoffile{COPYING} included +% in this package for further details. +% +% Currently, this package consists of the following files: +% \begin{itemize} +% \item \nameoffile{algorithms.ins}: the driver file +% \item \nameoffile{algorithms.dtx}: the source file +% \item \nameoffile{COPYING}: the license file +% \item \nameoffile{README}: remarks about the package +% \item \nameoffile{THANKS}: mentions of thanks for contributors to +% the package +% \end{itemize} +% +% Starting with with the 2009-08-24 release, the package is now +% versioned and this document corresponds to version~\fileversion. +% +% If you use this package, the author would kindly appreciate if you +% mentioned it in your documents, so as to let the package be better +% known and have more contributors, to make it better for the community +% itself. This is \emph{not} required by the license: it's just a +% friendly request. +% +%\section{Installation} +% +% The installation procedure of \textsf{algorithms} follows the usual +% practice of packages shipped with a pair of +% \nameoffile{.ins}/\nameoffile{.dtx}---simply type the comand: +% \begin{quote} +% \texttt{latex algorithms.ins} +% \end{quote} +% and the \nameoffile{.sty} files will be generated. Copy them to a +% place that is referenced by your \LaTeX{} distribution. To generate +% the documentation, type: +% \begin{quote} +% \texttt{latex algorithms.dtx} +% \end{quote} +% +% \section[Environment: \keyword{algorithmic}]% +% {The \keyword{algorithmic} Environment} +% \label{sec:algorithmic-envir} +% Within an \keyword{algorithmic} a number of commands for typesetting +% popular algorithmic constructs are available. In general, the +% commands provided can be arbitrarily nested to describe quite complex +% algorithms. An optional argument to the \verb+\begin{algorithmic}+ +% statement can be used to turn on line numbering by giving a positive +% integer indicating the required frequency of line numbering. For +% example, \verb+\begin{algorithmic}[5]+ would cause every fifth line +% to be numbered. +% +% \subsection{The Simple Statement} +% +% The simple statement takes the form +% \begin{verbatim} +% \STATE <text> +% \end{verbatim} +% and is used for simple statements. For example, +% \begin{verbatim} +% \begin{algorithmic} +% \STATE $S \leftarrow 0$ +% \end{algorithmic} +% \end{verbatim} +% would produce +% \begin{algorithmic} +% \STATE $S \leftarrow 0$ +% \end{algorithmic} +% With line numbering selected for every line, using, +% \begin{verbatim} +% \begin{algorithmic}[1] +% \STATE $S \leftarrow 0$ +% \end{algorithmic} +% \end{verbatim} +% we would get +% \begin{algorithmic}[1] +% \STATE $S \leftarrow 0$ +% \end{algorithmic} +% +% \begin{warning} +% For users of earlier versions of \keyword{algorithmic} this +% construct is a cause of an incompatibility. In the earlier version, +% instead of starting simple statements with the \verb+\STATE+ +% command, simple statements were entered as free text and terminated +% with \verb+\\+ command. Unfortunately, this simpler method failed +% to survive the modifications necessary for statement numbering. +% However, the \verb+\\+ command can still be used to force a line +% break within a simple statement. +% \end{warning} +% +%\subsection{The \emph{if-then-else} Statement} +% +% The \emph{if-then-else} construct takes the forms: +% \begin{verbatim} +% \IF{<condition>} <text> \ENDIF +% \IF{<condition>} <text1> \ELSE <text2> \ENDIF +% \IF{<condition1>} <text1> \ELSIF{<condition2>} <text2> \ELSE <text3> \ENDIF +% \end{verbatim} +% +% In the third of these forms there is no limit placed on the number of +% \verb+\ELSIF{<condition>}+ that may be used. For example, +% \begin{verbatim} +% \begin{algorithmic} +% \IF{some condition is true} +% \STATE do some processing +% \ELSIF{some other condition is true} +% \STATE do some different processing +% \ELSIF{some even more bizarre condition is met} +% \STATE do something else +% \ELSE +% \STATE do the default actions +% \ENDIF +% \end{algorithmic} +% \end{verbatim} +% would produce +% \begin{algorithmic} +% \IF{some condition is true} +% \STATE do some processing +% \ELSIF{some other condition is true} +% \STATE do some different processing +% \ELSIF{some even more bizarre condition is met} +% \STATE do something else +% \ELSE +% \STATE do the default actions +% \ENDIF +% \end{algorithmic} +% with appropriate indentations. +% +% \subsection{The \emph{for} Loop} +% +% The \emph{for} loop takes two forms. Namely: +% \begin{verbatim} +% \FOR{<condition>} <text> \ENDFOR +% \FORALL{<condition>} <text> \ENDFOR +% \end{verbatim} +% +% \noindent For example, +% \begin{verbatim} +% \begin{algorithmic} +% \FOR{$i=0$ to $10$} +% \STATE carry out some processing +% \ENDFOR +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic} +% \FOR{$i=0$ to $10$} +% \STATE carry out some processing +% \ENDFOR +% \end{algorithmic} +% and +% \begin{verbatim} +% \begin{algorithmic}[1] +% \FORALL{$i$ such that $0\leq i\leq 10$} +% \STATE carry out some processing +% \ENDFOR +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic}[1] +% \FORALL{$i$ such that $0\leq i\leq 10$} +% \STATE carry out some processing +% \ENDFOR +% \end{algorithmic} +% +% \subsubsection{The \emph{to} Connective} +% As may be clear from the usage of loops above, we usually want to +% specify ranges over which a variable will assume values. To help make +% this typographically distinct, the \keyword{algorithmic} package now +% supports the \algorithmicto{} connective, which can be used like: +% \begin{verbatim} +% \begin{algorithmic} +% \FOR{$i=0$ \TO $10$} +% \STATE carry out some processing +% \ENDFOR +% \end{algorithmic} +% \end{verbatim} +% to produce the output +% \begin{algorithmic} +% \FOR{$i=0$ \TO $10$} +% \STATE carry out some processing +% \ENDFOR +% \end{algorithmic} +% +% \subsection{The \emph{while} Loop} +% +% The \emph{while} loop takes the form +% \begin{verbatim} +% \WHILE{<condition>} <text> \ENDWHILE +% \end{verbatim} +% For example, +% \begin{verbatim} +% \begin{algorithmic} +% \WHILE{some condition holds} +% \STATE carry out some processing +% \ENDWHILE +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic} +% \WHILE{some condition holds} +% \STATE carry out some processing +% \ENDWHILE +% \end{algorithmic} +% +% \subsection{The \emph{repeat-until} Loop} +% +% The \emph{repeat-until} loop takes the form. +% \begin{verbatim} +% \REPEAT <text> \UNTIL{<condition>} +% \end{verbatim} +% For example, +% \begin{verbatim} +% \begin{algorithmic} +% \REPEAT +% \STATE carry out some processing +% \UNTIL{some condition is met} +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic} +% \REPEAT +% \STATE carry out some processing +% \UNTIL{some condition is met} +% \end{algorithmic} +% +% \subsection{The Infinite Loop} +% +% The infinite loop takes the form. +% \begin{verbatim} +% \LOOP <text> \ENDLOOP +% \end{verbatim} +% For example, +% \begin{verbatim} +% \begin{algorithmic} +% \LOOP +% \STATE this processing will be repeated forever +% \ENDLOOP +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic} +% \LOOP +% \STATE this processing will be repeated forever +% \ENDLOOP +% \end{algorithmic} +% +% \subsection{The Logical Connectives} +% +% The connectives \algorithmicand, \algorithmicor, \algorithmicxor{} and +% \algorithmicnot{} can be used in boolean expressions in the familiar, +% expected way: +% \begin{verbatim} +% <expression> \AND <expression> +% <expression> \OR <expression> +% <expression> \XOR <expression> +% \NOT <expression> +% \end{verbatim} +% according to their arity.\footnote{But there is nothing that prevents +% the user from violating the arity, from a syntatic point of view.} +% For example, +% \begin{verbatim} +% \begin{algorithmic} +% \IF{\NOT ($year \bmod 400$ \XOR $year \bmod 100$ \XOR $year \bmod 4$)} +% \STATE $year$ does not represent a leap year. +% \ENDIF +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic} +% \IF{\NOT ($year \bmod 400$ \XOR $year \bmod 100$ \XOR $year \bmod 4$)} +% \STATE $year$ does not represent a leap year. +% \ENDIF +% \end{algorithmic} +% +% \subsection{The Precondition} +% +% The precondition (that must be met if an algorithm is to correctly +% execute) takes the form: +% \begin{verbatim} +% \REQUIRE <text> +% \end{verbatim} +% For example, +% \begin{verbatim} +% \begin{algorithmic} +% \REQUIRE $x \neq 0$ and $n \geq 0$ +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic} +% \REQUIRE $x \neq 0$ and $n \geq 0$ +% \end{algorithmic} +% +% \subsection{The Postcondition} +% +% The postcondition (that must be met after an algorithm has correctly +% executed) takes the form: +% \begin{verbatim} +% \ENSURE <text> +% \end{verbatim} +% For example, +% \begin{verbatim} +% \begin{algorithmic} +% \ENSURE $x \neq 0$ and $n \geq 0$ +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic} +% \ENSURE $x \neq 0$ and $n \geq 0$ +% \end{algorithmic} +% +% \subsection{Returning Values} +% +% The \keyword{algorithmic} environment offers a special statement for +% explicitly returning values in algorithms. It has the syntax: +% \begin{verbatim} +% \RETURN <text> +% \end{verbatim} +% For example, +% \begin{verbatim} +% \begin{algorithmic} +% \RETURN $(x+y)/2$ +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic} +% \RETURN $(x+y)/2$ +% \end{algorithmic} +% +% +% \subsubsection{The ``true'' and ``false'' Values} +% +% Since many algorithms have the necessity of returning \emph{true} or +% \emph{false} values, \keyword{algorithms}, starting with version +% 2006-06-02, includes the keywords \verb+\TRUE+ and \verb+\FALSE+, +% which are intented to print the values in a standard fashion, like the +% following snippet of an algorithm to decide if an integer $n$ is even or +% odd: +% \begin{verbatim} +% \begin{algorithmic} +% \IF{$n$ is odd} +% \RETURN \TRUE +% \ELSE +% \RETURN \FALSE +% \ENDIF +% \end{algorithmic} +% \end{verbatim} +% The code above produces the following output: +% \begin{algorithmic} +% \IF{$n$ is odd} +% \RETURN \TRUE +% \ELSE +% \RETURN \FALSE +% \ENDIF +% \end{algorithmic} +% +% \subsection{Printing Messages} +% +% Another feature of the \keyword{algorithmic} environment is that it +% currently provides a standard way of printing values (which is an +% operation used enough to merit its own keyword). It has the syntax: +% \begin{verbatim} +% \PRINT <text> +% \end{verbatim} +% For example, +% \begin{verbatim} +% \begin{algorithmic} +% \PRINT \texttt{``Hello, World!''} +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic} +% \PRINT \texttt{``Hello, World!''} +% \end{algorithmic} +% +% \subsection{Comments} +% +% Comments may be inserted at most points in an algorithm using the form: +% \begin{verbatim} +% \COMMENT{<text>} +% \end{verbatim} +% For example, +% \begin{verbatim} +% \begin{algorithmic} +% \STATE do something \COMMENT{this is a comment} +% \end{algorithmic} +% \end{verbatim} +% produces +% \begin{algorithmic} +% \STATE do something \COMMENT{this is a comment} +% \end{algorithmic} +% Because the mechanisms used to build the various algorithmic structures +% make it difficult to use the above mechanism for placing comments at the +% end of the first line of a construct, the commands \verb+\IF+, +% \verb+\ELSIF+, \verb+\ELSE+, \verb+\WHILE+, \verb+\FOR+, \verb+\FORALL+, +% \verb+\REPEAT+ and \verb+\LOOP+ all take an optional argument which will +% be treated as a comment to be placed at the end of the line on which +% they appear. For example, +% \begin{algorithmic} +% \REPEAT[this is comment number one] +% \IF[this is comment number two]{condition one is met} +% \STATE do something +% \ELSIF[this is comment number three]{condition two is met} +% \STATE do something else +% \ELSE[this is comment number four] +% \STATE do nothing +% \ENDIF +% \UNTIL{hell freezes over} +% \end{algorithmic} +% +% \subsection{An Example} +% +% The following example demonstrates the use of the \keyword{algorithmic} +% environment to describe a complete algorithm. The following input +% \begin{verbatim} +% \begin{algorithmic} +% \REQUIRE $n \geq 0$ +% \ENSURE $y = x^n$ +% \STATE $y \leftarrow 1$ +% \STATE $X \leftarrow x$ +% \STATE $N \leftarrow n$ +% \WHILE{$N \neq 0$} +% \IF{$N$ is even} +% \STATE $X \leftarrow X \times X$ +% \STATE $N \leftarrow N / 2$ +% \ELSE[$N$ is odd] +% \STATE $y \leftarrow y \times X$ +% \STATE $N \leftarrow N - 1$ +% \ENDIF +% \ENDWHILE +% \end{algorithmic} +% \end{verbatim} +% will produce +% \begin{algorithmic} +% \REQUIRE $n \geq 0$ +% \ENSURE $y = x^n$ +% +% \STATE $y \leftarrow 1$ +% \STATE $X \leftarrow x$ +% \STATE $N \leftarrow n$ +% \WHILE{$N \neq 0$} +% \IF{$N$ is even} +% \STATE $X \leftarrow X \times X$ +% \STATE $N \leftarrow N / 2$ +% \ELSE[$N$ is odd] +% \STATE $y \leftarrow y \times X$ +% \STATE $N \leftarrow N - 1$ +% \ENDIF +% \ENDWHILE +% \end{algorithmic} +% which is an algorithm for finding the value of a number taken to a +% non-negative power. +% +% \subsection[Options/Customization]% +% {Options and Customization} +% +% There is a single option, \keyword{noend}\label{kwd:noend} that may be +% invoked when the \texttt{algorithmic} package is loaded. With this +% option invoked the \emph{end} statements are omitted in the output. +% This allows space to be saved in the output document when this is an +% issue. +% +% \subsubsection{Changing Indentation} +% \label{sec:changing-indentation} +% In the spirit of saving vertical space (which is especially important +% when submitting a paper for a journal, where space is frequently limited +% for authors), the \keyword{algorithmic} environment offers, beginning +% with the version released in 2005-05-08, a way to control the amount of +% indentation that is used by a given algorithm. +% +% The amount of indentation to be used is given by the command +% \begin{verbatim} +% \algsetup{indent=lenght} +% \end{verbatim} +% where \emph{length} is any valid length used by \TeX. The default value +% of the indentation used by the \keyword{algorithmic} environment is $1$ +% em (for ``backward compatibility reasons''), but a value of $2$ em or +% more is recommended, depending on the publication. For example, the +% snippet +% \begin{verbatim} +% \algsetup{indent=2em} +% \begin{algorithmic}[1] +% \STATE $a \leftarrow 1$ +% \IF{$a$ is even} +% \PRINT ``$a$ is even'' +% \ELSE +% \PRINT ``$a$ is odd'' +% \end{algorithmic} +% \end{verbatim} +% produces +% \algsetup{indent=2em} +% \begin{algorithmic}[1] +% \STATE $a \leftarrow 1$ +% \IF{$a$ is even} +% \PRINT ``$a$ is even'' +% \ELSE +% \PRINT ``$a$ is odd'' +% \ENDIF +% \end{algorithmic} +% while +% \begin{verbatim} +% \algsetup{indent=5em} +% \begin{algorithmic}[1] +% \STATE $a \leftarrow 1$ +% \IF{$a$ is even} +% \PRINT ``$a$ is even'' +% \ELSE +% \PRINT ``$a$ is odd'' +% \end{algorithmic} +% \end{verbatim} +% would produce +% \algsetup{indent=5em} +% \begin{algorithmic}[1] +% \STATE $a \leftarrow 1$ +% \IF{$a$ is even} +% \PRINT ``$a$ is even'' +% \ELSE +% \PRINT ``$a$ is odd'' +% \ENDIF +% \end{algorithmic} +% \algsetup{indent=1em} +% +% The intended use of this option is to allow the author to omit the +% \emph{end} (see Section~\ref{kwd:noend} for details) statements without +% loosing readability, by increasing the amount of indentation to a +% suitable level. +% +% \subsubsection{Changing Line Numbering} +% +% As mentioned in Section~\ref{sec:algorithmic-envir} and illustrated in +% Section~\ref{sec:changing-indentation}, \keyword{algorithms} already +% provides you with the possibility of numbering lines. +% +% Starting with the version released in 2005-07-05, you can now change two +% aspects of line numbering: the size of the line numbers (which, by +% default, is \verb+\footnotesize+) and the delimiter used to separate the +% line number from the code (which, by default, is \verb+:+, i.e., a +% colon). +% +% You can change the size of the line numbers using the command: +% \begin{verbatim} +% \algsetup{linenosize=size} +% \end{verbatim} +% where \emph{size} is any of the various commands provided by \LaTeX\ to +% change the size of the font to be used. Among others, useful values are +% \verb+\tiny+, \verb+\scriptsize+, \verb+\footnotesize+ and +% \verb+\small+. Please see the complete list of sizes in your \LaTeX\ +% documentation. +% +% As another frequently requested feature, you can change the delimiter +% used with the line numbers by issuing the command: +% \begin{verbatim} +% \algsetup{linenodelimiter=delimiter} +% \end{verbatim} +% where \emph{delimiter} is any ``well-formed'' string, including the +% empty string. With this command, you can change the colon to a period +% (\verb+.+) by issuing the command +% \begin{verbatim} +% \algsetup{linenodelimiter=.} +% \end{verbatim} +% or even omit the delimiter, by specifying the empty string or a space +% (\verb+\ +), whatever seems best for your document. +% +% As an example of such commands, the code produced by +% \begin{verbatim} +% \algsetup{ +% linenosize=\small, +% linenodelimiter=. +% } +% \begin{algorithmic}[1] +% \STATE $i \leftarrow 10$ +% \RETURN $i$ +% \end{algorithmic} +% \end{verbatim} +% would be something like +% +% \algsetup{ +% linenosize=\small, +% linenodelimiter=. +% } +% \begin{algorithmic}[1] +% \STATE $i \leftarrow 10$ +% \RETURN $i$ +% \end{algorithmic} +% \algsetup{linenosize=\footnotesize, +% linenodelimiter=:} +% +% \subsubsection{Customization} +% +% In order to facilitate the use of this package with foreign languages, +% all of the words in the output are produced via redefinable macro +% commands. The default definitions of these macros are: +% \begin{verbatim} +% \newcommand{\algorithmicrequire}{\textbf{Require:}} +% \newcommand{\algorithmicensure}{\textbf{Ensure:}} +% \newcommand{\algorithmicend}{\textbf{end}} +% \newcommand{\algorithmicif}{\textbf{if}} +% \newcommand{\algorithmicthen}{\textbf{then}} +% \newcommand{\algorithmicelse}{\textbf{else}} +% \newcommand{\algorithmicelsif}{\algorithmicelse\ \algorithmicif} +% \newcommand{\algorithmicendif}{\algorithmicend\ \algorithmicif} +% \newcommand{\algorithmicfor}{\textbf{for}} +% \newcommand{\algorithmicforall}{\textbf{for all}} +% \newcommand{\algorithmicdo}{\textbf{do}} +% \newcommand{\algorithmicendfor}{\algorithmicend\ \algorithmicfor} +% \newcommand{\algorithmicwhile}{\textbf{while}} +% \newcommand{\algorithmicendwhile}{\algorithmicend\ \algorithmicwhile} +% \newcommand{\algorithmicloop}{\textbf{loop}} +% \newcommand{\algorithmicendloop}{\algorithmicend\ \algorithmicloop} +% \newcommand{\algorithmicrepeat}{\textbf{repeat}} +% \newcommand{\algorithmicuntil}{\textbf{until}} +% \newcommand{\algorithmicprint}{\textbf{print}} +% \newcommand{\algorithmicreturn}{\textbf{return}} +% \newcommand{\algorithmictrue}{\textbf{true}} +% \newcommand{\algorithmicfalse}{\textbf{false}} +% \end{verbatim} +% +% If you would like to change the definition of these commands to another +% content, then you should use, in your own document, the standard +% \LaTeX{} command \keyword{renewcommand}, with an usage like this: +% \begin{verbatim} +% \renewcommand{\algorithmicrequire}{\textbf{Input:}} +% \renewcommand{\algorithmicensure}{\textbf{Output:}} +% \end{verbatim} +% +% \paragraph{About the Way Comments Are Formatted} +% +% The formatting of comments is implemented via a single argument command +% macro which may also be redefined. The default definition is +% \begin{verbatim} +% \newcommand{\algorithmiccomment}[1]{\{#1\}} +% \end{verbatim} +% and another option that may be interesting for users familiar with +% C-like languages is to redefine the comments to be +% \begin{verbatim} +% \renewcommand{\algorithmiccomment}[1]{// #1} +% \end{verbatim} +% Comments produced this way would be like this: +% \renewcommand{\algorithmiccomment}[1]{// #1} +% \begin{algorithmic} +% \STATE $i \leftarrow i + 1$ \COMMENT{Increments $i$} +% \end{algorithmic} +% This second way to present comments may become the default in a future +% version of this package. +% +% \section[Environment: \keyword{algorithm}]% +% {The \keyword{algorithm} Environment} +% +% \subsection{General} +% +% When placed within the text without being encapsulated in a floating +% environment \texttt{algorithmic} environments may be split over a page +% boundary, greatly detracting from their appearance.\footnote{This is the +% expected behaviour for floats in \LaTeX. If you don't care about +% having your algorithm split between pages, then one option that you +% have is to ignore the \texttt{algorithm} environment.} In addition, it +% is useful to have algorithms numbered for reference and for lists of +% algorithms to be appended to the list of contents. The +% \texttt{algorithm} environment is meant to address these concerns by +% providing a floating environment for algorithms. +% +% \subsection{An Example} +% To illustrate the use of the \texttt{algorithm} environment, the +% following text +% \begin{verbatim} +% \begin{algorithm} +% \caption{Calculate $y = x^n$} +% \label{alg1} +% \begin{algorithmic} +% \REQUIRE $n \geq 0 \vee x \neq 0$ +% \ENSURE $y = x^n$ +% \STATE $y \leftarrow 1$ +% \IF{$n < 0$} +% \STATE $X \leftarrow 1 / x$ +% \STATE $N \leftarrow -n$ +% \ELSE +% \STATE $X \leftarrow x$ +% \STATE $N \leftarrow n$ +% \ENDIF +% \WHILE{$N \neq 0$} +% \IF{$N$ is even} +% \STATE $X \leftarrow X \times X$ +% \STATE $N \leftarrow N / 2$ +% \ELSE[$N$ is odd] +% \STATE $y \leftarrow y \times X$ +% \STATE $N \leftarrow N - 1$ +% \ENDIF +% \ENDWHILE +% \end{algorithmic} +% \end{algorithm} +% \end{verbatim} +% produces Algorithm~\ref{alg1} which is a slightly modified version of +% the earlier algorithm for determining the value of a number taken to an +% integer power. In this case, provided the power may be negative +% provided the number is not zero. +% +% \begin{algorithm}[H] +% \caption{Calculate $y = x^n$} +% \label{alg1} +% \begin{algorithmic} +% \REQUIRE $n \geq 0 \vee x \neq 0$ +% \ENSURE $y = x^n$ +% +% \STATE $y \leftarrow 1$ +% \IF{$n < 0$} +% \STATE $X \leftarrow 1 / x$ +% \STATE $N \leftarrow -n$ +% \ELSE +% \STATE $X \leftarrow x$ +% \STATE $N \leftarrow n$ +% \ENDIF +% +% \WHILE{$N \neq 0$} +% \IF{$N$ is even} +% \STATE $X \leftarrow X \times X$ +% \STATE $N \leftarrow N / 2$ +% \ELSE[$N$ is odd] +% \STATE $y \leftarrow y \times X$ +% \STATE $N \leftarrow N - 1$ +% \ENDIF +% \ENDWHILE +% \end{algorithmic} +% \end{algorithm} +% +% The command \verb+\listofalgorithms+ may be used to produce a list of +% algorithms as part of the table contents as shown at the beginning of +% this document. An auxiliary file with a suffix of \texttt{.loa} is +% produced when this feature is used. +% +% \subsection{Options} +% +% The appearance of the typeset algorithm may be changed by use of the +% options: \texttt{plain}, \texttt{boxed} or \texttt{ruled} during the +% loading of the \texttt{algorithm} package. The default option is +% \texttt{ruled}. +% +% The numbering of algorithms can be influenced by providing the name of +% the document component within which numbering should be recommenced. +% The legal values for this option are: \texttt{part}, \texttt{chapter}, +% \texttt{section}, \texttt{subsection}, \texttt{subsubsection} or +% \texttt{nothing}. The default value is \texttt{nothing} which causes +% algorithms to be numbered sequentially throughout the document. +% +% \subsection{Customization} +% +% In order to facilitate the use of this package with foreign languages, +% methods have been provided to facilitate the necessary modifications. +% +% The title used in the caption within \texttt{algorithm} environment can +% be set by use of the standard \verb+\floatname+ command which is +% provided as part of the \texttt{float} package which was used to +% implement this package. For example, +% \begin{verbatim} +% \floatname{algorithm}{Procedure} +% \end{verbatim} +% would cause \textbf{Procedure} to be used instead of \textbf{Algorithm} +% within the caption of algorithms. +% +% In a manner analogous to that available for the built in floating +% environments, the heading used for the list of algorithms may be changed +% by redefining the command \verb+listalgorithmname+. The default +% definition for this command is +% \begin{verbatim} +% \newcommand{\listalgorithmname}{List of Algorithms} +% \end{verbatim} +% +% \subsubsection{Placement of Algorithms} +% +% One important fact that many users may not have noticed is that the +% \texttt{algorithm} environment is actually built with the \texttt{float} +% package and \texttt{float}, in turn, uses David Carlisle's \textsf{here} +% style option. This means that the floats generated by the +% \texttt{algorithm} environment accept a special option, namely, +% \textbf{[H]}, with a capital `H', instead of the usual `h' offered by +% plain \LaTeX. +% +% This option works as a stronger request of ``please put the float +% here'': instead of just a suggestion for \LaTeX, it actually means ``put +% this float HERE'', which is something desired by many. The two +% algorithms typeset in this document use this option. +% +% \medskip +% \begin{warning} +% You \emph{can't} use the `H' positioning option together with the +% usual `h' (for ``here''), `b' (for ``bottom'') etc. This is a +% limitation (as far as I know) of the \texttt{float.sty} package. +% \end{warning} +% +% \section[References in Algorithms]% +% {Labels and References in Algorithms} +% +% With the release of 2005-07-05, now \keyword{algorithmic} accepts labels +% and references to specific lines of a given algorithm, so you don't have +% to hardcode the line numbers yourself when trying to explain what the +% code does in your texts. Thanks to Arnaud Legrand for the suggestion +% and patch for this highly missed feature. +% +% An example of its use is shown in Algorithm~\ref{alg2}. +% \begin{algorithm}[H] +% \caption{Calculate $y = x^n$} +% \label{alg2} +% \begin{algorithmic}[1] +% \REQUIRE $n \geq 0 \vee x \neq 0$ +% \ENSURE $y = x^n$ +% \STATE $y \leftarrow 1$ +% \IF{$n < 0$} +% \STATE $X \leftarrow 1 / x$ +% \STATE $N \leftarrow -n$ +% \ELSE +% \STATE $X \leftarrow x$ +% \STATE $N \leftarrow n$ +% \ENDIF +% \WHILE{$N \neq 0$} +% \IF{$N$ is even}\label{alg:n-is-even} +% \STATE $X \leftarrow X \times X$ +% \STATE $N \leftarrow N / 2$ +% \ELSE\label{alg:n-is-odd} +% \STATE $y \leftarrow y \times X$ +% \STATE $N \leftarrow N - 1$ +% \ENDIF +% \ENDWHILE +% \end{algorithmic} +% \end{algorithm} +% See that, in line~\ref{alg:n-is-even}, we deal with the case of $N$ +% being even, while, in line~\ref{alg:n-is-odd}, we give treatment to the +% case of $N$ being odd. The numbers you see on this document were +% generated automatically from the source document. +% +% +% \section[Known Issues]{Issues Between \texttt{algorithms} and +% \href{http://www.ctan.org/tex-archive/help/Catalogue/entries/tocbibind.html}{\texttt{tocbibind}} +% or \href{http://www.ctan.org/tex-archive/help/Catalogue/entries/memoir.html}{\texttt{memoir}}} +% +% It +% \href{http://groups.google.com/group/comp.text.tex/browse_thread/thread/4094e0c4f4fbd83e/a80a3f4666c794f0?fwc=1}{has +% been discussed} in late 2005 that \texttt{algorithms} may have bad +% interactions with the +% \href{http://www.ctan.org/tex-archive/help/Catalogue/entries/tocbibind.html}{\texttt{tocbibind}} +% or the +% \href{http://www.ctan.org/tex-archive/help/Catalogue/entries/memoir.html}{\texttt{memoir}} +% package (which includes \texttt{tocbibind}). +% +% A workaround has been suggested for the problem. After including +% something like +% \begin{verbatim} +% \usepackage[nottoc]{tocbibind} +% \end{verbatim} +% in the preamble of your document, you can put, after +% \verb+\begin{document}+, the following snippet of code: +% \begin{verbatim} +% \renewcommand{\listofalgorithms}{\begingroup +% \tocfile{List of Algorithms}{loa} +% \endgroup} +% +% \makeatletter +% \let\l@algorithm\l@figure +% \makeatother +% \end{verbatim} +% which should make the command \verb+\listofalgorithms+ work as expected. +% +% \section[General Hints]{Hints for Typesetting Algorithms} +% +% Here are some short hints on typesetting algorithms: +% \begin{itemize} +% \item Don't overcomment your pseudo-code. If you feel that you need to +% comment too much, then you are probably doing something wrong: you should +% probably detail the inner workings of the algorithm in regular text +% rather than in the pseudo-code; +% \item Similarly, don't regard pseudo-code as a low-level programming +% language: \emph{don't pollute your algorithms} with punctuation marks +% like semi-colons, which are necessary in C, C++ and Java, but not in +% pseudo-code. Remember: your readers \emph{are not} compilers; +% \item Always document what the algorithm receives as an input and what it +% returns as a solution. Don't care to say in the \verb+\REQUIRE+ or in the +% \verb+\ENSURE+ commands \emph{how} the algorithm does what it does. Put +% this in the regular text of your book/paper/lecture notes; +% \item If you feel that your pseudo-code is getting too big, just break it +% into sub-algorithms, perhaps abstracting some tasks. Your readers will +% probably thank you. +% \end{itemize} +% +% Of course, you should follow those hints with common sense. Well, anything +% should be done with common sense. +% +% \addtocontents{toc}{\protect\end{multicols}} +% \end{document} +% +%\StopEventually{} +%<algorithm>\RequirePackage{float} +%<algorithm>\RequirePackage{ifthen} +%<algorithm>\newcommand{\ALG@within}{nothing} +%<algorithm>\newboolean{ALG@within} +%<algorithm>\setboolean{ALG@within}{false} +%<algorithm>\newcommand{\ALG@floatstyle}{ruled} +%<algorithm>\newcommand{\ALG@name}{Algorithm} +%<algorithm>\newcommand{\listalgorithmname}{List of \ALG@name s} +% +%<algorithm>% Declare Options: +%<algorithm>% * first: appearance +%<algorithm>\DeclareOption{plain}{ +%<algorithm> \renewcommand{\ALG@floatstyle}{plain} +%<algorithm>} +%<algorithm>\DeclareOption{ruled}{ +%<algorithm> \renewcommand{\ALG@floatstyle}{ruled} +%<algorithm>} +%<algorithm>\DeclareOption{boxed}{ +%<algorithm> \renewcommand{\ALG@floatstyle}{boxed} +%<algorithm>} +%<algorithm>% * then: numbering convention +%<algorithm>\DeclareOption{part}{ +%<algorithm> \renewcommand{\ALG@within}{part} +%<algorithm> \setboolean{ALG@within}{true} +%<algorithm>} +%<algorithm>\DeclareOption{chapter}{ +%<algorithm> \renewcommand{\ALG@within}{chapter} +%<algorithm> \setboolean{ALG@within}{true} +%<algorithm>} +%<algorithm>\DeclareOption{section}{ +%<algorithm> \renewcommand{\ALG@within}{section} +%<algorithm> \setboolean{ALG@within}{true} +%<algorithm>} +%<algorithm>\DeclareOption{subsection}{ +%<algorithm> \renewcommand{\ALG@within}{subsection} +%<algorithm> \setboolean{ALG@within}{true} +%<algorithm>} +%<algorithm>\DeclareOption{subsubsection}{ +%<algorithm> \renewcommand{\ALG@within}{subsubsection} +%<algorithm> \setboolean{ALG@within}{true} +%<algorithm>} +%<algorithm>\DeclareOption{nothing}{ +%<algorithm> \renewcommand{\ALG@within}{nothing} +%<algorithm> \setboolean{ALG@within}{true} +%<algorithm>} +%<algorithm>\DeclareOption*{\edef\ALG@name{\CurrentOption}} +% +%<algorithm>% ALGORITHM +%<algorithm>% +%<algorithm>\ProcessOptions +%<algorithm>\floatstyle{\ALG@floatstyle} +%<algorithm>\ifthenelse{\boolean{ALG@within}}{ +%<algorithm> \ifthenelse{\equal{\ALG@within}{part}} +%<algorithm> {\newfloat{algorithm}{htbp}{loa}[part]}{} +%<algorithm> \ifthenelse{\equal{\ALG@within}{chapter}} +%<algorithm> {\newfloat{algorithm}{htbp}{loa}[chapter]}{} +%<algorithm> \ifthenelse{\equal{\ALG@within}{section}} +%<algorithm> {\newfloat{algorithm}{htbp}{loa}[section]}{} +%<algorithm> \ifthenelse{\equal{\ALG@within}{subsection}} +%<algorithm> {\newfloat{algorithm}{htbp}{loa}[subsection]}{} +%<algorithm> \ifthenelse{\equal{\ALG@within}{subsubsection}} +%<algorithm> {\newfloat{algorithm}{htbp}{loa}[subsubsection]}{} +%<algorithm> \ifthenelse{\equal{\ALG@within}{nothing}} +%<algorithm> {\newfloat{algorithm}{htbp}{loa}}{} +%<algorithm>}{ +%<algorithm> \newfloat{algorithm}{htbp}{loa} +%<algorithm>} +%<algorithm>\floatname{algorithm}{\ALG@name} +% +%<algorithm>\newcommand{\listofalgorithms}{\listof{algorithm}{\listalgorithmname}} +% +% +%<algorithmic>% The algorithmic.sty package: +% +%<algorithmic>\RequirePackage{ifthen} +%<algorithmic>\RequirePackage{keyval} +%<algorithmic>\newboolean{ALC@noend} +%<algorithmic>\setboolean{ALC@noend}{false} +%<algorithmic>\newcounter{ALC@unique} % new counter to make lines numbers be internally +%<algorithmic>\setcounter{ALC@unique}{0} % different in different algorithms +%<algorithmic>\newcounter{ALC@line} % counter for current line +%<algorithmic>\newcounter{ALC@rem} % counter for lines not printed +%<algorithmic>\newcounter{ALC@depth} +%<algorithmic>\newlength{\ALC@tlm} +%<algorithmic>% +%<algorithmic>\DeclareOption{noend}{\setboolean{ALC@noend}{true}} +%<algorithmic>% +%<algorithmic>\ProcessOptions +%<algorithmic>% +%<algorithmic>% For keyval-style options +%<algorithmic>\def\algsetup{\setkeys{ALG}} +%<algorithmic>% +%<algorithmic>% For indentation of algorithms +%<algorithmic>\newlength{\algorithmicindent} +%<algorithmic>\setlength{\algorithmicindent}{0pt} +%<algorithmic>\define@key{ALG}{indent}{\setlength{\algorithmicindent}{#1}} +%<algorithmic>\ifthenelse{\lengthtest{\algorithmicindent=0pt}}% +%<algorithmic> {\setlength{\algorithmicindent}{1em}}{} +%<algorithmic>% +%<algorithmic>% For line numbers' delimiters +%<algorithmic>\newcommand{\ALC@linenodelimiter}{:} +%<algorithmic>\define@key{ALG}{linenodelimiter}{\renewcommand{\ALC@linenodelimiter}{#1}} +% +%<algorithmic>% +%<algorithmic>% For line numbers' size +%<algorithmic>\newcommand{\ALC@linenosize}{\footnotesize} +%<algorithmic>\define@key{ALG}{linenosize}{\renewcommand{\ALC@linenosize}{#1}} +% +%<algorithmic>% +%<algorithmic>% ALGORITHMIC +%<algorithmic>\newcommand{\algorithmicrequire}{\textbf{Require:}} +%<algorithmic>\newcommand{\algorithmicensure}{\textbf{Ensure:}} +%<algorithmic>\newcommand{\algorithmiccomment}[1]{\{#1\}} +%<algorithmic>\newcommand{\algorithmicend}{\textbf{end}} +%<algorithmic>\newcommand{\algorithmicif}{\textbf{if}} +%<algorithmic>\newcommand{\algorithmicthen}{\textbf{then}} +%<algorithmic>\newcommand{\algorithmicelse}{\textbf{else}} +%<algorithmic>\newcommand{\algorithmicelsif}{\algorithmicelse\ \algorithmicif} +%<algorithmic>\newcommand{\algorithmicendif}{\algorithmicend\ \algorithmicif} +%<algorithmic>\newcommand{\algorithmicfor}{\textbf{for}} +%<algorithmic>\newcommand{\algorithmicforall}{\textbf{for all}} +%<algorithmic>\newcommand{\algorithmicdo}{\textbf{do}} +%<algorithmic>\newcommand{\algorithmicendfor}{\algorithmicend\ \algorithmicfor} +%<algorithmic>\newcommand{\algorithmicwhile}{\textbf{while}} +%<algorithmic>\newcommand{\algorithmicendwhile}{\algorithmicend\ \algorithmicwhile} +%<algorithmic>\newcommand{\algorithmicloop}{\textbf{loop}} +%<algorithmic>\newcommand{\algorithmicendloop}{\algorithmicend\ \algorithmicloop} +%<algorithmic>\newcommand{\algorithmicrepeat}{\textbf{repeat}} +%<algorithmic>\newcommand{\algorithmicuntil}{\textbf{until}} +%<algorithmic>\newcommand{\algorithmicprint}{\textbf{print}} +%<algorithmic>\newcommand{\algorithmicreturn}{\textbf{return}} +%<algorithmic>\newcommand{\algorithmicand}{\textbf{and}} +%<algorithmic>\newcommand{\algorithmicor}{\textbf{or}} +%<algorithmic>\newcommand{\algorithmicxor}{\textbf{xor}} +%<algorithmic>\newcommand{\algorithmicnot}{\textbf{not}} +%<algorithmic>\newcommand{\algorithmicto}{\textbf{to}} +%<algorithmic>\newcommand{\algorithmicinputs}{\textbf{inputs}} +%<algorithmic>\newcommand{\algorithmicoutputs}{\textbf{outputs}} +%<algorithmic>\newcommand{\algorithmicglobals}{\textbf{globals}} +%<algorithmic>\newcommand{\algorithmicbody}{\textbf{do}} +%<algorithmic>\newcommand{\algorithmictrue}{\textbf{true}} +%<algorithmic>\newcommand{\algorithmicfalse}{\textbf{false}} +%<algorithmic>\def\ALC@item[#1]{% +%<algorithmic>\if@noparitem \@donoparitem +%<algorithmic> \else \if@inlabel \indent \par \fi +%<algorithmic> \ifhmode \unskip\unskip \par \fi +%<algorithmic> \if@newlist \if@nobreak \@nbitem \else +%<algorithmic> \addpenalty\@beginparpenalty +%<algorithmic> \addvspace\@topsep \addvspace{-\parskip}\fi +%<algorithmic> \else \addpenalty\@itempenalty \addvspace\itemsep +%<algorithmic> \fi +%<algorithmic> \global\@inlabeltrue +%<algorithmic>\fi +%<algorithmic>\everypar{\global\@minipagefalse\global\@newlistfalse +%<algorithmic> \if@inlabel\global\@inlabelfalse \hskip -\parindent \box\@labels +%<algorithmic> \penalty\z@ \fi +%<algorithmic> \everypar{}}\global\@nobreakfalse +%<algorithmic>\if@noitemarg \@noitemargfalse \if@nmbrlist \refstepcounter{\@listctr}\fi \fi +%<algorithmic>\sbox\@tempboxa{\makelabel{#1}}% +%<algorithmic>\global\setbox\@labels +%<algorithmic> \hbox{\unhbox\@labels \hskip \itemindent +%<algorithmic> \hskip -\labelwidth \hskip -\ALC@tlm +%<algorithmic> \ifdim \wd\@tempboxa >\labelwidth +%<algorithmic> \box\@tempboxa +%<algorithmic> \else \hbox to\labelwidth {\unhbox\@tempboxa}\fi +%<algorithmic> \hskip \ALC@tlm}\ignorespaces} +%<algorithmic>% +%<algorithmic>\newenvironment{algorithmic}[1][0]{ +%<algorithmic>\setcounter{ALC@depth}{\@listdepth}% +%<algorithmic>\let\@listdepth\c@ALC@depth% +%<algorithmic>\let\@item\ALC@item% +%<algorithmic> \newcommand{\ALC@lno}{% +%<algorithmic>\ifthenelse{\equal{\arabic{ALC@rem}}{0}} +%<algorithmic>{{\ALC@linenosize \arabic{ALC@line}\ALC@linenodelimiter}}{}% +%<algorithmic>} +%<algorithmic>\let\@listii\@listi +%<algorithmic>\let\@listiii\@listi +%<algorithmic>\let\@listiv\@listi +%<algorithmic>\let\@listv\@listi +%<algorithmic>\let\@listvi\@listi +%<algorithmic>\let\@listvii\@listi +%<algorithmic> \newenvironment{ALC@g}{ +%<algorithmic> \begin{list}{\ALC@lno}{ \itemsep\z@ \itemindent\z@ +%<algorithmic> \listparindent\z@ \rightmargin\z@ +%<algorithmic> \topsep\z@ \partopsep\z@ \parskip\z@\parsep\z@ +%<algorithmic> \leftmargin \algorithmicindent%1em +%<algorithmic> \addtolength{\ALC@tlm}{\leftmargin} +%<algorithmic> } +%<algorithmic> } +%<algorithmic> {\end{list}} +%<algorithmic> \newcommand{\ALC@it}{% +%<algorithmic> \stepcounter{ALC@rem}% +%<algorithmic> \ifthenelse{\equal{\arabic{ALC@rem}}{#1}}{\setcounter{ALC@rem}{0}}{}% +%<algorithmic> \stepcounter{ALC@line}% +%<algorithmic> \refstepcounter{ALC@unique}% +%<algorithmic> \item\def\@currentlabel{\theALC@line}% +%<algorithmic> } +%<algorithmic> \newcommand{\ALC@com}[1]{\ifthenelse{\equal{##1}{default}}% +%<algorithmic>{}{\ \algorithmiccomment{##1}}} +%<algorithmic> \newcommand{\REQUIRE}{\item[\algorithmicrequire]} +%<algorithmic> \newcommand{\ENSURE}{\item[\algorithmicensure]} +%<algorithmic> \newcommand{\PRINT}{\ALC@it\algorithmicprint{} \ } +%<algorithmic> \newcommand{\RETURN}{\ALC@it\algorithmicreturn{} \ } +%<algorithmic> \newcommand{\TRUE}{\algorithmictrue{}} +%<algorithmic> \newcommand{\FALSE}{\algorithmicfalse{}} +%<algorithmic> \newcommand{\AND}{\algorithmicand{} } +%<algorithmic> \newcommand{\OR}{\algorithmicor{} } +%<algorithmic> \newcommand{\XOR}{\algorithmicxor{} } +%<algorithmic> \newcommand{\NOT}{\algorithmicnot{} } +%<algorithmic> \newcommand{\TO}{\algorithmicto{} } +%<algorithmic> \newcommand{\STATE}{\ALC@it} +%<algorithmic> \newcommand{\STMT}{\ALC@it} +%<algorithmic> \newcommand{\COMMENT}[1]{\algorithmiccomment{##1}} +%<algorithmic> \newenvironment{ALC@inputs}{\begin{ALC@g}}{\end{ALC@g}} +%<algorithmic> \newenvironment{ALC@outputs}{\begin{ALC@g}}{\end{ALC@g}} +%<algorithmic> \newenvironment{ALC@globals}{\begin{ALC@g}}{\end{ALC@g}} +%<algorithmic> \newenvironment{ALC@body}{\begin{ALC@g}}{\end{ALC@g}} +%<algorithmic> \newenvironment{ALC@if}{\begin{ALC@g}}{\end{ALC@g}} +%<algorithmic> \newenvironment{ALC@for}{\begin{ALC@g}}{\end{ALC@g}} +%<algorithmic> \newenvironment{ALC@whl}{\begin{ALC@g}}{\end{ALC@g}} +%<algorithmic> \newenvironment{ALC@loop}{\begin{ALC@g}}{\end{ALC@g}} +%<algorithmic> \newenvironment{ALC@rpt}{\begin{ALC@g}}{\end{ALC@g}} +%<algorithmic> \renewcommand{\\}{\@centercr} +%<algorithmic> \newcommand{\INPUTS}[1][default]{\ALC@it\algorithmicinputs\ \ALC@com{##1}\begin{ALC@inputs}} +%<algorithmic> \newcommand{\ENDINPUTS}{\end{ALC@inputs}} +%<algorithmic> \newcommand{\OUTPUTS}[1][default]{\ALC@it\algorithmicoutputs\ \ALC@com{##1}\begin{ALC@outputs}} +%<algorithmic> \newcommand{\ENDOUTPUTS}{\end{ALC@outputs}} +%<algorithmic> \newcommand{\GLOBALS}{\ALC@it\algorithmicglobals\ } +%<algorithmic> \newcommand{\BODY}[1][default]{\ALC@it\algorithmicbody\ \ALC@com{##1}\begin{ALC@body}} +%<algorithmic> \newcommand{\ENDBODY}{\end{ALC@body}} +%<algorithmic> \newcommand{\IF}[2][default]{\ALC@it\algorithmicif\ ##2\ \algorithmicthen% +%<algorithmic>\ALC@com{##1}\begin{ALC@if}} +%<algorithmic> \newcommand{\ELSE}[1][default]{\end{ALC@if}\ALC@it\algorithmicelse% +%<algorithmic>\ALC@com{##1}\begin{ALC@if}} +%<algorithmic> \newcommand{\ELSIF}[2][default]% +%<algorithmic>{\end{ALC@if}\ALC@it\algorithmicelsif\ ##2\ \algorithmicthen% +%<algorithmic>\ALC@com{##1}\begin{ALC@if}} +%<algorithmic> \newcommand{\FOR}[2][default]{\ALC@it\algorithmicfor\ ##2\ \algorithmicdo% +%<algorithmic>\ALC@com{##1}\begin{ALC@for}} +%<algorithmic> \newcommand{\FORALL}[2][default]{\ALC@it\algorithmicforall\ ##2\ % +%<algorithmic>\algorithmicdo% +%<algorithmic>\ALC@com{##1}\begin{ALC@for}} +%<algorithmic> \newcommand{\WHILE}[2][default]{\ALC@it\algorithmicwhile\ ##2\ % +%<algorithmic>\algorithmicdo% +%<algorithmic>\ALC@com{##1}\begin{ALC@whl}} +%<algorithmic> \newcommand{\LOOP}[1][default]{\ALC@it\algorithmicloop% +%<algorithmic>\ALC@com{##1}\begin{ALC@loop}} +%<algorithmic> \newcommand{\REPEAT}[1][default]{\ALC@it\algorithmicrepeat% +%<algorithmic>\ALC@com{##1}\begin{ALC@rpt}} +%<algorithmic> \newcommand{\UNTIL}[1]{\end{ALC@rpt}\ALC@it\algorithmicuntil\ ##1} +%<algorithmic> \ifthenelse{\boolean{ALC@noend}}{ +%<algorithmic> \newcommand{\ENDIF}{\end{ALC@if}} +%<algorithmic> \newcommand{\ENDFOR}{\end{ALC@for}} +%<algorithmic> \newcommand{\ENDWHILE}{\end{ALC@whl}} +%<algorithmic> \newcommand{\ENDLOOP}{\end{ALC@loop}} +%<algorithmic> }{ +%<algorithmic> \newcommand{\ENDIF}{\end{ALC@if}\ALC@it\algorithmicendif} +%<algorithmic> \newcommand{\ENDFOR}{\end{ALC@for}\ALC@it\algorithmicendfor} +%<algorithmic> \newcommand{\ENDWHILE}{\end{ALC@whl}\ALC@it\algorithmicendwhile} +%<algorithmic> \newcommand{\ENDLOOP}{\end{ALC@loop}\ALC@it\algorithmicendloop} +%<algorithmic> } +%<algorithmic> \renewcommand{\@toodeep}{} +%<algorithmic> \begin{list}{\ALC@lno}{\setcounter{ALC@rem}{0}\setcounter{ALC@line}{0}% +%<algorithmic> \itemsep\z@ \itemindent\z@ \listparindent\z@% +%<algorithmic> \partopsep\z@ \parskip\z@ \parsep\z@% +%<algorithmic> \labelsep 0.5em \topsep 0.2em% +%<algorithmic>\ifthenelse{\equal{#1}{0}} +%<algorithmic> {\labelwidth 0.5em } +%<algorithmic> {\labelwidth 1.2em } +%<algorithmic>\leftmargin\labelwidth \addtolength{\leftmargin}{\labelsep} +%<algorithmic> \ALC@tlm\labelsep +%<algorithmic> } +%<algorithmic>} +%<algorithmic>{\end{list}} +%\Finale +%\PrintChanges +%\PrintIndex |