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Web","\u002Fsnt-2nde\u002Fsb-web","0.snt-2nde\u002Fsb-web\u002F0.index",[41,42,46,50,54,58,62],{"title":37,"path":38,"stem":39},{"title":43,"path":44,"stem":45},"Histoire du Web","\u002Fsnt-2nde\u002Fsb-web\u002Fhistoire-web","0.snt-2nde\u002Fsb-web\u002F1.histoire-web",{"title":47,"path":48,"stem":49},"URL et hypertexte","\u002Fsnt-2nde\u002Fsb-web\u002Furl-hypertexte","0.snt-2nde\u002Fsb-web\u002F2.url-hypertexte",{"title":51,"path":52,"stem":53},"HTML et CSS — le contenu et la présentation","\u002Fsnt-2nde\u002Fsb-web\u002Fhtml-css","0.snt-2nde\u002Fsb-web\u002F3.html-css",{"title":55,"path":56,"stem":57},"Client-serveur et requêtes HTTP","\u002Fsnt-2nde\u002Fsb-web\u002Fclient-serveur-http","0.snt-2nde\u002Fsb-web\u002F4.client-serveur-http",{"title":59,"path":60,"stem":61},"Moteurs de recherche","\u002Fsnt-2nde\u002Fsb-web\u002Fmoteurs-recherche","0.snt-2nde\u002Fsb-web\u002F5.moteurs-recherche",{"title":63,"path":64,"stem":65},"Sécurité du navigateur et notions juridiques","\u002Fsnt-2nde\u002Fsb-web\u002Fsecurite-droits","0.snt-2nde\u002Fsb-web\u002F6.securite-droits",{"title":67,"path":68,"stem":69,"children":70},"Les réseaux sociaux","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F0.index",[71,72,76,80,84,88],{"title":67,"path":68,"stem":69},{"title":73,"path":74,"stem":75},"Panorama des réseaux sociaux","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fpanorama-rs","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F1.panorama-rs",{"title":77,"path":78,"stem":79},"Identité numérique et authentification","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fidentite-numerique","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F2.identite-numerique",{"title":81,"path":82,"stem":83},"Le modèle économique des réseaux sociaux","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fmodele-economique","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F3.modele-economique",{"title":85,"path":86,"stem":87},"Petit monde et graphes","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fpetit-monde-graphes","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F4.petit-monde-graphes",{"title":89,"path":90,"stem":91},"La cyberviolence","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fcyberviolence","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F5.cyberviolence",{"title":93,"path":94,"stem":95,"children":96},"Les données structurées et leur traitement","\u002Fsnt-2nde\u002Fsd-donnees-structurees","0.snt-2nde\u002Fsd-donnees-structurees\u002F0.index",[97,98,102,106,110,114],{"title":93,"path":94,"stem":95},{"title":99,"path":100,"stem":101},"Données et formats","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fdonnees-formats","0.snt-2nde\u002Fsd-donnees-structurees\u002F1.donnees-formats",{"title":103,"path":104,"stem":105},"Données 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position","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fconfidentialite-position","0.snt-2nde\u002Fse-localisation-cartographie\u002F5.confidentialite-position",{"title":145,"path":146,"stem":147,"children":148},"Informatique embarquée et objets connectés","\u002Fsnt-2nde\u002Fsf-info-embarquee","0.snt-2nde\u002Fsf-info-embarquee\u002F0.index",[149,150,154,158],{"title":145,"path":146,"stem":147},{"title":151,"path":152,"stem":153},"Systèmes informatiques embarqués","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fsystemes-embarques","0.snt-2nde\u002Fsf-info-embarquee\u002F1.systemes-embarques",{"title":155,"path":156,"stem":157},"Capteurs et actionneurs","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fcapteurs-actionneurs","0.snt-2nde\u002Fsf-info-embarquee\u002F2.capteurs-actionneurs",{"title":159,"path":160,"stem":161},"IHM et objets connectés","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fihm-objet-connecte","0.snt-2nde\u002Fsf-info-embarquee\u002F3.ihm-objet-connecte",{"title":163,"path":164,"stem":165,"children":166},"Photographie numérique","\u002Fsnt-2nde\u002Fsg-photo-numerique","0.snt-2nde\u002Fsg-photo-numerique\u002F0.index",[167,168,172,176,180],{"title":163,"path":164,"stem":165},{"title":169,"path":170,"stem":171},"Photosites, pixels et résolution","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Fpixels-resolution","0.snt-2nde\u002Fsg-photo-numerique\u002F1.pixels-resolution",{"title":173,"path":174,"stem":175},"Les algorithmes de l'appareil photo","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Falgorithmes-photo","0.snt-2nde\u002Fsg-photo-numerique\u002F2.algorithmes-photo",{"title":177,"path":178,"stem":179},"Les métadonnées EXIF","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Fmetadonnees-exif","0.snt-2nde\u002Fsg-photo-numerique\u002F3.metadonnees-exif",{"title":181,"path":182,"stem":183},"Traiter une image en Python","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Ftraitement-rgb","0.snt-2nde\u002Fsg-photo-numerique\u002F4.traitement-rgb",{"title":185,"path":186,"stem":187,"children":188},"Notions transversales de programmation","\u002Fsnt-2nde\u002Fsh-prog-notions","0.snt-2nde\u002Fsh-prog-notions\u002F0.index",[189,190,194,198,202],{"title":185,"path":186,"stem":187},{"title":191,"path":192,"stem":193},"Séquences d'instructions et variables","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fsequences-affectations","0.snt-2nde\u002Fsh-prog-notions\u002F1.sequences-affectations",{"title":195,"path":196,"stem":197},"Instructions conditionnelles","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fconditionnelles","0.snt-2nde\u002Fsh-prog-notions\u002F2.conditionnelles",{"title":199,"path":200,"stem":201},"Boucles bornées et non bornées","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fboucles","0.snt-2nde\u002Fsh-prog-notions\u002F3.boucles",{"title":203,"path":204,"stem":205},"Définitions et appels de fonctions","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Ffonctions","0.snt-2nde\u002Fsh-prog-notions\u002F4.fonctions",{"title":207,"path":208,"stem":209,"children":210},"Démo des widgets MDC","\u002Fsnt-2nde\u002Fzz-demo-widgets","0.snt-2nde\u002Fzz-demo-widgets\u002F0.index",[211,212,216,220],{"title":207,"path":208,"stem":209},{"title":213,"path":214,"stem":215},"Démo statique — callouts, code, BO, illustration","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fstatique","0.snt-2nde\u002Fzz-demo-widgets\u002F1.statique",{"title":217,"path":218,"stem":219},"Démo interactive — self-eval et python-snippet","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Finteractif","0.snt-2nde\u002Fzz-demo-widgets\u002F2.interactif",{"title":221,"path":222,"stem":223},"Démo · 14 widgets de manipulation NSI","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fwidgets-manipulation","0.snt-2nde\u002Fzz-demo-widgets\u002F3.widgets-manipulation",{"title":225,"path":226,"stem":227,"children":228},"NSI — Première","\u002Fnsi-1ere","1.nsi-1ere\u002F0.index",[229,230,234,256,282,304,328,354,380,410],{"title":225,"path":226,"stem":227},{"title":231,"path":232,"stem":233},"Relecture pédagogique — 8 chapitres NSI 1ère (PA → PH)","\u002Fnsi-1ere\u002Freview","1.nsi-1ere\u002FREVIEW",{"title":235,"path":236,"stem":237,"children":238},"Histoire de l'informatique","\u002Fnsi-1ere\u002Fpa-histoire-info","1.nsi-1ere\u002Fpa-histoire-info\u002F0.index",[239,240,244,248,252],{"title":235,"path":236,"stem":237},{"title":241,"path":242,"stem":243},"De la préantiquité aux machines à calculer","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fpreantiquite-aux-machines","1.nsi-1ere\u002Fpa-histoire-info\u002F1.preantiquite-aux-machines",{"title":245,"path":246,"stem":247},"La machine universelle (1930-1950)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fmachine-universelle","1.nsi-1ere\u002Fpa-histoire-info\u002F2.machine-universelle",{"title":249,"path":250,"stem":251},"Les ordinateurs modernes 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deux","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fentiers-relatifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F2.entiers-relatifs",{"title":271,"path":272,"stem":273},"Nombres flottants et virgule flottante","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fflottants","1.nsi-1ere\u002Fpb-types-valeurs\u002F3.flottants",{"title":275,"path":276,"stem":277},"Textes et encodages — ASCII, ISO-8859-1, Unicode","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Ftextes-encodages","1.nsi-1ere\u002Fpb-types-valeurs\u002F4.textes-encodages",{"title":279,"path":280,"stem":281},"Valeurs booléennes et opérateurs logiques","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fbooleens","1.nsi-1ere\u002Fpb-types-valeurs\u002F5.booleens",{"title":283,"path":284,"stem":285,"children":286},"Représentation des données : types construits","\u002Fnsi-1ere\u002Fpc-types-construits","1.nsi-1ere\u002Fpc-types-construits\u002F0.index",[287,288,292,296,300],{"title":283,"path":284,"stem":285},{"title":289,"path":290,"stem":291},"Tableaux et listes","\u002Fnsi-1ere\u002Fpc-types-construits\u002Ftableaux-listes","1.nsi-1ere\u002Fpc-types-construits\u002F1.tableaux-listes",{"title":293,"path":294,"stem":295},"Listes en compréhension","\u002Fnsi-1ere\u002Fpc-types-construits\u002Fcomprehension","1.nsi-1ere\u002Fpc-types-construits\u002F2.comprehension",{"title":297,"path":298,"stem":299},"Tuples et p-uplets nommés","\u002Fnsi-1ere\u002Fpc-types-construits\u002Ftuples","1.nsi-1ere\u002Fpc-types-construits\u002F3.tuples",{"title":301,"path":302,"stem":303},"Dictionnaires","\u002Fnsi-1ere\u002Fpc-types-construits\u002Fdictionnaires","1.nsi-1ere\u002Fpc-types-construits\u002F4.dictionnaires",{"title":305,"path":306,"stem":307,"children":308},"Traitement de données en tables","\u002Fnsi-1ere\u002Fpd-tables-donnees","1.nsi-1ere\u002Fpd-tables-donnees\u002F0.index",[309,310,314,318,322],{"title":305,"path":306,"stem":307},{"title":311,"path":312,"stem":313},"Tables et CSV","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftables-csv","1.nsi-1ere\u002Fpd-tables-donnees\u002F1.tables-csv",{"title":315,"path":316,"stem":317},"Recherche et filtrage","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Frecherche","1.nsi-1ere\u002Fpd-tables-donnees\u002F2.recherche",{"title":319,"path":320,"stem":321},"Trier une table","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftri","1.nsi-1ere\u002Fpd-tables-donnees\u002F3.tri",{"title":323,"path":324,"stem":325,"children":326},"Fusion et indexation","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ffusion-indexation","1.nsi-1ere\u002Fpd-tables-donnees\u002F4.fusion-indexation",[327],{"title":323,"path":324,"stem":325},{"title":329,"path":330,"stem":331,"children":332},"IHM sur le Web","\u002Fnsi-1ere\u002Fpe-ihm-web","1.nsi-1ere\u002Fpe-ihm-web\u002F0.index",[333,334,338,342,346,350],{"title":329,"path":330,"stem":331},{"title":335,"path":336,"stem":337},"HTML et CSS — rappel de structure","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fhtml-css-bases","1.nsi-1ere\u002Fpe-ihm-web\u002F1.html-css-bases",{"title":339,"path":340,"stem":341},"Formulaires HTML","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fformulaires","1.nsi-1ere\u002Fpe-ihm-web\u002F2.formulaires",{"title":343,"path":344,"stem":345},"Événements JavaScript","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fevenements-js","1.nsi-1ere\u002Fpe-ihm-web\u002F3.evenements-js",{"title":347,"path":348,"stem":349},"Manipulation du DOM","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fdom-interaction","1.nsi-1ere\u002Fpe-ihm-web\u002F4.dom-interaction",{"title":351,"path":352,"stem":353},"Client, serveur et HTTP","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fclient-serveur-http","1.nsi-1ere\u002Fpe-ihm-web\u002F5.client-serveur-http",{"title":355,"path":356,"stem":357,"children":358},"Architectures matérielles et systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os","1.nsi-1ere\u002Fpf-archi-os\u002F0.index",[359,360,364,368,372,376],{"title":355,"path":356,"stem":357},{"title":361,"path":362,"stem":363},"Le modèle de von Neumann","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fvon-neumann","1.nsi-1ere\u002Fpf-archi-os\u002F1.von-neumann",{"title":365,"path":366,"stem":367},"Périphériques et interface homme-machine","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fperipheriques-ihm","1.nsi-1ere\u002Fpf-archi-os\u002F2.peripheriques-ihm",{"title":369,"path":370,"stem":371},"Les systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fsystemes-exploitation","1.nsi-1ere\u002Fpf-archi-os\u002F3.systemes-exploitation",{"title":373,"path":374,"stem":375},"Linux et le shell","\u002Fnsi-1ere\u002Fpf-archi-os\u002Flinux-shell","1.nsi-1ere\u002Fpf-archi-os\u002F4.linux-shell",{"title":377,"path":378,"stem":379},"Réseaux et protocoles","\u002Fnsi-1ere\u002Fpf-archi-os\u002Freseaux","1.nsi-1ere\u002Fpf-archi-os\u002F5.reseaux",{"title":381,"path":382,"stem":383,"children":384},"Langages et programmation","\u002Fnsi-1ere\u002Fpg-langages-prog","1.nsi-1ere\u002Fpg-langages-prog\u002F0.index",[385,386,390,394,398,402,406],{"title":381,"path":382,"stem":383},{"title":387,"path":388,"stem":389},"Diversité et unité des langages de programmation","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fdiversite-langages","1.nsi-1ere\u002Fpg-langages-prog\u002F1.diversite-langages",{"title":391,"path":392,"stem":393},"Constructions élémentaires","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fconstructions-elementaires","1.nsi-1ere\u002Fpg-langages-prog\u002F2.constructions-elementaires",{"title":395,"path":396,"stem":397},"Fonctions","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Ffonctions","1.nsi-1ere\u002Fpg-langages-prog\u002F3.fonctions",{"title":399,"path":400,"stem":401},"Spécification d'une fonction","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fspecification","1.nsi-1ere\u002Fpg-langages-prog\u002F4.specification",{"title":403,"path":404,"stem":405},"Mise au point des programmes","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fmise-au-point","1.nsi-1ere\u002Fpg-langages-prog\u002F5.mise-au-point",{"title":407,"path":408,"stem":409},"Utilisation de bibliothèques","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fbibliotheques","1.nsi-1ere\u002Fpg-langages-prog\u002F6.bibliotheques",{"title":411,"path":412,"stem":413,"children":414},"Algorithmique","\u002Fnsi-1ere\u002Fph-algorithmique","1.nsi-1ere\u002Fph-algorithmique\u002F0.index",[415,416,420,424,428,432,436],{"title":411,"path":412,"stem":413},{"title":417,"path":418,"stem":419},"Parcours séquentiel d'un tableau","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fparcours-sequentiel","1.nsi-1ere\u002Fph-algorithmique\u002F1.parcours-sequentiel",{"title":421,"path":422,"stem":423},"Bases de la complexité","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fcomplexite-bases","1.nsi-1ere\u002Fph-algorithmique\u002F2.complexite-bases",{"title":425,"path":426,"stem":427},"Tris par sélection et par insertion","\u002Fnsi-1ere\u002Fph-algorithmique\u002Ftris","1.nsi-1ere\u002Fph-algorithmique\u002F3.tris",{"title":429,"path":430,"stem":431},"Recherche dichotomique","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fdichotomie","1.nsi-1ere\u002Fph-algorithmique\u002F4.dichotomie",{"title":433,"path":434,"stem":435},"Algorithmes gloutons","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fgloutons","1.nsi-1ere\u002Fph-algorithmique\u002F5.gloutons",{"title":437,"path":438,"stem":439},"Les k plus proches voisins (k-NN)","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fknn","1.nsi-1ere\u002Fph-algorithmique\u002F6.knn",{"title":441,"path":442,"stem":443,"children":444},"NSI — Terminale","\u002Fnsi-tale","2.nsi-tale\u002F0.index",[445,446,450,476,498,536,560],{"title":441,"path":442,"stem":443},{"title":447,"path":448,"stem":449},"Review pédagogique — chapitres NSI Terminale (TA, TB, TC, TD, TE)","\u002Fnsi-tale\u002Freview","2.nsi-tale\u002FREVIEW",{"title":451,"path":452,"stem":453,"children":454},"Structures de données","\u002Fnsi-tale\u002Fta-structures-donnees","2.nsi-tale\u002Fta-structures-donnees\u002F0.index",[455,456,460,464,468,472],{"title":451,"path":452,"stem":453},{"title":457,"path":458,"stem":459},"Objet, classe, interface","\u002Fnsi-tale\u002Fta-structures-donnees\u002Finterface-implementation","2.nsi-tale\u002Fta-structures-donnees\u002F1.interface-implementation",{"title":461,"path":462,"stem":463},"Implémenter une structure — l'exemple de la file FIFO","\u002Fnsi-tale\u002Fta-structures-donnees\u002Fimplementer-une-structure","2.nsi-tale\u002Fta-structures-donnees\u002F2.implementer-une-structure",{"title":465,"path":466,"stem":467},"Listes, piles, files, dictionnaires","\u002Fnsi-tale\u002Fta-structures-donnees\u002Flistes-piles-files-dict","2.nsi-tale\u002Fta-structures-donnees\u002F3.listes-piles-files-dict",{"title":469,"path":470,"stem":471},"Arbres binaires","\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires","2.nsi-tale\u002Fta-structures-donnees\u002F4.arbres-binaires",{"title":473,"path":474,"stem":475},"Graphes","\u002Fnsi-tale\u002Fta-structures-donnees\u002Fgraphes","2.nsi-tale\u002Fta-structures-donnees\u002F5.graphes",{"title":477,"path":478,"stem":479,"children":480},"Bases de données","\u002Fnsi-tale\u002Ftb-bases-de-donnees","2.nsi-tale\u002Ftb-bases-de-donnees\u002F0.index",[481,482,486,490,494],{"title":477,"path":478,"stem":479},{"title":483,"path":484,"stem":485},"Le modèle relationnel","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fmodele-relationnel","2.nsi-tale\u002Ftb-bases-de-donnees\u002F1.modele-relationnel",{"title":487,"path":488,"stem":489},"Bases de données relationnelles et anomalies de schéma","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fbase-relationnelle","2.nsi-tale\u002Ftb-bases-de-donnees\u002F2.base-relationnelle",{"title":491,"path":492,"stem":493},"Le langage SQL","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fsql","2.nsi-tale\u002Ftb-bases-de-donnees\u002F3.sql",{"title":495,"path":496,"stem":497},"Les systèmes de gestion de bases de données","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fsgbd","2.nsi-tale\u002Ftb-bases-de-donnees\u002F4.sgbd",{"title":499,"path":500,"stem":501,"children":502},"Architectures matérielles, systèmes d'exploitation et réseaux","\u002Fnsi-tale\u002Ftc-archi-os-reseaux","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F0.index",[503,504,508,512,516,520,524,528,532],{"title":499,"path":500,"stem":501},{"title":505,"path":506,"stem":507},"Le système sur puce (SoC)","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fsysteme-sur-puce","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F1.systeme-sur-puce",{"title":509,"path":510,"stem":511},"Processus et ordonnancement par l'OS","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fprocessus-os","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F2.processus-os",{"title":513,"path":514,"stem":515},"L'interblocage (deadlock)","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Finterblocage","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F3.interblocage",{"title":517,"path":518,"stem":519},"Principes du routage","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Froutage-principes","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F4.routage-principes",{"title":521,"path":522,"stem":523},"Protocoles de routage RIP et OSPF","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fprotocoles-rip-ospf","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F5.protocoles-rip-ospf",{"title":525,"path":526,"stem":527},"Chiffrement symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-symetrique","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F6.chiffrement-symetrique",{"title":529,"path":530,"stem":531},"Chiffrement asymétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-asymetrique","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F7.chiffrement-asymetrique",{"title":533,"path":534,"stem":535},"HTTPS — l'échange de clé symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fhttps-tls","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F8.https-tls",{"title":381,"path":537,"stem":538,"children":539},"\u002Fnsi-tale\u002Ftd-langages-prog","2.nsi-tale\u002Ftd-langages-prog\u002F0.index",[540,541,544,548,552,556],{"title":381,"path":537,"stem":538},{"title":403,"path":542,"stem":543},"\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmise-au-point","2.nsi-tale\u002Ftd-langages-prog\u002F1.mise-au-point",{"title":545,"path":546,"stem":547},"Modularité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmodularite","2.nsi-tale\u002Ftd-langages-prog\u002F2.modularite",{"title":549,"path":550,"stem":551},"Récursivité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Frecursivite","2.nsi-tale\u002Ftd-langages-prog\u002F3.recursivite",{"title":553,"path":554,"stem":555},"Paradigmes de programmation","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fparadigmes","2.nsi-tale\u002Ftd-langages-prog\u002F4.paradigmes",{"title":557,"path":558,"stem":559},"Programme comme donnée — calculabilité et indécidabilité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fprogramme-comme-donnee","2.nsi-tale\u002Ftd-langages-prog\u002F5.programme-comme-donnee",{"title":411,"path":561,"stem":562,"children":563},"\u002Fnsi-tale\u002Fte-algorithmique","2.nsi-tale\u002Fte-algorithmique\u002F0.index",[564,565,569,573,577,581],{"title":411,"path":561,"stem":562},{"title":566,"path":567,"stem":568},"Algorithmes sur les arbres binaires","\u002Fnsi-tale\u002Fte-algorithmique\u002Farbres-binaires-algos","2.nsi-tale\u002Fte-algorithmique\u002F1.arbres-binaires-algos",{"title":570,"path":571,"stem":572},"Parcours de graphes — DFS, BFS, cycles, chemins","\u002Fnsi-tale\u002Fte-algorithmique\u002Fgraphes-parcours","2.nsi-tale\u002Fte-algorithmique\u002F2.graphes-parcours",{"title":574,"path":575,"stem":576},"Diviser pour régner","\u002Fnsi-tale\u002Fte-algorithmique\u002Fdiviser-pour-regner","2.nsi-tale\u002Fte-algorithmique\u002F3.diviser-pour-regner",{"title":578,"path":579,"stem":580},"Programmation dynamique","\u002Fnsi-tale\u002Fte-algorithmique\u002Fprogrammation-dynamique","2.nsi-tale\u002Fte-algorithmique\u002F4.programmation-dynamique",{"title":582,"path":583,"stem":584},"Recherche textuelle — l'algorithme de Boyer-Moore","\u002Fnsi-tale\u002Fte-algorithmique\u002Frecherche-textuelle","2.nsi-tale\u002Fte-algorithmique\u002F5.recherche-textuelle",{"id":586,"title":137,"bo":587,"body":589,"description":1395,"eval":1396,"extension":1397,"labo":1396,"meta":1398,"navigation":1399,"path":138,"quizzes":1400,"readingTime":1409,"seo":1410,"stem":139,"tp":1396,"__hash__":1411},"cours\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes.md",[588],"SE01",{"type":590,"value":591,"toc":1384},"minimark",[592,597,606,609,613,620,639,642,665,672,683,709,713,731,798,812,832,836,977],[593,594,596],"h2",{"id":595},"introduction","Introduction",[598,599,600,601,605],"p",{},"Vous demandez à votre téléphone un itinéraire de chez vous au lycée. En une\nseconde, il vous propose un trajet, une durée estimée, parfois trois\nvariantes : le plus rapide, le plus court, le plus économe. Comment une\nmachine prend-elle cette décision ? La réponse mêle géographie numérique\n(cours précédent) et un objet mathématique fondamental en informatique : le\n",[602,603,604],"strong",{},"graphe",".",[607,608],"bo-ref",{"code":588},[593,610,612],{"id":611},"dun-plan-à-un-graphe","D'un plan à un graphe",[598,614,615,616,619],{},"Sur un plan de ville, vous voyez des rues, des intersections, des places, des\nronds-points. Un logiciel de calcul d'itinéraire, lui, ne « voit » rien de\ntout cela. Il manipule une ",[602,617,618],{},"représentation abstraite"," : le graphe.",[621,622,625],"card",{"icon":623,"title":624},"i-lucide-share-2","Le graphe en deux mots",[598,626,627,628,630,631,634,635,638],{},"Un ",[602,629,604],{}," est une collection de ",[602,632,633],{},"sommets"," (les points) reliés par des\n",[602,636,637],{},"arêtes"," (les liens). C'est tout. Ni plus, ni moins.",[598,640,641],{},"Pour transformer un plan en graphe :",[643,644,645,656],"ul",{},[646,647,648,649,652,653,605],"li",{},"Chaque ",[602,650,651],{},"intersection"," devient un ",[602,654,655],{},"sommet",[646,657,648,658,661,662,605],{},[602,659,660],{},"tronçon de rue"," entre deux intersections devient une ",[602,663,664],{},"arête",[666,667],"illustration",{"alt":668,"kind":669,"src":670,"svg":671},"Passage d'un plan de quartier à un graphe","schema","\u002Fillustrations\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002Fplan-vers-graphe.svg","\u003Csvg class=\"illustration-svg\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 520 260\" role=\"img\" aria-label=\"Double représentation. À gauche, un plan de quartier : quatre intersections A, B, C, D reliées par des rues. Une flèche « modélisation » mène à droite, au graphe correspondant : quatre sommets A, B, C, D reliés par cinq arêtes.\">\n  \u003Ctitle>Du plan de quartier au graphe\u003C\u002Ftitle>\n  \u003Cstyle>\n    .pg-title  { fill: var(--diagram-text); font-family: Geist, Inter, system-ui, sans-serif; font-size: 13px; font-weight: 600; }\n    .pg-block  { fill: var(--diagram-surface-alt); stroke: var(--diagram-border); stroke-width: 1.5; }\n    .pg-street { stroke: var(--diagram-line); stroke-width: 7; stroke-linecap: round; }\n    .pg-inter  { fill: var(--diagram-node-bg); stroke: var(--diagram-node-border); stroke-width: 1.5; }\n    .pg-edge   { stroke: var(--diagram-line); stroke-width: 1.5; }\n    .pg-node   { fill: var(--diagram-node-bg); stroke: var(--diagram-node-border); stroke-width: 1.5; }\n    .pg-vlbl   { fill: var(--diagram-text); font-family: 'JetBrains Mono', monospace; font-size: 12px; font-weight: 600; }\n    .pg-modlbl { fill: var(--diagram-text); font-family: Geist, Inter, system-ui, sans-serif; font-size: 12px; font-weight: 500; font-style: italic; }\n    .pg-arrow-line { stroke: var(--diagram-line); stroke-width: 1.5; fill: none; }\n    .pg-arrow-head { fill: var(--diagram-line); }\n  \u003C\u002Fstyle>\n\n  \u003C!-- ░░ GAUCHE : plan de quartier ░░ -->\n  \u003Ctext x=\"110\" y=\"26\" text-anchor=\"middle\" class=\"pg-title\">plan de quartier\u003C\u002Ftext>\n\n  \u003C!-- îlots (blocs de bâti) pour donner l'idée d'un plan -->\n  \u003Crect class=\"pg-block\" x=\"58\"  y=\"62\"  width=\"44\" height=\"44\" rx=\"3\"\u002F>\n  \u003Crect class=\"pg-block\" x=\"118\" y=\"62\"  width=\"44\" height=\"44\" rx=\"3\"\u002F>\n  \u003Crect class=\"pg-block\" x=\"58\"  y=\"154\" width=\"44\" height=\"44\" rx=\"3\"\u002F>\n  \u003Crect class=\"pg-block\" x=\"118\" y=\"154\" width=\"44\" height=\"44\" rx=\"3\"\u002F>\n\n  \u003C!-- rues (entre les îlots) — coords des intersections :\n       A(50,50) B(170,50) C(50,210) D(170,210) -->\n  \u003Cline class=\"pg-street\" x1=\"50\"  y1=\"50\"  x2=\"170\" y2=\"50\"\u002F>   \u003C!-- A-B -->\n  \u003Cline class=\"pg-street\" x1=\"50\"  y1=\"50\"  x2=\"50\"  y2=\"210\"\u002F>  \u003C!-- A-C -->\n  \u003Cline class=\"pg-street\" x1=\"170\" y1=\"50\"  x2=\"170\" y2=\"210\"\u002F>  \u003C!-- B-D -->\n  \u003Cline class=\"pg-street\" x1=\"50\"  y1=\"210\" x2=\"170\" y2=\"210\"\u002F>  \u003C!-- C-D -->\n  \u003Cline class=\"pg-street\" x1=\"170\" y1=\"50\"  x2=\"50\"  y2=\"210\"\u002F>  \u003C!-- B-C (diagonale) -->\n\n  \u003C!-- intersections -->\n  \u003Cg>\n    \u003Ccircle class=\"pg-inter\" cx=\"50\"  cy=\"50\"  r=\"11\"\u002F>\u003Ctext x=\"50\"  y=\"54\"  text-anchor=\"middle\" class=\"pg-vlbl\">A\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-inter\" cx=\"170\" cy=\"50\"  r=\"11\"\u002F>\u003Ctext x=\"170\" y=\"54\"  text-anchor=\"middle\" class=\"pg-vlbl\">B\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-inter\" cx=\"50\"  cy=\"210\" r=\"11\"\u002F>\u003Ctext x=\"50\"  y=\"214\" text-anchor=\"middle\" class=\"pg-vlbl\">C\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-inter\" cx=\"170\" cy=\"210\" r=\"11\"\u002F>\u003Ctext x=\"170\" y=\"214\" text-anchor=\"middle\" class=\"pg-vlbl\">D\u003C\u002Ftext>\n  \u003C\u002Fg>\n\n  \u003C!-- ░░ FLÈCHE modélisation ░░ -->\n  \u003Cpath class=\"pg-arrow-line\" d=\"M 222 130 L 296 130\"\u002F>\n  \u003Cpolygon class=\"pg-arrow-head\" points=\"310,130 296,124 296,136\"\u002F>\n  \u003Ctext x=\"262\" y=\"120\" text-anchor=\"middle\" class=\"pg-modlbl\">modélisation\u003C\u002Ftext>\n\n  \u003C!-- ░░ DROITE : graphe ░░ -->\n  \u003Ctext x=\"410\" y=\"26\" text-anchor=\"middle\" class=\"pg-title\">graphe\u003C\u002Ftext>\n\n  \u003C!-- arêtes (5) — coords des sommets :\n       A(350,60) B(470,60) C(350,200) D(470,200) -->\n  \u003Cline class=\"pg-edge\" x1=\"350\" y1=\"60\"  x2=\"470\" y2=\"60\"\u002F>   \u003C!-- A-B -->\n  \u003Cline class=\"pg-edge\" x1=\"350\" y1=\"60\"  x2=\"350\" y2=\"200\"\u002F>  \u003C!-- A-C -->\n  \u003Cline class=\"pg-edge\" x1=\"470\" y1=\"60\"  x2=\"470\" y2=\"200\"\u002F>  \u003C!-- B-D -->\n  \u003Cline class=\"pg-edge\" x1=\"350\" y1=\"200\" x2=\"470\" y2=\"200\"\u002F>  \u003C!-- C-D -->\n  \u003Cline class=\"pg-edge\" x1=\"470\" y1=\"60\"  x2=\"350\" y2=\"200\"\u002F>  \u003C!-- B-C -->\n\n  \u003C!-- sommets -->\n  \u003Cg>\n    \u003Ccircle class=\"pg-node\" cx=\"350\" cy=\"60\"  r=\"15\"\u002F>\u003Ctext x=\"350\" y=\"65\"  text-anchor=\"middle\" class=\"pg-vlbl\">A\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-node\" cx=\"470\" cy=\"60\"  r=\"15\"\u002F>\u003Ctext x=\"470\" y=\"65\"  text-anchor=\"middle\" class=\"pg-vlbl\">B\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-node\" cx=\"350\" cy=\"200\" r=\"15\"\u002F>\u003Ctext x=\"350\" y=\"205\" text-anchor=\"middle\" class=\"pg-vlbl\">C\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-node\" cx=\"470\" cy=\"200\" r=\"15\"\u002F>\u003Ctext x=\"470\" y=\"205\" text-anchor=\"middle\" class=\"pg-vlbl\">D\u003C\u002Ftext>\n  \u003C\u002Fg>\n\u003C\u002Fsvg>\n",[598,673,674,675,678,679,682],{},"Sur ce graphe, ",[602,676,677],{},"trouver un itinéraire"," entre deux points, c'est trouver une\n",[602,680,681],{},"suite d'arêtes"," qui mène du sommet de départ au sommet d'arrivée.",[684,685,689,696],"self-eval-qcm",{"correct":686,"explanation":687,"slug":688},"1","Un sommet = un point du réseau, en général une intersection. Les rues entre intersections deviennent des arêtes.","itineraires-graphes-c1",[690,691,693],"template",{"v-slot:question":692},"",[598,694,695],{},"Sur un graphe représentant une ville, que représente un sommet ?",[690,697,698],{"v-slot:choices":692},[643,699,700,703,706],{},[646,701,702],{},"Un tronçon de rue",[646,704,705],{},"Une intersection ou un carrefour",[646,707,708],{},"Une voiture en mouvement",[593,710,712],{"id":711},"pondérer-les-arêtes","Pondérer les arêtes",[598,714,715,716,719,720,723,724,727,728,605],{},"Toutes les rues ne se valent pas. 50 mètres dans une zone piétonne, ce n'est\npas la même chose que 50 mètres sur un boulevard à 50 km\u002Fh. Pour en tenir\ncompte, on ",[602,717,718],{},"étiquette chaque arête avec un poids"," : ce poids représente le\n",[602,721,722],{},"coût"," du tronçon — typiquement la ",[602,725,726],{},"durée"," ou la ",[602,729,730],{},"distance",[732,733,734,753],"table",{},[735,736,737],"thead",{},[738,739,740,744,747,750],"tr",{},[741,742,743],"th",{},"Arête",[741,745,746],{},"Distance (m)",[741,748,749],{},"Vitesse (km\u002Fh)",[741,751,752],{},"Durée (s)",[754,755,756,771,785],"tbody",{},[738,757,758,762,765,768],{},[759,760,761],"td",{},"A → B",[759,763,764],{},"400",[759,766,767],{},"50",[759,769,770],{},"29",[738,772,773,776,779,782],{},[759,774,775],{},"B → C",[759,777,778],{},"150",[759,780,781],{},"30",[759,783,784],{},"18",[738,786,787,790,793,795],{},[759,788,789],{},"A → C",[759,791,792],{},"600",[759,794,767],{},[759,796,797],{},"43",[598,799,800,801,804,805,808,809,605],{},"On obtient un ",[602,802,803],{},"graphe pondéré",". La question devient alors : « quelle est la\nsuite d'arêtes qui ",[602,806,807],{},"minimise la somme des poids"," entre le départ et\nl'arrivée ? » C'est ce qu'on appelle le ",[602,810,811],{},"plus court chemin",[813,814,815],"note",{},[598,816,817,818,820,821,823,824,827,828,831],{},"Le poids n'est pas forcément une distance. Selon ce que l'utilisateur\nchoisit, on peut pondérer par : la ",[602,819,726],{}," (le plus rapide), la\n",[602,822,730],{}," (le plus court), la ",[602,825,826],{},"consommation"," (le plus économe), le\n",[602,829,830],{},"dénivelé"," (le moins fatigant à vélo)... Le graphe sous-jacent ne change\npas — seule la valeur du poids change.",[593,833,835],{"id":834},"lidée-du-plus-court-chemin","L'idée du plus court chemin",[598,837,838,839,885,886,885,916,885,946,976],{},"Imaginons le mini-graphe suivant — quatre points ",[840,841,844,866],"span",{"className":842},[843],"katex",[840,845,848],{"className":846},[847],"katex-mathml",[849,850,852],"math",{"xmlns":851},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[853,854,855,862],"semantics",{},[856,857,858],"mrow",{},[859,860,861],"mi",{},"A",[863,864,861],"annotation",{"encoding":865},"application\u002Fx-tex",[840,867,871],{"className":868,"ariaHidden":870},[869],"katex-html","true",[840,872,875,880],{"className":873},[874],"base",[840,876],{"className":877,"style":879},[878],"strut","height:0.6833em;",[840,881,861],{"className":882},[883,884],"mord","mathnormal",", ",[840,887,889,903],{"className":888},[843],[840,890,892],{"className":891},[847],[849,893,894],{"xmlns":851},[853,895,896,901],{},[856,897,898],{},[859,899,900],{},"B",[863,902,900],{"encoding":865},[840,904,906],{"className":905,"ariaHidden":870},[869],[840,907,909,912],{"className":908},[874],[840,910],{"className":911,"style":879},[878],[840,913,900],{"className":914,"style":915},[883,884],"margin-right:0.0502em;",[840,917,919,933],{"className":918},[843],[840,920,922],{"className":921},[847],[849,923,924],{"xmlns":851},[853,925,926,931],{},[856,927,928],{},[859,929,930],{},"C",[863,932,930],{"encoding":865},[840,934,936],{"className":935,"ariaHidden":870},[869],[840,937,939,942],{"className":938},[874],[840,940],{"className":941,"style":879},[878],[840,943,930],{"className":944,"style":945},[883,884],"margin-right:0.0715em;",[840,947,949,963],{"className":948},[843],[840,950,952],{"className":951},[847],[849,953,954],{"xmlns":851},[853,955,956,961],{},[856,957,958],{},[859,959,960],{},"D",[863,962,960],{"encoding":865},[840,964,966],{"className":965,"ariaHidden":870},[869],[840,967,969,972],{"className":968},[874],[840,970],{"className":971,"style":879},[878],[840,973,960],{"className":974,"style":975},[883,884],"margin-right:0.0278em;"," avec\nleurs durées en minutes :",[666,978,982,1043,1076,1150,1172,1176,1183,1196,1203,1207,1210,1244,1247,1261,1265,1268,1351,1373,1377],{"alt":979,"kind":669,"src":980,"svg":981},"Mini-graphe à quatre sommets A, B, C, D : A—B de coût 2, A—C de coût 3, B—D de coût 1, C—D de coût 4","\u002Fillustrations\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002Fmini-graphe-pondere.svg","\u003Csvg class=\"illustration-svg\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 320 240\" role=\"img\" aria-label=\"Mini-graphe pondéré à quatre sommets A, B, C, D. A est relié à B par une arête de coût 2, A à C par une arête de coût 3, B à D par une arête de coût 1, et C à D par une arête de coût 4.\">\n  \u003Ctitle>Mini-graphe pondéré à quatre sommets\u003C\u002Ftitle>\n  \u003Cstyle>\n    .mg-edge { stroke: var(--diagram-line); stroke-width: 1.5; }\n    .mg-node { fill: var(--diagram-node-bg); stroke: var(--diagram-node-border); stroke-width: 1.5; }\n    .mg-vlbl { fill: var(--diagram-text); font-family: 'JetBrains Mono', monospace; font-size: 13px; font-weight: 600; }\n    .mg-wpill { fill: var(--diagram-surface); stroke: var(--diagram-border); stroke-width: 1; }\n    .mg-wlbl { fill: var(--diagram-text); font-family: 'JetBrains Mono', monospace; font-size: 12px; font-weight: 600; }\n  \u003C\u002Fstyle>\n\n  \u003C!-- arêtes — sommets : A(80,60) B(240,60) C(80,180) D(240,180) -->\n  \u003Cline class=\"mg-edge\" x1=\"80\"  y1=\"60\"  x2=\"240\" y2=\"60\"\u002F>   \u003C!-- A-B -->\n  \u003Cline class=\"mg-edge\" x1=\"80\"  y1=\"60\"  x2=\"80\"  y2=\"180\"\u002F>  \u003C!-- A-C -->\n  \u003Cline class=\"mg-edge\" x1=\"240\" y1=\"60\"  x2=\"240\" y2=\"180\"\u002F>  \u003C!-- B-D -->\n  \u003Cline class=\"mg-edge\" x1=\"80\"  y1=\"180\" x2=\"240\" y2=\"180\"\u002F>  \u003C!-- C-D -->\n\n  \u003C!-- poids (pastilles au milieu des arêtes) -->\n  \u003Cg>\n    \u003Crect class=\"mg-wpill\" x=\"149\" y=\"51\"  width=\"22\" height=\"18\" rx=\"4\"\u002F>\u003Ctext x=\"160\" y=\"64\"  text-anchor=\"middle\" class=\"mg-wlbl\">2\u003C\u002Ftext>\n    \u003Crect class=\"mg-wpill\" x=\"69\"  y=\"111\" width=\"22\" height=\"18\" rx=\"4\"\u002F>\u003Ctext x=\"80\"  y=\"124\" text-anchor=\"middle\" class=\"mg-wlbl\">3\u003C\u002Ftext>\n    \u003Crect class=\"mg-wpill\" x=\"229\" y=\"111\" width=\"22\" height=\"18\" rx=\"4\"\u002F>\u003Ctext x=\"240\" y=\"124\" text-anchor=\"middle\" class=\"mg-wlbl\">1\u003C\u002Ftext>\n    \u003Crect class=\"mg-wpill\" x=\"149\" y=\"171\" width=\"22\" height=\"18\" rx=\"4\"\u002F>\u003Ctext x=\"160\" y=\"184\" text-anchor=\"middle\" class=\"mg-wlbl\">4\u003C\u002Ftext>\n  \u003C\u002Fg>\n\n  \u003C!-- sommets -->\n  \u003Cg>\n    \u003Ccircle class=\"mg-node\" cx=\"80\"  cy=\"60\"  r=\"15\"\u002F>\u003Ctext x=\"80\"  y=\"65\"  text-anchor=\"middle\" class=\"mg-vlbl\">A\u003C\u002Ftext>\n    \u003Ccircle class=\"mg-node\" cx=\"240\" cy=\"60\"  r=\"15\"\u002F>\u003Ctext x=\"240\" y=\"65\"  text-anchor=\"middle\" class=\"mg-vlbl\">B\u003C\u002Ftext>\n    \u003Ccircle class=\"mg-node\" cx=\"80\"  cy=\"180\" r=\"15\"\u002F>\u003Ctext x=\"80\"  y=\"185\" text-anchor=\"middle\" class=\"mg-vlbl\">C\u003C\u002Ftext>\n    \u003Ccircle class=\"mg-node\" cx=\"240\" cy=\"180\" r=\"15\"\u002F>\u003Ctext x=\"240\" y=\"185\" text-anchor=\"middle\" class=\"mg-vlbl\">D\u003C\u002Ftext>\n  \u003C\u002Fg>\n\u003C\u002Fsvg>\n",[598,983,984,985,1013,1014,1042],{},"Quatre arêtes au total : A — B de coût 2, A — C de coût 3, B — D de coût 1,\nC — D de coût 4. Plusieurs trajets relient ",[840,986,988,1001],{"className":987},[843],[840,989,991],{"className":990},[847],[849,992,993],{"xmlns":851},[853,994,995,999],{},[856,996,997],{},[859,998,861],{},[863,1000,861],{"encoding":865},[840,1002,1004],{"className":1003,"ariaHidden":870},[869],[840,1005,1007,1010],{"className":1006},[874],[840,1008],{"className":1009,"style":879},[878],[840,1011,861],{"className":1012},[883,884]," à ",[840,1015,1017,1030],{"className":1016},[843],[840,1018,1020],{"className":1019},[847],[849,1021,1022],{"xmlns":851},[853,1023,1024,1028],{},[856,1025,1026],{},[859,1027,960],{},[863,1029,960],{"encoding":865},[840,1031,1033],{"className":1032,"ariaHidden":870},[869],[840,1034,1036,1039],{"className":1035},[874],[840,1037],{"className":1038,"style":879},[878],[840,1040,960],{"className":1041,"style":975},[883,884]," :",[732,1044,1045,1055],{},[735,1046,1047],{},[738,1048,1049,1052],{},[741,1050,1051],{},"Trajet",[741,1053,1054],{},"Coût total",[754,1056,1057,1068],{},[738,1058,1059,1062],{},[759,1060,1061],{},"A → B → D",[759,1063,1064,1065],{},"2 + 1 = ",[602,1066,1067],{},"3",[738,1069,1070,1073],{},[759,1071,1072],{},"A → C → D",[759,1074,1075],{},"3 + 4 = 7",[598,1077,1078,1079,1013,1107,1135,1136,1138,1139,1142,1143,1146,1147,605],{},"Le plus court chemin de ",[840,1080,1082,1095],{"className":1081},[843],[840,1083,1085],{"className":1084},[847],[849,1086,1087],{"xmlns":851},[853,1088,1089,1093],{},[856,1090,1091],{},[859,1092,861],{},[863,1094,861],{"encoding":865},[840,1096,1098],{"className":1097,"ariaHidden":870},[869],[840,1099,1101,1104],{"className":1100},[874],[840,1102],{"className":1103,"style":879},[878],[840,1105,861],{"className":1106},[883,884],[840,1108,1110,1123],{"className":1109},[843],[840,1111,1113],{"className":1112},[847],[849,1114,1115],{"xmlns":851},[853,1116,1117,1121],{},[856,1118,1119],{},[859,1120,960],{},[863,1122,960],{"encoding":865},[840,1124,1126],{"className":1125,"ariaHidden":870},[869],[840,1127,1129,1132],{"className":1128},[874],[840,1130],{"className":1131,"style":879},[878],[840,1133,960],{"className":1134,"style":975},[883,884]," est donc ",[602,1137,1061],{}," pour un coût total\nde ",[602,1140,1141],{},"3 minutes",". Sur un mini-graphe, on trouve cela à l'œil. Sur un graphe\nde plusieurs ",[602,1144,1145],{},"millions de sommets"," (une ville moyenne en compte autour de\n50 000 intersections, un pays plusieurs millions), il faut un ",[602,1148,1149],{},"algorithme",[684,1151,1154,1159],{"correct":686,"explanation":1152,"slug":1153},"Le 'plus court' est en fait le 'moins coûteux' au sens du poids choisi — ici, la durée totale. Un chemin avec plus d'intersections mais des tronçons rapides peut être préférable.","itineraires-graphes-c2",[690,1155,1156],{"v-slot:question":692},[598,1157,1158],{},"Dans un graphe routier pondéré par la durée, le plus court chemin entre deux points est…",[690,1160,1161],{"v-slot:choices":692},[643,1162,1163,1166,1169],{},[646,1164,1165],{},"la suite d arêtes la plus directe à vol d oiseau",[646,1167,1168],{},"la suite d arêtes dont la somme des durées est minimale",[646,1170,1171],{},"la suite d arêtes contenant le moins d intersections",[593,1173,1175],{"id":1174},"lidée-dun-algorithme-de-plus-court-chemin","L'idée d'un algorithme de plus court chemin",[598,1177,1178,1179,1182],{},"Sans entrer dans le détail, l'idée intuitive est la suivante : on part du\nsommet de départ et on ",[602,1180,1181],{},"propage la distance minimale"," vers les voisins,\nvoisins des voisins, etc., en notant à chaque étape la meilleure manière\nconnue d'atteindre chaque sommet. À la fin, on connaît le plus court chemin\nvers tous les autres sommets — et donc en particulier vers l'arrivée.",[1184,1185,1186],"tip",{},[598,1187,1188,1189,1192,1193,605],{},"Cet algorithme s'appelle ",[602,1190,1191],{},"Dijkstra"," (du nom du Néerlandais Edsger Dijkstra\nqui l'a publié en 1959). C'est le moteur historique des calculateurs\nd'itinéraire. Vous\nen étudierez le fonctionnement précis en NSI Terminale, dans le chapitre sur\n",[602,1194,1195],{},"l'algorithmique sur les graphes",[598,1197,1198,1199,1202],{},"Aujourd'hui, les services comme Google Maps, Mapbox ou OpenRouteService\nutilisent des variantes plus rapides (A*, ",[602,1200,1201],{},"contraction hierarchies",", etc.),\nmais l'idée fondamentale reste la même : un graphe pondéré, et un calcul de\nplus court chemin.",[593,1204,1206],{"id":1205},"que-prend-en-compte-un-calculateur-moderne","Que prend en compte un calculateur moderne ?",[598,1208,1209],{},"Sur le papier, un graphe routier suffirait. En pratique, un calculateur\nd'itinéraire moderne enrichit le calcul avec :",[643,1211,1212,1219,1225,1232,1238],{},[646,1213,1214,1215,1218],{},"Les ",[602,1216,1217],{},"sens uniques"," (arêtes orientées, qu'on ne peut emprunter que dans un\nsens).",[646,1220,1214,1221,1224],{},[602,1222,1223],{},"interdictions de tourner"," (à une intersection, certains\nenchaînements sont interdits).",[646,1226,1227,1228,1231],{},"Le ",[602,1229,1230],{},"mode de transport"," (à pied, à vélo, en voiture, en transports en\ncommun — chaque mode ignore certaines arêtes).",[646,1233,1227,1234,1237],{},[602,1235,1236],{},"trafic en temps réel"," (les poids changent selon l'heure et la\ncongestion mesurée).",[646,1239,1214,1240,1243],{},[602,1241,1242],{},"péages"," et tarifs.",[598,1245,1246],{},"Tout cela enrichit le graphe sans en changer la nature : c'est toujours des\nsommets, des arêtes, des poids.",[1248,1249,1250],"warning",{},[598,1251,1252,1253,1256,1257,1260],{},"Un calculateur d'itinéraire ne ",[602,1254,1255],{},"mesure rien"," par lui-même. Il calcule sur\nles ",[602,1258,1259],{},"données qu'on lui fournit",". Si la carte n'est pas à jour, un trajet\npeut vous emmener dans une rue désormais piétonne, ou ignorer un raccourci\nrécemment ouvert. La qualité du calcul dépend de la qualité du graphe.",[593,1262,1264],{"id":1263},"le-graphe-au-delà-des-routes","Le graphe au-delà des routes",[598,1266,1267],{},"Le graphe sert bien plus que les itinéraires routiers. Quelques exemples :",[732,1269,1270,1283],{},[735,1271,1272],{},[738,1273,1274,1277,1280],{},[741,1275,1276],{},"Domaine",[741,1278,1279],{},"Sommets",[741,1281,1282],{},"Arêtes",[754,1284,1285,1296,1307,1318,1329,1340],{},[738,1286,1287,1290,1293],{},[759,1288,1289],{},"Réseau social",[759,1291,1292],{},"profils",[759,1294,1295],{},"amitiés \u002F abonnements",[738,1297,1298,1301,1304],{},[759,1299,1300],{},"Web",[759,1302,1303],{},"pages",[759,1305,1306],{},"hyperliens",[738,1308,1309,1312,1315],{},[759,1310,1311],{},"Transport ferroviaire",[759,1313,1314],{},"gares",[759,1316,1317],{},"lignes",[738,1319,1320,1323,1326],{},[759,1321,1322],{},"Métro",[759,1324,1325],{},"stations",[759,1327,1328],{},"tronçons",[738,1330,1331,1334,1337],{},[759,1332,1333],{},"Internet (cours SA)",[759,1335,1336],{},"routeurs",[759,1338,1339],{},"liens physiques",[738,1341,1342,1345,1348],{},[759,1343,1344],{},"Recommandation Netflix",[759,1346,1347],{},"films",[759,1349,1350],{},"partagent des spectateurs",[684,1352,1355,1360],{"correct":686,"explanation":1353,"slug":1354},"Une station = un sommet ; un tronçon entre deux stations consécutives = une arête. Une correspondance peut être modélisée comme une arête supplémentaire à l'intérieur d'une station.","itineraires-graphes-c3",[690,1356,1357],{"v-slot:question":692},[598,1358,1359],{},"Quand vous calculez un itinéraire en métro, que représente un sommet ?",[690,1361,1362],{"v-slot:choices":692},[643,1363,1364,1367,1370],{},[646,1365,1366],{},"Une rame de métro",[646,1368,1369],{},"Une station",[646,1371,1372],{},"Une correspondance entre deux lignes",[593,1374,1376],{"id":1375},"pour-aller-plus-loin","Pour aller plus loin",[598,1378,1379,1380,1383],{},"L'algorithme de Dijkstra a une ",[602,1381,1382],{},"complexité polynomiale"," : il termine en un\ntemps raisonnable même sur des graphes de plusieurs millions de sommets. La\nrecherche d'un itinéraire entre Paris et Marseille tient en quelques\nmillisecondes sur un serveur. C'est une réussite mathématique parmi les plus\ndiscrètes — vous l'utilisez probablement plusieurs fois par semaine sans le\nsavoir.",{"title":692,"searchDepth":1385,"depth":1385,"links":1386},2,[1387,1388,1389,1390,1391,1392,1393,1394],{"id":595,"depth":1385,"text":596},{"id":611,"depth":1385,"text":612},{"id":711,"depth":1385,"text":712},{"id":834,"depth":1385,"text":835},{"id":1174,"depth":1385,"text":1175},{"id":1205,"depth":1385,"text":1206},{"id":1263,"depth":1385,"text":1264},{"id":1375,"depth":1385,"text":1376},"Du plan de ville au plus court chemin, comment un logiciel calcule l'itinéraire que vous suivez en voiture ou à pied.",null,"md",{},true,[1401,1405,1407],{"slug":688,"kind":1402,"question":695,"choices":1403,"correct":686,"multi":1404,"explanation":687},"qcm",[702,705,708],false,{"slug":1153,"kind":1402,"question":1158,"choices":1406,"correct":686,"multi":1404,"explanation":1152},[1165,1168,1171],{"slug":1354,"kind":1402,"question":1359,"choices":1408,"correct":686,"multi":1404,"explanation":1353},[1366,1369,1372],1,{"title":137,"description":1395},"HWbayOZvGnO_l8nGxtUgq3Pcsof8UMkqKaGEQYWGwxo",{"id":1413,"title":1414,"bo":1415,"body":1416,"description":1583,"eval":1396,"extension":1397,"labo":1396,"meta":1584,"navigation":1404,"path":1585,"quizzes":1586,"readingTime":1409,"seo":1587,"stem":1588,"tp":1396,"__hash__":1589},"coursMemo\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes.memo.md","Itinéraires et graphes — l'essentiel",[588],{"type":590,"value":1417,"toc":1576},[1418,1422,1429,1433,1474,1478,1523,1527,1546,1550],[593,1419,1421],{"id":1420},"en-une-phrase","En une phrase",[598,1423,1424,1425,1428],{},"Un calcul d'itinéraire = la recherche du ",[602,1426,1427],{},"plus court chemin dans un graphe\npondéré"," dont les sommets sont les intersections et les arêtes les rues.",[593,1430,1432],{"id":1431},"à-mémoriser","À mémoriser",[643,1434,1435,1441,1446,1452,1458,1468],{},[646,1436,1437,1440],{},[602,1438,1439],{},"Sommet"," : un point du réseau (intersection, station, profil…).",[646,1442,1443,1445],{},[602,1444,743],{}," : un lien entre deux sommets (rue, ligne, amitié…).",[646,1447,1448,1451],{},[602,1449,1450],{},"Poids"," d'une arête : son coût (durée, distance, dénivelé…).",[646,1453,1454,1457],{},[602,1455,1456],{},"Graphe pondéré"," : graphe dont les arêtes portent un poids.",[646,1459,1460,1463,1464,1467],{},[602,1461,1462],{},"Plus court chemin"," : la suite d'arêtes dont la ",[602,1465,1466],{},"somme des poids est\nminimale"," entre deux sommets.",[646,1469,1470,1471,1473],{},"Algorithme historique : ",[602,1472,1191],{}," (1959).",[593,1475,1477],{"id":1476},"à-savoir-reconnaître","À savoir reconnaître",[732,1479,1480,1490],{},[735,1481,1482],{},[738,1483,1484,1487],{},[741,1485,1486],{},"Vous voyez",[741,1488,1489],{},"C'est un graphe avec…",[754,1491,1492,1500,1508,1516],{},[738,1493,1494,1497],{},[759,1495,1496],{},"Un plan de ville",[759,1498,1499],{},"sommets = intersections, arêtes = rues",[738,1501,1502,1505],{},[759,1503,1504],{},"Un plan de métro",[759,1506,1507],{},"sommets = stations, arêtes = tronçons",[738,1509,1510,1513],{},[759,1511,1512],{},"Un réseau social",[759,1514,1515],{},"sommets = profils, arêtes = amitiés",[738,1517,1518,1520],{},[759,1519,37],{},[759,1521,1522],{},"sommets = pages, arêtes = hyperliens",[593,1524,1526],{"id":1525},"pièges-courants","Pièges courants",[643,1528,1529,1536,1539],{},[646,1530,1531,1532,1535],{},"« Le plus court » = le plus court ",[602,1533,1534],{},"selon le poids choisi",", pas toujours\nà vol d'oiseau.",[646,1537,1538],{},"Un même graphe peut être pondéré différemment selon le besoin (durée,\ndistance, dénivelé…).",[646,1540,1541,1542,1545],{},"Un calculateur d'itinéraire ",[602,1543,1544],{},"dépend des données de la carte"," : carte\npérimée ⇒ trajet inadapté.",[593,1547,1549],{"id":1548},"à-enrichir-le-graphe-routier","À enrichir le graphe routier",[643,1551,1552,1558,1564,1570],{},[646,1553,1554,1557],{},[602,1555,1556],{},"Sens uniques"," → arêtes orientées.",[646,1559,1560,1563],{},[602,1561,1562],{},"Interdictions de tourner"," → règles aux intersections.",[646,1565,1566,1569],{},[602,1567,1568],{},"Mode de transport"," → certaines arêtes sont ignorées (piéton, voiture, vélo).",[646,1571,1572,1575],{},[602,1573,1574],{},"Trafic temps réel"," → poids variables selon l'heure.",{"title":692,"searchDepth":1385,"depth":1385,"links":1577},[1578,1579,1580,1581,1582],{"id":1420,"depth":1385,"text":1421},{"id":1431,"depth":1385,"text":1432},{"id":1476,"depth":1385,"text":1477},{"id":1525,"depth":1385,"text":1526},{"id":1548,"depth":1385,"text":1549},"Mémo de révision sur la modélisation d'un itinéraire comme problème sur un graphe.",{},"\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fitineraires-graphes.memo",[],{"title":1414,"description":1583},"0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes.memo","Eo_16M11MIFFrEHb2ugUxKqPIcDWMeTqbyeGJTGtvtI",{"id":1591,"title":1592,"body":1593,"description":1897,"extension":1397,"meta":1898,"navigation":1404,"path":1899,"seo":1900,"stem":1901,"__hash__":1902},"coursSlides\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes.slides.md","Itinéraires et graphes — diapositives",{"type":590,"value":1594,"toc":1895},[1595,1599,1602,1605,1607,1610,1622,1627,1629,1631,1638,1688,1693,1695,1699],[1596,1597,137],"h1",{"id":1598},"itinéraires-et-graphes",[598,1600,1601],{},"Comment une machine choisit-elle votre trajet ?",[1603,1604],"hr",{},[1596,1606,612],{"id":611},[666,1608],{"alt":1609,"kind":669,"src":670,"svg":671},"Plan vers graphe",[643,1611,1612,1617],{},[646,1613,1614,1616],{},[602,1615,1439],{}," : une intersection",[646,1618,1619,1621],{},[602,1620,743],{}," : un tronçon de rue",[598,1623,1624,1625,605],{},"Trouver un itinéraire ⇒ trouver une ",[602,1626,681],{},[1603,1628],{},[1596,1630,712],{"id":711},[598,1632,1633,1634,1637],{},"Chaque arête porte un ",[602,1635,1636],{},"poids"," = son coût.",[732,1639,1640,1653],{},[735,1641,1642],{},[738,1643,1644,1647,1650],{},[741,1645,1646],{},"Tronçon",[741,1648,1649],{},"Distance",[741,1651,1652],{},"Durée",[754,1654,1655,1666,1677],{},[738,1656,1657,1660,1663],{},[759,1658,1659],{},"A→B",[759,1661,1662],{},"400 m",[759,1664,1665],{},"29 s",[738,1667,1668,1671,1674],{},[759,1669,1670],{},"B→C",[759,1672,1673],{},"150 m",[759,1675,1676],{},"18 s",[738,1678,1679,1682,1685],{},[759,1680,1681],{},"A→C",[759,1683,1684],{},"600 m",[759,1686,1687],{},"43 s",[598,1689,627,1690,1692],{},[602,1691,803],{}," = graphe + poids sur les arêtes.",[1603,1694],{},[1596,1696,1698],{"id":1697},"plus-court-chemin-exemple","Plus court chemin — exemple",[666,1700,1701,1713,1720,1722,1726,1733,1736,1760,1763,1765,1769,1776,1783,1789,1795,1797,1801,1817,1823,1825,1829,1876,1883,1885,1889],{"alt":979,"kind":669,"src":980,"svg":981},[643,1702,1703,1710],{},[646,1704,1705,1706,1709],{},"A → B → D : ",[602,1707,1708],{},"2 + 1 = 3"," ✓",[646,1711,1712],{},"A → C → D : 3 + 4 = 7",[598,1714,1715,1716,1719],{},"Le plus court chemin minimise la ",[602,1717,1718],{},"somme"," des poids.",[1603,1721],{},[1596,1723,1725],{"id":1724},"le-sens-du-plus-court","Le sens du « plus court »",[598,1727,1728,1729,1732],{},"« Plus court » = ",[602,1730,1731],{},"plus petit coût"," au sens du poids choisi.",[598,1734,1735],{},"Poids possibles :",[643,1737,1738,1744,1749,1754],{},[646,1739,1740,1741,1743],{},"la ",[602,1742,726],{}," → le plus rapide",[646,1745,1740,1746,1748],{},[602,1747,730],{}," → le plus court",[646,1750,1740,1751,1753],{},[602,1752,826],{}," → le plus économe",[646,1755,1756,1757,1759],{},"le ",[602,1758,830],{}," → le moins fatigant à vélo",[598,1761,1762],{},"Même graphe, plusieurs réponses possibles.",[1603,1764],{},[1596,1766,1768],{"id":1767},"lidée-dun-algorithme","L'idée d'un algorithme",[598,1770,1771,1772,1775],{},"On part du départ et on ",[602,1773,1774],{},"propage"," la distance minimale aux voisins, puis\naux voisins des voisins…",[598,1777,1778,1779,1782],{},"À la fin, on connaît le plus court chemin vers ",[602,1780,1781],{},"tous"," les sommets.",[598,1784,1785,1786,1473],{},"Nom : ",[602,1787,1788],{},"algorithme de Dijkstra",[598,1790,1791,1792,605],{},"Vu en détail en ",[602,1793,1794],{},"NSI Terminale",[1603,1796],{},[1596,1798,1800],{"id":1799},"un-calculateur-moderne-tient-compte-de","Un calculateur moderne tient compte de…",[643,1802,1803,1806,1808,1811,1814],{},[646,1804,1805],{},"sens uniques (arêtes orientées)",[646,1807,1223],{},[646,1809,1810],{},"mode de transport (piéton, vélo, voiture, TC)",[646,1812,1813],{},"trafic temps réel",[646,1815,1816],{},"péages et tarifs",[598,1818,1819,1820,605],{},"Toujours le même squelette : ",[602,1821,1822],{},"graphe + poids",[1603,1824],{},[1596,1826,1828],{"id":1827},"le-graphe-partout","Le graphe partout",[732,1830,1831,1841],{},[735,1832,1833],{},[738,1834,1835,1837,1839],{},[741,1836,1276],{},[741,1838,1279],{},[741,1840,1282],{},[754,1842,1843,1851,1860,1868],{},[738,1844,1845,1847,1849],{},[759,1846,1322],{},[759,1848,1325],{},[759,1850,1328],{},[738,1852,1853,1855,1857],{},[759,1854,1289],{},[759,1856,1292],{},[759,1858,1859],{},"amitiés",[738,1861,1862,1864,1866],{},[759,1863,1300],{},[759,1865,1303],{},[759,1867,1306],{},[738,1869,1870,1872,1874],{},[759,1871,15],{},[759,1873,1336],{},[759,1875,1339],{},[598,1877,1878,1879,1882],{},"Le graphe est un ",[602,1880,1881],{},"outil universel"," en informatique.",[1603,1884],{},[1596,1886,1888],{"id":1887},"à-retenir","À retenir",[598,1890,1891,1892,1894],{},"Un calculateur d'itinéraire ne « voit » pas une carte.\nIl calcule sur un ",[602,1893,803],{}," la suite d'arêtes la moins coûteuse.\nC'est la qualité du graphe qui fait la qualité du trajet.",{"title":692,"searchDepth":1385,"depth":1385,"links":1896},[],"Deck projetable pour la séance sur le calcul 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