% !TeX encoding = UTF-8
% Ce fichier contient le code de l'extension "dijkstra"
%
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% %
\def\dijkname {dijkstra} %
\def\dijkver {0.13} %
% %
\def\dijkdate {2022/10/01} %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% --------------------------------------------------------------------
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3c
% 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 2017-2022
% email: unbonpetit@netc.fr
% Commentaires, suggestions et signalement de bugs bienvenus !
% Comments, bug reports and suggestions are welcome.
% --------------------------------------------------------------------
% L'extension dijkstra est compos��e des 4 fichiers suivants :
% - code : dijkstra.sty
% - manuel en fran��ais : dijkstra-fr.tex & dijkstra-fr.pdf
% - fichier lisezmoi : README
% --------------------------------------------------------------------
%
\csname dijkloadonce\endcsname
\let\dijkloadonce\endinput
\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{}
\long\def\dijk_first#1#2{#1}
\long\def\dijk_second#1#2{#2}
\long\def\dijk_earg#1#2{\expandafter\dijk_earg_i\expandafter{#2}{#1}}\let\dijk_exparg\dijk_earg
\long\def\dijk_eearg#1#2{\expandafter\expandafter\expandafter\dijk_earg_i\expandafter\expandafter\expandafter{#2}{#1}}
\long\def\dijk_earg_i#1#2{#2{#1}}
\long\def\dijk_ifx#1{\ifx#1\expandafter\dijk_first\else\expandafter\dijk_second\fi}
\long\def\dijk_ifempty#1{\dijk_ifempty_i#1\_nil\_nil\dijk_second\dijk_first\__nil}%
\long\def\dijk_ifempty_i#1#2\_nil#3#4#5\__nil{#4}
\def\dijk_ifcsname#1{\ifcsname#1\endcsname\expandafter\skv_first\else\expandafter\skv_second\fi}
\def\dijk_addtomacro#1#2{\expandafter\def\expandafter#1\expandafter{#1#2}}
\def\dijk_eaddtomacro#1#2{\dijk_exparg{\dijk_addtomacro#1}{#2}}
\def\dijk_eeaddtomacro#1#2{\dijk_eearg{\dijk_addtomacro#1}{#2}}
\long\def\dijk_exptwoargs#1#2#3{\dijk_exparg{\dijk_exparg{#1}{#2}}{#3}}
\def\dijk_ifnum#1{\ifnum#1\expandafter\dijk_first\else\expandafter\dijk_second\fi}
\def\dijk_swapargs#1#2#3{#1{#3}{#2}}
\def\dijk_ifstar#1#2{\def\dijk_ifstar_i{\dijk_ifx{*\dijk_nxttok}{\dijk_first{#1}}{#2}}\futurelet\dijk_nxttok\dijk_ifstar_i}
\def\dijk_ifopt#1#2{\def\dijk_ifopt_i{\dijk_ifx{[\dijk_nxttok}{#1}{#2}}\futurelet\dijk_nxttok\dijk_ifopt_i}
\def\dijk_stripsp#1%
{%
\long\def\dijk_stripsp##1{\expanded{\dijk_stripsp_i\_marksp##1\__nil\_marksp#1\_marksp\_nil}}%
\long\def\dijk_stripsp_i##1\_marksp#1##2\_marksp##3\_nil{\dijk_stripsp_ii##3##1##2\__nil#1\__nil\_nil}%
\long\def\dijk_stripsp_ii##1#1\__nil##2\_nil{\dijk_stripsp_iii##1##2\_nil}%
\long\def\dijk_stripsp_iii##1##2\__nil##3\_nil{\unexpanded{##2}}%
}
\dijk_stripsp{ }
\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}%
\dijk_ifx{\dijk_quark#1}
{%
}
{%
\dijk_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{\dijk_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 o�� l'on va enlever les espaces
\dijk_sanitizegraph#1,\dijk_quark[],% enlever tous les espaces ind��sirables et ��valuer les nombres dans l'argument #1
\expandafter\readgraph_b\dijk_graph,\dijk_quark[],%
}
\def\dijk_sanitizegraph#1,%
{%
\expandafter\expandafter\expandafter\dijk_sanitizegraph_i\dijk_stripsp{#1},% bugfix 0.12
}
\def\dijk_sanitizegraph_i#1[#2],%
{%
\dijk_ifx{\dijk_quark#1}
{%
\dijk_removelastcommainmacro\dijk_graph
}
{%
\dijk_eearg{\def\dijk_childnodes}{\dijk_stripsp{#1}[}%
\dijk_foreach\dijk_temp\in{#2}{\expandafter\dijk_sanitizegraph_ii\dijk_temp\_nil}%
\dijk_removelastcommainmacro\dijk_childnodes
\dijk_eaddtomacro\dijk_graph{\dijk_childnodes],}%
\dijk_sanitizegraph
}%
}
\def\dijk_sanitizegraph_ii#1=#2\_nil
{%
\dijk_eeaddtomacro\dijk_childnodes{\dijk_stripsp{#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,%
{%
\dijk_ifx{\dijk_quark#1}
{%
\dijk_exparg{\dijk_foreach\dijk_tempnodename\in}{\dijk_initlistofnodes}
{% pour chaque sommet
\dijk_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 orient��, ajouter les distances inverses
\dijk_exparg{\dijk_eearg\dijk_ifinst{\csname dijknode\dijk_currentnodechildname\endcsname}}{\dijk_tempnodename=}% si le parent est dans d��j�� 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 diff��rente : 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
\dijk_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
\dijk_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%
{% enl��ve le sommet #1 de la liste des sommets non vus
\dijk_exparg{\dijk_ifinst}{\expandafter,\dijk_nodestoexplore}{,#1,}
{%
\def\dijk_removenode_i##1,#1,##2\_nil{\dijk_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 d��part #2=sommet arriv��e
\begingroup
\dijk_ifempty{#1}{}{\setdijk{#1}}%
\let\dijk_listofnodes\dijk_initlistofnodes
\let\dijk_nodestoexplore\dijk_initlistofnodes
\dijk_cnt0
\dijk_eearg{\def\dijk_currentnode}{\dijk_stripsp{#2}}%
\dijk_eearg{\def\dijk_endnode}{\dijk_stripsp{#3}}%
\edef\dijk_tab
{%
\noexpand\dijk_pre_tab
\noexpand\begin{tabular}[\dijk_v_position]{%
*{\dijk_numberofnodes}{|\dijk_col_type}|%
\ifboolKV[\dijkname]{show-lastcol}
{\noexpand\dijk_last_col_type}
{}%
}%
\noexpand\hline
}%
\def\dijk_autoamp{\def\dijk_autoamp{\dijk_addtomacro\dijk_tab&}}%
\dijk_exparg{\dijk_foreach\dijk_tempnodename\in}\dijk_listofnodes
{% pour tous le sommets du graphe
\dijk_autoamp% ajouter "&", sauf la premi��re fois
\dijk_cscmd\let{dist_\dijk_tempnodename}\dijk_maxint% toutes les distances �� +inf
\dijk_cscmd\let{prev_\dijk_tempnodename}\dijk_quark% tous les pr��decesseurs �� <quark>
\dijk_eaddtomacro\dijk_tab{\dijk_tempnodename}% peupler 1re ligne du tableau
}%
\ifboolKV[\dijkname]{show-lastcol}
{\dijk_eaddtomacro\dijk_tab{\expandafter&\dijk_lastcol_label}}
{}%
\dijk_addtomacro\dijk_tab{\\\hline}%
\dijk_cscmd\def{dist_\dijk_currentnode}{0}% distance sommet de d��part = 0
\dijk_whilenotempty\dijk_nodestoexplore
{%
\dijk_findmindist\dijk_currentnode% retourne \dijk_currentnode : le sommet enfant ayant la distance la plus faible
\dijk_ifx{\dijk_quark\dijk_currentnode}
{% si le sommet n'est pas trouv�� (graphe non connexe)
\global\let\dijkdist\dijk_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
\dijk_ifx{\dijk_currentnode\dijk_endnode}
{% si le sommet de sortie est atteint
\let\dijk_nodestoexplore\empty% sortir de la boucle
}
{% sinon
\dijk_exparg\dijk_removenode\dijk_currentnode% enlever ce sommet du graphe �� explorer
\dijk_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_eaddtomacro\dijk_tab{\dijk_post_tab}%
\dijk_ifx{\dijk_quark\dijk_currentnode}
{\global\let\dijkpath\dijk_nopath_string}
{\dijk_exparg\dijk_createpath\dijk_currentnode}% calculer le chemin sauf s'il est impossible �� 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
\dijk_eearg{\def\dijk_temp}{\csname prev_#1\endcsname}%
\dijk_ifx{\dijk_quark\dijk_temp}
{%
}
{%
\xdef\dijkpath{\dijk_temp\dijk_path_sep\dijkpath}%
\dijk_exparg\dijk_createpathi\dijk_temp
}%
}
\def\dijk_findmindist#1%
{% trouve dans "sommets �� explorer" celui ayant la distance mini
\let\dijk_mindist\dijk_maxint
\let#1\dijk_quark
\dijk_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, ex��cuter #2
\dijk_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&}}%
\dijk_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_eaddtomacro\dijk_tab{\dijk_infinity_code}%
\else
\dijk_ifx{\dijk_temp\dijk_currentnode}% si c'est le sommet fix��, le mettre en valeur
{%
\dijk_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_eaddtomacro\dijk_tab{\dijk_no_revisit_code}% sommet d��j�� fix��
}%
}%
\ifboolKV[\dijkname]{show-lastcol}
{\dijk_eaddtomacro\dijk_tab{\expandafter&\detokenize\expandafter{\dijk_currentnode}}}% ajout du sommet fix��
{}%
\dijk_addtomacro\dijk_tab{\\}%
\ifboolKV[\dijkname]{h-rules}
{\dijk_addtomacro\dijk_tab\hline}
{}%
}
\def\dijk_highlightnode\formatnodewithprev{\highlightnode}
\defKV[\dijkname]{%
v-position = \def\dijk_v_position {#1},
pre-tab = \def\dijk_pre_tab {#1},
post-tab = \def\dijk_post_tab {#1},
col-type = \def\dijk_col_type {#1},
infinity-code = \def\dijk_infinity_code {#1},
norevisit-code = \def\dijk_no_revisit_code{#1},
lastcol-type = \def\dijk_last_col_type {#1},
lastcol-label = \def\dijk_lastcol_label {#1},
nopath-string = \def\dijk_nopath_string {#1},
path-sep = \def\dijk_path_sep {#1}
}
\dijk_restorecatcode
\def\initdijk{\restoreKV[\dijkname]}
% Macros permettant de modifier les <valeurs> des <cl��s>
\def\setdijk#{\setKV[\dijkname]}
% ... ainsi que les <valeurs> par d��faut
\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 apr��s 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 pr��alablement fix��s
h-rules = false,% pas de filets entre les lignes des ��tapes
show-lastcol = false,% si vrai : mettre en plus la colonne "sommet fix��"
lastcol-type = c|,% derni��re colonne
lastcol-label = sommet fix\'e,
nopath-string = Pas de chemin possible,% si chemin impossible
path-sep = -,% s��parateur entre sommets dans le chemin
}
\endinput
Versions :
_____________________________________________________________________________
| Version | Date | Changements |
|---------+------------+------------------------------------------------------|
| 0.1 | 06/09/2017 | Premi��re version |
|---------+------------+------------------------------------------------------|
| 0.11 | 09/09/2017 | - retrait d'un \show, laiss�� par oubli apr��s les |
| | | phases de d��bogage |
| | | - petit nettoyage du code |
|---------+------------+------------------------------------------------------|
| 0.12 | 25/06/2020 | - bugfix : le package est rendu compatible avec la |
| | | version 0.2 de simplekv |
| | | - bugfix : mauvaise gestion des espaces dans la macro|
| | | \dijk_sanitizegraph |
|---------+------------+------------------------------------------------------|
| 0.13 | 01/10/2022 | - le package est rendu compatible avec la version |
| | | 0.2a de simplekv |
| | | - code en UFT8 |
|---------+------------+------------------------------------------------------|