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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/dijkstra/dijkstra.sty
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+% !TeX encoding = ISO-8859-1
+% Ce fichier contient le code de l'extension "dijkstra"
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+\def\dijkname {dijkstra} %
+\def\dijkver {0.11} %
+% %
+\def\dijkdate {2017/09/09} %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% --------------------------------------------------------------------
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%
+% % http://www.latex-project.org/lppl.txt
+%
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% --------------------------------------------------------------------
+% This work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Christian Tellechea
+% Copyright : Christian Tellechea 2017
+% email: unbonpetit@netc.fr
+% Commentaires, suggestions et signalement de bugs bienvenus !
+% Comments, bug reports and suggestions are welcome.
+% Copyright: Christian Tellechea 2017
+% --------------------------------------------------------------------
+% L'extension dijkstra est composée des 4 fichiers suivants :
+% - code : dijkstra.sty
+% - manuel en français : dijkstra-fr.tex & dijkstra-fr.pdf
+% - fichier lisezmoi : README
+% --------------------------------------------------------------------
+%
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{dijkstra}[\dijkdate\space v\dijkver\space Dijkstra Algorithm (CT)]
+\RequirePackage{simplekv}
+
+\expandafter\edef\csname dijk_restorecatcode\endcsname{\expandafter\catcode\number`\_=\number\catcode`\_\relax}
+\catcode`\_=11
+
+\newcount\dijk_nest
+\newcount\dijk_cnt
+\newif\ifdijk_oriented
+
+\def\dijk_maxint{1073741823}
+\def\dijk_quark{\dijk_quark}
+\def\dijk_cscmd#1#2{\expandafter#1\csname#2\endcsname}
+\def\dijk_gobarg#1{}
+\def\dijk_addtomacro#1#2{\expandafter\def\expandafter#1\expandafter{#1#2}}
+\def\dijk_eaddtomacro#1#2{\skv_exparg{\dijk_addtomacro#1}{#2}}
+\def\dijk_eeaddtomacro#1#2{\skv_eearg{\dijk_addtomacro#1}{#2}}
+\long\def\dijk_exptwoargs#1#2#3{\skv_exparg{\skv_exparg{#1}{#2}}{#3}}
+\def\dijk_ifnum#1{\ifnum#1\expandafter\skv_first\else\expandafter\skv_second\fi}
+\def\dijk_swapargs#1#2#3{#1{#3}{#2}}
+\def\dijk_ifstar#1#2{\def\dijk_ifstar_i{\skv_ifx{*\dijk_nxttok}{\skv_first{#1}}{#2}}\futurelet\dijk_nxttok\dijk_ifstar_i}
+\def\dijk_ifopt#1#2{\def\dijk_ifopt_i{\skv_ifx{[\dijk_nxttok}{#1}{#2}}\futurelet\dijk_nxttok\dijk_ifopt_i}
+
+\def\dijk_foreach#1\in#2#3%
+{%
+ \global\advance\dijk_nest1
+ \dijk_cscmd\def{dijk_loopcode_\number\dijk_nest}{#3}%
+ \dijk_foreach_i#1#2,\dijk_quark,%
+ \dijk_cscmd\let{dijk_loopcode_\number\dijk_nest}\empty
+ \global\advance\dijk_nest-1
+}%
+
+\def\dijk_foreach_i#1#2,%
+{%
+ \def#1{#2}%
+ \skv_ifx{\dijk_quark#1}
+ {}
+ {%
+ \skv_ifx{#1\empty}{}{\csname dijk_loopcode_\number\dijk_nest\endcsname}%
+ \dijk_foreach_i#1%
+ }%
+}%
+
+\def\dijk_ifinst#1#2%
+{% #2 est-il dans #1 ?
+ \def\dijk_ifinst_i##1#2##2\_nil{\dijk_swapargs{\skv_ifempty{##2}}}%
+ \dijk_ifinst_i#1#2\_nil
+}
+
+\def\readgraph
+{%
+ \dijk_ifstar{\dijk_orientedtrue\readgraph_a}{\dijk_orientedfalse\readgraph_a}%
+}
+
+\def\readgraph_a#1%
+{%
+ \let\dijk_initlistofnodes\empty% liste des sommets
+ \let\dijk_graph\empty% argument #1 où l'on va enlever les espaces
+ \dijk_sanitizegraph#1,\dijk_quark[],% enlever tous les espaces indésirables et évaluer les nombres dans l'argument #1
+ \expandafter\readgraph_b\dijk_graph,\dijk_quark[],%
+}
+
+\def\dijk_sanitizegraph#1[#2],%
+{%
+ \skv_ifx{\dijk_quark#1}
+ {%
+ \dijk_removelastcommainmacro\dijk_graph
+ }
+ {%
+ \skv_eearg{\def\dijk_childnodes}{\skv_removeextremespaces{#1}[}%
+ \dijk_foreach\dijk_temp\in{#2}{\expandafter\dijk_sanitizegraph_i\dijk_temp\_nil}%
+ \dijk_removelastcommainmacro\dijk_childnodes
+ \dijk_eaddtomacro\dijk_graph{\dijk_childnodes],}%
+ \dijk_sanitizegraph
+ }%
+}
+
+\def\dijk_sanitizegraph_i#1=#2\_nil
+{%
+ \dijk_eeaddtomacro\dijk_childnodes{\skv_removeextremespaces{#1}=}%
+ \dijk_eaddtomacro\dijk_childnodes{\the\numexpr#2\relax,}%
+}
+
+\def\dijk_removelastcommainmacro#1%
+{%
+ \expandafter\dijk_removelastcommainmacro_i#1\_nil#1%
+}
+
+\def\dijk_removelastcommainmacro_i#1,\_nil#2%
+{%
+ \def#2{#1}%
+}
+
+\def\readgraph_b#1#2[#3]#4,%
+{%
+ \skv_ifx{\dijk_quark#1}
+ {%
+ \skv_exparg{\dijk_foreach\dijk_tempnodename\in}{\dijk_initlistofnodes}
+ {% pour chaque sommet
+ \skv_eearg{\dijk_foreach\dijk_tempnodechild\in}{\csname dijknode\dijk_tempnodename\endcsname}
+ {% pour chaque enfant
+ \expandafter\readgraph_c\dijk_tempnodechild\_nil\dijk_currentnodechildname\dijk_currentnodechilddist% capturer nom et distance de l'enfant
+ \dijk_exptwoargs\dijk_ifinst\dijk_initlistofnodes{\dijk_currentnodechildname,}% si l'enfant n'est pas dans la liste des sommets
+ {}%
+ {%
+ \dijk_eaddtomacro\dijk_initlistofnodes{\dijk_currentnodechildname,}% l'y mettre
+ \dijk_cscmd\let{dijknode\dijk_currentnodechildname}\empty% et initialiser la liste de ses enfants
+ }%
+ \unless\ifdijk_oriented% si graphe non orienté, ajouter les distances inverses
+ \skv_exparg{\skv_eearg\dijk_ifinst{\csname dijknode\dijk_currentnodechildname\endcsname}}{\dijk_tempnodename=}% si le parent est dans déjà un des enfants de l'enfant
+ {%
+ \expandafter\def\expandafter\readgraph_d\expandafter########\expandafter1\dijk_tempnodename=########2,########3\_nil{%
+ \unless\ifnum########2=\dijk_currentnodechilddist\relax% si distance différente : erreur, c'est pas normal
+ \errmessage{Distance "\dijk_tempnodename=########2" incorrecte dans \dijk_currentnodechildname{} comprise comme "\dijk_tempnodename=\dijk_currentnodechilddist"}%
+ \dijk_cscmd\edef{dijknode\dijk_currentnodechildname}{########1\dijk_tempnodename=\dijk_currentnodechilddist,########3}%
+ \fi
+ }%
+ \expandafter\expandafter\expandafter\readgraph_d\csname dijknode\dijk_currentnodechildname\endcsname\_nil
+ }%
+ {% sinon, l'y mettre
+ \dijk_cscmd\edef{dijknode\dijk_currentnodechildname}{\dijk_tempnodename=\dijk_currentnodechilddist,\csname dijknode\dijk_currentnodechildname\endcsname}%
+ }%
+ \fi
+ }%
+ }%
+ \dijk_cnt0
+ \skv_exparg{\dijk_foreach\dijk_tempnodename\in}{\dijk_initlistofnodes}
+ {% pour chaque sommet, construire la liste de ses enfants
+ \advance\dijk_cnt1
+ \dijk_cscmd\let{listofchilds_\dijk_tempnodename}\empty
+ \skv_eearg{\dijk_foreach\dijk_tempnodechild\in}{\csname dijknode\dijk_tempnodename\endcsname}
+ {%
+ \expandafter\readgraph_c\dijk_tempnodechild\_nil\dijk_currentnodechildname\dijk_currentnodechilddist
+ \expandafter\dijk_eaddtomacro\csname listofchilds_\dijk_tempnodename\endcsname{\dijk_currentnodechildname,}%
+ }%
+ }%
+ \edef\dijk_numberofnodes{\the\dijk_cnt}%
+ }%
+ {%
+ \def\dijk_currentnodename{#1}%
+ \dijk_eaddtomacro\dijk_initlistofnodes{\dijk_currentnodename,}%
+ \dijk_cscmd\def{dijknode\dijk_currentnodename}{#3,}%
+ \readgraph_b
+ }%
+}%
+
+\def\readgraph_c#1=#2\_nil#3#4%
+{%
+ \def#3{#1}\edef#4{\number\numexpr#2\relax}%
+}
+
+\def\dijk_nodedist#1#2#3%
+{% renvoit la distance du sommet #1 vers #2 dans la macro #3
+ \def\dijk_nodedist_i##1#2=##2,##3\_nil{\def#3{##2}}%
+ \expandafter\expandafter\expandafter\dijk_nodedist_i\csname dijknode#1\endcsname,#2=1073741823,\_nil%
+}
+
+\def\dijk_removenode#1%
+{% enlève le sommet #1 de la liste des sommets non vus
+ \skv_exparg{\dijk_ifinst}{\expandafter,\dijk_nodestoexplore}{,#1,}
+ {\def\dijk_removenode_i##1,#1,##2\_nil{\skv_exparg{\def\dijk_nodestoexplore}{\dijk_gobarg##1,##2}}%
+ \expandafter\dijk_removenode_i\expandafter,\dijk_nodestoexplore\_nil}
+ {}%
+}
+
+\def\dijkstra
+{%
+ \dijk_ifopt{\dijkstra_i}{\dijkstra_i[]}%
+}
+\def\dijkstra_i[#1]#2#3%
+{% #1=sommet départ #2=sommet arrivée
+ \begingroup
+ \skv_ifempty{#1}{}{\setdijk{#1}}%
+ \let\dijk_listofnodes\dijk_initlistofnodes
+ \let\dijk_nodestoexplore\dijk_initlistofnodes
+ \dijk_cnt0
+ \skv_eearg{\def\dijk_currentnode}{\skv_removeextremespaces{#2}}%
+ \skv_eearg{\def\dijk_endnode}{\skv_removeextremespaces{#3}}%
+ \edef\dijk_tab{%
+ \unexpanded\expandafter\expandafter\expandafter{\useKV[\dijkname]{pre-tab}}%
+ \noexpand
+ \begin{tabular}[\useKV[\dijkname]{v-position}]{%
+ *{\dijk_numberofnodes}{|c}|%
+ \ifboolKV[\dijkname]{show-lastcol}
+ {\unexpanded\expandafter\expandafter\expandafter{\useKV[\dijkname]{lastcol-type}}}
+ {}%
+ }%
+ \noexpand\hline
+ }%
+ \def\dijk_autoamp{\def\dijk_autoamp{\dijk_addtomacro\dijk_tab&}}%
+ \skv_exparg{\dijk_foreach\dijk_tempnodename\in}\dijk_listofnodes
+ {% pour tous le sommets du graphe
+ \dijk_autoamp% ajouter "&", sauf la première fois
+ \dijk_cscmd\let{dist_\dijk_tempnodename}\dijk_maxint% toutes les distances à +inf
+ \dijk_cscmd\let{prev_\dijk_tempnodename}\dijk_quark% tous les prédecesseurs à <quark>
+ \dijk_eaddtomacro\dijk_tab{\dijk_tempnodename}% peupler 1re ligne du tableau
+ }%
+ \ifboolKV[\dijkname]{show-lastcol}
+ {\dijk_eaddtomacro\dijk_tab{\expandafter&\unexpanded\expandafter\expandafter\expandafter{\useKV[\dijkname]{lastcol-label}}}}
+ {}%
+ \dijk_addtomacro\dijk_tab{\\\hline}%
+ \dijk_cscmd\def{dist_\dijk_currentnode}{0}% distance sommet de départ = 0
+ \dijk_whilenotempty\dijk_nodestoexplore
+ {%
+ \dijk_findmindist\dijk_currentnode% retourne \dijk_currentnode : le sommet enfant ayant la distance la plus faible
+ \skv_ifx{\dijk_quark\dijk_currentnode}
+ {% si le sommet n'est pas trouvé (graphe non connexe)
+ \skv_eearg{\gdef\dijkdist}{\useKV[\dijkname]{infinity-code}}%
+ \let\dijk_nodestoexplore\empty% sortir de la boucle
+ }
+ {%
+ \xdef\dijkdist{\csname dist_\dijk_currentnode\endcsname}%
+ \unless\ifx\dijk_nodestoexplore\empty
+ \dijk_addstep
+ \fi
+ \skv_ifx{\dijk_currentnode\dijk_endnode}
+ {% si le sommet de sortie est atteint
+ \let\dijk_nodestoexplore\empty% sortir de la boucle
+ }
+ {% sinon
+ \skv_exparg\dijk_removenode\dijk_currentnode% enlever ce sommet du graphe à explorer
+ \skv_eearg{\dijk_foreach\dijk_temp\in}{\csname listofchilds_\dijk_currentnode\endcsname}
+ {%
+ \dijk_exptwoargs\dijk_ifinst\dijk_nodestoexplore{\dijk_temp,}
+ {%
+ \dijk_exptwoargs\dijk_updatedist\dijk_currentnode\dijk_temp
+ }%
+ {}%
+ }%
+ \advance\dijk_cnt1
+ }%
+ }%
+ }%
+ \ifboolKV[\dijkname]{h-rules}
+ {}
+ {\dijk_addtomacro\dijk_tab\hline}%
+ \dijk_addtomacro\dijk_tab{\end{tabular}}%
+ \dijk_eeaddtomacro\dijk_tab{\useKV[\dijkname]{post-tab}}%
+ \skv_ifx{\dijk_quark\dijk_currentnode}
+ {\skv_eearg{\gdef\dijkpath}{\useKV[\dijkname]{nopath-string}}}
+ {\skv_exparg\dijk_createpath\dijk_currentnode}% calculer le chemin sauf s'il est impossible à trouver
+ \ifboolKV[\dijkname]{show-tab}\dijk_tab{}% afficher le tableau
+ \endgroup
+}
+
+\def\dijk_createpath
+{%
+ \global\let\dijkpath\dijk_currentnode
+ \dijk_createpathi
+}
+\def\dijk_createpathi#1%
+{% #1=sommet en cours
+ \skv_eearg{\def\dijk_temp}{\csname prev_#1\endcsname}%
+ \skv_ifx{\dijk_quark\dijk_temp}
+ {}
+ {\xdef\dijkpath{\dijk_temp\useKV[\dijkname]{path-sep}\dijkpath}%
+ \skv_exparg\dijk_createpathi\dijk_temp
+ }%
+}
+
+\def\dijk_findmindist#1%
+{% trouve dans "sommets à explorer" celui ayant la distance mini
+ \let\dijk_mindist\dijk_maxint
+ \let#1\dijk_quark
+ \skv_exparg{\dijk_foreach\dijk_currentnodechildname\in}\dijk_nodestoexplore
+ {%
+ \ifnum\csname dist_\dijk_currentnodechildname\endcsname<\dijk_mindist\relax
+ \expandafter\let\expandafter\dijk_mindist\csname dist_\dijk_currentnodechildname\endcsname
+ \let#1\dijk_currentnodechildname
+ \fi
+ }%
+}
+
+\def\dijk_whilenotempty#1#2%
+{% tant que la macro #1 n'est pas \ifx-vide, exécuter #2
+ \skv_ifx{#1\empty}{}{#2\dijk_whilenotempty#1{#2}}%
+}
+
+\def\dijk_updatedist#1#2%
+{%
+ \dijk_nodedist{#1}{#2}\tempdist
+ \ifnum\numexpr\csname dist_#1\endcsname+\tempdist\relax<\csname dist_#2\endcsname\relax
+ \dijk_cscmd\edef{dist_#2}{\the\numexpr\csname dist_#1\endcsname+\tempdist\relax}%
+ \dijk_cscmd\edef{distwithprev_#2}{\noexpand\formatnodewithprev{\the\numexpr\csname dist_#1\endcsname+\tempdist\relax}{\unexpanded{#1}}}%
+ \dijk_cscmd\def{prev_#2}{#1}%
+ \fi
+}
+
+\def\dijk_addstep
+{%
+ \def\dijk_autoamp{\def\dijk_autoamp{\dijk_addtomacro\dijk_tab&}}%
+ \skv_exparg{\dijk_foreach\dijk_temp\in}\dijk_listofnodes
+ {%
+ \dijk_autoamp
+ \dijk_exptwoargs\dijk_ifinst\dijk_nodestoexplore\dijk_temp
+ {%
+ \ifnum\csname dist_\dijk_temp\endcsname=\dijk_maxint\relax
+ \dijk_eeaddtomacro\dijk_tab{\useKV[\dijkname]{infinity-code}}%
+ \else
+ \skv_ifx{\dijk_temp\dijk_currentnode}% si c'est le sommet fixé, le mettre en valeur
+ {%
+ \skv_ifcsname{distwithprev_\dijk_temp}
+ {%
+ \dijk_eeaddtomacro\dijk_tab{\expandafter\expandafter\expandafter\dijk_highlightnode
+ \csname distwithprev_\dijk_temp\endcsname}% forme \dijk_highlightnode\formatnodewithprev{<dist>}{<sommet>}
+ }
+ {%
+ \dijk_eeaddtomacro\dijk_tab{\expandafter\expandafter\expandafter
+ \highlightfirstnode\expandafter\expandafter\expandafter
+ {\csname dist_\dijk_temp\endcsname}}% forme \highlightfirstnode{0}
+ }%
+ }
+ {% sinon, afficher normalement (forme \formatnodewithprev{<dist>}{<sommet>})
+ \dijk_eeaddtomacro\dijk_tab{\csname dist\ifcsname distwithprev_\dijk_temp\endcsname withprev\fi _\dijk_temp\endcsname}%
+ }%
+ \fi
+ }%
+ {%
+ \dijk_eeaddtomacro\dijk_tab{\useKV[\dijkname]{norevisit-code}}% sommet déjà fixé
+ }%
+ }%
+ \ifboolKV[\dijkname]{show-lastcol}
+ {\dijk_eaddtomacro\dijk_tab{\expandafter&\detokenize\expandafter{\dijk_currentnode}}}% ajout du sommet fixé
+ {}%
+ \dijk_addtomacro\dijk_tab{\\}%
+ \ifboolKV[\dijkname]{h-rules}
+ {\dijk_addtomacro\dijk_tab\hline}
+ {}%
+}
+
+\def\dijk_highlightnode\formatnodewithprev{\highlightnode}
+
+\dijk_restorecatcode
+
+\expandafter\let\expandafter\initdijk\csname skv_[\dijkname]\endcsname
+
+% Macros permettant de modifier les <valeurs> des <clés>
+\def\setdijk#{\setKV[\dijkname]}
+
+% ... ainsi que les <valeurs> par défaut
+\def\setdijkdefault#{\setKVdefault[\dijkname]}
+
+\newcommand*\formatnodewithprev[2]%
+{% #1=distance, #2=nom du noeud de provenance
+ $#1_{\mathrm{#2}}$%
+}
+
+\newcommand*\highlightnode[2]%
+{% #1=distance, #2=nom du noeud de provenance
+ $\mathbf{#1}_{\mathrm{\mathbf{#2}}}$%
+}
+
+\newcommand*\highlightfirstnode[1]%
+{%
+ $\mathbf{#1}$%
+}
+
+\setdijkdefault{
+ show-tab = true,% afficher le tableau
+ v-position = c,% argument optionnel de \begin{tabular}[<arg>]
+ pre-tab = {},% juste avant le \begin{tabular}
+ post-tab = {},% juste après le \end{tabular}
+ col-type = c,% colonnes de type "c" pour les colonnes de distances
+ infinity-code = $\infty$,% pour distance infinie
+ norevisit-code = ---,% pour les sommets préalablement fixés
+ h-rules = false,% pas de filets entre les lignes des étapes
+ show-lastcol = false,% si vrai : mettre en plus la colonne "sommet fixé"
+ lastcol-type = c|,% dernière colonne
+ lastcol-label = sommet fix\'e,
+ nopath-string = Pas de chemin possible,% si chemin impossible
+ path-sep = -,% séparateur entre sommets dans le chemin
+}
+
+\endinput
+
+Versions :
+ _____________________________________________________________________________
+| Version | Date | Changements |
+|---------+------------+------------------------------------------------------|
+| 0.1 | 06/09/2017 | Première version |
+|---------+------------+------------------------------------------------------|
+| 0.11 | 09/09/2017 | - retrait d'un \show, laissé par oubli après les |
+| | | phases de débogage |
+| | | - petit nettoyage du code |
+|---------+------------+------------------------------------------------------| \ No newline at end of file