[{"data":1,"prerenderedAt":12531},["ShallowReactive",2],{"navigation":3,"\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires":585,"\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires__counterpart":5929,"\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires__slides":7414,"annexes-memo:\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires":9293,"annexes-slides:\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires":10720},[4,224,440],{"title":5,"path":6,"stem":7,"children":8},"SNT — Seconde","\u002Fsnt-2nde","0.snt-2nde\u002F0.index",[9,10,14,36,66,92,118,144,162,184,206],{"title":5,"path":6,"stem":7},{"title":11,"path":12,"stem":13},"REVIEW pédagogique — SNT 2nde","\u002Fsnt-2nde\u002Freview","0.snt-2nde\u002FREVIEW",{"title":15,"path":16,"stem":17,"children":18},"Internet","\u002Fsnt-2nde\u002Fsa-internet","0.snt-2nde\u002Fsa-internet\u002F0.index",[19,20,24,28,32],{"title":15,"path":16,"stem":17},{"title":21,"path":22,"stem":23},"Adresses symboliques et DNS","\u002Fsnt-2nde\u002Fsa-internet\u002Fadresses-dns","0.snt-2nde\u002Fsa-internet\u002F1.adresses-dns",{"title":25,"path":26,"stem":27},"Internet et les réseaux physiques","\u002Fsnt-2nde\u002Fsa-internet\u002Freseaux-physiques","0.snt-2nde\u002Fsa-internet\u002F2.reseaux-physiques",{"title":29,"path":30,"stem":31},"Protocoles TCP\u002FIP et routage des paquets","\u002Fsnt-2nde\u002Fsa-internet\u002Ftcp-ip-routage","0.snt-2nde\u002Fsa-internet\u002F3.tcp-ip-routage",{"title":33,"path":34,"stem":35},"Réseaux pair-à-pair","\u002Fsnt-2nde\u002Fsa-internet\u002Fpair-a-pair","0.snt-2nde\u002Fsa-internet\u002F4.pair-a-pair",{"title":37,"path":38,"stem":39,"children":40},"Le 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 structurées","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fdonnees-structurees","0.snt-2nde\u002Fsd-donnees-structurees\u002F2.donnees-structurees",{"title":107,"path":108,"stem":109},"Métadonnées","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fmetadonnees","0.snt-2nde\u002Fsd-donnees-structurees\u002F3.metadonnees",{"title":111,"path":112,"stem":113},"Traitement de tables","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Ftraitement-tables","0.snt-2nde\u002Fsd-donnees-structurees\u002F4.traitement-tables",{"title":115,"path":116,"stem":117},"Le cloud","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fcloud","0.snt-2nde\u002Fsd-donnees-structurees\u002F5.cloud",{"title":119,"path":120,"stem":121,"children":122},"Localisation, cartographie et mobilité","\u002Fsnt-2nde\u002Fse-localisation-cartographie","0.snt-2nde\u002Fse-localisation-cartographie\u002F0.index",[123,124,128,132,136,140],{"title":119,"path":120,"stem":121},{"title":125,"path":126,"stem":127},"GPS et Galileo — se situer grâce aux satellites","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fgps-galileo","0.snt-2nde\u002Fse-localisation-cartographie\u002F1.gps-galileo",{"title":129,"path":130,"stem":131},"Décoder une trame NMEA","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Ftrame-nmea","0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea",{"title":133,"path":134,"stem":135},"Cartes numériques — GeoPortail et OpenStreetMap","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fcartes-numeriques","0.snt-2nde\u002Fse-localisation-cartographie\u002F3.cartes-numeriques",{"title":137,"path":138,"stem":139},"Itinéraires et graphes","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fitineraires-graphes","0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes",{"title":141,"path":142,"stem":143},"Confidentialité de la 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 (1947-1990)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fordinateurs-modernes","1.nsi-1ere\u002Fpa-histoire-info\u002F3.ordinateurs-modernes",{"title":253,"path":254,"stem":255},"Réseaux, Web et IA (1969 à aujourd'hui)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Freseaux-et-web","1.nsi-1ere\u002Fpa-histoire-info\u002F4.reseaux-et-web",{"title":257,"path":258,"stem":259,"children":260},"Représentation des données — types et valeurs","\u002Fnsi-1ere\u002Fpb-types-valeurs","1.nsi-1ere\u002Fpb-types-valeurs\u002F0.index",[261,262,266,270,274,278],{"title":257,"path":258,"stem":259},{"title":263,"path":264,"stem":265},"Bases de numération et entiers positifs","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fbases-entiers-positifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F1.bases-entiers-positifs",{"title":267,"path":268,"stem":269},"Entiers relatifs et complément à 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":469,"bo":587,"body":589,"description":5915,"eval":5916,"extension":5917,"labo":5916,"meta":5918,"navigation":999,"path":470,"quizzes":5919,"readingTime":974,"seo":5927,"stem":471,"tp":5916,"__hash__":5928},"cours\u002F2.nsi-tale\u002Fta-structures-donnees\u002F4.arbres-binaires.md",[588],"TA01",{"type":590,"value":591,"toc":5901},"minimark",[592,597,614,621,632,636,823,950,954,962,1113,1116,1179,1201,1205,1209,1212,1702,1758,1761,2216,2423,2473,2477,2596,3048,3052,3248,3623,4092,4728,5125,5129,5759,5832,5836,5895,5897],[593,594,596],"h2",{"id":595},"introduction","Introduction",[598,599,600,601,605,606,609,610,613],"p",{},"Quand les données ont une ",[602,603,604],"strong",{},"hiérarchie naturelle"," — un système de fichiers, un\narbre généalogique, le DOM d'une page web, la décomposition syntaxique d'une\nexpression — les structures linéaires ne suffisent plus. On utilise alors un\n",[602,607,608],{},"arbre"," : un ensemble de nœuds organisés autour d'une ",[602,611,612],{},"racine",", où chaque\nnœud porte un nombre fini d'enfants.",[598,615,616,617,620],{},"L'image la plus familière est l'",[602,618,619],{},"arbre généalogique"," : une personne en haut,\nses descendants qui se ramifient à mesure qu'on descend. La racine informatique\nest en haut par convention — les arbres en informatique poussent vers le bas,\ncontrairement à leurs cousins botaniques.",[598,622,623,624,627,628,631],{},"Ce cours traite spécifiquement des ",[602,625,626],{},"arbres binaires"," (chaque nœud a au plus\ndeux enfants), conformément à ",[629,630],"bo-ref",{"code":588},". Les algorithmes associés\n(parcours préfixe, infixe, suffixe, BFS, DFS) sont abordés au chapitre TE.",[593,633,635],{"id":634},"vocabulaire","Vocabulaire",[637,638,639,652],"table",{},[640,641,642],"thead",{},[643,644,645,649],"tr",{},[646,647,648],"th",{},"Terme",[646,650,651],{},"Définition",[653,654,655,666,676,686,696,706,716,773,813],"tbody",{},[643,656,657,663],{},[658,659,660],"td",{},[602,661,662],{},"Nœud",[658,664,665],{},"Élément de l'arbre, portant une valeur.",[643,667,668,673],{},[658,669,670],{},[602,671,672],{},"Racine",[658,674,675],{},"Nœud sans parent — point d'entrée unique de l'arbre.",[643,677,678,683],{},[658,679,680],{},[602,681,682],{},"Feuille",[658,684,685],{},"Nœud sans enfant.",[643,687,688,693],{},[658,689,690],{},[602,691,692],{},"Sous-arbre gauche",[658,694,695],{},"Arbre enraciné au fils gauche d'un nœud.",[643,697,698,703],{},[658,699,700],{},[602,701,702],{},"Sous-arbre droit",[658,704,705],{},"Arbre enraciné au fils droit.",[643,707,708,713],{},[658,709,710],{},[602,711,712],{},"Arête",[658,714,715],{},"Lien entre un parent et un de ses enfants.",[643,717,718,770],{},[658,719,720,723,724],{},[602,721,722],{},"Taille"," ",[725,726,729,751],"span",{"className":727},[728],"katex",[725,730,733],{"className":731},[732],"katex-mathml",[734,735,737],"math",{"xmlns":736},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[738,739,740,747],"semantics",{},[741,742,743],"mrow",{},[744,745,746],"mi",{},"n",[748,749,746],"annotation",{"encoding":750},"application\u002Fx-tex",[725,752,756],{"className":753,"ariaHidden":755},[754],"katex-html","true",[725,757,760,765],{"className":758},[759],"base",[725,761],{"className":762,"style":764},[763],"strut","height:0.4306em;",[725,766,746],{"className":767},[768,769],"mord","mathnormal",[658,771,772],{},"Nombre total de nœuds de l'arbre.",[643,774,775,810],{},[658,776,777,723,780],{},[602,778,779],{},"Hauteur",[725,781,783,797],{"className":782},[728],[725,784,786],{"className":785},[732],[734,787,788],{"xmlns":736},[738,789,790,795],{},[741,791,792],{},[744,793,794],{},"h",[748,796,794],{"encoding":750},[725,798,800],{"className":799,"ariaHidden":755},[754],[725,801,803,807],{"className":802},[759],[725,804],{"className":805,"style":806},[763],"height:0.6944em;",[725,808,794],{"className":809},[768,769],[658,811,812],{},"Longueur (en arêtes) du plus long chemin de la racine à une feuille.",[643,814,815,820],{},[658,816,817],{},[602,818,819],{},"Profondeur d'un nœud",[658,821,822],{},"Longueur du chemin de la racine à ce nœud.",[824,825,826],"warning",{},[598,827,828,829,832,833,836,837,896,897,949],{},"Attention aux ",[602,830,831],{},"conventions de hauteur",". Certains auteurs comptent en nombre\nde niveaux (racine = niveau 1) ; d'autres en arêtes (racine = hauteur 0). Nous\nadoptons ici la convention ",[602,834,835],{},"en arêtes"," : un arbre réduit à sa racine a une\nhauteur ",[725,838,840,862],{"className":839},[728],[725,841,843],{"className":842},[732],[734,844,845],{"xmlns":736},[738,846,847,859],{},[741,848,849,851,855],{},[744,850,794],{},[852,853,854],"mo",{},"=",[856,857,858],"mn",{},"0",[748,860,861],{"encoding":750},"h = 0",[725,863,865,886],{"className":864,"ariaHidden":755},[754],[725,866,868,871,874,879,883],{"className":867},[759],[725,869],{"className":870,"style":806},[763],[725,872,794],{"className":873},[768,769],[725,875],{"className":876,"style":878},[877],"mspace","margin-right:0.2778em;",[725,880,854],{"className":881},[882],"mrel",[725,884],{"className":885,"style":878},[877],[725,887,889,893],{"className":888},[759],[725,890],{"className":891,"style":892},[763],"height:0.6444em;",[725,894,858],{"className":895},[768],", une taille ",[725,898,900,919],{"className":899},[728],[725,901,903],{"className":902},[732],[734,904,905],{"xmlns":736},[738,906,907,916],{},[741,908,909,911,913],{},[744,910,746],{},[852,912,854],{},[856,914,915],{},"1",[748,917,918],{"encoding":750},"n = 1",[725,920,922,940],{"className":921,"ariaHidden":755},[754],[725,923,925,928,931,934,937],{"className":924},[759],[725,926],{"className":927,"style":764},[763],[725,929,746],{"className":930},[768,769],[725,932],{"className":933,"style":878},[877],[725,935,854],{"className":936},[882],[725,938],{"className":939,"style":878},[877],[725,941,943,946],{"className":942},[759],[725,944],{"className":945,"style":892},[763],[725,947,915],{"className":948},[768],".",[593,951,953],{"id":952},"implémentation-python","Implémentation Python",[598,955,956,957,961],{},"On reprend l'outil objet du cours précédent. Un nœud est un objet portant une\nvaleur, un fils gauche et un fils droit (qui sont eux-mêmes des nœuds ou ",[958,959,960],"code",{},"None",").",[963,964,969],"pre",{"className":965,"code":966,"language":967,"meta":968,"style":968},"language-python shiki shiki-themes github-light github-light github-dark","class Noeud:\n    \"\"\"Nœud d'un arbre binaire.\"\"\"\n\n    def __init__(self, valeur, gauche=None, droite=None):\n        self.valeur = valeur\n        self.gauche = gauche\n        self.droite = droite\n\n    def est_feuille(self):\n        return self.gauche is None and self.droite is None\n","python","",[958,970,971,987,994,1001,1028,1042,1055,1068,1073,1084],{"__ignoreMap":968},[725,972,975,979,983],{"class":973,"line":974},"line",1,[725,976,978],{"class":977},"s8jYJ","class",[725,980,982],{"class":981},"snPdu"," Noeud",[725,984,986],{"class":985},"sxrX7",":\n",[725,988,990],{"class":973,"line":989},2,[725,991,993],{"class":992},"sIIMD","    \"\"\"Nœud d'un arbre binaire.\"\"\"\n",[725,995,997],{"class":973,"line":996},3,[725,998,1000],{"emptyLinePlaceholder":999},true,"\n",[725,1002,1004,1007,1011,1014,1016,1018,1021,1023,1025],{"class":973,"line":1003},4,[725,1005,1006],{"class":977},"    def",[725,1008,1010],{"class":1009},"sBjJW"," __init__",[725,1012,1013],{"class":985},"(self, valeur, gauche",[725,1015,854],{"class":977},[725,1017,960],{"class":1009},[725,1019,1020],{"class":985},", droite",[725,1022,854],{"class":977},[725,1024,960],{"class":1009},[725,1026,1027],{"class":985},"):\n",[725,1029,1031,1034,1037,1039],{"class":973,"line":1030},5,[725,1032,1033],{"class":1009},"        self",[725,1035,1036],{"class":985},".valeur ",[725,1038,854],{"class":977},[725,1040,1041],{"class":985}," valeur\n",[725,1043,1045,1047,1050,1052],{"class":973,"line":1044},6,[725,1046,1033],{"class":1009},[725,1048,1049],{"class":985},".gauche ",[725,1051,854],{"class":977},[725,1053,1054],{"class":985}," gauche\n",[725,1056,1058,1060,1063,1065],{"class":973,"line":1057},7,[725,1059,1033],{"class":1009},[725,1061,1062],{"class":985},".droite ",[725,1064,854],{"class":977},[725,1066,1067],{"class":985}," droite\n",[725,1069,1071],{"class":973,"line":1070},8,[725,1072,1000],{"emptyLinePlaceholder":999},[725,1074,1076,1078,1081],{"class":973,"line":1075},9,[725,1077,1006],{"class":977},[725,1079,1080],{"class":981}," est_feuille",[725,1082,1083],{"class":985},"(self):\n",[725,1085,1087,1090,1093,1095,1098,1101,1104,1106,1108,1110],{"class":973,"line":1086},10,[725,1088,1089],{"class":977},"        return",[725,1091,1092],{"class":1009}," self",[725,1094,1049],{"class":985},[725,1096,1097],{"class":977},"is",[725,1099,1100],{"class":1009}," None",[725,1102,1103],{"class":977}," and",[725,1105,1092],{"class":1009},[725,1107,1062],{"class":985},[725,1109,1097],{"class":977},[725,1111,1112],{"class":1009}," None\n",[598,1114,1115],{},"Création d'un petit arbre :",[963,1117,1119],{"className":965,"code":1118,"language":967,"meta":968,"style":968},"#       1\n#      \u002F \\\n#     2   3\n#    \u002F\n#   4\narbre = Noeud(1, Noeud(2, Noeud(4)), Noeud(3))\n",[958,1120,1121,1127,1132,1137,1142,1147],{"__ignoreMap":968},[725,1122,1123],{"class":973,"line":974},[725,1124,1126],{"class":1125},"sCsY4","#       1\n",[725,1128,1129],{"class":973,"line":989},[725,1130,1131],{"class":1125},"#      \u002F \\\n",[725,1133,1134],{"class":973,"line":996},[725,1135,1136],{"class":1125},"#     2   3\n",[725,1138,1139],{"class":973,"line":1003},[725,1140,1141],{"class":1125},"#    \u002F\n",[725,1143,1144],{"class":973,"line":1030},[725,1145,1146],{"class":1125},"#   4\n",[725,1148,1149,1152,1154,1157,1159,1162,1165,1167,1170,1173,1176],{"class":973,"line":1044},[725,1150,1151],{"class":985},"arbre ",[725,1153,854],{"class":977},[725,1155,1156],{"class":985}," Noeud(",[725,1158,915],{"class":1009},[725,1160,1161],{"class":985},", Noeud(",[725,1163,1164],{"class":1009},"2",[725,1166,1161],{"class":985},[725,1168,1169],{"class":1009},"4",[725,1171,1172],{"class":985},")), Noeud(",[725,1174,1175],{"class":1009},"3",[725,1177,1178],{"class":985},"))\n",[1180,1181,1183,1189],"self-eval-qcm",{"correct":1164,"slug":1182},"arbres-binaires-c1",[1184,1185,1186],"template",{"v-slot:question":968},[598,1187,1188],{},"Dans l'arbre ci-dessus, combien de feuilles ?",[1184,1190,1191],{"v-slot:choices":968},[1192,1193,1194,1197,1199],"ul",{},[1195,1196,915],"li",{},[1195,1198,1164],{},[1195,1200,1175],{},[593,1202,1204],{"id":1203},"mesurer-un-arbre-binaire","Mesurer un arbre binaire",[1206,1207,722],"h3",{"id":1208},"taille",[598,1210,1211],{},"Le nombre total de nœuds, défini récursivement :",[725,1213,1216],{"className":1214},[1215],"katex-display",[725,1217,1219,1374],{"className":1218},[728],[725,1220,1222],{"className":1221},[732],[734,1223,1225],{"xmlns":736,"display":1224},"block",[738,1226,1227,1371],{},[741,1228,1229,1249,1253,1256,1259,1261],{},[741,1230,1231,1235,1238,1241,1244,1246],{},[744,1232,1234],{"mathvariant":1233},"normal","t",[744,1236,1237],{"mathvariant":1233},"a",[744,1239,1240],{"mathvariant":1233},"i",[744,1242,1243],{"mathvariant":1233},"l",[744,1245,1243],{"mathvariant":1233},[744,1247,1248],{"mathvariant":1233},"e",[852,1250,1252],{"stretchy":1251},"false","(",[744,1254,1255],{},"A",[852,1257,1258],{"stretchy":1251},")",[852,1260,854],{},[741,1262,1263,1266],{},[852,1264,1265],{"fence":755},"{",[1267,1268,1272,1298],"mtable",{"rowspacing":1269,"columnalign":1270,"columnspacing":1271},"0.36em","left left","1em",[1273,1274,1275,1283],"mtr",{},[1276,1277,1278],"mtd",{},[1279,1280,1281],"mstyle",{"scriptlevel":858,"displaystyle":1251},[856,1282,858],{},[1276,1284,1285],{},[1279,1286,1287],{"scriptlevel":858,"displaystyle":1251},[741,1288,1289,1293,1295],{},[1290,1291,1292],"mtext",{},"si ",[744,1294,1255],{},[1290,1296,1297],{}," est vide",[1273,1299,1300,1364],{},[1276,1301,1302],{},[1279,1303,1304],{"scriptlevel":858,"displaystyle":1251},[741,1305,1306,1308,1311,1325,1327,1335,1337,1339,1353,1355,1362],{},[856,1307,915],{},[852,1309,1310],{},"+",[741,1312,1313,1315,1317,1319,1321,1323],{},[744,1314,1234],{"mathvariant":1233},[744,1316,1237],{"mathvariant":1233},[744,1318,1240],{"mathvariant":1233},[744,1320,1243],{"mathvariant":1233},[744,1322,1243],{"mathvariant":1233},[744,1324,1248],{"mathvariant":1233},[852,1326,1252],{"stretchy":1251},[1328,1329,1330,1332],"msub",{},[744,1331,1255],{},[744,1333,1334],{},"g",[852,1336,1258],{"stretchy":1251},[852,1338,1310],{},[741,1340,1341,1343,1345,1347,1349,1351],{},[744,1342,1234],{"mathvariant":1233},[744,1344,1237],{"mathvariant":1233},[744,1346,1240],{"mathvariant":1233},[744,1348,1243],{"mathvariant":1233},[744,1350,1243],{"mathvariant":1233},[744,1352,1248],{"mathvariant":1233},[852,1354,1252],{"stretchy":1251},[1328,1356,1357,1359],{},[744,1358,1255],{},[744,1360,1361],{},"d",[852,1363,1258],{"stretchy":1251},[1276,1365,1366],{},[1279,1367,1368],{"scriptlevel":858,"displaystyle":1251},[1290,1369,1370],{},"sinon",[748,1372,1373],{"encoding":750},"\\mathrm{taille}(A) =\n\\begin{cases}\n0 & \\text{si } A \\text{ est vide} \\\\\n1 + \\mathrm{taille}(A_g) + \\mathrm{taille}(A_d) & \\text{sinon}\n\\end{cases}",[725,1375,1377,1411],{"className":1376,"ariaHidden":755},[754],[725,1378,1380,1384,1391,1395,1398,1402,1405,1408],{"className":1379},[759],[725,1381],{"className":1382,"style":1383},[763],"height:1em;vertical-align:-0.25em;",[725,1385,1387],{"className":1386},[768],[725,1388,1208],{"className":1389},[768,1390],"mathrm",[725,1392,1252],{"className":1393},[1394],"mopen",[725,1396,1255],{"className":1397},[768,769],[725,1399,1258],{"className":1400},[1401],"mclose",[725,1403],{"className":1404,"style":878},[877],[725,1406,854],{"className":1407},[882],[725,1409],{"className":1410,"style":878},[877],[725,1412,1414,1418],{"className":1413},[759],[725,1415],{"className":1416,"style":1417},[763],"height:3em;vertical-align:-1.25em;",[725,1419,1422,1432,1698],{"className":1420},[1421],"minner",[725,1423,1427],{"className":1424,"style":1426},[1394,1425],"delimcenter","top:0em;",[725,1428,1265],{"className":1429},[1430,1431],"delimsizing","size4",[725,1433,1435],{"className":1434},[768],[725,1436,1438,1632,1637],{"className":1437},[1267],[725,1439,1442],{"className":1440},[1441],"col-align-l",[725,1443,1447,1623],{"className":1444},[1445,1446],"vlist-t","vlist-t2",[725,1448,1451,1620],{"className":1449},[1450],"vlist-r",[725,1452,1456,1470],{"className":1453,"style":1455},[1454],"vlist","height:1.69em;",[725,1457,1459,1464],{"style":1458},"top:-3.69em;",[725,1460],{"className":1461,"style":1463},[1462],"pstrut","height:3.008em;",[725,1465,1467],{"className":1466},[768],[725,1468,858],{"className":1469},[768],[725,1471,1473,1476],{"style":1472},"top:-2.25em;",[725,1474],{"className":1475,"style":1463},[1462],[725,1477,1479,1482,1486,1490,1493,1499,1502,1554,1557,1560,1563,1566,1572,1575,1617],{"className":1478},[768],[725,1480,915],{"className":1481},[768],[725,1483],{"className":1484,"style":1485},[877],"margin-right:0.2222em;",[725,1487,1310],{"className":1488},[1489],"mbin",[725,1491],{"className":1492,"style":1485},[877],[725,1494,1496],{"className":1495},[768],[725,1497,1208],{"className":1498},[768,1390],[725,1500,1252],{"className":1501},[1394],[725,1503,1505,1508],{"className":1504},[768],[725,1506,1255],{"className":1507},[768,769],[725,1509,1512],{"className":1510},[1511],"msupsub",[725,1513,1515,1545],{"className":1514},[1445,1446],[725,1516,1518,1540],{"className":1517},[1450],[725,1519,1522],{"className":1520,"style":1521},[1454],"height:0.1514em;",[725,1523,1525,1529],{"style":1524},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[725,1526],{"className":1527,"style":1528},[1462],"height:2.7em;",[725,1530,1536],{"className":1531},[1532,1533,1534,1535],"sizing","reset-size6","size3","mtight",[725,1537,1334],{"className":1538,"style":1539},[768,769,1535],"margin-right:0.0359em;",[725,1541,1544],{"className":1542},[1543],"vlist-s","​",[725,1546,1548],{"className":1547},[1450],[725,1549,1552],{"className":1550,"style":1551},[1454],"height:0.2861em;",[725,1553],{},[725,1555,1258],{"className":1556},[1401],[725,1558],{"className":1559,"style":1485},[877],[725,1561,1310],{"className":1562},[1489],[725,1564],{"className":1565,"style":1485},[877],[725,1567,1569],{"className":1568},[768],[725,1570,1208],{"className":1571},[768,1390],[725,1573,1252],{"className":1574},[1394],[725,1576,1578,1581],{"className":1577},[768],[725,1579,1255],{"className":1580},[768,769],[725,1582,1584],{"className":1583},[1511],[725,1585,1587,1608],{"className":1586},[1445,1446],[725,1588,1590,1605],{"className":1589},[1450],[725,1591,1594],{"className":1592,"style":1593},[1454],"height:0.3361em;",[725,1595,1596,1599],{"style":1524},[725,1597],{"className":1598,"style":1528},[1462],[725,1600,1602],{"className":1601},[1532,1533,1534,1535],[725,1603,1361],{"className":1604},[768,769,1535],[725,1606,1544],{"className":1607},[1543],[725,1609,1611],{"className":1610},[1450],[725,1612,1615],{"className":1613,"style":1614},[1454],"height:0.15em;",[725,1616],{},[725,1618,1258],{"className":1619},[1401],[725,1621,1544],{"className":1622},[1543],[725,1624,1626],{"className":1625},[1450],[725,1627,1630],{"className":1628,"style":1629},[1454],"height:1.19em;",[725,1631],{},[725,1633],{"className":1634,"style":1636},[1635],"arraycolsep","width:1em;",[725,1638,1640],{"className":1639},[1441],[725,1641,1643,1690],{"className":1642},[1445,1446],[725,1644,1646,1687],{"className":1645},[1450],[725,1647,1649,1673],{"className":1648,"style":1455},[1454],[725,1650,1651,1654],{"style":1458},[725,1652],{"className":1653,"style":1463},[1462],[725,1655,1657,1664,1667],{"className":1656},[768],[725,1658,1661],{"className":1659},[768,1660],"text",[725,1662,1292],{"className":1663},[768],[725,1665,1255],{"className":1666},[768,769],[725,1668,1670],{"className":1669},[768,1660],[725,1671,1297],{"className":1672},[768],[725,1674,1675,1678],{"style":1472},[725,1676],{"className":1677,"style":1463},[1462],[725,1679,1681],{"className":1680},[768],[725,1682,1684],{"className":1683},[768,1660],[725,1685,1370],{"className":1686},[768],[725,1688,1544],{"className":1689},[1543],[725,1691,1693],{"className":1692},[1450],[725,1694,1696],{"className":1695,"style":1629},[1454],[725,1697],{},[725,1699],{"className":1700},[1401,1701],"nulldelimiter",[963,1703,1705],{"className":965,"code":1704,"language":967,"meta":968,"style":968},"def taille(noeud):\n    if noeud is None:\n        return 0\n    return 1 + taille(noeud.gauche) + taille(noeud.droite)\n",[958,1706,1707,1718,1732,1739],{"__ignoreMap":968},[725,1708,1709,1712,1715],{"class":973,"line":974},[725,1710,1711],{"class":977},"def",[725,1713,1714],{"class":981}," taille",[725,1716,1717],{"class":985},"(noeud):\n",[725,1719,1720,1723,1726,1728,1730],{"class":973,"line":989},[725,1721,1722],{"class":977},"    if",[725,1724,1725],{"class":985}," noeud ",[725,1727,1097],{"class":977},[725,1729,1100],{"class":1009},[725,1731,986],{"class":985},[725,1733,1734,1736],{"class":973,"line":996},[725,1735,1089],{"class":977},[725,1737,1738],{"class":1009}," 0\n",[725,1740,1741,1744,1747,1750,1753,1755],{"class":973,"line":1003},[725,1742,1743],{"class":977},"    return",[725,1745,1746],{"class":1009}," 1",[725,1748,1749],{"class":977}," +",[725,1751,1752],{"class":985}," taille(noeud.gauche) ",[725,1754,1310],{"class":977},[725,1756,1757],{"class":985}," taille(noeud.droite)\n",[1206,1759,779],{"id":1760},"hauteur",[725,1762,1764],{"className":1763},[1215],[725,1765,1767,1919],{"className":1766},[728],[725,1768,1770],{"className":1769},[732],[734,1771,1772],{"xmlns":736,"display":1224},[738,1773,1774,1916],{},[741,1775,1776,1794,1796,1798,1800,1802],{},[741,1777,1778,1780,1782,1785,1787,1789,1791],{},[744,1779,794],{"mathvariant":1233},[744,1781,1237],{"mathvariant":1233},[744,1783,1784],{"mathvariant":1233},"u",[744,1786,1234],{"mathvariant":1233},[744,1788,1248],{"mathvariant":1233},[744,1790,1784],{"mathvariant":1233},[744,1792,1793],{"mathvariant":1233},"r",[852,1795,1252],{"stretchy":1251},[744,1797,1255],{},[852,1799,1258],{"stretchy":1251},[852,1801,854],{},[741,1803,1804,1806],{},[852,1805,1265],{"fence":755},[1267,1807,1808,1833],{"rowspacing":1269,"columnalign":1270,"columnspacing":1271},[1273,1809,1810,1821],{},[1276,1811,1812],{},[1279,1813,1814],{"scriptlevel":858,"displaystyle":1251},[741,1815,1816,1819],{},[852,1817,1818],{},"−",[856,1820,915],{},[1276,1822,1823],{},[1279,1824,1825],{"scriptlevel":858,"displaystyle":1251},[741,1826,1827,1829,1831],{},[1290,1828,1292],{},[744,1830,1255],{},[1290,1832,1297],{},[1273,1834,1835,1910],{},[1276,1836,1837],{},[1279,1838,1839],{"scriptlevel":858,"displaystyle":1251},[741,1840,1841,1843,1845,1848,1851,1853,1869,1871,1877,1879,1882,1898,1900,1906,1908],{},[856,1842,915],{},[852,1844,1310],{},[744,1846,1847],{},"max",[852,1849,1850],{},"⁡",[852,1852,1252],{"stretchy":1251},[741,1854,1855,1857,1859,1861,1863,1865,1867],{},[744,1856,794],{"mathvariant":1233},[744,1858,1237],{"mathvariant":1233},[744,1860,1784],{"mathvariant":1233},[744,1862,1234],{"mathvariant":1233},[744,1864,1248],{"mathvariant":1233},[744,1866,1784],{"mathvariant":1233},[744,1868,1793],{"mathvariant":1233},[852,1870,1252],{"stretchy":1251},[1328,1872,1873,1875],{},[744,1874,1255],{},[744,1876,1334],{},[852,1878,1258],{"stretchy":1251},[852,1880,1881],{"separator":755},",",[741,1883,1884,1886,1888,1890,1892,1894,1896],{},[744,1885,794],{"mathvariant":1233},[744,1887,1237],{"mathvariant":1233},[744,1889,1784],{"mathvariant":1233},[744,1891,1234],{"mathvariant":1233},[744,1893,1248],{"mathvariant":1233},[744,1895,1784],{"mathvariant":1233},[744,1897,1793],{"mathvariant":1233},[852,1899,1252],{"stretchy":1251},[1328,1901,1902,1904],{},[744,1903,1255],{},[744,1905,1361],{},[852,1907,1258],{"stretchy":1251},[852,1909,1258],{"stretchy":1251},[1276,1911,1912],{},[1279,1913,1914],{"scriptlevel":858,"displaystyle":1251},[1290,1915,1370],{},[748,1917,1918],{"encoding":750},"\\mathrm{hauteur}(A) =\n\\begin{cases}\n-1 & \\text{si } A \\text{ est vide} \\\\\n1 + \\max(\\mathrm{hauteur}(A_g), \\mathrm{hauteur}(A_d)) & \\text{sinon}\n\\end{cases}",[725,1920,1922,1952],{"className":1921,"ariaHidden":755},[754],[725,1923,1925,1928,1934,1937,1940,1943,1946,1949],{"className":1924},[759],[725,1926],{"className":1927,"style":1383},[763],[725,1929,1931],{"className":1930},[768],[725,1932,1760],{"className":1933},[768,1390],[725,1935,1252],{"className":1936},[1394],[725,1938,1255],{"className":1939},[768,769],[725,1941,1258],{"className":1942},[1401],[725,1944],{"className":1945,"style":878},[877],[725,1947,854],{"className":1948},[882],[725,1950],{"className":1951,"style":878},[877],[725,1953,1955,1958],{"className":1954},[759],[725,1956],{"className":1957,"style":1417},[763],[725,1959,1961,1967,2213],{"className":1960},[1421],[725,1962,1964],{"className":1963,"style":1426},[1394,1425],[725,1965,1265],{"className":1966},[1430,1431],[725,1968,1970],{"className":1969},[768],[725,1971,1973,2150,2153],{"className":1972},[1267],[725,1974,1976],{"className":1975},[1441],[725,1977,1979,2142],{"className":1978},[1445,1446],[725,1980,1982,2139],{"className":1981},[1450],[725,1983,1985,1999],{"className":1984,"style":1455},[1454],[725,1986,1987,1990],{"style":1458},[725,1988],{"className":1989,"style":1463},[1462],[725,1991,1993,1996],{"className":1992},[768],[725,1994,1818],{"className":1995},[768],[725,1997,915],{"className":1998},[768],[725,2000,2001,2004],{"style":1472},[725,2002],{"className":2003,"style":1463},[1462],[725,2005,2007,2010,2013,2016,2019,2023,2026,2032,2035,2075,2078,2082,2086,2092,2095,2135],{"className":2006},[768],[725,2008,915],{"className":2009},[768],[725,2011],{"className":2012,"style":1485},[877],[725,2014,1310],{"className":2015},[1489],[725,2017],{"className":2018,"style":1485},[877],[725,2020,1847],{"className":2021},[2022],"mop",[725,2024,1252],{"className":2025},[1394],[725,2027,2029],{"className":2028},[768],[725,2030,1760],{"className":2031},[768,1390],[725,2033,1252],{"className":2034},[1394],[725,2036,2038,2041],{"className":2037},[768],[725,2039,1255],{"className":2040},[768,769],[725,2042,2044],{"className":2043},[1511],[725,2045,2047,2067],{"className":2046},[1445,1446],[725,2048,2050,2064],{"className":2049},[1450],[725,2051,2053],{"className":2052,"style":1521},[1454],[725,2054,2055,2058],{"style":1524},[725,2056],{"className":2057,"style":1528},[1462],[725,2059,2061],{"className":2060},[1532,1533,1534,1535],[725,2062,1334],{"className":2063,"style":1539},[768,769,1535],[725,2065,1544],{"className":2066},[1543],[725,2068,2070],{"className":2069},[1450],[725,2071,2073],{"className":2072,"style":1551},[1454],[725,2074],{},[725,2076,1258],{"className":2077},[1401],[725,2079,1881],{"className":2080},[2081],"mpunct",[725,2083],{"className":2084,"style":2085},[877],"margin-right:0.1667em;",[725,2087,2089],{"className":2088},[768],[725,2090,1760],{"className":2091},[768,1390],[725,2093,1252],{"className":2094},[1394],[725,2096,2098,2101],{"className":2097},[768],[725,2099,1255],{"className":2100},[768,769],[725,2102,2104],{"className":2103},[1511],[725,2105,2107,2127],{"className":2106},[1445,1446],[725,2108,2110,2124],{"className":2109},[1450],[725,2111,2113],{"className":2112,"style":1593},[1454],[725,2114,2115,2118],{"style":1524},[725,2116],{"className":2117,"style":1528},[1462],[725,2119,2121],{"className":2120},[1532,1533,1534,1535],[725,2122,1361],{"className":2123},[768,769,1535],[725,2125,1544],{"className":2126},[1543],[725,2128,2130],{"className":2129},[1450],[725,2131,2133],{"className":2132,"style":1614},[1454],[725,2134],{},[725,2136,2138],{"className":2137},[1401],"))",[725,2140,1544],{"className":2141},[1543],[725,2143,2145],{"className":2144},[1450],[725,2146,2148],{"className":2147,"style":1629},[1454],[725,2149],{},[725,2151],{"className":2152,"style":1636},[1635],[725,2154,2156],{"className":2155},[1441],[725,2157,2159,2205],{"className":2158},[1445,1446],[725,2160,2162,2202],{"className":2161},[1450],[725,2163,2165,2188],{"className":2164,"style":1455},[1454],[725,2166,2167,2170],{"style":1458},[725,2168],{"className":2169,"style":1463},[1462],[725,2171,2173,2179,2182],{"className":2172},[768],[725,2174,2176],{"className":2175},[768,1660],[725,2177,1292],{"className":2178},[768],[725,2180,1255],{"className":2181},[768,769],[725,2183,2185],{"className":2184},[768,1660],[725,2186,1297],{"className":2187},[768],[725,2189,2190,2193],{"style":1472},[725,2191],{"className":2192,"style":1463},[1462],[725,2194,2196],{"className":2195},[768],[725,2197,2199],{"className":2198},[768,1660],[725,2200,1370],{"className":2201},[768],[725,2203,1544],{"className":2204},[1543],[725,2206,2208],{"className":2207},[1450],[725,2209,2211],{"className":2210,"style":1629},[1454],[725,2212],{},[725,2214],{"className":2215},[1401,1701],[598,2217,2218,2219,2309,2310,949],{},"La convention ",[725,2220,2222,2263],{"className":2221},[728],[725,2223,2225],{"className":2224},[732],[734,2226,2227],{"xmlns":736},[738,2228,2229,2260],{},[741,2230,2231,2247,2249,2252,2254,2256,2258],{},[741,2232,2233,2235,2237,2239,2241,2243,2245],{},[744,2234,794],{"mathvariant":1233},[744,2236,1237],{"mathvariant":1233},[744,2238,1784],{"mathvariant":1233},[744,2240,1234],{"mathvariant":1233},[744,2242,1248],{"mathvariant":1233},[744,2244,1784],{"mathvariant":1233},[744,2246,1793],{"mathvariant":1233},[852,2248,1252],{"stretchy":1251},[744,2250,2251],{"mathvariant":1233},"∅",[852,2253,1258],{"stretchy":1251},[852,2255,854],{},[852,2257,1818],{},[856,2259,915],{},[748,2261,2262],{"encoding":750},"\\mathrm{hauteur}(\\emptyset) = -1",[725,2264,2266,2296],{"className":2265,"ariaHidden":755},[754],[725,2267,2269,2272,2278,2281,2284,2287,2290,2293],{"className":2268},[759],[725,2270],{"className":2271,"style":1383},[763],[725,2273,2275],{"className":2274},[768],[725,2276,1760],{"className":2277},[768,1390],[725,2279,1252],{"className":2280},[1394],[725,2282,2251],{"className":2283},[768],[725,2285,1258],{"className":2286},[1401],[725,2288],{"className":2289,"style":878},[877],[725,2291,854],{"className":2292},[882],[725,2294],{"className":2295,"style":878},[877],[725,2297,2299,2303,2306],{"className":2298},[759],[725,2300],{"className":2301,"style":2302},[763],"height:0.7278em;vertical-align:-0.0833em;",[725,2304,1818],{"className":2305},[768],[725,2307,915],{"className":2308},[768]," rend la formule cohérente : un\narbre à un seul nœud a alors une hauteur ",[725,2311,2313,2351],{"className":2312},[728],[725,2314,2316],{"className":2315},[732],[734,2317,2318],{"xmlns":736},[738,2319,2320,2348],{},[741,2321,2322,2324,2326,2328,2330,2332,2334,2336,2338,2340,2342,2344,2346],{},[856,2323,915],{},[852,2325,1310],{},[744,2327,1847],{},[852,2329,1850],{},[852,2331,1252],{"stretchy":1251},[852,2333,1818],{},[856,2335,915],{},[852,2337,1881],{"separator":755},[852,2339,1818],{},[856,2341,915],{},[852,2343,1258],{"stretchy":1251},[852,2345,854],{},[856,2347,858],{},[748,2349,2350],{"encoding":750},"1 + \\max(-1, -1) = 0",[725,2352,2354,2372,2414],{"className":2353,"ariaHidden":755},[754],[725,2355,2357,2360,2363,2366,2369],{"className":2356},[759],[725,2358],{"className":2359,"style":2302},[763],[725,2361,915],{"className":2362},[768],[725,2364],{"className":2365,"style":1485},[877],[725,2367,1310],{"className":2368},[1489],[725,2370],{"className":2371,"style":1485},[877],[725,2373,2375,2378,2381,2384,2387,2390,2393,2396,2399,2402,2405,2408,2411],{"className":2374},[759],[725,2376],{"className":2377,"style":1383},[763],[725,2379,1847],{"className":2380},[2022],[725,2382,1252],{"className":2383},[1394],[725,2385,1818],{"className":2386},[768],[725,2388,915],{"className":2389},[768],[725,2391,1881],{"className":2392},[2081],[725,2394],{"className":2395,"style":2085},[877],[725,2397,1818],{"className":2398},[768],[725,2400,915],{"className":2401},[768],[725,2403,1258],{"className":2404},[1401],[725,2406],{"className":2407,"style":878},[877],[725,2409,854],{"className":2410},[882],[725,2412],{"className":2413,"style":878},[877],[725,2415,2417,2420],{"className":2416},[759],[725,2418],{"className":2419,"style":892},[763],[725,2421,858],{"className":2422},[768],[963,2424,2426],{"className":965,"code":2425,"language":967,"meta":968,"style":968},"def hauteur(noeud):\n    if noeud is None:\n        return -1\n    return 1 + max(hauteur(noeud.gauche), hauteur(noeud.droite))\n",[958,2427,2428,2437,2449,2459],{"__ignoreMap":968},[725,2429,2430,2432,2435],{"class":973,"line":974},[725,2431,1711],{"class":977},[725,2433,2434],{"class":981}," hauteur",[725,2436,1717],{"class":985},[725,2438,2439,2441,2443,2445,2447],{"class":973,"line":989},[725,2440,1722],{"class":977},[725,2442,1725],{"class":985},[725,2444,1097],{"class":977},[725,2446,1100],{"class":1009},[725,2448,986],{"class":985},[725,2450,2451,2453,2456],{"class":973,"line":996},[725,2452,1089],{"class":977},[725,2454,2455],{"class":977}," -",[725,2457,2458],{"class":1009},"1\n",[725,2460,2461,2463,2465,2467,2470],{"class":973,"line":1003},[725,2462,1743],{"class":977},[725,2464,1746],{"class":1009},[725,2466,1749],{"class":977},[725,2468,2469],{"class":1009}," max",[725,2471,2472],{"class":985},"(hauteur(noeud.gauche), hauteur(noeud.droite))\n",[593,2474,2476],{"id":2475},"encadrement-de-la-hauteur","Encadrement de la hauteur",[598,2478,2479,2480,2508,2509,2537,2538,2566,2567,2595],{},"Question canonique du BO : pour un arbre binaire de taille ",[725,2481,2483,2496],{"className":2482},[728],[725,2484,2486],{"className":2485},[732],[734,2487,2488],{"xmlns":736},[738,2489,2490,2494],{},[741,2491,2492],{},[744,2493,746],{},[748,2495,746],{"encoding":750},[725,2497,2499],{"className":2498,"ariaHidden":755},[754],[725,2500,2502,2505],{"className":2501},[759],[725,2503],{"className":2504,"style":764},[763],[725,2506,746],{"className":2507},[768,769]," et de hauteur\n",[725,2510,2512,2525],{"className":2511},[728],[725,2513,2515],{"className":2514},[732],[734,2516,2517],{"xmlns":736},[738,2518,2519,2523],{},[741,2520,2521],{},[744,2522,794],{},[748,2524,794],{"encoding":750},[725,2526,2528],{"className":2527,"ariaHidden":755},[754],[725,2529,2531,2534],{"className":2530},[759],[725,2532],{"className":2533,"style":806},[763],[725,2535,794],{"className":2536},[768,769],", peut-on borner ",[725,2539,2541,2554],{"className":2540},[728],[725,2542,2544],{"className":2543},[732],[734,2545,2546],{"xmlns":736},[738,2547,2548,2552],{},[741,2549,2550],{},[744,2551,794],{},[748,2553,794],{"encoding":750},[725,2555,2557],{"className":2556,"ariaHidden":755},[754],[725,2558,2560,2563],{"className":2559},[759],[725,2561],{"className":2562,"style":806},[763],[725,2564,794],{"className":2565},[768,769]," en fonction de ",[725,2568,2570,2583],{"className":2569},[728],[725,2571,2573],{"className":2572},[732],[734,2574,2575],{"xmlns":736},[738,2576,2577,2581],{},[741,2578,2579],{},[744,2580,746],{},[748,2582,746],{"encoding":750},[725,2584,2586],{"className":2585,"ariaHidden":755},[754],[725,2587,2589,2592],{"className":2588},[759],[725,2590],{"className":2591,"style":764},[763],[725,2593,746],{"className":2594},[768,769]," ?",[2597,2598,2601,2662,2875,2878],"card",{"icon":2599,"title":2600},"i-lucide-target","Théorème",[598,2602,2603,2604,2632,2633,2661],{},"Pour tout arbre binaire non vide de taille ",[725,2605,2607,2620],{"className":2606},[728],[725,2608,2610],{"className":2609},[732],[734,2611,2612],{"xmlns":736},[738,2613,2614,2618],{},[741,2615,2616],{},[744,2617,746],{},[748,2619,746],{"encoding":750},[725,2621,2623],{"className":2622,"ariaHidden":755},[754],[725,2624,2626,2629],{"className":2625},[759],[725,2627],{"className":2628,"style":764},[763],[725,2630,746],{"className":2631},[768,769]," et de hauteur ",[725,2634,2636,2649],{"className":2635},[728],[725,2637,2639],{"className":2638},[732],[734,2640,2641],{"xmlns":736},[738,2642,2643,2647],{},[741,2644,2645],{},[744,2646,794],{},[748,2648,794],{"encoding":750},[725,2650,2652],{"className":2651,"ariaHidden":755},[754],[725,2653,2655,2658],{"className":2654},[759],[725,2656],{"className":2657,"style":806},[763],[725,2659,794],{"className":2660},[768,769]," :",[598,2663,2664],{},[725,2665,2667,2717],{"className":2666},[728],[725,2668,2670],{"className":2669},[732],[734,2671,2672],{"xmlns":736},[738,2673,2674,2714],{},[741,2675,2676,2687,2689,2691,2693,2695,2697,2699,2701,2704,2706,2708,2710,2712],{},[1328,2677,2678,2685],{},[741,2679,2680,2683],{},[744,2681,2682],{},"log",[852,2684,1850],{},[856,2686,1164],{},[852,2688,1252],{"stretchy":1251},[744,2690,746],{},[852,2692,1310],{},[856,2694,915],{},[852,2696,1258],{"stretchy":1251},[852,2698,1818],{},[856,2700,915],{},[852,2702,2703],{},"≤",[744,2705,794],{},[852,2707,2703],{},[744,2709,746],{},[852,2711,1818],{},[856,2713,915],{},[748,2715,2716],{"encoding":750},"\\log_2(n+1) - 1 \\le h \\le n - 1",[725,2718,2720,2788,2809,2828,2847,2866],{"className":2719,"ariaHidden":755},[754],[725,2721,2723,2726,2773,2776,2779,2782,2785],{"className":2722},[759],[725,2724],{"className":2725,"style":1383},[763],[725,2727,2729,2736],{"className":2728},[2022],[725,2730,2732,2733],{"className":2731},[2022],"lo",[725,2734,1334],{"style":2735},"margin-right:0.0139em;",[725,2737,2739],{"className":2738},[1511],[725,2740,2742,2764],{"className":2741},[1445,1446],[725,2743,2745,2761],{"className":2744},[1450],[725,2746,2749],{"className":2747,"style":2748},[1454],"height:0.207em;",[725,2750,2752,2755],{"style":2751},"top:-2.4559em;margin-right:0.05em;",[725,2753],{"className":2754,"style":1528},[1462],[725,2756,2758],{"className":2757},[1532,1533,1534,1535],[725,2759,1164],{"className":2760},[768,1535],[725,2762,1544],{"className":2763},[1543],[725,2765,2767],{"className":2766},[1450],[725,2768,2771],{"className":2769,"style":2770},[1454],"height:0.2441em;",[725,2772],{},[725,2774,1252],{"className":2775},[1394],[725,2777,746],{"className":2778},[768,769],[725,2780],{"className":2781,"style":1485},[877],[725,2783,1310],{"className":2784},[1489],[725,2786],{"className":2787,"style":1485},[877],[725,2789,2791,2794,2797,2800,2803,2806],{"className":2790},[759],[725,2792],{"className":2793,"style":1383},[763],[725,2795,915],{"className":2796},[768],[725,2798,1258],{"className":2799},[1401],[725,2801],{"className":2802,"style":1485},[877],[725,2804,1818],{"className":2805},[1489],[725,2807],{"className":2808,"style":1485},[877],[725,2810,2812,2816,2819,2822,2825],{"className":2811},[759],[725,2813],{"className":2814,"style":2815},[763],"height:0.7804em;vertical-align:-0.136em;",[725,2817,915],{"className":2818},[768],[725,2820],{"className":2821,"style":878},[877],[725,2823,2703],{"className":2824},[882],[725,2826],{"className":2827,"style":878},[877],[725,2829,2831,2835,2838,2841,2844],{"className":2830},[759],[725,2832],{"className":2833,"style":2834},[763],"height:0.8304em;vertical-align:-0.136em;",[725,2836,794],{"className":2837},[768,769],[725,2839],{"className":2840,"style":878},[877],[725,2842,2703],{"className":2843},[882],[725,2845],{"className":2846,"style":878},[877],[725,2848,2850,2854,2857,2860,2863],{"className":2849},[759],[725,2851],{"className":2852,"style":2853},[763],"height:0.6667em;vertical-align:-0.0833em;",[725,2855,746],{"className":2856},[768,769],[725,2858],{"className":2859,"style":1485},[877],[725,2861,1818],{"className":2862},[1489],[725,2864],{"className":2865,"style":1485},[877],[725,2867,2869,2872],{"className":2868},[759],[725,2870],{"className":2871,"style":892},[763],[725,2873,915],{"className":2874},[768],[598,2876,2877],{},"de manière équivalente :",[598,2879,2880],{},[725,2881,2883,2924],{"className":2882},[728],[725,2884,2886],{"className":2885},[732],[734,2887,2888],{"xmlns":736},[738,2889,2890,2921],{},[741,2891,2892,2894,2896,2898,2900,2902,2904,2917,2919],{},[744,2893,794],{},[852,2895,1310],{},[856,2897,915],{},[852,2899,2703],{},[744,2901,746],{},[852,2903,2703],{},[2905,2906,2907,2909],"msup",{},[856,2908,1164],{},[741,2910,2911,2913,2915],{},[744,2912,794],{},[852,2914,1310],{},[856,2916,915],{},[852,2918,1818],{},[856,2920,915],{},[748,2922,2923],{"encoding":750},"h + 1 \\le n \\le 2^{h+1} - 1",[725,2925,2927,2946,2964,2983,3039],{"className":2926,"ariaHidden":755},[754],[725,2928,2930,2934,2937,2940,2943],{"className":2929},[759],[725,2931],{"className":2932,"style":2933},[763],"height:0.7778em;vertical-align:-0.0833em;",[725,2935,794],{"className":2936},[768,769],[725,2938],{"className":2939,"style":1485},[877],[725,2941,1310],{"className":2942},[1489],[725,2944],{"className":2945,"style":1485},[877],[725,2947,2949,2952,2955,2958,2961],{"className":2948},[759],[725,2950],{"className":2951,"style":2815},[763],[725,2953,915],{"className":2954},[768],[725,2956],{"className":2957,"style":878},[877],[725,2959,2703],{"className":2960},[882],[725,2962],{"className":2963,"style":878},[877],[725,2965,2967,2971,2974,2977,2980],{"className":2966},[759],[725,2968],{"className":2969,"style":2970},[763],"height:0.7719em;vertical-align:-0.136em;",[725,2972,746],{"className":2973},[768,769],[725,2975],{"className":2976,"style":878},[877],[725,2978,2703],{"className":2979},[882],[725,2981],{"className":2982,"style":878},[877],[725,2984,2986,2990,3030,3033,3036],{"className":2985},[759],[725,2987],{"className":2988,"style":2989},[763],"height:0.9324em;vertical-align:-0.0833em;",[725,2991,2993,2996],{"className":2992},[768],[725,2994,1164],{"className":2995},[768],[725,2997,2999],{"className":2998},[1511],[725,3000,3002],{"className":3001},[1445],[725,3003,3005],{"className":3004},[1450],[725,3006,3009],{"className":3007,"style":3008},[1454],"height:0.8491em;",[725,3010,3012,3015],{"style":3011},"top:-3.063em;margin-right:0.05em;",[725,3013],{"className":3014,"style":1528},[1462],[725,3016,3018],{"className":3017},[1532,1533,1534,1535],[725,3019,3021,3024,3027],{"className":3020},[768,1535],[725,3022,794],{"className":3023},[768,769,1535],[725,3025,1310],{"className":3026},[1489,1535],[725,3028,915],{"className":3029},[768,1535],[725,3031],{"className":3032,"style":1485},[877],[725,3034,1818],{"className":3035},[1489],[725,3037],{"className":3038,"style":1485},[877],[725,3040,3042,3045],{"className":3041},[759],[725,3043],{"className":3044,"style":892},[763],[725,3046,915],{"className":3047},[768],[1206,3049,3051],{"id":3050},"preuve-par-récurrence","Preuve par récurrence",[598,3053,3054,3057,3058,3086,3087,949],{},[602,3055,3056],{},"Montrons"," : un arbre binaire de hauteur ",[725,3059,3061,3074],{"className":3060},[728],[725,3062,3064],{"className":3063},[732],[734,3065,3066],{"xmlns":736},[738,3067,3068,3072],{},[741,3069,3070],{},[744,3071,794],{},[748,3073,794],{"encoding":750},[725,3075,3077],{"className":3076,"ariaHidden":755},[754],[725,3078,3080,3083],{"className":3079},[759],[725,3081],{"className":3082,"style":806},[763],[725,3084,794],{"className":3085},[768,769]," vérifie ",[725,3088,3090,3129],{"className":3089},[728],[725,3091,3093],{"className":3092},[732],[734,3094,3095],{"xmlns":736},[738,3096,3097,3127],{},[741,3098,3099,3101,3103,3105,3107,3109,3111,3123,3125],{},[744,3100,794],{},[852,3102,1310],{},[856,3104,915],{},[852,3106,2703],{},[744,3108,746],{},[852,3110,2703],{},[2905,3112,3113,3115],{},[856,3114,1164],{},[741,3116,3117,3119,3121],{},[744,3118,794],{},[852,3120,1310],{},[856,3122,915],{},[852,3124,1818],{},[856,3126,915],{},[748,3128,2923],{"encoding":750},[725,3130,3132,3150,3168,3186,3239],{"className":3131,"ariaHidden":755},[754],[725,3133,3135,3138,3141,3144,3147],{"className":3134},[759],[725,3136],{"className":3137,"style":2933},[763],[725,3139,794],{"className":3140},[768,769],[725,3142],{"className":3143,"style":1485},[877],[725,3145,1310],{"className":3146},[1489],[725,3148],{"className":3149,"style":1485},[877],[725,3151,3153,3156,3159,3162,3165],{"className":3152},[759],[725,3154],{"className":3155,"style":2815},[763],[725,3157,915],{"className":3158},[768],[725,3160],{"className":3161,"style":878},[877],[725,3163,2703],{"className":3164},[882],[725,3166],{"className":3167,"style":878},[877],[725,3169,3171,3174,3177,3180,3183],{"className":3170},[759],[725,3172],{"className":3173,"style":2970},[763],[725,3175,746],{"className":3176},[768,769],[725,3178],{"className":3179,"style":878},[877],[725,3181,2703],{"className":3182},[882],[725,3184],{"className":3185,"style":878},[877],[725,3187,3189,3192,3230,3233,3236],{"className":3188},[759],[725,3190],{"className":3191,"style":2989},[763],[725,3193,3195,3198],{"className":3194},[768],[725,3196,1164],{"className":3197},[768],[725,3199,3201],{"className":3200},[1511],[725,3202,3204],{"className":3203},[1445],[725,3205,3207],{"className":3206},[1450],[725,3208,3210],{"className":3209,"style":3008},[1454],[725,3211,3212,3215],{"style":3011},[725,3213],{"className":3214,"style":1528},[1462],[725,3216,3218],{"className":3217},[1532,1533,1534,1535],[725,3219,3221,3224,3227],{"className":3220},[768,1535],[725,3222,794],{"className":3223},[768,769,1535],[725,3225,1310],{"className":3226},[1489,1535],[725,3228,915],{"className":3229},[768,1535],[725,3231],{"className":3232,"style":1485},[877],[725,3234,1818],{"className":3235},[1489],[725,3237],{"className":3238,"style":1485},[877],[725,3240,3242,3245],{"className":3241},[759],[725,3243],{"className":3244,"style":892},[763],[725,3246,915],{"className":3247},[768],[598,3249,3250,3253,3254,3304,3305,3355,3356,3429,3430,3548,3549,3622],{},[602,3251,3252],{},"Initialisation"," (",[725,3255,3257,3274],{"className":3256},[728],[725,3258,3260],{"className":3259},[732],[734,3261,3262],{"xmlns":736},[738,3263,3264,3272],{},[741,3265,3266,3268,3270],{},[744,3267,794],{},[852,3269,854],{},[856,3271,858],{},[748,3273,861],{"encoding":750},[725,3275,3277,3295],{"className":3276,"ariaHidden":755},[754],[725,3278,3280,3283,3286,3289,3292],{"className":3279},[759],[725,3281],{"className":3282,"style":806},[763],[725,3284,794],{"className":3285},[768,769],[725,3287],{"className":3288,"style":878},[877],[725,3290,854],{"className":3291},[882],[725,3293],{"className":3294,"style":878},[877],[725,3296,3298,3301],{"className":3297},[759],[725,3299],{"className":3300,"style":892},[763],[725,3302,858],{"className":3303},[768],"). L'arbre est réduit à sa racine. On a ",[725,3306,3308,3325],{"className":3307},[728],[725,3309,3311],{"className":3310},[732],[734,3312,3313],{"xmlns":736},[738,3314,3315,3323],{},[741,3316,3317,3319,3321],{},[744,3318,746],{},[852,3320,854],{},[856,3322,915],{},[748,3324,918],{"encoding":750},[725,3326,3328,3346],{"className":3327,"ariaHidden":755},[754],[725,3329,3331,3334,3337,3340,3343],{"className":3330},[759],[725,3332],{"className":3333,"style":764},[763],[725,3335,746],{"className":3336},[768,769],[725,3338],{"className":3339,"style":878},[877],[725,3341,854],{"className":3342},[882],[725,3344],{"className":3345,"style":878},[877],[725,3347,3349,3352],{"className":3348},[759],[725,3350],{"className":3351,"style":892},[763],[725,3353,915],{"className":3354},[768],", et\n",[725,3357,3359,3381],{"className":3358},[728],[725,3360,3362],{"className":3361},[732],[734,3363,3364],{"xmlns":736},[738,3365,3366,3378],{},[741,3367,3368,3370,3372,3374,3376],{},[744,3369,794],{},[852,3371,1310],{},[856,3373,915],{},[852,3375,854],{},[856,3377,915],{},[748,3379,3380],{"encoding":750},"h + 1 = 1",[725,3382,3384,3402,3420],{"className":3383,"ariaHidden":755},[754],[725,3385,3387,3390,3393,3396,3399],{"className":3386},[759],[725,3388],{"className":3389,"style":2933},[763],[725,3391,794],{"className":3392},[768,769],[725,3394],{"className":3395,"style":1485},[877],[725,3397,1310],{"className":3398},[1489],[725,3400],{"className":3401,"style":1485},[877],[725,3403,3405,3408,3411,3414,3417],{"className":3404},[759],[725,3406],{"className":3407,"style":892},[763],[725,3409,915],{"className":3410},[768],[725,3412],{"className":3413,"style":878},[877],[725,3415,854],{"className":3416},[882],[725,3418],{"className":3419,"style":878},[877],[725,3421,3423,3426],{"className":3422},[759],[725,3424],{"className":3425,"style":892},[763],[725,3427,915],{"className":3428},[768],", et ",[725,3431,3433,3465],{"className":3432},[728],[725,3434,3436],{"className":3435},[732],[734,3437,3438],{"xmlns":736},[738,3439,3440,3462],{},[741,3441,3442,3454,3456,3458,3460],{},[2905,3443,3444,3446],{},[856,3445,1164],{},[741,3447,3448,3450,3452],{},[744,3449,794],{},[852,3451,1310],{},[856,3453,915],{},[852,3455,1818],{},[856,3457,915],{},[852,3459,854],{},[856,3461,915],{},[748,3463,3464],{"encoding":750},"2^{h+1} - 1 = 1",[725,3466,3468,3521,3539],{"className":3467,"ariaHidden":755},[754],[725,3469,3471,3474,3512,3515,3518],{"className":3470},[759],[725,3472],{"className":3473,"style":2989},[763],[725,3475,3477,3480],{"className":3476},[768],[725,3478,1164],{"className":3479},[768],[725,3481,3483],{"className":3482},[1511],[725,3484,3486],{"className":3485},[1445],[725,3487,3489],{"className":3488},[1450],[725,3490,3492],{"className":3491,"style":3008},[1454],[725,3493,3494,3497],{"style":3011},[725,3495],{"className":3496,"style":1528},[1462],[725,3498,3500],{"className":3499},[1532,1533,1534,1535],[725,3501,3503,3506,3509],{"className":3502},[768,1535],[725,3504,794],{"className":3505},[768,769,1535],[725,3507,1310],{"className":3508},[1489,1535],[725,3510,915],{"className":3511},[768,1535],[725,3513],{"className":3514,"style":1485},[877],[725,3516,1818],{"className":3517},[1489],[725,3519],{"className":3520,"style":1485},[877],[725,3522,3524,3527,3530,3533,3536],{"className":3523},[759],[725,3525],{"className":3526,"style":892},[763],[725,3528,915],{"className":3529},[768],[725,3531],{"className":3532,"style":878},[877],[725,3534,854],{"className":3535},[882],[725,3537],{"className":3538,"style":878},[877],[725,3540,3542,3545],{"className":3541},[759],[725,3543],{"className":3544,"style":892},[763],[725,3546,915],{"className":3547},[768],". L'inégalité ",[725,3550,3552,3574],{"className":3551},[728],[725,3553,3555],{"className":3554},[732],[734,3556,3557],{"xmlns":736},[738,3558,3559,3571],{},[741,3560,3561,3563,3565,3567,3569],{},[856,3562,915],{},[852,3564,2703],{},[856,3566,915],{},[852,3568,2703],{},[856,3570,915],{},[748,3572,3573],{"encoding":750},"1 \\le 1 \\le 1",[725,3575,3577,3595,3613],{"className":3576,"ariaHidden":755},[754],[725,3578,3580,3583,3586,3589,3592],{"className":3579},[759],[725,3581],{"className":3582,"style":2815},[763],[725,3584,915],{"className":3585},[768],[725,3587],{"className":3588,"style":878},[877],[725,3590,2703],{"className":3591},[882],[725,3593],{"className":3594,"style":878},[877],[725,3596,3598,3601,3604,3607,3610],{"className":3597},[759],[725,3599],{"className":3600,"style":2815},[763],[725,3602,915],{"className":3603},[768],[725,3605],{"className":3606,"style":878},[877],[725,3608,2703],{"className":3609},[882],[725,3611],{"className":3612,"style":878},[877],[725,3614,3616,3619],{"className":3615},[759],[725,3617],{"className":3618,"style":892},[763],[725,3620,915],{"className":3621},[768]," tient.",[598,3624,3625,3628,3629,3657,3658,3710,3711,3740,3741,3769,3770,3841,3842,3913,3914,3429,3979,3982,3983,4034,4035,4063,4064,961],{},[602,3626,3627],{},"Hérédité."," Supposons la propriété vraie pour toute hauteur strictement\ninférieure à ",[725,3630,3632,3645],{"className":3631},[728],[725,3633,3635],{"className":3634},[732],[734,3636,3637],{"xmlns":736},[738,3638,3639,3643],{},[741,3640,3641],{},[744,3642,794],{},[748,3644,794],{"encoding":750},[725,3646,3648],{"className":3647,"ariaHidden":755},[754],[725,3649,3651,3654],{"className":3650},[759],[725,3652],{"className":3653,"style":806},[763],[725,3655,794],{"className":3656},[768,769]," (avec ",[725,3659,3661,3680],{"className":3660},[728],[725,3662,3664],{"className":3663},[732],[734,3665,3666],{"xmlns":736},[738,3667,3668,3677],{},[741,3669,3670,3672,3675],{},[744,3671,794],{},[852,3673,3674],{},"≥",[856,3676,915],{},[748,3678,3679],{"encoding":750},"h \\ge 1",[725,3681,3683,3701],{"className":3682,"ariaHidden":755},[754],[725,3684,3686,3689,3692,3695,3698],{"className":3685},[759],[725,3687],{"className":3688,"style":2834},[763],[725,3690,794],{"className":3691},[768,769],[725,3693],{"className":3694,"style":878},[877],[725,3696,3674],{"className":3697},[882],[725,3699],{"className":3700,"style":878},[877],[725,3702,3704,3707],{"className":3703},[759],[725,3705],{"className":3706,"style":892},[763],[725,3708,915],{"className":3709},[768],"). Soit ",[725,3712,3714,3727],{"className":3713},[728],[725,3715,3717],{"className":3716},[732],[734,3718,3719],{"xmlns":736},[738,3720,3721,3725],{},[741,3722,3723],{},[744,3724,1255],{},[748,3726,1255],{"encoding":750},[725,3728,3730],{"className":3729,"ariaHidden":755},[754],[725,3731,3733,3737],{"className":3732},[759],[725,3734],{"className":3735,"style":3736},[763],"height:0.6833em;",[725,3738,1255],{"className":3739},[768,769]," un arbre binaire de hauteur ",[725,3742,3744,3757],{"className":3743},[728],[725,3745,3747],{"className":3746},[732],[734,3748,3749],{"xmlns":736},[738,3750,3751,3755],{},[741,3752,3753],{},[744,3754,794],{},[748,3756,794],{"encoding":750},[725,3758,3760],{"className":3759,"ariaHidden":755},[754],[725,3761,3763,3766],{"className":3762},[759],[725,3764],{"className":3765,"style":806},[763],[725,3767,794],{"className":3768},[768,769],".\nSes sous-arbres ",[725,3771,3773,3791],{"className":3772},[728],[725,3774,3776],{"className":3775},[732],[734,3777,3778],{"xmlns":736},[738,3779,3780,3788],{},[741,3781,3782],{},[1328,3783,3784,3786],{},[744,3785,1255],{},[744,3787,1334],{},[748,3789,3790],{"encoding":750},"A_g",[725,3792,3794],{"className":3793,"ariaHidden":755},[754],[725,3795,3797,3801],{"className":3796},[759],[725,3798],{"className":3799,"style":3800},[763],"height:0.9694em;vertical-align:-0.2861em;",[725,3802,3804,3807],{"className":3803},[768],[725,3805,1255],{"className":3806},[768,769],[725,3808,3810],{"className":3809},[1511],[725,3811,3813,3833],{"className":3812},[1445,1446],[725,3814,3816,3830],{"className":3815},[1450],[725,3817,3819],{"className":3818,"style":1521},[1454],[725,3820,3821,3824],{"style":1524},[725,3822],{"className":3823,"style":1528},[1462],[725,3825,3827],{"className":3826},[1532,1533,1534,1535],[725,3828,1334],{"className":3829,"style":1539},[768,769,1535],[725,3831,1544],{"className":3832},[1543],[725,3834,3836],{"className":3835},[1450],[725,3837,3839],{"className":3838,"style":1551},[1454],[725,3840],{}," et ",[725,3843,3845,3863],{"className":3844},[728],[725,3846,3848],{"className":3847},[732],[734,3849,3850],{"xmlns":736},[738,3851,3852,3860],{},[741,3853,3854],{},[1328,3855,3856,3858],{},[744,3857,1255],{},[744,3859,1361],{},[748,3861,3862],{"encoding":750},"A_d",[725,3864,3866],{"className":3865,"ariaHidden":755},[754],[725,3867,3869,3873],{"className":3868},[759],[725,3870],{"className":3871,"style":3872},[763],"height:0.8333em;vertical-align:-0.15em;",[725,3874,3876,3879],{"className":3875},[768],[725,3877,1255],{"className":3878},[768,769],[725,3880,3882],{"className":3881},[1511],[725,3883,3885,3905],{"className":3884},[1445,1446],[725,3886,3888,3902],{"className":3887},[1450],[725,3889,3891],{"className":3890,"style":1593},[1454],[725,3892,3893,3896],{"style":1524},[725,3894],{"className":3895,"style":1528},[1462],[725,3897,3899],{"className":3898},[1532,1533,1534,1535],[725,3900,1361],{"className":3901},[768,769,1535],[725,3903,1544],{"className":3904},[1543],[725,3906,3908],{"className":3907},[1450],[725,3909,3911],{"className":3910,"style":1614},[1454],[725,3912],{}," ont chacun une hauteur ",[725,3915,3917,3937],{"className":3916},[728],[725,3918,3920],{"className":3919},[732],[734,3921,3922],{"xmlns":736},[738,3923,3924,3934],{},[741,3925,3926,3928,3930,3932],{},[852,3927,2703],{},[744,3929,794],{},[852,3931,1818],{},[856,3933,915],{},[748,3935,3936],{"encoding":750},"\\le h - 1",[725,3938,3940,3952,3970],{"className":3939,"ariaHidden":755},[754],[725,3941,3943,3946,3949],{"className":3942},[759],[725,3944],{"className":3945,"style":2970},[763],[725,3947,2703],{"className":3948},[882],[725,3950],{"className":3951,"style":878},[877],[725,3953,3955,3958,3961,3964,3967],{"className":3954},[759],[725,3956],{"className":3957,"style":2933},[763],[725,3959,794],{"className":3960},[768,769],[725,3962],{"className":3963,"style":1485},[877],[725,3965,1818],{"className":3966},[1489],[725,3968],{"className":3969,"style":1485},[877],[725,3971,3973,3976],{"className":3972},[759],[725,3974],{"className":3975,"style":892},[763],[725,3977,915],{"className":3978},[768],[602,3980,3981],{},"au\nmoins l'un des deux"," atteint ",[725,3984,3986,4004],{"className":3985},[728],[725,3987,3989],{"className":3988},[732],[734,3990,3991],{"xmlns":736},[738,3992,3993,4001],{},[741,3994,3995,3997,3999],{},[744,3996,794],{},[852,3998,1818],{},[856,4000,915],{},[748,4002,4003],{"encoding":750},"h - 1",[725,4005,4007,4025],{"className":4006,"ariaHidden":755},[754],[725,4008,4010,4013,4016,4019,4022],{"className":4009},[759],[725,4011],{"className":4012,"style":2933},[763],[725,4014,794],{"className":4015},[768,769],[725,4017],{"className":4018,"style":1485},[877],[725,4020,1818],{"className":4021},[1489],[725,4023],{"className":4024,"style":1485},[877],[725,4026,4028,4031],{"className":4027},[759],[725,4029],{"className":4030,"style":892},[763],[725,4032,915],{"className":4033},[768]," (sinon ",[725,4036,4038,4051],{"className":4037},[728],[725,4039,4041],{"className":4040},[732],[734,4042,4043],{"xmlns":736},[738,4044,4045,4049],{},[741,4046,4047],{},[744,4048,1255],{},[748,4050,1255],{"encoding":750},[725,4052,4054],{"className":4053,"ariaHidden":755},[754],[725,4055,4057,4060],{"className":4056},[759],[725,4058],{"className":4059,"style":3736},[763],[725,4061,1255],{"className":4062},[768,769]," aurait une hauteur strictement\ninférieure à ",[725,4065,4067,4080],{"className":4066},[728],[725,4068,4070],{"className":4069},[732],[734,4071,4072],{"xmlns":736},[738,4073,4074,4078],{},[741,4075,4076],{},[744,4077,794],{},[748,4079,794],{"encoding":750},[725,4081,4083],{"className":4082,"ariaHidden":755},[754],[725,4084,4086,4089],{"className":4085},[759],[725,4087],{"className":4088,"style":806},[763],[725,4090,794],{"className":4091},[768,769],[1192,4093,4094,4403],{},[1195,4095,4096,4099,4100,4150,4151,4256,4257,4285,4286,949],{},[602,4097,4098],{},"Minoration."," Le sous-arbre qui atteint ",[725,4101,4103,4120],{"className":4102},[728],[725,4104,4106],{"className":4105},[732],[734,4107,4108],{"xmlns":736},[738,4109,4110,4118],{},[741,4111,4112,4114,4116],{},[744,4113,794],{},[852,4115,1818],{},[856,4117,915],{},[748,4119,4003],{"encoding":750},[725,4121,4123,4141],{"className":4122,"ariaHidden":755},[754],[725,4124,4126,4129,4132,4135,4138],{"className":4125},[759],[725,4127],{"className":4128,"style":2933},[763],[725,4130,794],{"className":4131},[768,769],[725,4133],{"className":4134,"style":1485},[877],[725,4136,1818],{"className":4137},[1489],[725,4139],{"className":4140,"style":1485},[877],[725,4142,4144,4147],{"className":4143},[759],[725,4145],{"className":4146,"style":892},[763],[725,4148,915],{"className":4149},[768]," contient au moins\n",[725,4152,4154,4184],{"className":4153},[728],[725,4155,4157],{"className":4156},[732],[734,4158,4159],{"xmlns":736},[738,4160,4161,4181],{},[741,4162,4163,4165,4167,4169,4171,4173,4175,4177,4179],{},[852,4164,1252],{"stretchy":1251},[744,4166,794],{},[852,4168,1818],{},[856,4170,915],{},[852,4172,1258],{"stretchy":1251},[852,4174,1310],{},[856,4176,915],{},[852,4178,854],{},[744,4180,794],{},[748,4182,4183],{"encoding":750},"(h - 1) + 1 = h",[725,4185,4187,4208,4229,4247],{"className":4186,"ariaHidden":755},[754],[725,4188,4190,4193,4196,4199,4202,4205],{"className":4189},[759],[725,4191],{"className":4192,"style":1383},[763],[725,4194,1252],{"className":4195},[1394],[725,4197,794],{"className":4198},[768,769],[725,4200],{"className":4201,"style":1485},[877],[725,4203,1818],{"className":4204},[1489],[725,4206],{"className":4207,"style":1485},[877],[725,4209,4211,4214,4217,4220,4223,4226],{"className":4210},[759],[725,4212],{"className":4213,"style":1383},[763],[725,4215,915],{"className":4216},[768],[725,4218,1258],{"className":4219},[1401],[725,4221],{"className":4222,"style":1485},[877],[725,4224,1310],{"className":4225},[1489],[725,4227],{"className":4228,"style":1485},[877],[725,4230,4232,4235,4238,4241,4244],{"className":4231},[759],[725,4233],{"className":4234,"style":892},[763],[725,4236,915],{"className":4237},[768],[725,4239],{"className":4240,"style":878},[877],[725,4242,854],{"className":4243},[882],[725,4245],{"className":4246,"style":878},[877],[725,4248,4250,4253],{"className":4249},[759],[725,4251],{"className":4252,"style":806},[763],[725,4254,794],{"className":4255},[768,769]," nœuds par hypothèse de récurrence. Avec la racine de ",[725,4258,4260,4273],{"className":4259},[728],[725,4261,4263],{"className":4262},[732],[734,4264,4265],{"xmlns":736},[738,4266,4267,4271],{},[741,4268,4269],{},[744,4270,1255],{},[748,4272,1255],{"encoding":750},[725,4274,4276],{"className":4275,"ariaHidden":755},[754],[725,4277,4279,4282],{"className":4278},[759],[725,4280],{"className":4281,"style":3736},[763],[725,4283,1255],{"className":4284},[768,769],",\non a donc ",[725,4287,4289,4319],{"className":4288},[728],[725,4290,4292],{"className":4291},[732],[734,4293,4294],{"xmlns":736},[738,4295,4296,4316],{},[741,4297,4298,4300,4302,4304,4306,4308,4310,4312,4314],{},[744,4299,746],{},[852,4301,3674],{},[856,4303,915],{},[852,4305,1310],{},[744,4307,794],{},[852,4309,854],{},[744,4311,794],{},[852,4313,1310],{},[856,4315,915],{},[748,4317,4318],{"encoding":750},"n \\ge 1 + h = h + 1",[725,4320,4322,4340,4358,4376,4394],{"className":4321,"ariaHidden":755},[754],[725,4323,4325,4328,4331,4334,4337],{"className":4324},[759],[725,4326],{"className":4327,"style":2970},[763],[725,4329,746],{"className":4330},[768,769],[725,4332],{"className":4333,"style":878},[877],[725,4335,3674],{"className":4336},[882],[725,4338],{"className":4339,"style":878},[877],[725,4341,4343,4346,4349,4352,4355],{"className":4342},[759],[725,4344],{"className":4345,"style":2302},[763],[725,4347,915],{"className":4348},[768],[725,4350],{"className":4351,"style":1485},[877],[725,4353,1310],{"className":4354},[1489],[725,4356],{"className":4357,"style":1485},[877],[725,4359,4361,4364,4367,4370,4373],{"className":4360},[759],[725,4362],{"className":4363,"style":806},[763],[725,4365,794],{"className":4366},[768,769],[725,4368],{"className":4369,"style":878},[877],[725,4371,854],{"className":4372},[882],[725,4374],{"className":4375,"style":878},[877],[725,4377,4379,4382,4385,4388,4391],{"className":4378},[759],[725,4380],{"className":4381,"style":2933},[763],[725,4383,794],{"className":4384},[768,769],[725,4386],{"className":4387,"style":1485},[877],[725,4389,1310],{"className":4390},[1489],[725,4392],{"className":4393,"style":1485},[877],[725,4395,4397,4400],{"className":4396},[759],[725,4398],{"className":4399,"style":892},[763],[725,4401,915],{"className":4402},[768],[1195,4404,4405,4408,4409,4493,4494],{},[602,4406,4407],{},"Majoration."," Chaque sous-arbre a au plus ",[725,4410,4412,4434],{"className":4411},[728],[725,4413,4415],{"className":4414},[732],[734,4416,4417],{"xmlns":736},[738,4418,4419,4431],{},[741,4420,4421,4427,4429],{},[2905,4422,4423,4425],{},[856,4424,1164],{},[744,4426,794],{},[852,4428,1818],{},[856,4430,915],{},[748,4432,4433],{"encoding":750},"2^{h} - 1",[725,4435,4437,4484],{"className":4436,"ariaHidden":755},[754],[725,4438,4440,4443,4475,4478,4481],{"className":4439},[759],[725,4441],{"className":4442,"style":2989},[763],[725,4444,4446,4449],{"className":4445},[768],[725,4447,1164],{"className":4448},[768],[725,4450,4452],{"className":4451},[1511],[725,4453,4455],{"className":4454},[1445],[725,4456,4458],{"className":4457},[1450],[725,4459,4461],{"className":4460,"style":3008},[1454],[725,4462,4463,4466],{"style":3011},[725,4464],{"className":4465,"style":1528},[1462],[725,4467,4469],{"className":4468},[1532,1533,1534,1535],[725,4470,4472],{"className":4471},[768,1535],[725,4473,794],{"className":4474},[768,769,1535],[725,4476],{"className":4477,"style":1485},[877],[725,4479,1818],{"className":4480},[1489],[725,4482],{"className":4483,"style":1485},[877],[725,4485,4487,4490],{"className":4486},[759],[725,4488],{"className":4489,"style":892},[763],[725,4491,915],{"className":4492},[768]," nœuds par hypothèse de\nrécurrence. Donc\n",[725,4495,4497,4552],{"className":4496},[728],[725,4498,4500],{"className":4499},[732],[734,4501,4502],{"xmlns":736},[738,4503,4504,4549],{},[741,4505,4506,4508,4510,4512,4514,4516,4518,4524,4526,4528,4530,4532,4544,4546],{},[744,4507,746],{},[852,4509,2703],{},[856,4511,915],{},[852,4513,1310],{},[856,4515,1164],{},[852,4517,1252],{"stretchy":1251},[2905,4519,4520,4522],{},[856,4521,1164],{},[744,4523,794],{},[852,4525,1818],{},[856,4527,915],{},[852,4529,1258],{"stretchy":1251},[852,4531,854],{},[2905,4533,4534,4536],{},[856,4535,1164],{},[741,4537,4538,4540,4542],{},[744,4539,794],{},[852,4541,1310],{},[856,4543,915],{},[852,4545,1818],{},[856,4547,4548],{},"1.",[748,4550,4551],{"encoding":750},"n \\le 1 + 2(2^{h} - 1) = 2^{h+1} - 1.",[725,4553,4555,4573,4591,4645,4666,4719],{"className":4554,"ariaHidden":755},[754],[725,4556,4558,4561,4564,4567,4570],{"className":4557},[759],[725,4559],{"className":4560,"style":2970},[763],[725,4562,746],{"className":4563},[768,769],[725,4565],{"className":4566,"style":878},[877],[725,4568,2703],{"className":4569},[882],[725,4571],{"className":4572,"style":878},[877],[725,4574,4576,4579,4582,4585,4588],{"className":4575},[759],[725,4577],{"className":4578,"style":2302},[763],[725,4580,915],{"className":4581},[768],[725,4583],{"className":4584,"style":1485},[877],[725,4586,1310],{"className":4587},[1489],[725,4589],{"className":4590,"style":1485},[877],[725,4592,4594,4598,4601,4604,4636,4639,4642],{"className":4593},[759],[725,4595],{"className":4596,"style":4597},[763],"height:1.0991em;vertical-align:-0.25em;",[725,4599,1164],{"className":4600},[768],[725,4602,1252],{"className":4603},[1394],[725,4605,4607,4610],{"className":4606},[768],[725,4608,1164],{"className":4609},[768],[725,4611,4613],{"className":4612},[1511],[725,4614,4616],{"className":4615},[1445],[725,4617,4619],{"className":4618},[1450],[725,4620,4622],{"className":4621,"style":3008},[1454],[725,4623,4624,4627],{"style":3011},[725,4625],{"className":4626,"style":1528},[1462],[725,4628,4630],{"className":4629},[1532,1533,1534,1535],[725,4631,4633],{"className":4632},[768,1535],[725,4634,794],{"className":4635},[768,769,1535],[725,4637],{"className":4638,"style":1485},[877],[725,4640,1818],{"className":4641},[1489],[725,4643],{"className":4644,"style":1485},[877],[725,4646,4648,4651,4654,4657,4660,4663],{"className":4647},[759],[725,4649],{"className":4650,"style":1383},[763],[725,4652,915],{"className":4653},[768],[725,4655,1258],{"className":4656},[1401],[725,4658],{"className":4659,"style":878},[877],[725,4661,854],{"className":4662},[882],[725,4664],{"className":4665,"style":878},[877],[725,4667,4669,4672,4710,4713,4716],{"className":4668},[759],[725,4670],{"className":4671,"style":2989},[763],[725,4673,4675,4678],{"className":4674},[768],[725,4676,1164],{"className":4677},[768],[725,4679,4681],{"className":4680},[1511],[725,4682,4684],{"className":4683},[1445],[725,4685,4687],{"className":4686},[1450],[725,4688,4690],{"className":4689,"style":3008},[1454],[725,4691,4692,4695],{"style":3011},[725,4693],{"className":4694,"style":1528},[1462],[725,4696,4698],{"className":4697},[1532,1533,1534,1535],[725,4699,4701,4704,4707],{"className":4700},[768,1535],[725,4702,794],{"className":4703},[768,769,1535],[725,4705,1310],{"className":4706},[1489,1535],[725,4708,915],{"className":4709},[768,1535],[725,4711],{"className":4712,"style":1485},[877],[725,4714,1818],{"className":4715},[1489],[725,4717],{"className":4718,"style":1485},[877],[725,4720,4722,4725],{"className":4721},[759],[725,4723],{"className":4724,"style":892},[763],[725,4726,4548],{"className":4727},[768],[598,4729,4730,4731,4759,4760,4763,4764,4815,4816,4934,4935,5092,5093],{},"L'inégalité est démontrée pour la hauteur ",[725,4732,4734,4747],{"className":4733},[728],[725,4735,4737],{"className":4736},[732],[734,4738,4739],{"xmlns":736},[738,4740,4741,4745],{},[741,4742,4743],{},[744,4744,794],{},[748,4746,794],{"encoding":750},[725,4748,4750],{"className":4749,"ariaHidden":755},[754],[725,4751,4753,4756],{"className":4752},[759],[725,4754],{"className":4755,"style":806},[763],[725,4757,794],{"className":4758},[768,769],". ",[602,4761,4762],{},"Par récurrence",", elle est\nvraie pour tout ",[725,4765,4767,4785],{"className":4766},[728],[725,4768,4770],{"className":4769},[732],[734,4771,4772],{"xmlns":736},[738,4773,4774,4782],{},[741,4775,4776,4778,4780],{},[744,4777,794],{},[852,4779,3674],{},[856,4781,858],{},[748,4783,4784],{"encoding":750},"h \\ge 0",[725,4786,4788,4806],{"className":4787,"ariaHidden":755},[754],[725,4789,4791,4794,4797,4800,4803],{"className":4790},[759],[725,4792],{"className":4793,"style":2834},[763],[725,4795,794],{"className":4796},[768,769],[725,4798],{"className":4799,"style":878},[877],[725,4801,3674],{"className":4802},[882],[725,4804],{"className":4805,"style":878},[877],[725,4807,4809,4812],{"className":4808},[759],[725,4810],{"className":4811,"style":892},[763],[725,4813,858],{"className":4814},[768],". Par passage au logarithme dans la majoration\n",[725,4817,4819,4851],{"className":4818},[728],[725,4820,4822],{"className":4821},[732],[734,4823,4824],{"xmlns":736},[738,4825,4826,4848],{},[741,4827,4828,4830,4832,4844,4846],{},[744,4829,746],{},[852,4831,2703],{},[2905,4833,4834,4836],{},[856,4835,1164],{},[741,4837,4838,4840,4842],{},[744,4839,794],{},[852,4841,1310],{},[856,4843,915],{},[852,4845,1818],{},[856,4847,915],{},[748,4849,4850],{"encoding":750},"n \\le 2^{h+1} - 1",[725,4852,4854,4872,4925],{"className":4853,"ariaHidden":755},[754],[725,4855,4857,4860,4863,4866,4869],{"className":4856},[759],[725,4858],{"className":4859,"style":2970},[763],[725,4861,746],{"className":4862},[768,769],[725,4864],{"className":4865,"style":878},[877],[725,4867,2703],{"className":4868},[882],[725,4870],{"className":4871,"style":878},[877],[725,4873,4875,4878,4916,4919,4922],{"className":4874},[759],[725,4876],{"className":4877,"style":2989},[763],[725,4879,4881,4884],{"className":4880},[768],[725,4882,1164],{"className":4883},[768],[725,4885,4887],{"className":4886},[1511],[725,4888,4890],{"className":4889},[1445],[725,4891,4893],{"className":4892},[1450],[725,4894,4896],{"className":4895,"style":3008},[1454],[725,4897,4898,4901],{"style":3011},[725,4899],{"className":4900,"style":1528},[1462],[725,4902,4904],{"className":4903},[1532,1533,1534,1535],[725,4905,4907,4910,4913],{"className":4906},[768,1535],[725,4908,794],{"className":4909},[768,769,1535],[725,4911,1310],{"className":4912},[1489,1535],[725,4914,915],{"className":4915},[768,1535],[725,4917],{"className":4918,"style":1485},[877],[725,4920,1818],{"className":4921},[1489],[725,4923],{"className":4924,"style":1485},[877],[725,4926,4928,4931],{"className":4927},[759],[725,4929],{"className":4930,"style":892},[763],[725,4932,915],{"className":4933},[768],", on obtient ",[725,4936,4938,4978],{"className":4937},[728],[725,4939,4941],{"className":4940},[732],[734,4942,4943],{"xmlns":736},[738,4944,4945,4975],{},[741,4946,4947,4949,4951,4961,4963,4965,4967,4969,4971,4973],{},[744,4948,794],{},[852,4950,3674],{},[1328,4952,4953,4959],{},[741,4954,4955,4957],{},[744,4956,2682],{},[852,4958,1850],{},[856,4960,1164],{},[852,4962,1252],{"stretchy":1251},[744,4964,746],{},[852,4966,1310],{},[856,4968,915],{},[852,4970,1258],{"stretchy":1251},[852,4972,1818],{},[856,4974,915],{},[748,4976,4977],{"encoding":750},"h \\ge \\log_2(n+1) - 1",[725,4979,4981,4999,5062,5083],{"className":4980,"ariaHidden":755},[754],[725,4982,4984,4987,4990,4993,4996],{"className":4983},[759],[725,4985],{"className":4986,"style":2834},[763],[725,4988,794],{"className":4989},[768,769],[725,4991],{"className":4992,"style":878},[877],[725,4994,3674],{"className":4995},[882],[725,4997],{"className":4998,"style":878},[877],[725,5000,5002,5005,5047,5050,5053,5056,5059],{"className":5001},[759],[725,5003],{"className":5004,"style":1383},[763],[725,5006,5008,5013],{"className":5007},[2022],[725,5009,2732,5011],{"className":5010},[2022],[725,5012,1334],{"style":2735},[725,5014,5016],{"className":5015},[1511],[725,5017,5019,5039],{"className":5018},[1445,1446],[725,5020,5022,5036],{"className":5021},[1450],[725,5023,5025],{"className":5024,"style":2748},[1454],[725,5026,5027,5030],{"style":2751},[725,5028],{"className":5029,"style":1528},[1462],[725,5031,5033],{"className":5032},[1532,1533,1534,1535],[725,5034,1164],{"className":5035},[768,1535],[725,5037,1544],{"className":5038},[1543],[725,5040,5042],{"className":5041},[1450],[725,5043,5045],{"className":5044,"style":2770},[1454],[725,5046],{},[725,5048,1252],{"className":5049},[1394],[725,5051,746],{"className":5052},[768,769],[725,5054],{"className":5055,"style":1485},[877],[725,5057,1310],{"className":5058},[1489],[725,5060],{"className":5061,"style":1485},[877],[725,5063,5065,5068,5071,5074,5077,5080],{"className":5064},[759],[725,5066],{"className":5067,"style":1383},[763],[725,5069,915],{"className":5070},[768],[725,5072,1258],{"className":5073},[1401],[725,5075],{"className":5076,"style":1485},[877],[725,5078,1818],{"className":5079},[1489],[725,5081],{"className":5082,"style":1485},[877],[725,5084,5086,5089],{"className":5085},[759],[725,5087],{"className":5088,"style":892},[763],[725,5090,915],{"className":5091},[768],", ce qui ferme\nl'équivalence annoncée. ",[725,5094,5096,5111],{"className":5095},[728],[725,5097,5099],{"className":5098},[732],[734,5100,5101],{"xmlns":736},[738,5102,5103,5108],{},[741,5104,5105],{},[744,5106,5107],{"mathvariant":1233},"■",[748,5109,5110],{"encoding":750},"\\blacksquare",[725,5112,5114],{"className":5113,"ariaHidden":755},[754],[725,5115,5117,5121],{"className":5116},[759],[725,5118],{"className":5119,"style":5120},[763],"height:0.675em;",[725,5122,5107],{"className":5123},[768,5124],"amsrm",[1206,5126,5128],{"id":5127},"conséquences","Conséquences",[1192,5130,5131,5285,5651],{},[1195,5132,5133,5134,5137,5138,5211,5212,949],{},"Un arbre ",[602,5135,5136],{},"filiforme"," (chaque nœud n'a qu'un seul enfant) atteint la borne\nbasse : ",[725,5139,5141,5163],{"className":5140},[728],[725,5142,5144],{"className":5143},[732],[734,5145,5146],{"xmlns":736},[738,5147,5148,5160],{},[741,5149,5150,5152,5154,5156,5158],{},[744,5151,746],{},[852,5153,854],{},[744,5155,794],{},[852,5157,1310],{},[856,5159,915],{},[748,5161,5162],{"encoding":750},"n = h + 1",[725,5164,5166,5184,5202],{"className":5165,"ariaHidden":755},[754],[725,5167,5169,5172,5175,5178,5181],{"className":5168},[759],[725,5170],{"className":5171,"style":764},[763],[725,5173,746],{"className":5174},[768,769],[725,5176],{"className":5177,"style":878},[877],[725,5179,854],{"className":5180},[882],[725,5182],{"className":5183,"style":878},[877],[725,5185,5187,5190,5193,5196,5199],{"className":5186},[759],[725,5188],{"className":5189,"style":2933},[763],[725,5191,794],{"className":5192},[768,769],[725,5194],{"className":5195,"style":1485},[877],[725,5197,1310],{"className":5198},[1489],[725,5200],{"className":5201,"style":1485},[877],[725,5203,5205,5208],{"className":5204},[759],[725,5206],{"className":5207,"style":892},[763],[725,5209,915],{"className":5210},[768],", donc ",[725,5213,5215,5237],{"className":5214},[728],[725,5216,5218],{"className":5217},[732],[734,5219,5220],{"xmlns":736},[738,5221,5222,5234],{},[741,5223,5224,5226,5228,5230,5232],{},[744,5225,794],{},[852,5227,854],{},[744,5229,746],{},[852,5231,1818],{},[856,5233,915],{},[748,5235,5236],{"encoding":750},"h = n - 1",[725,5238,5240,5258,5276],{"className":5239,"ariaHidden":755},[754],[725,5241,5243,5246,5249,5252,5255],{"className":5242},[759],[725,5244],{"className":5245,"style":806},[763],[725,5247,794],{"className":5248},[768,769],[725,5250],{"className":5251,"style":878},[877],[725,5253,854],{"className":5254},[882],[725,5256],{"className":5257,"style":878},[877],[725,5259,5261,5264,5267,5270,5273],{"className":5260},[759],[725,5262],{"className":5263,"style":2853},[763],[725,5265,746],{"className":5266},[768,769],[725,5268],{"className":5269,"style":1485},[877],[725,5271,1818],{"className":5272},[1489],[725,5274],{"className":5275,"style":1485},[877],[725,5277,5279,5282],{"className":5278},[759],[725,5280],{"className":5281,"style":892},[763],[725,5283,915],{"className":5284},[768],[1195,5286,5133,5287,5290,5291,5211,5409,5566,5567,949],{},[602,5288,5289],{},"parfaitement équilibré et complet"," atteint la borne haute :\n",[725,5292,5294,5326],{"className":5293},[728],[725,5295,5297],{"className":5296},[732],[734,5298,5299],{"xmlns":736},[738,5300,5301,5323],{},[741,5302,5303,5305,5307,5319,5321],{},[744,5304,746],{},[852,5306,854],{},[2905,5308,5309,5311],{},[856,5310,1164],{},[741,5312,5313,5315,5317],{},[744,5314,794],{},[852,5316,1310],{},[856,5318,915],{},[852,5320,1818],{},[856,5322,915],{},[748,5324,5325],{"encoding":750},"n = 2^{h+1} - 1",[725,5327,5329,5347,5400],{"className":5328,"ariaHidden":755},[754],[725,5330,5332,5335,5338,5341,5344],{"className":5331},[759],[725,5333],{"className":5334,"style":764},[763],[725,5336,746],{"className":5337},[768,769],[725,5339],{"className":5340,"style":878},[877],[725,5342,854],{"className":5343},[882],[725,5345],{"className":5346,"style":878},[877],[725,5348,5350,5353,5391,5394,5397],{"className":5349},[759],[725,5351],{"className":5352,"style":2989},[763],[725,5354,5356,5359],{"className":5355},[768],[725,5357,1164],{"className":5358},[768],[725,5360,5362],{"className":5361},[1511],[725,5363,5365],{"className":5364},[1445],[725,5366,5368],{"className":5367},[1450],[725,5369,5371],{"className":5370,"style":3008},[1454],[725,5372,5373,5376],{"style":3011},[725,5374],{"className":5375,"style":1528},[1462],[725,5377,5379],{"className":5378},[1532,1533,1534,1535],[725,5380,5382,5385,5388],{"className":5381},[768,1535],[725,5383,794],{"className":5384},[768,769,1535],[725,5386,1310],{"className":5387},[1489,1535],[725,5389,915],{"className":5390},[768,1535],[725,5392],{"className":5393,"style":1485},[877],[725,5395,1818],{"className":5396},[1489],[725,5398],{"className":5399,"style":1485},[877],[725,5401,5403,5406],{"className":5402},[759],[725,5404],{"className":5405,"style":892},[763],[725,5407,915],{"className":5408},[768],[725,5410,5412,5452],{"className":5411},[728],[725,5413,5415],{"className":5414},[732],[734,5416,5417],{"xmlns":736},[738,5418,5419,5449],{},[741,5420,5421,5423,5425,5435,5437,5439,5441,5443,5445,5447],{},[744,5422,794],{},[852,5424,854],{},[1328,5426,5427,5433],{},[741,5428,5429,5431],{},[744,5430,2682],{},[852,5432,1850],{},[856,5434,1164],{},[852,5436,1252],{"stretchy":1251},[744,5438,746],{},[852,5440,1310],{},[856,5442,915],{},[852,5444,1258],{"stretchy":1251},[852,5446,1818],{},[856,5448,915],{},[748,5450,5451],{"encoding":750},"h = \\log_2(n+1) - 1",[725,5453,5455,5473,5536,5557],{"className":5454,"ariaHidden":755},[754],[725,5456,5458,5461,5464,5467,5470],{"className":5457},[759],[725,5459],{"className":5460,"style":806},[763],[725,5462,794],{"className":5463},[768,769],[725,5465],{"className":5466,"style":878},[877],[725,5468,854],{"className":5469},[882],[725,5471],{"className":5472,"style":878},[877],[725,5474,5476,5479,5521,5524,5527,5530,5533],{"className":5475},[759],[725,5477],{"className":5478,"style":1383},[763],[725,5480,5482,5487],{"className":5481},[2022],[725,5483,2732,5485],{"className":5484},[2022],[725,5486,1334],{"style":2735},[725,5488,5490],{"className":5489},[1511],[725,5491,5493,5513],{"className":5492},[1445,1446],[725,5494,5496,5510],{"className":5495},[1450],[725,5497,5499],{"className":5498,"style":2748},[1454],[725,5500,5501,5504],{"style":2751},[725,5502],{"className":5503,"style":1528},[1462],[725,5505,5507],{"className":5506},[1532,1533,1534,1535],[725,5508,1164],{"className":5509},[768,1535],[725,5511,1544],{"className":5512},[1543],[725,5514,5516],{"className":5515},[1450],[725,5517,5519],{"className":5518,"style":2770},[1454],[725,5520],{},[725,5522,1252],{"className":5523},[1394],[725,5525,746],{"className":5526},[768,769],[725,5528],{"className":5529,"style":1485},[877],[725,5531,1310],{"className":5532},[1489],[725,5534],{"className":5535,"style":1485},[877],[725,5537,5539,5542,5545,5548,5551,5554],{"className":5538},[759],[725,5540],{"className":5541,"style":1383},[763],[725,5543,915],{"className":5544},[768],[725,5546,1258],{"className":5547},[1401],[725,5549],{"className":5550,"style":1485},[877],[725,5552,1818],{"className":5553},[1489],[725,5555],{"className":5556,"style":1485},[877],[725,5558,5560,5563],{"className":5559},[759],[725,5561],{"className":5562,"style":892},[763],[725,5564,915],{"className":5565},[768],", soit ",[725,5568,5570,5601],{"className":5569},[728],[725,5571,5573],{"className":5572},[732],[734,5574,5575],{"xmlns":736},[738,5576,5577,5598],{},[741,5578,5579,5581,5584,5588,5590,5592,5594,5596],{},[744,5580,794],{},[852,5582,5583],{},"∈",[744,5585,5587],{"mathvariant":5586},"script","O",[852,5589,1252],{"stretchy":1251},[744,5591,2682],{},[852,5593,1850],{},[744,5595,746],{},[852,5597,1258],{"stretchy":1251},[748,5599,5600],{"encoding":750},"h \\in \\mathcal{O}(\\log n)",[725,5602,5604,5623],{"className":5603,"ariaHidden":755},[754],[725,5605,5607,5611,5614,5617,5620],{"className":5606},[759],[725,5608],{"className":5609,"style":5610},[763],"height:0.7335em;vertical-align:-0.0391em;",[725,5612,794],{"className":5613},[768,769],[725,5615],{"className":5616,"style":878},[877],[725,5618,5583],{"className":5619},[882],[725,5621],{"className":5622,"style":878},[877],[725,5624,5626,5629,5634,5637,5642,5645,5648],{"className":5625},[759],[725,5627],{"className":5628,"style":1383},[763],[725,5630,5587],{"className":5631,"style":5633},[768,5632],"mathcal","margin-right:0.0278em;",[725,5635,1252],{"className":5636},[1394],[725,5638,2732,5640],{"className":5639},[2022],[725,5641,1334],{"style":2735},[725,5643],{"className":5644,"style":2085},[877],[725,5646,746],{"className":5647},[768,769],[725,5649,1258],{"className":5650},[1401],[1195,5652,5653,5654,5657,5658,5714,5715,949],{},"C'est pour cela que les structures arborescentes ",[602,5655,5656],{},"équilibrées"," sont\nrecherchées : leurs opérations sont en ",[725,5659,5661,5685],{"className":5660},[728],[725,5662,5664],{"className":5663},[732],[734,5665,5666],{"xmlns":736},[738,5667,5668,5682],{},[741,5669,5670,5672,5674,5676,5678,5680],{},[744,5671,5587],{"mathvariant":5586},[852,5673,1252],{"stretchy":1251},[744,5675,2682],{},[852,5677,1850],{},[744,5679,746],{},[852,5681,1258],{"stretchy":1251},[748,5683,5684],{"encoding":750},"\\mathcal{O}(\\log n)",[725,5686,5688],{"className":5687,"ariaHidden":755},[754],[725,5689,5691,5694,5697,5700,5705,5708,5711],{"className":5690},[759],[725,5692],{"className":5693,"style":1383},[763],[725,5695,5587],{"className":5696,"style":5633},[768,5632],[725,5698,1252],{"className":5699},[1394],[725,5701,2732,5703],{"className":5702},[2022],[725,5704,1334],{"style":2735},[725,5706],{"className":5707,"style":2085},[877],[725,5709,746],{"className":5710},[768,769],[725,5712,1258],{"className":5713},[1401]," au lieu de\n",[725,5716,5718,5738],{"className":5717},[728],[725,5719,5721],{"className":5720},[732],[734,5722,5723],{"xmlns":736},[738,5724,5725,5735],{},[741,5726,5727,5729,5731,5733],{},[744,5728,5587],{"mathvariant":5586},[852,5730,1252],{"stretchy":1251},[744,5732,746],{},[852,5734,1258],{"stretchy":1251},[748,5736,5737],{"encoding":750},"\\mathcal{O}(n)",[725,5739,5741],{"className":5740,"ariaHidden":755},[754],[725,5742,5744,5747,5750,5753,5756],{"className":5743},[759],[725,5745],{"className":5746,"style":1383},[763],[725,5748,5587],{"className":5749,"style":5633},[768,5632],[725,5751,1252],{"className":5752},[1394],[725,5754,746],{"className":5755},[768,769],[725,5757,1258],{"className":5758},[1401],[1180,5760,5762,5819],{"correct":915,"slug":5761},"arbres-binaires-c2",[1184,5763,5764],{"v-slot:question":968},[598,5765,5766,5767,5818],{},"Un arbre binaire de hauteur ",[725,5768,5770,5788],{"className":5769},[728],[725,5771,5773],{"className":5772},[732],[734,5774,5775],{"xmlns":736},[738,5776,5777,5785],{},[741,5778,5779,5781,5783],{},[744,5780,794],{},[852,5782,854],{},[856,5784,1175],{},[748,5786,5787],{"encoding":750},"h = 3",[725,5789,5791,5809],{"className":5790,"ariaHidden":755},[754],[725,5792,5794,5797,5800,5803,5806],{"className":5793},[759],[725,5795],{"className":5796,"style":806},[763],[725,5798,794],{"className":5799},[768,769],[725,5801],{"className":5802,"style":878},[877],[725,5804,854],{"className":5805},[882],[725,5807],{"className":5808,"style":878},[877],[725,5810,5812,5815],{"className":5811},[759],[725,5813],{"className":5814,"style":892},[763],[725,5816,1175],{"className":5817},[768]," contient au plus combien de nœuds ?",[1184,5820,5821],{"v-slot:choices":968},[1192,5822,5823,5826,5829],{},[1195,5824,5825],{},"7",[1195,5827,5828],{},"15",[1195,5830,5831],{},"8",[593,5833,5835],{"id":5834},"pour-aller-plus-loin","Pour aller plus loin",[598,5837,5838,5839,5894],{},"Les arbres binaires de recherche (ABR), les tas binaires et les arbres\néquilibrés (AVL, rouge-noir) exploitent cette propriété d'encadrement pour\ngarantir des opérations en ",[725,5840,5842,5865],{"className":5841},[728],[725,5843,5845],{"className":5844},[732],[734,5846,5847],{"xmlns":736},[738,5848,5849,5863],{},[741,5850,5851,5853,5855,5857,5859,5861],{},[744,5852,5587],{"mathvariant":5586},[852,5854,1252],{"stretchy":1251},[744,5856,2682],{},[852,5858,1850],{},[744,5860,746],{},[852,5862,1258],{"stretchy":1251},[748,5864,5684],{"encoding":750},[725,5866,5868],{"className":5867,"ariaHidden":755},[754],[725,5869,5871,5874,5877,5880,5885,5888,5891],{"className":5870},[759],[725,5872],{"className":5873,"style":1383},[763],[725,5875,5587],{"className":5876,"style":5633},[768,5632],[725,5878,1252],{"className":5879},[1394],[725,5881,2732,5883],{"className":5882},[2022],[725,5884,1334],{"style":2735},[725,5886],{"className":5887,"style":2085},[877],[725,5889,746],{"className":5890},[768,769],[725,5892,1258],{"className":5893},[1401],". Vous reviendrez sur certains\nd'entre eux au chapitre TE.",[629,5896],{"code":588},[5898,5899,5900],"style",{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}",{"title":968,"searchDepth":989,"depth":989,"links":5902},[5903,5904,5905,5906,5910,5914],{"id":595,"depth":989,"text":596},{"id":634,"depth":989,"text":635},{"id":952,"depth":989,"text":953},{"id":1203,"depth":989,"text":1204,"children":5907},[5908,5909],{"id":1208,"depth":996,"text":722},{"id":1760,"depth":996,"text":779},{"id":2475,"depth":989,"text":2476,"children":5911},[5912,5913],{"id":3050,"depth":996,"text":3051},{"id":5127,"depth":996,"text":5128},{"id":5834,"depth":989,"text":5835},"Structures hiérarchiques — vocabulaire, mesures, encadrement de la hauteur, classe Noeud en Python.",null,"md",{},[5920,5924],{"slug":1182,"kind":5921,"question":1188,"choices":5922,"correct":1164,"multi":5923,"explanation":968},"qcm",[915,1164,1175],false,{"slug":5761,"kind":5921,"question":5925,"choices":5926,"correct":915,"multi":5923,"explanation":968},"Un arbre binaire de hauteur h=3h = 3h=3 contient au plus combien de nœuds ?",[5825,5828,5831],{"title":469,"description":5915},"lfLNnwL1886RhYf98Gry79MIyqtEA4zlmRsjXulC3iw",{"id":5930,"title":5931,"bo":5932,"body":5933,"description":7407,"eval":5916,"extension":5917,"labo":5916,"meta":7408,"navigation":5923,"path":7409,"quizzes":7410,"readingTime":974,"seo":7411,"stem":7412,"tp":5916,"__hash__":7413},"coursMemo\u002F2.nsi-tale\u002Fta-structures-donnees\u002F4.arbres-binaires.memo.md","Arbres binaires — l'essentiel",[588],{"type":590,"value":5934,"toc":7400},[5935,5939,6163,6167,6902,6906,7226,7230,7246,7250,7397],[593,5936,5938],{"id":5937},"en-une-phrase","En une phrase",[598,5940,5941],{},[602,5942,5943,5944,5972,5973,6001,6002,949],{},"Un arbre binaire est une structure hiérarchique où chaque nœud a au plus deux enfants ; sa hauteur ",[725,5945,5947,5960],{"className":5946},[728],[725,5948,5950],{"className":5949},[732],[734,5951,5952],{"xmlns":736},[738,5953,5954,5958],{},[741,5955,5956],{},[744,5957,794],{},[748,5959,794],{"encoding":750},[725,5961,5963],{"className":5962,"ariaHidden":755},[754],[725,5964,5966,5969],{"className":5965},[759],[725,5967],{"className":5968,"style":806},[763],[725,5970,794],{"className":5971},[768,769]," et sa taille ",[725,5974,5976,5989],{"className":5975},[728],[725,5977,5979],{"className":5978},[732],[734,5980,5981],{"xmlns":736},[738,5982,5983,5987],{},[741,5984,5985],{},[744,5986,746],{},[748,5988,746],{"encoding":750},[725,5990,5992],{"className":5991,"ariaHidden":755},[754],[725,5993,5995,5998],{"className":5994},[759],[725,5996],{"className":5997,"style":764},[763],[725,5999,746],{"className":6000},[768,769]," sont liées par ",[725,6003,6005,6044],{"className":6004},[728],[725,6006,6008],{"className":6007},[732],[734,6009,6010],{"xmlns":736},[738,6011,6012,6042],{},[741,6013,6014,6016,6018,6020,6022,6024,6026,6038,6040],{},[744,6015,794],{},[852,6017,1310],{},[856,6019,915],{},[852,6021,2703],{},[744,6023,746],{},[852,6025,2703],{},[2905,6027,6028,6030],{},[856,6029,1164],{},[741,6031,6032,6034,6036],{},[744,6033,794],{},[852,6035,1310],{},[856,6037,915],{},[852,6039,1818],{},[856,6041,915],{},[748,6043,2923],{"encoding":750},[725,6045,6047,6065,6083,6101,6154],{"className":6046,"ariaHidden":755},[754],[725,6048,6050,6053,6056,6059,6062],{"className":6049},[759],[725,6051],{"className":6052,"style":2933},[763],[725,6054,794],{"className":6055},[768,769],[725,6057],{"className":6058,"style":1485},[877],[725,6060,1310],{"className":6061},[1489],[725,6063],{"className":6064,"style":1485},[877],[725,6066,6068,6071,6074,6077,6080],{"className":6067},[759],[725,6069],{"className":6070,"style":2815},[763],[725,6072,915],{"className":6073},[768],[725,6075],{"className":6076,"style":878},[877],[725,6078,2703],{"className":6079},[882],[725,6081],{"className":6082,"style":878},[877],[725,6084,6086,6089,6092,6095,6098],{"className":6085},[759],[725,6087],{"className":6088,"style":2970},[763],[725,6090,746],{"className":6091},[768,769],[725,6093],{"className":6094,"style":878},[877],[725,6096,2703],{"className":6097},[882],[725,6099],{"className":6100,"style":878},[877],[725,6102,6104,6107,6145,6148,6151],{"className":6103},[759],[725,6105],{"className":6106,"style":2989},[763],[725,6108,6110,6113],{"className":6109},[768],[725,6111,1164],{"className":6112},[768],[725,6114,6116],{"className":6115},[1511],[725,6117,6119],{"className":6118},[1445],[725,6120,6122],{"className":6121},[1450],[725,6123,6125],{"className":6124,"style":3008},[1454],[725,6126,6127,6130],{"style":3011},[725,6128],{"className":6129,"style":1528},[1462],[725,6131,6133],{"className":6132},[1532,1533,1534,1535],[725,6134,6136,6139,6142],{"className":6135},[768,1535],[725,6137,794],{"className":6138},[768,769,1535],[725,6140,1310],{"className":6141},[1489,1535],[725,6143,915],{"className":6144},[768,1535],[725,6146],{"className":6147,"style":1485},[877],[725,6149,1818],{"className":6150},[1489],[725,6152],{"className":6153,"style":1485},[877],[725,6155,6157,6160],{"className":6156},[759],[725,6158],{"className":6159,"style":892},[763],[725,6161,915],{"className":6162},[768],[593,6164,6166],{"id":6165},"à-mémoriser","À mémoriser",[1192,6168,6169,6178,6242,6302,6670],{},[1195,6170,6171,6173,6174,6177],{},[602,6172,672],{}," = nœud sans parent ; ",[602,6175,6176],{},"feuille"," = nœud sans enfant.",[1195,6179,6180,723,6182,6210,6211,723,6213,6241],{},[602,6181,722],{},[725,6183,6185,6198],{"className":6184},[728],[725,6186,6188],{"className":6187},[732],[734,6189,6190],{"xmlns":736},[738,6191,6192,6196],{},[741,6193,6194],{},[744,6195,746],{},[748,6197,746],{"encoding":750},[725,6199,6201],{"className":6200,"ariaHidden":755},[754],[725,6202,6204,6207],{"className":6203},[759],[725,6205],{"className":6206,"style":764},[763],[725,6208,746],{"className":6209},[768,769]," = nombre de nœuds ; ",[602,6212,1760],{},[725,6214,6216,6229],{"className":6215},[728],[725,6217,6219],{"className":6218},[732],[734,6220,6221],{"xmlns":736},[738,6222,6223,6227],{},[741,6224,6225],{},[744,6226,794],{},[748,6228,794],{"encoding":750},[725,6230,6232],{"className":6231,"ariaHidden":755},[754],[725,6233,6235,6238],{"className":6234},[759],[725,6236],{"className":6237,"style":806},[763],[725,6239,794],{"className":6240},[768,769]," = longueur du plus long chemin racine → feuille (en arêtes).",[1195,6243,6244,6245,6301],{},"Convention : arbre vide → ",[725,6246,6248,6268],{"className":6247},[728],[725,6249,6251],{"className":6250},[732],[734,6252,6253],{"xmlns":736},[738,6254,6255,6265],{},[741,6256,6257,6259,6261,6263],{},[744,6258,794],{},[852,6260,854],{},[852,6262,1818],{},[856,6264,915],{},[748,6266,6267],{"encoding":750},"h = -1",[725,6269,6271,6289],{"className":6270,"ariaHidden":755},[754],[725,6272,6274,6277,6280,6283,6286],{"className":6273},[759],[725,6275],{"className":6276,"style":806},[763],[725,6278,794],{"className":6279},[768,769],[725,6281],{"className":6282,"style":878},[877],[725,6284,854],{"className":6285},[882],[725,6287],{"className":6288,"style":878},[877],[725,6290,6292,6295,6298],{"className":6291},[759],[725,6293],{"className":6294,"style":2302},[763],[725,6296,1818],{"className":6297},[768],[725,6299,915],{"className":6300},[768],", taille = 0.",[1195,6303,6304,6307,6308,6469,6470,949],{},[602,6305,6306],{},"Encadrement"," : ",[725,6309,6311,6350],{"className":6310},[728],[725,6312,6314],{"className":6313},[732],[734,6315,6316],{"xmlns":736},[738,6317,6318,6348],{},[741,6319,6320,6322,6324,6326,6328,6330,6332,6344,6346],{},[744,6321,794],{},[852,6323,1310],{},[856,6325,915],{},[852,6327,2703],{},[744,6329,746],{},[852,6331,2703],{},[2905,6333,6334,6336],{},[856,6335,1164],{},[741,6337,6338,6340,6342],{},[744,6339,794],{},[852,6341,1310],{},[856,6343,915],{},[852,6345,1818],{},[856,6347,915],{},[748,6349,2923],{"encoding":750},[725,6351,6353,6371,6389,6407,6460],{"className":6352,"ariaHidden":755},[754],[725,6354,6356,6359,6362,6365,6368],{"className":6355},[759],[725,6357],{"className":6358,"style":2933},[763],[725,6360,794],{"className":6361},[768,769],[725,6363],{"className":6364,"style":1485},[877],[725,6366,1310],{"className":6367},[1489],[725,6369],{"className":6370,"style":1485},[877],[725,6372,6374,6377,6380,6383,6386],{"className":6373},[759],[725,6375],{"className":6376,"style":2815},[763],[725,6378,915],{"className":6379},[768],[725,6381],{"className":6382,"style":878},[877],[725,6384,2703],{"className":6385},[882],[725,6387],{"className":6388,"style":878},[877],[725,6390,6392,6395,6398,6401,6404],{"className":6391},[759],[725,6393],{"className":6394,"style":2970},[763],[725,6396,746],{"className":6397},[768,769],[725,6399],{"className":6400,"style":878},[877],[725,6402,2703],{"className":6403},[882],[725,6405],{"className":6406,"style":878},[877],[725,6408,6410,6413,6451,6454,6457],{"className":6409},[759],[725,6411],{"className":6412,"style":2989},[763],[725,6414,6416,6419],{"className":6415},[768],[725,6417,1164],{"className":6418},[768],[725,6420,6422],{"className":6421},[1511],[725,6423,6425],{"className":6424},[1445],[725,6426,6428],{"className":6427},[1450],[725,6429,6431],{"className":6430,"style":3008},[1454],[725,6432,6433,6436],{"style":3011},[725,6434],{"className":6435,"style":1528},[1462],[725,6437,6439],{"className":6438},[1532,1533,1534,1535],[725,6440,6442,6445,6448],{"className":6441},[768,1535],[725,6443,794],{"className":6444},[768,769,1535],[725,6446,1310],{"className":6447},[1489,1535],[725,6449,915],{"className":6450},[768,1535],[725,6452],{"className":6453,"style":1485},[877],[725,6455,1818],{"className":6456},[1489],[725,6458],{"className":6459,"style":1485},[877],[725,6461,6463,6466],{"className":6462},[759],[725,6464],{"className":6465,"style":892},[763],[725,6467,915],{"className":6468},[768],", ou ",[725,6471,6473,6520],{"className":6472},[728],[725,6474,6476],{"className":6475},[732],[734,6477,6478],{"xmlns":736},[738,6479,6480,6518],{},[741,6481,6482,6492,6494,6496,6498,6500,6502,6504,6506,6508,6510,6512,6514,6516],{},[1328,6483,6484,6490],{},[741,6485,6486,6488],{},[744,6487,2682],{},[852,6489,1850],{},[856,6491,1164],{},[852,6493,1252],{"stretchy":1251},[744,6495,746],{},[852,6497,1310],{},[856,6499,915],{},[852,6501,1258],{"stretchy":1251},[852,6503,1818],{},[856,6505,915],{},[852,6507,2703],{},[744,6509,794],{},[852,6511,2703],{},[744,6513,746],{},[852,6515,1818],{},[856,6517,915],{},[748,6519,2716],{"encoding":750},[725,6521,6523,6586,6607,6625,6643,6661],{"className":6522,"ariaHidden":755},[754],[725,6524,6526,6529,6571,6574,6577,6580,6583],{"className":6525},[759],[725,6527],{"className":6528,"style":1383},[763],[725,6530,6532,6537],{"className":6531},[2022],[725,6533,2732,6535],{"className":6534},[2022],[725,6536,1334],{"style":2735},[725,6538,6540],{"className":6539},[1511],[725,6541,6543,6563],{"className":6542},[1445,1446],[725,6544,6546,6560],{"className":6545},[1450],[725,6547,6549],{"className":6548,"style":2748},[1454],[725,6550,6551,6554],{"style":2751},[725,6552],{"className":6553,"style":1528},[1462],[725,6555,6557],{"className":6556},[1532,1533,1534,1535],[725,6558,1164],{"className":6559},[768,1535],[725,6561,1544],{"className":6562},[1543],[725,6564,6566],{"className":6565},[1450],[725,6567,6569],{"className":6568,"style":2770},[1454],[725,6570],{},[725,6572,1252],{"className":6573},[1394],[725,6575,746],{"className":6576},[768,769],[725,6578],{"className":6579,"style":1485},[877],[725,6581,1310],{"className":6582},[1489],[725,6584],{"className":6585,"style":1485},[877],[725,6587,6589,6592,6595,6598,6601,6604],{"className":6588},[759],[725,6590],{"className":6591,"style":1383},[763],[725,6593,915],{"className":6594},[768],[725,6596,1258],{"className":6597},[1401],[725,6599],{"className":6600,"style":1485},[877],[725,6602,1818],{"className":6603},[1489],[725,6605],{"className":6606,"style":1485},[877],[725,6608,6610,6613,6616,6619,6622],{"className":6609},[759],[725,6611],{"className":6612,"style":2815},[763],[725,6614,915],{"className":6615},[768],[725,6617],{"className":6618,"style":878},[877],[725,6620,2703],{"className":6621},[882],[725,6623],{"className":6624,"style":878},[877],[725,6626,6628,6631,6634,6637,6640],{"className":6627},[759],[725,6629],{"className":6630,"style":2834},[763],[725,6632,794],{"className":6633},[768,769],[725,6635],{"className":6636,"style":878},[877],[725,6638,2703],{"className":6639},[882],[725,6641],{"className":6642,"style":878},[877],[725,6644,6646,6649,6652,6655,6658],{"className":6645},[759],[725,6647],{"className":6648,"style":2853},[763],[725,6650,746],{"className":6651},[768,769],[725,6653],{"className":6654,"style":1485},[877],[725,6656,1818],{"className":6657},[1489],[725,6659],{"className":6660,"style":1485},[877],[725,6662,6664,6667],{"className":6663},[759],[725,6665],{"className":6666,"style":892},[763],[725,6668,915],{"className":6669},[768],[1195,6671,6672,6673,6745,6746,949],{},"Cas filiforme : ",[725,6674,6676,6697],{"className":6675},[728],[725,6677,6679],{"className":6678},[732],[734,6680,6681],{"xmlns":736},[738,6682,6683,6695],{},[741,6684,6685,6687,6689,6691,6693],{},[744,6686,794],{},[852,6688,854],{},[744,6690,746],{},[852,6692,1818],{},[856,6694,915],{},[748,6696,5236],{"encoding":750},[725,6698,6700,6718,6736],{"className":6699,"ariaHidden":755},[754],[725,6701,6703,6706,6709,6712,6715],{"className":6702},[759],[725,6704],{"className":6705,"style":806},[763],[725,6707,794],{"className":6708},[768,769],[725,6710],{"className":6711,"style":878},[877],[725,6713,854],{"className":6714},[882],[725,6716],{"className":6717,"style":878},[877],[725,6719,6721,6724,6727,6730,6733],{"className":6720},[759],[725,6722],{"className":6723,"style":2853},[763],[725,6725,746],{"className":6726},[768,769],[725,6728],{"className":6729,"style":1485},[877],[725,6731,1818],{"className":6732},[1489],[725,6734],{"className":6735,"style":1485},[877],[725,6737,6739,6742],{"className":6738},[759],[725,6740],{"className":6741,"style":892},[763],[725,6743,915],{"className":6744},[768]," ; cas parfait : ",[725,6747,6749,6788],{"className":6748},[728],[725,6750,6752],{"className":6751},[732],[734,6753,6754],{"xmlns":736},[738,6755,6756,6786],{},[741,6757,6758,6760,6762,6772,6774,6776,6778,6780,6782,6784],{},[744,6759,794],{},[852,6761,854],{},[1328,6763,6764,6770],{},[741,6765,6766,6768],{},[744,6767,2682],{},[852,6769,1850],{},[856,6771,1164],{},[852,6773,1252],{"stretchy":1251},[744,6775,746],{},[852,6777,1310],{},[856,6779,915],{},[852,6781,1258],{"stretchy":1251},[852,6783,1818],{},[856,6785,915],{},[748,6787,5451],{"encoding":750},[725,6789,6791,6809,6872,6893],{"className":6790,"ariaHidden":755},[754],[725,6792,6794,6797,6800,6803,6806],{"className":6793},[759],[725,6795],{"className":6796,"style":806},[763],[725,6798,794],{"className":6799},[768,769],[725,6801],{"className":6802,"style":878},[877],[725,6804,854],{"className":6805},[882],[725,6807],{"className":6808,"style":878},[877],[725,6810,6812,6815,6857,6860,6863,6866,6869],{"className":6811},[759],[725,6813],{"className":6814,"style":1383},[763],[725,6816,6818,6823],{"className":6817},[2022],[725,6819,2732,6821],{"className":6820},[2022],[725,6822,1334],{"style":2735},[725,6824,6826],{"className":6825},[1511],[725,6827,6829,6849],{"className":6828},[1445,1446],[725,6830,6832,6846],{"className":6831},[1450],[725,6833,6835],{"className":6834,"style":2748},[1454],[725,6836,6837,6840],{"style":2751},[725,6838],{"className":6839,"style":1528},[1462],[725,6841,6843],{"className":6842},[1532,1533,1534,1535],[725,6844,1164],{"className":6845},[768,1535],[725,6847,1544],{"className":6848},[1543],[725,6850,6852],{"className":6851},[1450],[725,6853,6855],{"className":6854,"style":2770},[1454],[725,6856],{},[725,6858,1252],{"className":6859},[1394],[725,6861,746],{"className":6862},[768,769],[725,6864],{"className":6865,"style":1485},[877],[725,6867,1310],{"className":6868},[1489],[725,6870],{"className":6871,"style":1485},[877],[725,6873,6875,6878,6881,6884,6887,6890],{"className":6874},[759],[725,6876],{"className":6877,"style":1383},[763],[725,6879,915],{"className":6880},[768],[725,6882,1258],{"className":6883},[1401],[725,6885],{"className":6886,"style":1485},[877],[725,6888,1818],{"className":6889},[1489],[725,6891],{"className":6892,"style":1485},[877],[725,6894,6896,6899],{"className":6895},[759],[725,6897],{"className":6898,"style":892},[763],[725,6900,915],{"className":6901},[768],[593,6903,6905],{"id":6904},"à-savoir-reconnaître","À savoir reconnaître",[637,6907,6908,6946],{},[640,6909,6910],{},[643,6911,6912,6915],{},[646,6913,6914],{},"Forme",[646,6916,6917,6918],{},"Hauteur en fonction de ",[725,6919,6921,6934],{"className":6920},[728],[725,6922,6924],{"className":6923},[732],[734,6925,6926],{"xmlns":736},[738,6927,6928,6932],{},[741,6929,6930],{},[744,6931,746],{},[748,6933,746],{"encoding":750},[725,6935,6937],{"className":6936,"ariaHidden":755},[754],[725,6938,6940,6943],{"className":6939},[759],[725,6941],{"className":6942,"style":764},[763],[725,6944,746],{"className":6945},[768,769],[653,6947,6948,7027,7142],{},[643,6949,6950,6953],{},[658,6951,6952],{},"Filiforme (peigne)",[658,6954,6955],{},[725,6956,6958,6979],{"className":6957},[728],[725,6959,6961],{"className":6960},[732],[734,6962,6963],{"xmlns":736},[738,6964,6965,6977],{},[741,6966,6967,6969,6971,6973,6975],{},[744,6968,794],{},[852,6970,854],{},[744,6972,746],{},[852,6974,1818],{},[856,6976,915],{},[748,6978,5236],{"encoding":750},[725,6980,6982,7000,7018],{"className":6981,"ariaHidden":755},[754],[725,6983,6985,6988,6991,6994,6997],{"className":6984},[759],[725,6986],{"className":6987,"style":806},[763],[725,6989,794],{"className":6990},[768,769],[725,6992],{"className":6993,"style":878},[877],[725,6995,854],{"className":6996},[882],[725,6998],{"className":6999,"style":878},[877],[725,7001,7003,7006,7009,7012,7015],{"className":7002},[759],[725,7004],{"className":7005,"style":2853},[763],[725,7007,746],{"className":7008},[768,769],[725,7010],{"className":7011,"style":1485},[877],[725,7013,1818],{"className":7014},[1489],[725,7016],{"className":7017,"style":1485},[877],[725,7019,7021,7024],{"className":7020},[759],[725,7022],{"className":7023,"style":892},[763],[725,7025,915],{"className":7026},[768],[643,7028,7029,7032],{},[658,7030,7031],{},"Parfaitement équilibré",[658,7033,7034],{},[725,7035,7037,7066],{"className":7036},[728],[725,7038,7040],{"className":7039},[732],[734,7041,7042],{"xmlns":736},[738,7043,7044,7063],{},[741,7045,7046,7048,7051,7061],{},[744,7047,794],{},[852,7049,7050],{},"≈",[1328,7052,7053,7059],{},[741,7054,7055,7057],{},[744,7056,2682],{},[852,7058,1850],{},[856,7060,1164],{},[744,7062,746],{},[748,7064,7065],{"encoding":750},"h \\approx \\log_2 n",[725,7067,7069,7087],{"className":7068,"ariaHidden":755},[754],[725,7070,7072,7075,7078,7081,7084],{"className":7071},[759],[725,7073],{"className":7074,"style":806},[763],[725,7076,794],{"className":7077},[768,769],[725,7079],{"className":7080,"style":878},[877],[725,7082,7050],{"className":7083},[882],[725,7085],{"className":7086,"style":878},[877],[725,7088,7090,7094,7136,7139],{"className":7089},[759],[725,7091],{"className":7092,"style":7093},[763],"height:0.9386em;vertical-align:-0.2441em;",[725,7095,7097,7102],{"className":7096},[2022],[725,7098,2732,7100],{"className":7099},[2022],[725,7101,1334],{"style":2735},[725,7103,7105],{"className":7104},[1511],[725,7106,7108,7128],{"className":7107},[1445,1446],[725,7109,7111,7125],{"className":7110},[1450],[725,7112,7114],{"className":7113,"style":2748},[1454],[725,7115,7116,7119],{"style":2751},[725,7117],{"className":7118,"style":1528},[1462],[725,7120,7122],{"className":7121},[1532,1533,1534,1535],[725,7123,1164],{"className":7124},[768,1535],[725,7126,1544],{"className":7127},[1543],[725,7129,7131],{"className":7130},[1450],[725,7132,7134],{"className":7133,"style":2770},[1454],[725,7135],{},[725,7137],{"className":7138,"style":2085},[877],[725,7140,746],{"className":7141},[768,769],[643,7143,7144,7147],{},[658,7145,7146],{},"Quelconque équilibré",[658,7148,7149],{},[725,7150,7152,7179],{"className":7151},[728],[725,7153,7155],{"className":7154},[732],[734,7156,7157],{"xmlns":736},[738,7158,7159,7177],{},[741,7160,7161,7163,7165,7167,7169,7171,7173,7175],{},[744,7162,794],{},[852,7164,5583],{},[744,7166,5587],{"mathvariant":5586},[852,7168,1252],{"stretchy":1251},[744,7170,2682],{},[852,7172,1850],{},[744,7174,746],{},[852,7176,1258],{"stretchy":1251},[748,7178,5600],{"encoding":750},[725,7180,7182,7200],{"className":7181,"ariaHidden":755},[754],[725,7183,7185,7188,7191,7194,7197],{"className":7184},[759],[725,7186],{"className":7187,"style":5610},[763],[725,7189,794],{"className":7190},[768,769],[725,7192],{"className":7193,"style":878},[877],[725,7195,5583],{"className":7196},[882],[725,7198],{"className":7199,"style":878},[877],[725,7201,7203,7206,7209,7212,7217,7220,7223],{"className":7202},[759],[725,7204],{"className":7205,"style":1383},[763],[725,7207,5587],{"className":7208,"style":5633},[768,5632],[725,7210,1252],{"className":7211},[1394],[725,7213,2732,7215],{"className":7214},[2022],[725,7216,1334],{"style":2735},[725,7218],{"className":7219,"style":2085},[877],[725,7221,746],{"className":7222},[768,769],[725,7224,1258],{"className":7225},[1401],[593,7227,7229],{"id":7228},"pièges-courants","Pièges courants",[1192,7231,7232,7235,7243],{},[1195,7233,7234],{},"Confondre hauteur en arêtes et en niveaux.",[1195,7236,7237,7238,7240,7241,949],{},"Oublier le cas vide dans la définition récursive de ",[958,7239,1208],{}," ou ",[958,7242,1760],{},[1195,7244,7245],{},"Croire qu'un arbre binaire est forcément équilibré.",[593,7247,7249],{"id":7248},"syntaxe-python","Syntaxe Python",[963,7251,7253],{"className":965,"code":7252,"language":967,"meta":968,"style":968},"class Noeud:\n    def __init__(self, valeur, gauche=None, droite=None):\n        self.valeur, self.gauche, self.droite = valeur, gauche, droite\n\ndef taille(n):\n    if n is None: return 0\n    return 1 + taille(n.gauche) + taille(n.droite)\n\ndef hauteur(n):\n    if n is None: return -1\n    return 1 + max(hauteur(n.gauche), hauteur(n.droite))\n",[958,7254,7255,7263,7283,7305,7309,7318,7337,7353,7357,7365,7383],{"__ignoreMap":968},[725,7256,7257,7259,7261],{"class":973,"line":974},[725,7258,978],{"class":977},[725,7260,982],{"class":981},[725,7262,986],{"class":985},[725,7264,7265,7267,7269,7271,7273,7275,7277,7279,7281],{"class":973,"line":989},[725,7266,1006],{"class":977},[725,7268,1010],{"class":1009},[725,7270,1013],{"class":985},[725,7272,854],{"class":977},[725,7274,960],{"class":1009},[725,7276,1020],{"class":985},[725,7278,854],{"class":977},[725,7280,960],{"class":1009},[725,7282,1027],{"class":985},[725,7284,7285,7287,7290,7293,7296,7298,7300,7302],{"class":973,"line":996},[725,7286,1033],{"class":1009},[725,7288,7289],{"class":985},".valeur, ",[725,7291,7292],{"class":1009},"self",[725,7294,7295],{"class":985},".gauche, ",[725,7297,7292],{"class":1009},[725,7299,1062],{"class":985},[725,7301,854],{"class":977},[725,7303,7304],{"class":985}," valeur, gauche, droite\n",[725,7306,7307],{"class":973,"line":1003},[725,7308,1000],{"emptyLinePlaceholder":999},[725,7310,7311,7313,7315],{"class":973,"line":1030},[725,7312,1711],{"class":977},[725,7314,1714],{"class":981},[725,7316,7317],{"class":985},"(n):\n",[725,7319,7320,7322,7325,7327,7329,7332,7335],{"class":973,"line":1044},[725,7321,1722],{"class":977},[725,7323,7324],{"class":985}," n ",[725,7326,1097],{"class":977},[725,7328,1100],{"class":1009},[725,7330,7331],{"class":985},": ",[725,7333,7334],{"class":977},"return",[725,7336,1738],{"class":1009},[725,7338,7339,7341,7343,7345,7348,7350],{"class":973,"line":1057},[725,7340,1743],{"class":977},[725,7342,1746],{"class":1009},[725,7344,1749],{"class":977},[725,7346,7347],{"class":985}," taille(n.gauche) ",[725,7349,1310],{"class":977},[725,7351,7352],{"class":985}," taille(n.droite)\n",[725,7354,7355],{"class":973,"line":1070},[725,7356,1000],{"emptyLinePlaceholder":999},[725,7358,7359,7361,7363],{"class":973,"line":1075},[725,7360,1711],{"class":977},[725,7362,2434],{"class":981},[725,7364,7317],{"class":985},[725,7366,7367,7369,7371,7373,7375,7377,7379,7381],{"class":973,"line":1086},[725,7368,1722],{"class":977},[725,7370,7324],{"class":985},[725,7372,1097],{"class":977},[725,7374,1100],{"class":1009},[725,7376,7331],{"class":985},[725,7378,7334],{"class":977},[725,7380,2455],{"class":977},[725,7382,2458],{"class":1009},[725,7384,7386,7388,7390,7392,7394],{"class":973,"line":7385},11,[725,7387,1743],{"class":977},[725,7389,1746],{"class":1009},[725,7391,1749],{"class":977},[725,7393,2469],{"class":1009},[725,7395,7396],{"class":985},"(hauteur(n.gauche), hauteur(n.droite))\n",[5898,7398,7399],{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":968,"searchDepth":989,"depth":989,"links":7401},[7402,7403,7404,7405,7406],{"id":5937,"depth":989,"text":5938},{"id":6165,"depth":989,"text":6166},{"id":6904,"depth":989,"text":6905},{"id":7228,"depth":989,"text":7229},{"id":7248,"depth":989,"text":7249},"Mémo de révision sur le vocabulaire, les mesures et l'encadrement de la hauteur.",{},"\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires.memo",[],{"title":5931,"description":7407},"2.nsi-tale\u002Fta-structures-donnees\u002F4.arbres-binaires.memo","ztZnJEcPgrCVKqDRlDm9M7Q2AbUA1oAJZEY0gXGKHvs",{"id":7415,"title":7416,"body":7417,"description":9287,"extension":5917,"meta":9288,"navigation":5923,"path":9289,"seo":9290,"stem":9291,"__hash__":9292},"coursSlides\u002F2.nsi-tale\u002Fta-structures-donnees\u002F4.arbres-binaires.slides.md","Arbres binaires — diapositives",{"type":590,"value":7418,"toc":9285},[7419,7423,7429,7432,7434,7457,7459,7466,7534,7541,7543,7547,7817,7860,7862,7866,8095,8220,8222,8224,8449,8451,8455,8462,8649,8651,8655,9272,9274,9278,9283],[7420,7421,469],"h1",{"id":7422},"arbres-binaires",[598,7424,7425,7426,7428],{},"Item ",[629,7427],{"code":588}," — Hiérarchies à deux enfants par nœud.",[7430,7431],"hr",{},[7420,7433,635],{"id":634},[1192,7435,7436,7441,7446,7451],{},[1195,7437,7438,7440],{},[602,7439,662],{}," : élément porteur d'une valeur.",[1195,7442,7443,7445],{},[602,7444,672],{}," : nœud unique sans parent.",[1195,7447,7448,7450],{},[602,7449,682],{}," : nœud sans enfant.",[1195,7452,7453,7456],{},[602,7454,7455],{},"Sous-arbres"," gauche et droit.",[7430,7458],{},[7420,7460,7462,7463],{"id":7461},"classe-noeud","Classe ",[958,7464,7465],{},"Noeud",[963,7467,7469],{"className":965,"code":7468,"language":967,"meta":968,"style":968},"class Noeud:\n    def __init__(self, v, g=None, d=None):\n        self.valeur = v\n        self.gauche = g\n        self.droite = d\n",[958,7470,7471,7479,7501,7512,7523],{"__ignoreMap":968},[725,7472,7473,7475,7477],{"class":973,"line":974},[725,7474,978],{"class":977},[725,7476,982],{"class":981},[725,7478,986],{"class":985},[725,7480,7481,7483,7485,7488,7490,7492,7495,7497,7499],{"class":973,"line":989},[725,7482,1006],{"class":977},[725,7484,1010],{"class":1009},[725,7486,7487],{"class":985},"(self, v, g",[725,7489,854],{"class":977},[725,7491,960],{"class":1009},[725,7493,7494],{"class":985},", d",[725,7496,854],{"class":977},[725,7498,960],{"class":1009},[725,7500,1027],{"class":985},[725,7502,7503,7505,7507,7509],{"class":973,"line":996},[725,7504,1033],{"class":1009},[725,7506,1036],{"class":985},[725,7508,854],{"class":977},[725,7510,7511],{"class":985}," v\n",[725,7513,7514,7516,7518,7520],{"class":973,"line":1003},[725,7515,1033],{"class":1009},[725,7517,1049],{"class":985},[725,7519,854],{"class":977},[725,7521,7522],{"class":985}," g\n",[725,7524,7525,7527,7529,7531],{"class":973,"line":1030},[725,7526,1033],{"class":1009},[725,7528,1062],{"class":985},[725,7530,854],{"class":977},[725,7532,7533],{"class":985}," d\n",[598,7535,7536,7537,5566,7539,949],{},"Un fils est soit un ",[958,7538,7465],{},[958,7540,960],{},[7430,7542],{},[7420,7544,7546],{"id":7545},"taille-définition-récursive","Taille — définition récursive",[598,7548,7549],{},[725,7550,7552,7640],{"className":7551},[728],[725,7553,7555],{"className":7554},[732],[734,7556,7557],{"xmlns":736},[738,7558,7559,7637],{},[741,7560,7561,7575,7577,7579,7581,7583,7585,7587,7601,7603,7609,7611,7613,7627,7629,7635],{},[741,7562,7563,7565,7567,7569,7571,7573],{},[744,7564,1234],{"mathvariant":1233},[744,7566,1237],{"mathvariant":1233},[744,7568,1240],{"mathvariant":1233},[744,7570,1243],{"mathvariant":1233},[744,7572,1243],{"mathvariant":1233},[744,7574,1248],{"mathvariant":1233},[852,7576,1252],{"stretchy":1251},[744,7578,1255],{},[852,7580,1258],{"stretchy":1251},[852,7582,854],{},[856,7584,915],{},[852,7586,1310],{},[741,7588,7589,7591,7593,7595,7597,7599],{},[744,7590,1234],{"mathvariant":1233},[744,7592,1237],{"mathvariant":1233},[744,7594,1240],{"mathvariant":1233},[744,7596,1243],{"mathvariant":1233},[744,7598,1243],{"mathvariant":1233},[744,7600,1248],{"mathvariant":1233},[852,7602,1252],{"stretchy":1251},[1328,7604,7605,7607],{},[744,7606,1255],{},[744,7608,1334],{},[852,7610,1258],{"stretchy":1251},[852,7612,1310],{},[741,7614,7615,7617,7619,7621,7623,7625],{},[744,7616,1234],{"mathvariant":1233},[744,7618,1237],{"mathvariant":1233},[744,7620,1240],{"mathvariant":1233},[744,7622,1243],{"mathvariant":1233},[744,7624,1243],{"mathvariant":1233},[744,7626,1248],{"mathvariant":1233},[852,7628,1252],{"stretchy":1251},[1328,7630,7631,7633],{},[744,7632,1255],{},[744,7634,1361],{},[852,7636,1258],{"stretchy":1251},[748,7638,7639],{"encoding":750},"\\mathrm{taille}(A) = 1 + \\mathrm{taille}(A_g) + \\mathrm{taille}(A_d)",[725,7641,7643,7673,7691,7759],{"className":7642,"ariaHidden":755},[754],[725,7644,7646,7649,7655,7658,7661,7664,7667,7670],{"className":7645},[759],[725,7647],{"className":7648,"style":1383},[763],[725,7650,7652],{"className":7651},[768],[725,7653,1208],{"className":7654},[768,1390],[725,7656,1252],{"className":7657},[1394],[725,7659,1255],{"className":7660},[768,769],[725,7662,1258],{"className":7663},[1401],[725,7665],{"className":7666,"style":878},[877],[725,7668,854],{"className":7669},[882],[725,7671],{"className":7672,"style":878},[877],[725,7674,7676,7679,7682,7685,7688],{"className":7675},[759],[725,7677],{"className":7678,"style":2302},[763],[725,7680,915],{"className":7681},[768],[725,7683],{"className":7684,"style":1485},[877],[725,7686,1310],{"className":7687},[1489],[725,7689],{"className":7690,"style":1485},[877],[725,7692,7694,7698,7704,7707,7747,7750,7753,7756],{"className":7693},[759],[725,7695],{"className":7696,"style":7697},[763],"height:1.0361em;vertical-align:-0.2861em;",[725,7699,7701],{"className":7700},[768],[725,7702,1208],{"className":7703},[768,1390],[725,7705,1252],{"className":7706},[1394],[725,7708,7710,7713],{"className":7709},[768],[725,7711,1255],{"className":7712},[768,769],[725,7714,7716],{"className":7715},[1511],[725,7717,7719,7739],{"className":7718},[1445,1446],[725,7720,7722,7736],{"className":7721},[1450],[725,7723,7725],{"className":7724,"style":1521},[1454],[725,7726,7727,7730],{"style":1524},[725,7728],{"className":7729,"style":1528},[1462],[725,7731,7733],{"className":7732},[1532,1533,1534,1535],[725,7734,1334],{"className":7735,"style":1539},[768,769,1535],[725,7737,1544],{"className":7738},[1543],[725,7740,7742],{"className":7741},[1450],[725,7743,7745],{"className":7744,"style":1551},[1454],[725,7746],{},[725,7748,1258],{"className":7749},[1401],[725,7751],{"className":7752,"style":1485},[877],[725,7754,1310],{"className":7755},[1489],[725,7757],{"className":7758,"style":1485},[877],[725,7760,7762,7765,7771,7774,7814],{"className":7761},[759],[725,7763],{"className":7764,"style":1383},[763],[725,7766,7768],{"className":7767},[768],[725,7769,1208],{"className":7770},[768,1390],[725,7772,1252],{"className":7773},[1394],[725,7775,7777,7780],{"className":7776},[768],[725,7778,1255],{"className":7779},[768,769],[725,7781,7783],{"className":7782},[1511],[725,7784,7786,7806],{"className":7785},[1445,1446],[725,7787,7789,7803],{"className":7788},[1450],[725,7790,7792],{"className":7791,"style":1593},[1454],[725,7793,7794,7797],{"style":1524},[725,7795],{"className":7796,"style":1528},[1462],[725,7798,7800],{"className":7799},[1532,1533,1534,1535],[725,7801,1361],{"className":7802},[768,769,1535],[725,7804,1544],{"className":7805},[1543],[725,7807,7809],{"className":7808},[1450],[725,7810,7812],{"className":7811,"style":1614},[1454],[725,7813],{},[725,7815,1258],{"className":7816},[1401],[963,7818,7820],{"className":965,"code":7819,"language":967,"meta":968,"style":968},"def taille(n):\n    if n is None: return 0\n    return 1 + taille(n.gauche) + taille(n.droite)\n",[958,7821,7822,7830,7846],{"__ignoreMap":968},[725,7823,7824,7826,7828],{"class":973,"line":974},[725,7825,1711],{"class":977},[725,7827,1714],{"class":981},[725,7829,7317],{"class":985},[725,7831,7832,7834,7836,7838,7840,7842,7844],{"class":973,"line":989},[725,7833,1722],{"class":977},[725,7835,7324],{"class":985},[725,7837,1097],{"class":977},[725,7839,1100],{"class":1009},[725,7841,7331],{"class":985},[725,7843,7334],{"class":977},[725,7845,1738],{"class":1009},[725,7847,7848,7850,7852,7854,7856,7858],{"class":973,"line":996},[725,7849,1743],{"class":977},[725,7851,1746],{"class":1009},[725,7853,1749],{"class":977},[725,7855,7347],{"class":985},[725,7857,1310],{"class":977},[725,7859,7352],{"class":985},[7430,7861],{},[7420,7863,7865],{"id":7864},"hauteur-définition-récursive","Hauteur — définition récursive",[598,7867,7868],{},[725,7869,7871,7931],{"className":7870},[728],[725,7872,7874],{"className":7873},[732],[734,7875,7876],{"xmlns":736},[738,7877,7878,7928],{},[741,7879,7880,7882,7884,7886,7888,7890,7892,7894,7896,7898,7900,7902,7904,7910,7912,7914,7916,7918,7924,7926],{},[744,7881,794],{},[852,7883,1252],{"stretchy":1251},[744,7885,1255],{},[852,7887,1258],{"stretchy":1251},[852,7889,854],{},[856,7891,915],{},[852,7893,1310],{},[744,7895,1847],{},[852,7897,1850],{},[852,7899,1252],{"stretchy":1251},[744,7901,794],{},[852,7903,1252],{"stretchy":1251},[1328,7905,7906,7908],{},[744,7907,1255],{},[744,7909,1334],{},[852,7911,1258],{"stretchy":1251},[852,7913,1881],{"separator":755},[744,7915,794],{},[852,7917,1252],{"stretchy":1251},[1328,7919,7920,7922],{},[744,7921,1255],{},[744,7923,1361],{},[852,7925,1258],{"stretchy":1251},[852,7927,1258],{"stretchy":1251},[748,7929,7930],{"encoding":750},"h(A) = 1 + \\max(h(A_g), h(A_d))",[725,7932,7934,7961,7979],{"className":7933,"ariaHidden":755},[754],[725,7935,7937,7940,7943,7946,7949,7952,7955,7958],{"className":7936},[759],[725,7938],{"className":7939,"style":1383},[763],[725,7941,794],{"className":7942},[768,769],[725,7944,1252],{"className":7945},[1394],[725,7947,1255],{"className":7948},[768,769],[725,7950,1258],{"className":7951},[1401],[725,7953],{"className":7954,"style":878},[877],[725,7956,854],{"className":7957},[882],[725,7959],{"className":7960,"style":878},[877],[725,7962,7964,7967,7970,7973,7976],{"className":7963},[759],[725,7965],{"className":7966,"style":2302},[763],[725,7968,915],{"className":7969},[768],[725,7971],{"className":7972,"style":1485},[877],[725,7974,1310],{"className":7975},[1489],[725,7977],{"className":7978,"style":1485},[877],[725,7980,7982,7985,7988,7991,7994,7997,8037,8040,8043,8046,8049,8052,8092],{"className":7981},[759],[725,7983],{"className":7984,"style":7697},[763],[725,7986,1847],{"className":7987},[2022],[725,7989,1252],{"className":7990},[1394],[725,7992,794],{"className":7993},[768,769],[725,7995,1252],{"className":7996},[1394],[725,7998,8000,8003],{"className":7999},[768],[725,8001,1255],{"className":8002},[768,769],[725,8004,8006],{"className":8005},[1511],[725,8007,8009,8029],{"className":8008},[1445,1446],[725,8010,8012,8026],{"className":8011},[1450],[725,8013,8015],{"className":8014,"style":1521},[1454],[725,8016,8017,8020],{"style":1524},[725,8018],{"className":8019,"style":1528},[1462],[725,8021,8023],{"className":8022},[1532,1533,1534,1535],[725,8024,1334],{"className":8025,"style":1539},[768,769,1535],[725,8027,1544],{"className":8028},[1543],[725,8030,8032],{"className":8031},[1450],[725,8033,8035],{"className":8034,"style":1551},[1454],[725,8036],{},[725,8038,1258],{"className":8039},[1401],[725,8041,1881],{"className":8042},[2081],[725,8044],{"className":8045,"style":2085},[877],[725,8047,794],{"className":8048},[768,769],[725,8050,1252],{"className":8051},[1394],[725,8053,8055,8058],{"className":8054},[768],[725,8056,1255],{"className":8057},[768,769],[725,8059,8061],{"className":8060},[1511],[725,8062,8064,8084],{"className":8063},[1445,1446],[725,8065,8067,8081],{"className":8066},[1450],[725,8068,8070],{"className":8069,"style":1593},[1454],[725,8071,8072,8075],{"style":1524},[725,8073],{"className":8074,"style":1528},[1462],[725,8076,8078],{"className":8077},[1532,1533,1534,1535],[725,8079,1361],{"className":8080},[768,769,1535],[725,8082,1544],{"className":8083},[1543],[725,8085,8087],{"className":8086},[1450],[725,8088,8090],{"className":8089,"style":1614},[1454],[725,8091],{},[725,8093,2138],{"className":8094},[1401],[598,8096,8097,8098,8169,8170,949],{},"Convention : ",[725,8099,8101,8127],{"className":8100},[728],[725,8102,8104],{"className":8103},[732],[734,8105,8106],{"xmlns":736},[738,8107,8108,8124],{},[741,8109,8110,8112,8114,8116,8118,8120,8122],{},[744,8111,794],{},[852,8113,1252],{"stretchy":1251},[744,8115,2251],{"mathvariant":1233},[852,8117,1258],{"stretchy":1251},[852,8119,854],{},[852,8121,1818],{},[856,8123,915],{},[748,8125,8126],{"encoding":750},"h(\\emptyset) = -1",[725,8128,8130,8157],{"className":8129,"ariaHidden":755},[754],[725,8131,8133,8136,8139,8142,8145,8148,8151,8154],{"className":8132},[759],[725,8134],{"className":8135,"style":1383},[763],[725,8137,794],{"className":8138},[768,769],[725,8140,1252],{"className":8141},[1394],[725,8143,2251],{"className":8144},[768],[725,8146,1258],{"className":8147},[1401],[725,8149],{"className":8150,"style":878},[877],[725,8152,854],{"className":8153},[882],[725,8155],{"className":8156,"style":878},[877],[725,8158,8160,8163,8166],{"className":8159},[759],[725,8161],{"className":8162,"style":2302},[763],[725,8164,1818],{"className":8165},[768],[725,8167,915],{"className":8168},[768],", racine seule → ",[725,8171,8173,8190],{"className":8172},[728],[725,8174,8176],{"className":8175},[732],[734,8177,8178],{"xmlns":736},[738,8179,8180,8188],{},[741,8181,8182,8184,8186],{},[744,8183,794],{},[852,8185,854],{},[856,8187,858],{},[748,8189,861],{"encoding":750},[725,8191,8193,8211],{"className":8192,"ariaHidden":755},[754],[725,8194,8196,8199,8202,8205,8208],{"className":8195},[759],[725,8197],{"className":8198,"style":806},[763],[725,8200,794],{"className":8201},[768,769],[725,8203],{"className":8204,"style":878},[877],[725,8206,854],{"className":8207},[882],[725,8209],{"className":8210,"style":878},[877],[725,8212,8214,8217],{"className":8213},[759],[725,8215],{"className":8216,"style":892},[763],[725,8218,858],{"className":8219},[768],[7430,8221],{},[7420,8223,2476],{"id":2475},[2597,8225,8226,8286],{"title":2600},[598,8227,8228,8229,8257,8258,2661],{},"Pour tout arbre binaire de taille ",[725,8230,8232,8245],{"className":8231},[728],[725,8233,8235],{"className":8234},[732],[734,8236,8237],{"xmlns":736},[738,8238,8239,8243],{},[741,8240,8241],{},[744,8242,746],{},[748,8244,746],{"encoding":750},[725,8246,8248],{"className":8247,"ariaHidden":755},[754],[725,8249,8251,8254],{"className":8250},[759],[725,8252],{"className":8253,"style":764},[763],[725,8255,746],{"className":8256},[768,769]," et hauteur ",[725,8259,8261,8274],{"className":8260},[728],[725,8262,8264],{"className":8263},[732],[734,8265,8266],{"xmlns":736},[738,8267,8268,8272],{},[741,8269,8270],{},[744,8271,794],{},[748,8273,794],{"encoding":750},[725,8275,8277],{"className":8276,"ariaHidden":755},[754],[725,8278,8280,8283],{"className":8279},[759],[725,8281],{"className":8282,"style":806},[763],[725,8284,794],{"className":8285},[768,769],[598,8287,8288],{},[725,8289,8291,8330],{"className":8290},[728],[725,8292,8294],{"className":8293},[732],[734,8295,8296],{"xmlns":736},[738,8297,8298,8328],{},[741,8299,8300,8302,8304,8306,8308,8310,8312,8324,8326],{},[744,8301,794],{},[852,8303,1310],{},[856,8305,915],{},[852,8307,2703],{},[744,8309,746],{},[852,8311,2703],{},[2905,8313,8314,8316],{},[856,8315,1164],{},[741,8317,8318,8320,8322],{},[744,8319,794],{},[852,8321,1310],{},[856,8323,915],{},[852,8325,1818],{},[856,8327,915],{},[748,8329,2923],{"encoding":750},[725,8331,8333,8351,8369,8387,8440],{"className":8332,"ariaHidden":755},[754],[725,8334,8336,8339,8342,8345,8348],{"className":8335},[759],[725,8337],{"className":8338,"style":2933},[763],[725,8340,794],{"className":8341},[768,769],[725,8343],{"className":8344,"style":1485},[877],[725,8346,1310],{"className":8347},[1489],[725,8349],{"className":8350,"style":1485},[877],[725,8352,8354,8357,8360,8363,8366],{"className":8353},[759],[725,8355],{"className":8356,"style":2815},[763],[725,8358,915],{"className":8359},[768],[725,8361],{"className":8362,"style":878},[877],[725,8364,2703],{"className":8365},[882],[725,8367],{"className":8368,"style":878},[877],[725,8370,8372,8375,8378,8381,8384],{"className":8371},[759],[725,8373],{"className":8374,"style":2970},[763],[725,8376,746],{"className":8377},[768,769],[725,8379],{"className":8380,"style":878},[877],[725,8382,2703],{"className":8383},[882],[725,8385],{"className":8386,"style":878},[877],[725,8388,8390,8393,8431,8434,8437],{"className":8389},[759],[725,8391],{"className":8392,"style":2989},[763],[725,8394,8396,8399],{"className":8395},[768],[725,8397,1164],{"className":8398},[768],[725,8400,8402],{"className":8401},[1511],[725,8403,8405],{"className":8404},[1445],[725,8406,8408],{"className":8407},[1450],[725,8409,8411],{"className":8410,"style":3008},[1454],[725,8412,8413,8416],{"style":3011},[725,8414],{"className":8415,"style":1528},[1462],[725,8417,8419],{"className":8418},[1532,1533,1534,1535],[725,8420,8422,8425,8428],{"className":8421},[768,1535],[725,8423,794],{"className":8424},[768,769,1535],[725,8426,1310],{"className":8427},[1489,1535],[725,8429,915],{"className":8430},[768,1535],[725,8432],{"className":8433,"style":1485},[877],[725,8435,1818],{"className":8436},[1489],[725,8438],{"className":8439,"style":1485},[877],[725,8441,8443,8446],{"className":8442},[759],[725,8444],{"className":8445,"style":892},[763],[725,8447,915],{"className":8448},[768],[7430,8450],{},[7420,8452,8454],{"id":8453},"cas-extrêmes","Cas extrêmes",[8456,8457],"illustration",{"alt":8458,"kind":8459,"src":8460,"svg":8461},"Deux arbres binaires à 7 nœuds côte à côte : à gauche un arbre filiforme (peigne) de hauteur 6, à droite un arbre parfaitement équilibré de hauteur 2.","schema","\u002Fillustrations\u002F2.nsi-tale\u002Fta-structures-donnees\u002Farbres-degenere-equilibre.svg","\u003Csvg class=\"illustration-svg\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 480 320\" role=\"img\" aria-label=\"Deux arbres binaires de 7 nœuds côte à côte : à gauche un arbre filiforme (peigne) en escalier de hauteur 6 ; à droite un arbre parfaitement équilibré de hauteur 2\">\n  \u003Ctitle>Arbre filiforme (h = 6) vs arbre équilibré (h = 2)\u003C\u002Ftitle>\n  \u003Cstyle>\n    .ab-svg { font-family: Geist, Inter, system-ui, sans-serif; }\n    .ab-title  { fill: var(--diagram-text); font-size: 13px; font-weight: 600; }\n    .ab-sub    { fill: var(--diagram-line); font-family: 'JetBrains Mono', monospace; font-size: 11px; }\n    .ab-edge   { stroke: var(--diagram-line); stroke-width: 1.5; }\n    .ab-node   { fill: var(--diagram-node-bg); stroke: var(--diagram-node-border); stroke-width: 1.5; }\n    .ab-divider{ stroke: var(--diagram-border); stroke-width: 1.5; stroke-dasharray: 4 4; }\n  \u003C\u002Fstyle>\n\n  \u003Cg class=\"ab-svg\">\n    \u003Cline x1=\"240\" y1=\"40\" x2=\"240\" y2=\"300\" class=\"ab-divider\"\u002F>\n\n    \u003C!-- GAUCHE : peigne filiforme, hauteur 6 (7 nœuds en escalier) -->\n    \u003Ctext x=\"120\" y=\"26\" text-anchor=\"middle\" class=\"ab-title\">Filiforme (peigne)\u003C\u002Ftext>\n    \u003Ctext x=\"120\" y=\"44\" text-anchor=\"middle\" class=\"ab-sub\">h = 6\u003C\u002Ftext>\n\n    \u003C!-- arêtes en escalier -->\n    \u003Cline x1=\"60\"  y1=\"68\"  x2=\"80\"  y2=\"104\" class=\"ab-edge\"\u002F>\n    \u003Cline x1=\"80\"  y1=\"104\" x2=\"100\" y2=\"140\" class=\"ab-edge\"\u002F>\n    \u003Cline x1=\"100\" y1=\"140\" x2=\"120\" y2=\"176\" class=\"ab-edge\"\u002F>\n    \u003Cline x1=\"120\" y1=\"176\" x2=\"140\" y2=\"212\" class=\"ab-edge\"\u002F>\n    \u003Cline x1=\"140\" y1=\"212\" x2=\"160\" y2=\"248\" class=\"ab-edge\"\u002F>\n    \u003Cline x1=\"160\" y1=\"248\" x2=\"180\" y2=\"284\" class=\"ab-edge\"\u002F>\n    \u003C!-- nœuds -->\n    \u003Ccircle cx=\"60\"  cy=\"68\"  r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"80\"  cy=\"104\" r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"100\" cy=\"140\" r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"120\" cy=\"176\" r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"140\" cy=\"212\" r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"160\" cy=\"248\" r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"180\" cy=\"284\" r=\"11\" class=\"ab-node\"\u002F>\n\n    \u003C!-- DROITE : arbre parfait, hauteur 2 (7 nœuds) -->\n    \u003Ctext x=\"360\" y=\"26\" text-anchor=\"middle\" class=\"ab-title\">Équilibré (parfait)\u003C\u002Ftext>\n    \u003Ctext x=\"360\" y=\"44\" text-anchor=\"middle\" class=\"ab-sub\">h = 2\u003C\u002Ftext>\n\n    \u003C!-- niveau 0 → 1 -->\n    \u003Cline x1=\"360\" y1=\"80\"  x2=\"312\" y2=\"150\" class=\"ab-edge\"\u002F>\n    \u003Cline x1=\"360\" y1=\"80\"  x2=\"408\" y2=\"150\" class=\"ab-edge\"\u002F>\n    \u003C!-- niveau 1 → 2 -->\n    \u003Cline x1=\"312\" y1=\"150\" x2=\"288\" y2=\"220\" class=\"ab-edge\"\u002F>\n    \u003Cline x1=\"312\" y1=\"150\" x2=\"336\" y2=\"220\" class=\"ab-edge\"\u002F>\n    \u003Cline x1=\"408\" y1=\"150\" x2=\"384\" y2=\"220\" class=\"ab-edge\"\u002F>\n    \u003Cline x1=\"408\" y1=\"150\" x2=\"432\" y2=\"220\" class=\"ab-edge\"\u002F>\n    \u003C!-- nœuds -->\n    \u003Ccircle cx=\"360\" cy=\"80\"  r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"312\" cy=\"150\" r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"408\" cy=\"150\" r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"288\" cy=\"220\" r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"336\" cy=\"220\" r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"384\" cy=\"220\" r=\"11\" class=\"ab-node\"\u002F>\n    \u003Ccircle cx=\"432\" cy=\"220\" r=\"11\" class=\"ab-node\"\u002F>\n  \u003C\u002Fg>\n\u003C\u002Fsvg>\n",[1192,8463,8464,8540],{},[1195,8465,8466,8467,8539],{},"Filiforme : ",[725,8468,8470,8491],{"className":8469},[728],[725,8471,8473],{"className":8472},[732],[734,8474,8475],{"xmlns":736},[738,8476,8477,8489],{},[741,8478,8479,8481,8483,8485,8487],{},[744,8480,794],{},[852,8482,854],{},[744,8484,746],{},[852,8486,1818],{},[856,8488,915],{},[748,8490,5236],{"encoding":750},[725,8492,8494,8512,8530],{"className":8493,"ariaHidden":755},[754],[725,8495,8497,8500,8503,8506,8509],{"className":8496},[759],[725,8498],{"className":8499,"style":806},[763],[725,8501,794],{"className":8502},[768,769],[725,8504],{"className":8505,"style":878},[877],[725,8507,854],{"className":8508},[882],[725,8510],{"className":8511,"style":878},[877],[725,8513,8515,8518,8521,8524,8527],{"className":8514},[759],[725,8516],{"className":8517,"style":2853},[763],[725,8519,746],{"className":8520},[768,769],[725,8522],{"className":8523,"style":1485},[877],[725,8525,1818],{"className":8526},[1489],[725,8528],{"className":8529,"style":1485},[877],[725,8531,8533,8536],{"className":8532},[759],[725,8534],{"className":8535,"style":892},[763],[725,8537,915],{"className":8538},[768]," (linéaire).",[1195,8541,8542,8543,8648],{},"Parfait : ",[725,8544,8546,8573],{"className":8545},[728],[725,8547,8549],{"className":8548},[732],[734,8550,8551],{"xmlns":736},[738,8552,8553,8571],{},[741,8554,8555,8557,8559,8569],{},[744,8556,794],{},[852,8558,7050],{},[1328,8560,8561,8567],{},[741,8562,8563,8565],{},[744,8564,2682],{},[852,8566,1850],{},[856,8568,1164],{},[744,8570,746],{},[748,8572,7065],{"encoding":750},[725,8574,8576,8594],{"className":8575,"ariaHidden":755},[754],[725,8577,8579,8582,8585,8588,8591],{"className":8578},[759],[725,8580],{"className":8581,"style":806},[763],[725,8583,794],{"className":8584},[768,769],[725,8586],{"className":8587,"style":878},[877],[725,8589,7050],{"className":8590},[882],[725,8592],{"className":8593,"style":878},[877],[725,8595,8597,8600,8642,8645],{"className":8596},[759],[725,8598],{"className":8599,"style":7093},[763],[725,8601,8603,8608],{"className":8602},[2022],[725,8604,2732,8606],{"className":8605},[2022],[725,8607,1334],{"style":2735},[725,8609,8611],{"className":8610},[1511],[725,8612,8614,8634],{"className":8613},[1445,1446],[725,8615,8617,8631],{"className":8616},[1450],[725,8618,8620],{"className":8619,"style":2748},[1454],[725,8621,8622,8625],{"style":2751},[725,8623],{"className":8624,"style":1528},[1462],[725,8626,8628],{"className":8627},[1532,1533,1534,1535],[725,8629,1164],{"className":8630},[768,1535],[725,8632,1544],{"className":8633},[1543],[725,8635,8637],{"className":8636},[1450],[725,8638,8640],{"className":8639,"style":2770},[1454],[725,8641],{},[725,8643],{"className":8644,"style":2085},[877],[725,8646,746],{"className":8647},[768,769]," (logarithmique).",[7430,8650],{},[7420,8652,8654],{"id":8653},"preuve-par-récurrence-esquisse","Preuve par récurrence (esquisse)",[1192,8656,8657,8765],{},[1195,8658,8659,723,8662,6307,8713,8764],{},[602,8660,8661],{},"Init",[725,8663,8665,8683],{"className":8664},[728],[725,8666,8668],{"className":8667},[732],[734,8669,8670],{"xmlns":736},[738,8671,8672,8680],{},[741,8673,8674,8676,8678],{},[744,8675,794],{},[852,8677,854],{},[856,8679,858],{},[748,8681,8682],{"encoding":750},"h=0",[725,8684,8686,8704],{"className":8685,"ariaHidden":755},[754],[725,8687,8689,8692,8695,8698,8701],{"className":8688},[759],[725,8690],{"className":8691,"style":806},[763],[725,8693,794],{"className":8694},[768,769],[725,8696],{"className":8697,"style":878},[877],[725,8699,854],{"className":8700},[882],[725,8702],{"className":8703,"style":878},[877],[725,8705,8707,8710],{"className":8706},[759],[725,8708],{"className":8709,"style":892},[763],[725,8711,858],{"className":8712},[768],[725,8714,8716,8734],{"className":8715},[728],[725,8717,8719],{"className":8718},[732],[734,8720,8721],{"xmlns":736},[738,8722,8723,8731],{},[741,8724,8725,8727,8729],{},[744,8726,746],{},[852,8728,854],{},[856,8730,915],{},[748,8732,8733],{"encoding":750},"n=1",[725,8735,8737,8755],{"className":8736,"ariaHidden":755},[754],[725,8738,8740,8743,8746,8749,8752],{"className":8739},[759],[725,8741],{"className":8742,"style":764},[763],[725,8744,746],{"className":8745},[768,769],[725,8747],{"className":8748,"style":878},[877],[725,8750,854],{"className":8751},[882],[725,8753],{"className":8754,"style":878},[877],[725,8756,8758,8761],{"className":8757},[759],[725,8759],{"className":8760,"style":892},[763],[725,8762,915],{"className":8763},[768],", OK.",[1195,8766,8767,8770,8771,5211,8822,5566,8873,8946,8947,9042,9043,949],{},[602,8768,8769],{},"Hérédité"," : un sous-arbre atteint ",[725,8772,8774,8792],{"className":8773},[728],[725,8775,8777],{"className":8776},[732],[734,8778,8779],{"xmlns":736},[738,8780,8781,8789],{},[741,8782,8783,8785,8787],{},[744,8784,794],{},[852,8786,1818],{},[856,8788,915],{},[748,8790,8791],{"encoding":750},"h-1",[725,8793,8795,8813],{"className":8794,"ariaHidden":755},[754],[725,8796,8798,8801,8804,8807,8810],{"className":8797},[759],[725,8799],{"className":8800,"style":2933},[763],[725,8802,794],{"className":8803},[768,769],[725,8805],{"className":8806,"style":1485},[877],[725,8808,1818],{"className":8809},[1489],[725,8811],{"className":8812,"style":1485},[877],[725,8814,8816,8819],{"className":8815},[759],[725,8817],{"className":8818,"style":892},[763],[725,8820,915],{"className":8821},[768],[725,8823,8825,8843],{"className":8824},[728],[725,8826,8828],{"className":8827},[732],[734,8829,8830],{"xmlns":736},[738,8831,8832,8840],{},[741,8833,8834,8836,8838],{},[744,8835,746],{},[852,8837,3674],{},[744,8839,794],{},[748,8841,8842],{"encoding":750},"n \\ge h",[725,8844,8846,8864],{"className":8845,"ariaHidden":755},[754],[725,8847,8849,8852,8855,8858,8861],{"className":8848},[759],[725,8850],{"className":8851,"style":2970},[763],[725,8853,746],{"className":8854},[768,769],[725,8856],{"className":8857,"style":878},[877],[725,8859,3674],{"className":8860},[882],[725,8862],{"className":8863,"style":878},[877],[725,8865,8867,8870],{"className":8866},[759],[725,8868],{"className":8869,"style":806},[763],[725,8871,794],{"className":8872},[768,769],[725,8874,8876,8898],{"className":8875},[728],[725,8877,8879],{"className":8878},[732],[734,8880,8881],{"xmlns":736},[738,8882,8883,8895],{},[741,8884,8885,8887,8889,8891,8893],{},[744,8886,746],{},[852,8888,3674],{},[744,8890,794],{},[852,8892,1310],{},[856,8894,915],{},[748,8896,8897],{"encoding":750},"n \\ge h+1",[725,8899,8901,8919,8937],{"className":8900,"ariaHidden":755},[754],[725,8902,8904,8907,8910,8913,8916],{"className":8903},[759],[725,8905],{"className":8906,"style":2970},[763],[725,8908,746],{"className":8909},[768,769],[725,8911],{"className":8912,"style":878},[877],[725,8914,3674],{"className":8915},[882],[725,8917],{"className":8918,"style":878},[877],[725,8920,8922,8925,8928,8931,8934],{"className":8921},[759],[725,8923],{"className":8924,"style":2933},[763],[725,8926,794],{"className":8927},[768,769],[725,8929],{"className":8930,"style":1485},[877],[725,8932,1310],{"className":8933},[1489],[725,8935],{"className":8936,"style":1485},[877],[725,8938,8940,8943],{"className":8939},[759],[725,8941],{"className":8942,"style":892},[763],[725,8944,915],{"className":8945},[768],". Et chaque sous-arbre a ",[725,8948,8950,8974],{"className":8949},[728],[725,8951,8953],{"className":8952},[732],[734,8954,8955],{"xmlns":736},[738,8956,8957,8971],{},[741,8958,8959,8961,8967,8969],{},[852,8960,2703],{},[2905,8962,8963,8965],{},[856,8964,1164],{},[744,8966,794],{},[852,8968,1818],{},[856,8970,915],{},[748,8972,8973],{"encoding":750},"\\le 2^h - 1",[725,8975,8977,8989,9033],{"className":8976,"ariaHidden":755},[754],[725,8978,8980,8983,8986],{"className":8979},[759],[725,8981],{"className":8982,"style":2970},[763],[725,8984,2703],{"className":8985},[882],[725,8987],{"className":8988,"style":878},[877],[725,8990,8992,8995,9024,9027,9030],{"className":8991},[759],[725,8993],{"className":8994,"style":2989},[763],[725,8996,8998,9001],{"className":8997},[768],[725,8999,1164],{"className":9000},[768],[725,9002,9004],{"className":9003},[1511],[725,9005,9007],{"className":9006},[1445],[725,9008,9010],{"className":9009},[1450],[725,9011,9013],{"className":9012,"style":3008},[1454],[725,9014,9015,9018],{"style":3011},[725,9016],{"className":9017,"style":1528},[1462],[725,9019,9021],{"className":9020},[1532,1533,1534,1535],[725,9022,794],{"className":9023},[768,769,1535],[725,9025],{"className":9026,"style":1485},[877],[725,9028,1818],{"className":9029},[1489],[725,9031],{"className":9032,"style":1485},[877],[725,9034,9036,9039],{"className":9035},[759],[725,9037],{"className":9038,"style":892},[763],[725,9040,915],{"className":9041},[768]," nœuds, donc ",[725,9044,9046,9100],{"className":9045},[728],[725,9047,9049],{"className":9048},[732],[734,9050,9051],{"xmlns":736},[738,9052,9053,9097],{},[741,9054,9055,9057,9059,9061,9063,9065,9067,9073,9075,9077,9079,9081,9093,9095],{},[744,9056,746],{},[852,9058,2703],{},[856,9060,915],{},[852,9062,1310],{},[856,9064,1164],{},[852,9066,1252],{"stretchy":1251},[2905,9068,9069,9071],{},[856,9070,1164],{},[744,9072,794],{},[852,9074,1818],{},[856,9076,915],{},[852,9078,1258],{"stretchy":1251},[852,9080,854],{},[2905,9082,9083,9085],{},[856,9084,1164],{},[741,9086,9087,9089,9091],{},[744,9088,794],{},[852,9090,1310],{},[856,9092,915],{},[852,9094,1818],{},[856,9096,915],{},[748,9098,9099],{"encoding":750},"n \\le 1 + 2(2^h - 1) = 2^{h+1} - 1",[725,9101,9103,9121,9139,9189,9210,9263],{"className":9102,"ariaHidden":755},[754],[725,9104,9106,9109,9112,9115,9118],{"className":9105},[759],[725,9107],{"className":9108,"style":2970},[763],[725,9110,746],{"className":9111},[768,769],[725,9113],{"className":9114,"style":878},[877],[725,9116,2703],{"className":9117},[882],[725,9119],{"className":9120,"style":878},[877],[725,9122,9124,9127,9130,9133,9136],{"className":9123},[759],[725,9125],{"className":9126,"style":2302},[763],[725,9128,915],{"className":9129},[768],[725,9131],{"className":9132,"style":1485},[877],[725,9134,1310],{"className":9135},[1489],[725,9137],{"className":9138,"style":1485},[877],[725,9140,9142,9145,9148,9151,9180,9183,9186],{"className":9141},[759],[725,9143],{"className":9144,"style":4597},[763],[725,9146,1164],{"className":9147},[768],[725,9149,1252],{"className":9150},[1394],[725,9152,9154,9157],{"className":9153},[768],[725,9155,1164],{"className":9156},[768],[725,9158,9160],{"className":9159},[1511],[725,9161,9163],{"className":9162},[1445],[725,9164,9166],{"className":9165},[1450],[725,9167,9169],{"className":9168,"style":3008},[1454],[725,9170,9171,9174],{"style":3011},[725,9172],{"className":9173,"style":1528},[1462],[725,9175,9177],{"className":9176},[1532,1533,1534,1535],[725,9178,794],{"className":9179},[768,769,1535],[725,9181],{"className":9182,"style":1485},[877],[725,9184,1818],{"className":9185},[1489],[725,9187],{"className":9188,"style":1485},[877],[725,9190,9192,9195,9198,9201,9204,9207],{"className":9191},[759],[725,9193],{"className":9194,"style":1383},[763],[725,9196,915],{"className":9197},[768],[725,9199,1258],{"className":9200},[1401],[725,9202],{"className":9203,"style":878},[877],[725,9205,854],{"className":9206},[882],[725,9208],{"className":9209,"style":878},[877],[725,9211,9213,9216,9254,9257,9260],{"className":9212},[759],[725,9214],{"className":9215,"style":2989},[763],[725,9217,9219,9222],{"className":9218},[768],[725,9220,1164],{"className":9221},[768],[725,9223,9225],{"className":9224},[1511],[725,9226,9228],{"className":9227},[1445],[725,9229,9231],{"className":9230},[1450],[725,9232,9234],{"className":9233,"style":3008},[1454],[725,9235,9236,9239],{"style":3011},[725,9237],{"className":9238,"style":1528},[1462],[725,9240,9242],{"className":9241},[1532,1533,1534,1535],[725,9243,9245,9248,9251],{"className":9244},[768,1535],[725,9246,794],{"className":9247},[768,769,1535],[725,9249,1310],{"className":9250},[1489,1535],[725,9252,915],{"className":9253},[768,1535],[725,9255],{"className":9256,"style":1485},[877],[725,9258,1818],{"className":9259},[1489],[725,9261],{"className":9262,"style":1485},[877],[725,9264,9266,9269],{"className":9265},[759],[725,9267],{"className":9268,"style":892},[763],[725,9270,915],{"className":9271},[768],[7430,9273],{},[7420,9275,9277],{"id":9276},"à-retenir","À retenir",[598,9279,9280],{},[602,9281,9282],{},"Un arbre équilibré donne accès logarithmique à ses données. Le déséquilibre dégrade en linéaire.",[5898,9284,7399],{},{"title":968,"searchDepth":989,"depth":989,"links":9286},[],"Deck pour la séance sur les arbres binaires.",{},"\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires.slides",{"title":7416,"description":9287},"2.nsi-tale\u002Fta-structures-donnees\u002F4.arbres-binaires.slides","-U65sIaughSKdriFTjYdTLzPzpp0Mvbf2bC64bNb3wE",{"id":5930,"title":5931,"bo":9294,"body":9295,"description":7407,"eval":5916,"extension":5917,"labo":5916,"meta":10717,"navigation":5923,"path":7409,"quizzes":10718,"readingTime":974,"seo":10719,"stem":7412,"tp":5916,"__hash__":7413},[588],{"type":590,"value":9296,"toc":10710},[9297,9299,9520,9522,10244,10246,10558,10560,10572,10574,10708],[593,9298,5938],{"id":5937},[598,9300,9301],{},[602,9302,5943,9303,5972,9331,6001,9359,949],{},[725,9304,9306,9319],{"className":9305},[728],[725,9307,9309],{"className":9308},[732],[734,9310,9311],{"xmlns":736},[738,9312,9313,9317],{},[741,9314,9315],{},[744,9316,794],{},[748,9318,794],{"encoding":750},[725,9320,9322],{"className":9321,"ariaHidden":755},[754],[725,9323,9325,9328],{"className":9324},[759],[725,9326],{"className":9327,"style":806},[763],[725,9329,794],{"className":9330},[768,769],[725,9332,9334,9347],{"className":9333},[728],[725,9335,9337],{"className":9336},[732],[734,9338,9339],{"xmlns":736},[738,9340,9341,9345],{},[741,9342,9343],{},[744,9344,746],{},[748,9346,746],{"encoding":750},[725,9348,9350],{"className":9349,"ariaHidden":755},[754],[725,9351,9353,9356],{"className":9352},[759],[725,9354],{"className":9355,"style":764},[763],[725,9357,746],{"className":9358},[768,769],[725,9360,9362,9401],{"className":9361},[728],[725,9363,9365],{"className":9364},[732],[734,9366,9367],{"xmlns":736},[738,9368,9369,9399],{},[741,9370,9371,9373,9375,9377,9379,9381,9383,9395,9397],{},[744,9372,794],{},[852,9374,1310],{},[856,9376,915],{},[852,9378,2703],{},[744,9380,746],{},[852,9382,2703],{},[2905,9384,9385,9387],{},[856,9386,1164],{},[741,9388,9389,9391,9393],{},[744,9390,794],{},[852,9392,1310],{},[856,9394,915],{},[852,9396,1818],{},[856,9398,915],{},[748,9400,2923],{"encoding":750},[725,9402,9404,9422,9440,9458,9511],{"className":9403,"ariaHidden":755},[754],[725,9405,9407,9410,9413,9416,9419],{"className":9406},[759],[725,9408],{"className":9409,"style":2933},[763],[725,9411,794],{"className":9412},[768,769],[725,9414],{"className":9415,"style":1485},[877],[725,9417,1310],{"className":9418},[1489],[725,9420],{"className":9421,"style":1485},[877],[725,9423,9425,9428,9431,9434,9437],{"className":9424},[759],[725,9426],{"className":9427,"style":2815},[763],[725,9429,915],{"className":9430},[768],[725,9432],{"className":9433,"style":878},[877],[725,9435,2703],{"className":9436},[882],[725,9438],{"className":9439,"style":878},[877],[725,9441,9443,9446,9449,9452,9455],{"className":9442},[759],[725,9444],{"className":9445,"style":2970},[763],[725,9447,746],{"className":9448},[768,769],[725,9450],{"className":9451,"style":878},[877],[725,9453,2703],{"className":9454},[882],[725,9456],{"className":9457,"style":878},[877],[725,9459,9461,9464,9502,9505,9508],{"className":9460},[759],[725,9462],{"className":9463,"style":2989},[763],[725,9465,9467,9470],{"className":9466},[768],[725,9468,1164],{"className":9469},[768],[725,9471,9473],{"className":9472},[1511],[725,9474,9476],{"className":9475},[1445],[725,9477,9479],{"className":9478},[1450],[725,9480,9482],{"className":9481,"style":3008},[1454],[725,9483,9484,9487],{"style":3011},[725,9485],{"className":9486,"style":1528},[1462],[725,9488,9490],{"className":9489},[1532,1533,1534,1535],[725,9491,9493,9496,9499],{"className":9492},[768,1535],[725,9494,794],{"className":9495},[768,769,1535],[725,9497,1310],{"className":9498},[1489,1535],[725,9500,915],{"className":9501},[768,1535],[725,9503],{"className":9504,"style":1485},[877],[725,9506,1818],{"className":9507},[1489],[725,9509],{"className":9510,"style":1485},[877],[725,9512,9514,9517],{"className":9513},[759],[725,9515],{"className":9516,"style":892},[763],[725,9518,915],{"className":9519},[768],[593,9521,6166],{"id":6165},[1192,9523,9524,9530,9592,9649,10014],{},[1195,9525,9526,6173,9528,6177],{},[602,9527,672],{},[602,9529,6176],{},[1195,9531,9532,723,9534,6210,9562,723,9564,6241],{},[602,9533,722],{},[725,9535,9537,9550],{"className":9536},[728],[725,9538,9540],{"className":9539},[732],[734,9541,9542],{"xmlns":736},[738,9543,9544,9548],{},[741,9545,9546],{},[744,9547,746],{},[748,9549,746],{"encoding":750},[725,9551,9553],{"className":9552,"ariaHidden":755},[754],[725,9554,9556,9559],{"className":9555},[759],[725,9557],{"className":9558,"style":764},[763],[725,9560,746],{"className":9561},[768,769],[602,9563,1760],{},[725,9565,9567,9580],{"className":9566},[728],[725,9568,9570],{"className":9569},[732],[734,9571,9572],{"xmlns":736},[738,9573,9574,9578],{},[741,9575,9576],{},[744,9577,794],{},[748,9579,794],{"encoding":750},[725,9581,9583],{"className":9582,"ariaHidden":755},[754],[725,9584,9586,9589],{"className":9585},[759],[725,9587],{"className":9588,"style":806},[763],[725,9590,794],{"className":9591},[768,769],[1195,9593,6244,9594,6301],{},[725,9595,9597,9616],{"className":9596},[728],[725,9598,9600],{"className":9599},[732],[734,9601,9602],{"xmlns":736},[738,9603,9604,9614],{},[741,9605,9606,9608,9610,9612],{},[744,9607,794],{},[852,9609,854],{},[852,9611,1818],{},[856,9613,915],{},[748,9615,6267],{"encoding":750},[725,9617,9619,9637],{"className":9618,"ariaHidden":755},[754],[725,9620,9622,9625,9628,9631,9634],{"className":9621},[759],[725,9623],{"className":9624,"style":806},[763],[725,9626,794],{"className":9627},[768,769],[725,9629],{"className":9630,"style":878},[877],[725,9632,854],{"className":9633},[882],[725,9635],{"className":9636,"style":878},[877],[725,9638,9640,9643,9646],{"className":9639},[759],[725,9641],{"className":9642,"style":2302},[763],[725,9644,1818],{"className":9645},[768],[725,9647,915],{"className":9648},[768],[1195,9650,9651,6307,9653,6469,9814,949],{},[602,9652,6306],{},[725,9654,9656,9695],{"className":9655},[728],[725,9657,9659],{"className":9658},[732],[734,9660,9661],{"xmlns":736},[738,9662,9663,9693],{},[741,9664,9665,9667,9669,9671,9673,9675,9677,9689,9691],{},[744,9666,794],{},[852,9668,1310],{},[856,9670,915],{},[852,9672,2703],{},[744,9674,746],{},[852,9676,2703],{},[2905,9678,9679,9681],{},[856,9680,1164],{},[741,9682,9683,9685,9687],{},[744,9684,794],{},[852,9686,1310],{},[856,9688,915],{},[852,9690,1818],{},[856,9692,915],{},[748,9694,2923],{"encoding":750},[725,9696,9698,9716,9734,9752,9805],{"className":9697,"ariaHidden":755},[754],[725,9699,9701,9704,9707,9710,9713],{"className":9700},[759],[725,9702],{"className":9703,"style":2933},[763],[725,9705,794],{"className":9706},[768,769],[725,9708],{"className":9709,"style":1485},[877],[725,9711,1310],{"className":9712},[1489],[725,9714],{"className":9715,"style":1485},[877],[725,9717,9719,9722,9725,9728,9731],{"className":9718},[759],[725,9720],{"className":9721,"style":2815},[763],[725,9723,915],{"className":9724},[768],[725,9726],{"className":9727,"style":878},[877],[725,9729,2703],{"className":9730},[882],[725,9732],{"className":9733,"style":878},[877],[725,9735,9737,9740,9743,9746,9749],{"className":9736},[759],[725,9738],{"className":9739,"style":2970},[763],[725,9741,746],{"className":9742},[768,769],[725,9744],{"className":9745,"style":878},[877],[725,9747,2703],{"className":9748},[882],[725,9750],{"className":9751,"style":878},[877],[725,9753,9755,9758,9796,9799,9802],{"className":9754},[759],[725,9756],{"className":9757,"style":2989},[763],[725,9759,9761,9764],{"className":9760},[768],[725,9762,1164],{"className":9763},[768],[725,9765,9767],{"className":9766},[1511],[725,9768,9770],{"className":9769},[1445],[725,9771,9773],{"className":9772},[1450],[725,9774,9776],{"className":9775,"style":3008},[1454],[725,9777,9778,9781],{"style":3011},[725,9779],{"className":9780,"style":1528},[1462],[725,9782,9784],{"className":9783},[1532,1533,1534,1535],[725,9785,9787,9790,9793],{"className":9786},[768,1535],[725,9788,794],{"className":9789},[768,769,1535],[725,9791,1310],{"className":9792},[1489,1535],[725,9794,915],{"className":9795},[768,1535],[725,9797],{"className":9798,"style":1485},[877],[725,9800,1818],{"className":9801},[1489],[725,9803],{"className":9804,"style":1485},[877],[725,9806,9808,9811],{"className":9807},[759],[725,9809],{"className":9810,"style":892},[763],[725,9812,915],{"className":9813},[768],[725,9815,9817,9864],{"className":9816},[728],[725,9818,9820],{"className":9819},[732],[734,9821,9822],{"xmlns":736},[738,9823,9824,9862],{},[741,9825,9826,9836,9838,9840,9842,9844,9846,9848,9850,9852,9854,9856,9858,9860],{},[1328,9827,9828,9834],{},[741,9829,9830,9832],{},[744,9831,2682],{},[852,9833,1850],{},[856,9835,1164],{},[852,9837,1252],{"stretchy":1251},[744,9839,746],{},[852,9841,1310],{},[856,9843,915],{},[852,9845,1258],{"stretchy":1251},[852,9847,1818],{},[856,9849,915],{},[852,9851,2703],{},[744,9853,794],{},[852,9855,2703],{},[744,9857,746],{},[852,9859,1818],{},[856,9861,915],{},[748,9863,2716],{"encoding":750},[725,9865,9867,9930,9951,9969,9987,10005],{"className":9866,"ariaHidden":755},[754],[725,9868,9870,9873,9915,9918,9921,9924,9927],{"className":9869},[759],[725,9871],{"className":9872,"style":1383},[763],[725,9874,9876,9881],{"className":9875},[2022],[725,9877,2732,9879],{"className":9878},[2022],[725,9880,1334],{"style":2735},[725,9882,9884],{"className":9883},[1511],[725,9885,9887,9907],{"className":9886},[1445,1446],[725,9888,9890,9904],{"className":9889},[1450],[725,9891,9893],{"className":9892,"style":2748},[1454],[725,9894,9895,9898],{"style":2751},[725,9896],{"className":9897,"style":1528},[1462],[725,9899,9901],{"className":9900},[1532,1533,1534,1535],[725,9902,1164],{"className":9903},[768,1535],[725,9905,1544],{"className":9906},[1543],[725,9908,9910],{"className":9909},[1450],[725,9911,9913],{"className":9912,"style":2770},[1454],[725,9914],{},[725,9916,1252],{"className":9917},[1394],[725,9919,746],{"className":9920},[768,769],[725,9922],{"className":9923,"style":1485},[877],[725,9925,1310],{"className":9926},[1489],[725,9928],{"className":9929,"style":1485},[877],[725,9931,9933,9936,9939,9942,9945,9948],{"className":9932},[759],[725,9934],{"className":9935,"style":1383},[763],[725,9937,915],{"className":9938},[768],[725,9940,1258],{"className":9941},[1401],[725,9943],{"className":9944,"style":1485},[877],[725,9946,1818],{"className":9947},[1489],[725,9949],{"className":9950,"style":1485},[877],[725,9952,9954,9957,9960,9963,9966],{"className":9953},[759],[725,9955],{"className":9956,"style":2815},[763],[725,9958,915],{"className":9959},[768],[725,9961],{"className":9962,"style":878},[877],[725,9964,2703],{"className":9965},[882],[725,9967],{"className":9968,"style":878},[877],[725,9970,9972,9975,9978,9981,9984],{"className":9971},[759],[725,9973],{"className":9974,"style":2834},[763],[725,9976,794],{"className":9977},[768,769],[725,9979],{"className":9980,"style":878},[877],[725,9982,2703],{"className":9983},[882],[725,9985],{"className":9986,"style":878},[877],[725,9988,9990,9993,9996,9999,10002],{"className":9989},[759],[725,9991],{"className":9992,"style":2853},[763],[725,9994,746],{"className":9995},[768,769],[725,9997],{"className":9998,"style":1485},[877],[725,10000,1818],{"className":10001},[1489],[725,10003],{"className":10004,"style":1485},[877],[725,10006,10008,10011],{"className":10007},[759],[725,10009],{"className":10010,"style":892},[763],[725,10012,915],{"className":10013},[768],[1195,10015,6672,10016,6745,10088,949],{},[725,10017,10019,10040],{"className":10018},[728],[725,10020,10022],{"className":10021},[732],[734,10023,10024],{"xmlns":736},[738,10025,10026,10038],{},[741,10027,10028,10030,10032,10034,10036],{},[744,10029,794],{},[852,10031,854],{},[744,10033,746],{},[852,10035,1818],{},[856,10037,915],{},[748,10039,5236],{"encoding":750},[725,10041,10043,10061,10079],{"className":10042,"ariaHidden":755},[754],[725,10044,10046,10049,10052,10055,10058],{"className":10045},[759],[725,10047],{"className":10048,"style":806},[763],[725,10050,794],{"className":10051},[768,769],[725,10053],{"className":10054,"style":878},[877],[725,10056,854],{"className":10057},[882],[725,10059],{"className":10060,"style":878},[877],[725,10062,10064,10067,10070,10073,10076],{"className":10063},[759],[725,10065],{"className":10066,"style":2853},[763],[725,10068,746],{"className":10069},[768,769],[725,10071],{"className":10072,"style":1485},[877],[725,10074,1818],{"className":10075},[1489],[725,10077],{"className":10078,"style":1485},[877],[725,10080,10082,10085],{"className":10081},[759],[725,10083],{"className":10084,"style":892},[763],[725,10086,915],{"className":10087},[768],[725,10089,10091,10130],{"className":10090},[728],[725,10092,10094],{"className":10093},[732],[734,10095,10096],{"xmlns":736},[738,10097,10098,10128],{},[741,10099,10100,10102,10104,10114,10116,10118,10120,10122,10124,10126],{},[744,10101,794],{},[852,10103,854],{},[1328,10105,10106,10112],{},[741,10107,10108,10110],{},[744,10109,2682],{},[852,10111,1850],{},[856,10113,1164],{},[852,10115,1252],{"stretchy":1251},[744,10117,746],{},[852,10119,1310],{},[856,10121,915],{},[852,10123,1258],{"stretchy":1251},[852,10125,1818],{},[856,10127,915],{},[748,10129,5451],{"encoding":750},[725,10131,10133,10151,10214,10235],{"className":10132,"ariaHidden":755},[754],[725,10134,10136,10139,10142,10145,10148],{"className":10135},[759],[725,10137],{"className":10138,"style":806},[763],[725,10140,794],{"className":10141},[768,769],[725,10143],{"className":10144,"style":878},[877],[725,10146,854],{"className":10147},[882],[725,10149],{"className":10150,"style":878},[877],[725,10152,10154,10157,10199,10202,10205,10208,10211],{"className":10153},[759],[725,10155],{"className":10156,"style":1383},[763],[725,10158,10160,10165],{"className":10159},[2022],[725,10161,2732,10163],{"className":10162},[2022],[725,10164,1334],{"style":2735},[725,10166,10168],{"className":10167},[1511],[725,10169,10171,10191],{"className":10170},[1445,1446],[725,10172,10174,10188],{"className":10173},[1450],[725,10175,10177],{"className":10176,"style":2748},[1454],[725,10178,10179,10182],{"style":2751},[725,10180],{"className":10181,"style":1528},[1462],[725,10183,10185],{"className":10184},[1532,1533,1534,1535],[725,10186,1164],{"className":10187},[768,1535],[725,10189,1544],{"className":10190},[1543],[725,10192,10194],{"className":10193},[1450],[725,10195,10197],{"className":10196,"style":2770},[1454],[725,10198],{},[725,10200,1252],{"className":10201},[1394],[725,10203,746],{"className":10204},[768,769],[725,10206],{"className":10207,"style":1485},[877],[725,10209,1310],{"className":10210},[1489],[725,10212],{"className":10213,"style":1485},[877],[725,10215,10217,10220,10223,10226,10229,10232],{"className":10216},[759],[725,10218],{"className":10219,"style":1383},[763],[725,10221,915],{"className":10222},[768],[725,10224,1258],{"className":10225},[1401],[725,10227],{"className":10228,"style":1485},[877],[725,10230,1818],{"className":10231},[1489],[725,10233],{"className":10234,"style":1485},[877],[725,10236,10238,10241],{"className":10237},[759],[725,10239],{"className":10240,"style":892},[763],[725,10242,915],{"className":10243},[768],[593,10245,6905],{"id":6904},[637,10247,10248,10284],{},[640,10249,10250],{},[643,10251,10252,10254],{},[646,10253,6914],{},[646,10255,6917,10256],{},[725,10257,10259,10272],{"className":10258},[728],[725,10260,10262],{"className":10261},[732],[734,10263,10264],{"xmlns":736},[738,10265,10266,10270],{},[741,10267,10268],{},[744,10269,746],{},[748,10271,746],{"encoding":750},[725,10273,10275],{"className":10274,"ariaHidden":755},[754],[725,10276,10278,10281],{"className":10277},[759],[725,10279],{"className":10280,"style":764},[763],[725,10282,746],{"className":10283},[768,769],[653,10285,10286,10364,10475],{},[643,10287,10288,10290],{},[658,10289,6952],{},[658,10291,10292],{},[725,10293,10295,10316],{"className":10294},[728],[725,10296,10298],{"className":10297},[732],[734,10299,10300],{"xmlns":736},[738,10301,10302,10314],{},[741,10303,10304,10306,10308,10310,10312],{},[744,10305,794],{},[852,10307,854],{},[744,10309,746],{},[852,10311,1818],{},[856,10313,915],{},[748,10315,5236],{"encoding":750},[725,10317,10319,10337,10355],{"className":10318,"ariaHidden":755},[754],[725,10320,10322,10325,10328,10331,10334],{"className":10321},[759],[725,10323],{"className":10324,"style":806},[763],[725,10326,794],{"className":10327},[768,769],[725,10329],{"className":10330,"style":878},[877],[725,10332,854],{"className":10333},[882],[725,10335],{"className":10336,"style":878},[877],[725,10338,10340,10343,10346,10349,10352],{"className":10339},[759],[725,10341],{"className":10342,"style":2853},[763],[725,10344,746],{"className":10345},[768,769],[725,10347],{"className":10348,"style":1485},[877],[725,10350,1818],{"className":10351},[1489],[725,10353],{"className":10354,"style":1485},[877],[725,10356,10358,10361],{"className":10357},[759],[725,10359],{"className":10360,"style":892},[763],[725,10362,915],{"className":10363},[768],[643,10365,10366,10368],{},[658,10367,7031],{},[658,10369,10370],{},[725,10371,10373,10400],{"className":10372},[728],[725,10374,10376],{"className":10375},[732],[734,10377,10378],{"xmlns":736},[738,10379,10380,10398],{},[741,10381,10382,10384,10386,10396],{},[744,10383,794],{},[852,10385,7050],{},[1328,10387,10388,10394],{},[741,10389,10390,10392],{},[744,10391,2682],{},[852,10393,1850],{},[856,10395,1164],{},[744,10397,746],{},[748,10399,7065],{"encoding":750},[725,10401,10403,10421],{"className":10402,"ariaHidden":755},[754],[725,10404,10406,10409,10412,10415,10418],{"className":10405},[759],[725,10407],{"className":10408,"style":806},[763],[725,10410,794],{"className":10411},[768,769],[725,10413],{"className":10414,"style":878},[877],[725,10416,7050],{"className":10417},[882],[725,10419],{"className":10420,"style":878},[877],[725,10422,10424,10427,10469,10472],{"className":10423},[759],[725,10425],{"className":10426,"style":7093},[763],[725,10428,10430,10435],{"className":10429},[2022],[725,10431,2732,10433],{"className":10432},[2022],[725,10434,1334],{"style":2735},[725,10436,10438],{"className":10437},[1511],[725,10439,10441,10461],{"className":10440},[1445,1446],[725,10442,10444,10458],{"className":10443},[1450],[725,10445,10447],{"className":10446,"style":2748},[1454],[725,10448,10449,10452],{"style":2751},[725,10450],{"className":10451,"style":1528},[1462],[725,10453,10455],{"className":10454},[1532,1533,1534,1535],[725,10456,1164],{"className":10457},[768,1535],[725,10459,1544],{"className":10460},[1543],[725,10462,10464],{"className":10463},[1450],[725,10465,10467],{"className":10466,"style":2770},[1454],[725,10468],{},[725,10470],{"className":10471,"style":2085},[877],[725,10473,746],{"className":10474},[768,769],[643,10476,10477,10479],{},[658,10478,7146],{},[658,10480,10481],{},[725,10482,10484,10511],{"className":10483},[728],[725,10485,10487],{"className":10486},[732],[734,10488,10489],{"xmlns":736},[738,10490,10491,10509],{},[741,10492,10493,10495,10497,10499,10501,10503,10505,10507],{},[744,10494,794],{},[852,10496,5583],{},[744,10498,5587],{"mathvariant":5586},[852,10500,1252],{"stretchy":1251},[744,10502,2682],{},[852,10504,1850],{},[744,10506,746],{},[852,10508,1258],{"stretchy":1251},[748,10510,5600],{"encoding":750},[725,10512,10514,10532],{"className":10513,"ariaHidden":755},[754],[725,10515,10517,10520,10523,10526,10529],{"className":10516},[759],[725,10518],{"className":10519,"style":5610},[763],[725,10521,794],{"className":10522},[768,769],[725,10524],{"className":10525,"style":878},[877],[725,10527,5583],{"className":10528},[882],[725,10530],{"className":10531,"style":878},[877],[725,10533,10535,10538,10541,10544,10549,10552,10555],{"className":10534},[759],[725,10536],{"className":10537,"style":1383},[763],[725,10539,5587],{"className":10540,"style":5633},[768,5632],[725,10542,1252],{"className":10543},[1394],[725,10545,2732,10547],{"className":10546},[2022],[725,10548,1334],{"style":2735},[725,10550],{"className":10551,"style":2085},[877],[725,10553,746],{"className":10554},[768,769],[725,10556,1258],{"className":10557},[1401],[593,10559,7229],{"id":7228},[1192,10561,10562,10564,10570],{},[1195,10563,7234],{},[1195,10565,7237,10566,7240,10568,949],{},[958,10567,1208],{},[958,10569,1760],{},[1195,10571,7245],{},[593,10573,7249],{"id":7248},[963,10575,10576],{"className":965,"code":7252,"language":967,"meta":968,"style":968},[958,10577,10578,10586,10606,10624,10628,10636,10652,10666,10670,10678,10696],{"__ignoreMap":968},[725,10579,10580,10582,10584],{"class":973,"line":974},[725,10581,978],{"class":977},[725,10583,982],{"class":981},[725,10585,986],{"class":985},[725,10587,10588,10590,10592,10594,10596,10598,10600,10602,10604],{"class":973,"line":989},[725,10589,1006],{"class":977},[725,10591,1010],{"class":1009},[725,10593,1013],{"class":985},[725,10595,854],{"class":977},[725,10597,960],{"class":1009},[725,10599,1020],{"class":985},[725,10601,854],{"class":977},[725,10603,960],{"class":1009},[725,10605,1027],{"class":985},[725,10607,10608,10610,10612,10614,10616,10618,10620,10622],{"class":973,"line":996},[725,10609,1033],{"class":1009},[725,10611,7289],{"class":985},[725,10613,7292],{"class":1009},[725,10615,7295],{"class":985},[725,10617,7292],{"class":1009},[725,10619,1062],{"class":985},[725,10621,854],{"class":977},[725,10623,7304],{"class":985},[725,10625,10626],{"class":973,"line":1003},[725,10627,1000],{"emptyLinePlaceholder":999},[725,10629,10630,10632,10634],{"class":973,"line":1030},[725,10631,1711],{"class":977},[725,10633,1714],{"class":981},[725,10635,7317],{"class":985},[725,10637,10638,10640,10642,10644,10646,10648,10650],{"class":973,"line":1044},[725,10639,1722],{"class":977},[725,10641,7324],{"class":985},[725,10643,1097],{"class":977},[725,10645,1100],{"class":1009},[725,10647,7331],{"class":985},[725,10649,7334],{"class":977},[725,10651,1738],{"class":1009},[725,10653,10654,10656,10658,10660,10662,10664],{"class":973,"line":1057},[725,10655,1743],{"class":977},[725,10657,1746],{"class":1009},[725,10659,1749],{"class":977},[725,10661,7347],{"class":985},[725,10663,1310],{"class":977},[725,10665,7352],{"class":985},[725,10667,10668],{"class":973,"line":1070},[725,10669,1000],{"emptyLinePlaceholder":999},[725,10671,10672,10674,10676],{"class":973,"line":1075},[725,10673,1711],{"class":977},[725,10675,2434],{"class":981},[725,10677,7317],{"class":985},[725,10679,10680,10682,10684,10686,10688,10690,10692,10694],{"class":973,"line":1086},[725,10681,1722],{"class":977},[725,10683,7324],{"class":985},[725,10685,1097],{"class":977},[725,10687,1100],{"class":1009},[725,10689,7331],{"class":985},[725,10691,7334],{"class":977},[725,10693,2455],{"class":977},[725,10695,2458],{"class":1009},[725,10697,10698,10700,10702,10704,10706],{"class":973,"line":7385},[725,10699,1743],{"class":977},[725,10701,1746],{"class":1009},[725,10703,1749],{"class":977},[725,10705,2469],{"class":1009},[725,10707,7396],{"class":985},[5898,10709,7399],{},{"title":968,"searchDepth":989,"depth":989,"links":10711},[10712,10713,10714,10715,10716],{"id":5937,"depth":989,"text":5938},{"id":6165,"depth":989,"text":6166},{"id":6904,"depth":989,"text":6905},{"id":7228,"depth":989,"text":7229},{"id":7248,"depth":989,"text":7249},{},[],{"title":5931,"description":7407},{"id":7415,"title":7416,"body":10721,"description":9287,"extension":5917,"meta":12529,"navigation":5923,"path":9289,"seo":12530,"stem":9291,"__hash__":9292},{"type":590,"value":10722,"toc":12527},[10723,10725,10729,10731,10733,10751,10753,10757,10819,10825,10827,10829,11097,11139,11141,11143,11371,11493,11495,11497,11720,11722,11724,11726,11909,11911,11913,12517,12519,12521,12525],[7420,10724,469],{"id":7422},[598,10726,7425,10727,7428],{},[629,10728],{"code":588},[7430,10730],{},[7420,10732,635],{"id":634},[1192,10734,10735,10739,10743,10747],{},[1195,10736,10737,7440],{},[602,10738,662],{},[1195,10740,10741,7445],{},[602,10742,672],{},[1195,10744,10745,7450],{},[602,10746,682],{},[1195,10748,10749,7456],{},[602,10750,7455],{},[7430,10752],{},[7420,10754,7462,10755],{"id":7461},[958,10756,7465],{},[963,10758,10759],{"className":965,"code":7468,"language":967,"meta":968,"style":968},[958,10760,10761,10769,10789,10799,10809],{"__ignoreMap":968},[725,10762,10763,10765,10767],{"class":973,"line":974},[725,10764,978],{"class":977},[725,10766,982],{"class":981},[725,10768,986],{"class":985},[725,10770,10771,10773,10775,10777,10779,10781,10783,10785,10787],{"class":973,"line":989},[725,10772,1006],{"class":977},[725,10774,1010],{"class":1009},[725,10776,7487],{"class":985},[725,10778,854],{"class":977},[725,10780,960],{"class":1009},[725,10782,7494],{"class":985},[725,10784,854],{"class":977},[725,10786,960],{"class":1009},[725,10788,1027],{"class":985},[725,10790,10791,10793,10795,10797],{"class":973,"line":996},[725,10792,1033],{"class":1009},[725,10794,1036],{"class":985},[725,10796,854],{"class":977},[725,10798,7511],{"class":985},[725,10800,10801,10803,10805,10807],{"class":973,"line":1003},[725,10802,1033],{"class":1009},[725,10804,1049],{"class":985},[725,10806,854],{"class":977},[725,10808,7522],{"class":985},[725,10810,10811,10813,10815,10817],{"class":973,"line":1030},[725,10812,1033],{"class":1009},[725,10814,1062],{"class":985},[725,10816,854],{"class":977},[725,10818,7533],{"class":985},[598,10820,7536,10821,5566,10823,949],{},[958,10822,7465],{},[958,10824,960],{},[7430,10826],{},[7420,10828,7546],{"id":7545},[598,10830,10831],{},[725,10832,10834,10921],{"className":10833},[728],[725,10835,10837],{"className":10836},[732],[734,10838,10839],{"xmlns":736},[738,10840,10841,10919],{},[741,10842,10843,10857,10859,10861,10863,10865,10867,10869,10883,10885,10891,10893,10895,10909,10911,10917],{},[741,10844,10845,10847,10849,10851,10853,10855],{},[744,10846,1234],{"mathvariant":1233},[744,10848,1237],{"mathvariant":1233},[744,10850,1240],{"mathvariant":1233},[744,10852,1243],{"mathvariant":1233},[744,10854,1243],{"mathvariant":1233},[744,10856,1248],{"mathvariant":1233},[852,10858,1252],{"stretchy":1251},[744,10860,1255],{},[852,10862,1258],{"stretchy":1251},[852,10864,854],{},[856,10866,915],{},[852,10868,1310],{},[741,10870,10871,10873,10875,10877,10879,10881],{},[744,10872,1234],{"mathvariant":1233},[744,10874,1237],{"mathvariant":1233},[744,10876,1240],{"mathvariant":1233},[744,10878,1243],{"mathvariant":1233},[744,10880,1243],{"mathvariant":1233},[744,10882,1248],{"mathvariant":1233},[852,10884,1252],{"stretchy":1251},[1328,10886,10887,10889],{},[744,10888,1255],{},[744,10890,1334],{},[852,10892,1258],{"stretchy":1251},[852,10894,1310],{},[741,10896,10897,10899,10901,10903,10905,10907],{},[744,10898,1234],{"mathvariant":1233},[744,10900,1237],{"mathvariant":1233},[744,10902,1240],{"mathvariant":1233},[744,10904,1243],{"mathvariant":1233},[744,10906,1243],{"mathvariant":1233},[744,10908,1248],{"mathvariant":1233},[852,10910,1252],{"stretchy":1251},[1328,10912,10913,10915],{},[744,10914,1255],{},[744,10916,1361],{},[852,10918,1258],{"stretchy":1251},[748,10920,7639],{"encoding":750},[725,10922,10924,10954,10972,11039],{"className":10923,"ariaHidden":755},[754],[725,10925,10927,10930,10936,10939,10942,10945,10948,10951],{"className":10926},[759],[725,10928],{"className":10929,"style":1383},[763],[725,10931,10933],{"className":10932},[768],[725,10934,1208],{"className":10935},[768,1390],[725,10937,1252],{"className":10938},[1394],[725,10940,1255],{"className":10941},[768,769],[725,10943,1258],{"className":10944},[1401],[725,10946],{"className":10947,"style":878},[877],[725,10949,854],{"className":10950},[882],[725,10952],{"className":10953,"style":878},[877],[725,10955,10957,10960,10963,10966,10969],{"className":10956},[759],[725,10958],{"className":10959,"style":2302},[763],[725,10961,915],{"className":10962},[768],[725,10964],{"className":10965,"style":1485},[877],[725,10967,1310],{"className":10968},[1489],[725,10970],{"className":10971,"style":1485},[877],[725,10973,10975,10978,10984,10987,11027,11030,11033,11036],{"className":10974},[759],[725,10976],{"className":10977,"style":7697},[763],[725,10979,10981],{"className":10980},[768],[725,10982,1208],{"className":10983},[768,1390],[725,10985,1252],{"className":10986},[1394],[725,10988,10990,10993],{"className":10989},[768],[725,10991,1255],{"className":10992},[768,769],[725,10994,10996],{"className":10995},[1511],[725,10997,10999,11019],{"className":10998},[1445,1446],[725,11000,11002,11016],{"className":11001},[1450],[725,11003,11005],{"className":11004,"style":1521},[1454],[725,11006,11007,11010],{"style":1524},[725,11008],{"className":11009,"style":1528},[1462],[725,11011,11013],{"className":11012},[1532,1533,1534,1535],[725,11014,1334],{"className":11015,"style":1539},[768,769,1535],[725,11017,1544],{"className":11018},[1543],[725,11020,11022],{"className":11021},[1450],[725,11023,11025],{"className":11024,"style":1551},[1454],[725,11026],{},[725,11028,1258],{"className":11029},[1401],[725,11031],{"className":11032,"style":1485},[877],[725,11034,1310],{"className":11035},[1489],[725,11037],{"className":11038,"style":1485},[877],[725,11040,11042,11045,11051,11054,11094],{"className":11041},[759],[725,11043],{"className":11044,"style":1383},[763],[725,11046,11048],{"className":11047},[768],[725,11049,1208],{"className":11050},[768,1390],[725,11052,1252],{"className":11053},[1394],[725,11055,11057,11060],{"className":11056},[768],[725,11058,1255],{"className":11059},[768,769],[725,11061,11063],{"className":11062},[1511],[725,11064,11066,11086],{"className":11065},[1445,1446],[725,11067,11069,11083],{"className":11068},[1450],[725,11070,11072],{"className":11071,"style":1593},[1454],[725,11073,11074,11077],{"style":1524},[725,11075],{"className":11076,"style":1528},[1462],[725,11078,11080],{"className":11079},[1532,1533,1534,1535],[725,11081,1361],{"className":11082},[768,769,1535],[725,11084,1544],{"className":11085},[1543],[725,11087,11089],{"className":11088},[1450],[725,11090,11092],{"className":11091,"style":1614},[1454],[725,11093],{},[725,11095,1258],{"className":11096},[1401],[963,11098,11099],{"className":965,"code":7819,"language":967,"meta":968,"style":968},[958,11100,11101,11109,11125],{"__ignoreMap":968},[725,11102,11103,11105,11107],{"class":973,"line":974},[725,11104,1711],{"class":977},[725,11106,1714],{"class":981},[725,11108,7317],{"class":985},[725,11110,11111,11113,11115,11117,11119,11121,11123],{"class":973,"line":989},[725,11112,1722],{"class":977},[725,11114,7324],{"class":985},[725,11116,1097],{"class":977},[725,11118,1100],{"class":1009},[725,11120,7331],{"class":985},[725,11122,7334],{"class":977},[725,11124,1738],{"class":1009},[725,11126,11127,11129,11131,11133,11135,11137],{"class":973,"line":996},[725,11128,1743],{"class":977},[725,11130,1746],{"class":1009},[725,11132,1749],{"class":977},[725,11134,7347],{"class":985},[725,11136,1310],{"class":977},[725,11138,7352],{"class":985},[7430,11140],{},[7420,11142,7865],{"id":7864},[598,11144,11145],{},[725,11146,11148,11207],{"className":11147},[728],[725,11149,11151],{"className":11150},[732],[734,11152,11153],{"xmlns":736},[738,11154,11155,11205],{},[741,11156,11157,11159,11161,11163,11165,11167,11169,11171,11173,11175,11177,11179,11181,11187,11189,11191,11193,11195,11201,11203],{},[744,11158,794],{},[852,11160,1252],{"stretchy":1251},[744,11162,1255],{},[852,11164,1258],{"stretchy":1251},[852,11166,854],{},[856,11168,915],{},[852,11170,1310],{},[744,11172,1847],{},[852,11174,1850],{},[852,11176,1252],{"stretchy":1251},[744,11178,794],{},[852,11180,1252],{"stretchy":1251},[1328,11182,11183,11185],{},[744,11184,1255],{},[744,11186,1334],{},[852,11188,1258],{"stretchy":1251},[852,11190,1881],{"separator":755},[744,11192,794],{},[852,11194,1252],{"stretchy":1251},[1328,11196,11197,11199],{},[744,11198,1255],{},[744,11200,1361],{},[852,11202,1258],{"stretchy":1251},[852,11204,1258],{"stretchy":1251},[748,11206,7930],{"encoding":750},[725,11208,11210,11237,11255],{"className":11209,"ariaHidden":755},[754],[725,11211,11213,11216,11219,11222,11225,11228,11231,11234],{"className":11212},[759],[725,11214],{"className":11215,"style":1383},[763],[725,11217,794],{"className":11218},[768,769],[725,11220,1252],{"className":11221},[1394],[725,11223,1255],{"className":11224},[768,769],[725,11226,1258],{"className":11227},[1401],[725,11229],{"className":11230,"style":878},[877],[725,11232,854],{"className":11233},[882],[725,11235],{"className":11236,"style":878},[877],[725,11238,11240,11243,11246,11249,11252],{"className":11239},[759],[725,11241],{"className":11242,"style":2302},[763],[725,11244,915],{"className":11245},[768],[725,11247],{"className":11248,"style":1485},[877],[725,11250,1310],{"className":11251},[1489],[725,11253],{"className":11254,"style":1485},[877],[725,11256,11258,11261,11264,11267,11270,11273,11313,11316,11319,11322,11325,11328,11368],{"className":11257},[759],[725,11259],{"className":11260,"style":7697},[763],[725,11262,1847],{"className":11263},[2022],[725,11265,1252],{"className":11266},[1394],[725,11268,794],{"className":11269},[768,769],[725,11271,1252],{"className":11272},[1394],[725,11274,11276,11279],{"className":11275},[768],[725,11277,1255],{"className":11278},[768,769],[725,11280,11282],{"className":11281},[1511],[725,11283,11285,11305],{"className":11284},[1445,1446],[725,11286,11288,11302],{"className":11287},[1450],[725,11289,11291],{"className":11290,"style":1521},[1454],[725,11292,11293,11296],{"style":1524},[725,11294],{"className":11295,"style":1528},[1462],[725,11297,11299],{"className":11298},[1532,1533,1534,1535],[725,11300,1334],{"className":11301,"style":1539},[768,769,1535],[725,11303,1544],{"className":11304},[1543],[725,11306,11308],{"className":11307},[1450],[725,11309,11311],{"className":11310,"style":1551},[1454],[725,11312],{},[725,11314,1258],{"className":11315},[1401],[725,11317,1881],{"className":11318},[2081],[725,11320],{"className":11321,"style":2085},[877],[725,11323,794],{"className":11324},[768,769],[725,11326,1252],{"className":11327},[1394],[725,11329,11331,11334],{"className":11330},[768],[725,11332,1255],{"className":11333},[768,769],[725,11335,11337],{"className":11336},[1511],[725,11338,11340,11360],{"className":11339},[1445,1446],[725,11341,11343,11357],{"className":11342},[1450],[725,11344,11346],{"className":11345,"style":1593},[1454],[725,11347,11348,11351],{"style":1524},[725,11349],{"className":11350,"style":1528},[1462],[725,11352,11354],{"className":11353},[1532,1533,1534,1535],[725,11355,1361],{"className":11356},[768,769,1535],[725,11358,1544],{"className":11359},[1543],[725,11361,11363],{"className":11362},[1450],[725,11364,11366],{"className":11365,"style":1614},[1454],[725,11367],{},[725,11369,2138],{"className":11370},[1401],[598,11372,8097,11373,8169,11443,949],{},[725,11374,11376,11401],{"className":11375},[728],[725,11377,11379],{"className":11378},[732],[734,11380,11381],{"xmlns":736},[738,11382,11383,11399],{},[741,11384,11385,11387,11389,11391,11393,11395,11397],{},[744,11386,794],{},[852,11388,1252],{"stretchy":1251},[744,11390,2251],{"mathvariant":1233},[852,11392,1258],{"stretchy":1251},[852,11394,854],{},[852,11396,1818],{},[856,11398,915],{},[748,11400,8126],{"encoding":750},[725,11402,11404,11431],{"className":11403,"ariaHidden":755},[754],[725,11405,11407,11410,11413,11416,11419,11422,11425,11428],{"className":11406},[759],[725,11408],{"className":11409,"style":1383},[763],[725,11411,794],{"className":11412},[768,769],[725,11414,1252],{"className":11415},[1394],[725,11417,2251],{"className":11418},[768],[725,11420,1258],{"className":11421},[1401],[725,11423],{"className":11424,"style":878},[877],[725,11426,854],{"className":11427},[882],[725,11429],{"className":11430,"style":878},[877],[725,11432,11434,11437,11440],{"className":11433},[759],[725,11435],{"className":11436,"style":2302},[763],[725,11438,1818],{"className":11439},[768],[725,11441,915],{"className":11442},[768],[725,11444,11446,11463],{"className":11445},[728],[725,11447,11449],{"className":11448},[732],[734,11450,11451],{"xmlns":736},[738,11452,11453,11461],{},[741,11454,11455,11457,11459],{},[744,11456,794],{},[852,11458,854],{},[856,11460,858],{},[748,11462,861],{"encoding":750},[725,11464,11466,11484],{"className":11465,"ariaHidden":755},[754],[725,11467,11469,11472,11475,11478,11481],{"className":11468},[759],[725,11470],{"className":11471,"style":806},[763],[725,11473,794],{"className":11474},[768,769],[725,11476],{"className":11477,"style":878},[877],[725,11479,854],{"className":11480},[882],[725,11482],{"className":11483,"style":878},[877],[725,11485,11487,11490],{"className":11486},[759],[725,11488],{"className":11489,"style":892},[763],[725,11491,858],{"className":11492},[768],[7430,11494],{},[7420,11496,2476],{"id":2475},[2597,11498,11499,11557],{"title":2600},[598,11500,8228,11501,8257,11529,2661],{},[725,11502,11504,11517],{"className":11503},[728],[725,11505,11507],{"className":11506},[732],[734,11508,11509],{"xmlns":736},[738,11510,11511,11515],{},[741,11512,11513],{},[744,11514,746],{},[748,11516,746],{"encoding":750},[725,11518,11520],{"className":11519,"ariaHidden":755},[754],[725,11521,11523,11526],{"className":11522},[759],[725,11524],{"className":11525,"style":764},[763],[725,11527,746],{"className":11528},[768,769],[725,11530,11532,11545],{"className":11531},[728],[725,11533,11535],{"className":11534},[732],[734,11536,11537],{"xmlns":736},[738,11538,11539,11543],{},[741,11540,11541],{},[744,11542,794],{},[748,11544,794],{"encoding":750},[725,11546,11548],{"className":11547,"ariaHidden":755},[754],[725,11549,11551,11554],{"className":11550},[759],[725,11552],{"className":11553,"style":806},[763],[725,11555,794],{"className":11556},[768,769],[598,11558,11559],{},[725,11560,11562,11601],{"className":11561},[728],[725,11563,11565],{"className":11564},[732],[734,11566,11567],{"xmlns":736},[738,11568,11569,11599],{},[741,11570,11571,11573,11575,11577,11579,11581,11583,11595,11597],{},[744,11572,794],{},[852,11574,1310],{},[856,11576,915],{},[852,11578,2703],{},[744,11580,746],{},[852,11582,2703],{},[2905,11584,11585,11587],{},[856,11586,1164],{},[741,11588,11589,11591,11593],{},[744,11590,794],{},[852,11592,1310],{},[856,11594,915],{},[852,11596,1818],{},[856,11598,915],{},[748,11600,2923],{"encoding":750},[725,11602,11604,11622,11640,11658,11711],{"className":11603,"ariaHidden":755},[754],[725,11605,11607,11610,11613,11616,11619],{"className":11606},[759],[725,11608],{"className":11609,"style":2933},[763],[725,11611,794],{"className":11612},[768,769],[725,11614],{"className":11615,"style":1485},[877],[725,11617,1310],{"className":11618},[1489],[725,11620],{"className":11621,"style":1485},[877],[725,11623,11625,11628,11631,11634,11637],{"className":11624},[759],[725,11626],{"className":11627,"style":2815},[763],[725,11629,915],{"className":11630},[768],[725,11632],{"className":11633,"style":878},[877],[725,11635,2703],{"className":11636},[882],[725,11638],{"className":11639,"style":878},[877],[725,11641,11643,11646,11649,11652,11655],{"className":11642},[759],[725,11644],{"className":11645,"style":2970},[763],[725,11647,746],{"className":11648},[768,769],[725,11650],{"className":11651,"style":878},[877],[725,11653,2703],{"className":11654},[882],[725,11656],{"className":11657,"style":878},[877],[725,11659,11661,11664,11702,11705,11708],{"className":11660},[759],[725,11662],{"className":11663,"style":2989},[763],[725,11665,11667,11670],{"className":11666},[768],[725,11668,1164],{"className":11669},[768],[725,11671,11673],{"className":11672},[1511],[725,11674,11676],{"className":11675},[1445],[725,11677,11679],{"className":11678},[1450],[725,11680,11682],{"className":11681,"style":3008},[1454],[725,11683,11684,11687],{"style":3011},[725,11685],{"className":11686,"style":1528},[1462],[725,11688,11690],{"className":11689},[1532,1533,1534,1535],[725,11691,11693,11696,11699],{"className":11692},[768,1535],[725,11694,794],{"className":11695},[768,769,1535],[725,11697,1310],{"className":11698},[1489,1535],[725,11700,915],{"className":11701},[768,1535],[725,11703],{"className":11704,"style":1485},[877],[725,11706,1818],{"className":11707},[1489],[725,11709],{"className":11710,"style":1485},[877],[725,11712,11714,11717],{"className":11713},[759],[725,11715],{"className":11716,"style":892},[763],[725,11718,915],{"className":11719},[768],[7430,11721],{},[7420,11723,8454],{"id":8453},[8456,11725],{"alt":8458,"kind":8459,"src":8460,"svg":8461},[1192,11727,11728,11802],{},[1195,11729,8466,11730,8539],{},[725,11731,11733,11754],{"className":11732},[728],[725,11734,11736],{"className":11735},[732],[734,11737,11738],{"xmlns":736},[738,11739,11740,11752],{},[741,11741,11742,11744,11746,11748,11750],{},[744,11743,794],{},[852,11745,854],{},[744,11747,746],{},[852,11749,1818],{},[856,11751,915],{},[748,11753,5236],{"encoding":750},[725,11755,11757,11775,11793],{"className":11756,"ariaHidden":755},[754],[725,11758,11760,11763,11766,11769,11772],{"className":11759},[759],[725,11761],{"className":11762,"style":806},[763],[725,11764,794],{"className":11765},[768,769],[725,11767],{"className":11768,"style":878},[877],[725,11770,854],{"className":11771},[882],[725,11773],{"className":11774,"style":878},[877],[725,11776,11778,11781,11784,11787,11790],{"className":11777},[759],[725,11779],{"className":11780,"style":2853},[763],[725,11782,746],{"className":11783},[768,769],[725,11785],{"className":11786,"style":1485},[877],[725,11788,1818],{"className":11789},[1489],[725,11791],{"className":11792,"style":1485},[877],[725,11794,11796,11799],{"className":11795},[759],[725,11797],{"className":11798,"style":892},[763],[725,11800,915],{"className":11801},[768],[1195,11803,8542,11804,8648],{},[725,11805,11807,11834],{"className":11806},[728],[725,11808,11810],{"className":11809},[732],[734,11811,11812],{"xmlns":736},[738,11813,11814,11832],{},[741,11815,11816,11818,11820,11830],{},[744,11817,794],{},[852,11819,7050],{},[1328,11821,11822,11828],{},[741,11823,11824,11826],{},[744,11825,2682],{},[852,11827,1850],{},[856,11829,1164],{},[744,11831,746],{},[748,11833,7065],{"encoding":750},[725,11835,11837,11855],{"className":11836,"ariaHidden":755},[754],[725,11838,11840,11843,11846,11849,11852],{"className":11839},[759],[725,11841],{"className":11842,"style":806},[763],[725,11844,794],{"className":11845},[768,769],[725,11847],{"className":11848,"style":878},[877],[725,11850,7050],{"className":11851},[882],[725,11853],{"className":11854,"style":878},[877],[725,11856,11858,11861,11903,11906],{"className":11857},[759],[725,11859],{"className":11860,"style":7093},[763],[725,11862,11864,11869],{"className":11863},[2022],[725,11865,2732,11867],{"className":11866},[2022],[725,11868,1334],{"style":2735},[725,11870,11872],{"className":11871},[1511],[725,11873,11875,11895],{"className":11874},[1445,1446],[725,11876,11878,11892],{"className":11877},[1450],[725,11879,11881],{"className":11880,"style":2748},[1454],[725,11882,11883,11886],{"style":2751},[725,11884],{"className":11885,"style":1528},[1462],[725,11887,11889],{"className":11888},[1532,1533,1534,1535],[725,11890,1164],{"className":11891},[768,1535],[725,11893,1544],{"className":11894},[1543],[725,11896,11898],{"className":11897},[1450],[725,11899,11901],{"className":11900,"style":2770},[1454],[725,11902],{},[725,11904],{"className":11905,"style":2085},[877],[725,11907,746],{"className":11908},[768,769],[7430,11910],{},[7420,11912,8654],{"id":8653},[1192,11914,11915,12019],{},[1195,11916,11917,723,11919,6307,11969,8764],{},[602,11918,8661],{},[725,11920,11922,11939],{"className":11921},[728],[725,11923,11925],{"className":11924},[732],[734,11926,11927],{"xmlns":736},[738,11928,11929,11937],{},[741,11930,11931,11933,11935],{},[744,11932,794],{},[852,11934,854],{},[856,11936,858],{},[748,11938,8682],{"encoding":750},[725,11940,11942,11960],{"className":11941,"ariaHidden":755},[754],[725,11943,11945,11948,11951,11954,11957],{"className":11944},[759],[725,11946],{"className":11947,"style":806},[763],[725,11949,794],{"className":11950},[768,769],[725,11952],{"className":11953,"style":878},[877],[725,11955,854],{"className":11956},[882],[725,11958],{"className":11959,"style":878},[877],[725,11961,11963,11966],{"className":11962},[759],[725,11964],{"className":11965,"style":892},[763],[725,11967,858],{"className":11968},[768],[725,11970,11972,11989],{"className":11971},[728],[725,11973,11975],{"className":11974},[732],[734,11976,11977],{"xmlns":736},[738,11978,11979,11987],{},[741,11980,11981,11983,11985],{},[744,11982,746],{},[852,11984,854],{},[856,11986,915],{},[748,11988,8733],{"encoding":750},[725,11990,11992,12010],{"className":11991,"ariaHidden":755},[754],[725,11993,11995,11998,12001,12004,12007],{"className":11994},[759],[725,11996],{"className":11997,"style":764},[763],[725,11999,746],{"className":12000},[768,769],[725,12002],{"className":12003,"style":878},[877],[725,12005,854],{"className":12006},[882],[725,12008],{"className":12009,"style":878},[877],[725,12011,12013,12016],{"className":12012},[759],[725,12014],{"className":12015,"style":892},[763],[725,12017,915],{"className":12018},[768],[1195,12020,12021,8770,12023,5211,12073,5566,12123,8946,12195,9042,12289,949],{},[602,12022,8769],{},[725,12024,12026,12043],{"className":12025},[728],[725,12027,12029],{"className":12028},[732],[734,12030,12031],{"xmlns":736},[738,12032,12033,12041],{},[741,12034,12035,12037,12039],{},[744,12036,794],{},[852,12038,1818],{},[856,12040,915],{},[748,12042,8791],{"encoding":750},[725,12044,12046,12064],{"className":12045,"ariaHidden":755},[754],[725,12047,12049,12052,12055,12058,12061],{"className":12048},[759],[725,12050],{"className":12051,"style":2933},[763],[725,12053,794],{"className":12054},[768,769],[725,12056],{"className":12057,"style":1485},[877],[725,12059,1818],{"className":12060},[1489],[725,12062],{"className":12063,"style":1485},[877],[725,12065,12067,12070],{"className":12066},[759],[725,12068],{"className":12069,"style":892},[763],[725,12071,915],{"className":12072},[768],[725,12074,12076,12093],{"className":12075},[728],[725,12077,12079],{"className":12078},[732],[734,12080,12081],{"xmlns":736},[738,12082,12083,12091],{},[741,12084,12085,12087,12089],{},[744,12086,746],{},[852,12088,3674],{},[744,12090,794],{},[748,12092,8842],{"encoding":750},[725,12094,12096,12114],{"className":12095,"ariaHidden":755},[754],[725,12097,12099,12102,12105,12108,12111],{"className":12098},[759],[725,12100],{"className":12101,"style":2970},[763],[725,12103,746],{"className":12104},[768,769],[725,12106],{"className":12107,"style":878},[877],[725,12109,3674],{"className":12110},[882],[725,12112],{"className":12113,"style":878},[877],[725,12115,12117,12120],{"className":12116},[759],[725,12118],{"className":12119,"style":806},[763],[725,12121,794],{"className":12122},[768,769],[725,12124,12126,12147],{"className":12125},[728],[725,12127,12129],{"className":12128},[732],[734,12130,12131],{"xmlns":736},[738,12132,12133,12145],{},[741,12134,12135,12137,12139,12141,12143],{},[744,12136,746],{},[852,12138,3674],{},[744,12140,794],{},[852,12142,1310],{},[856,12144,915],{},[748,12146,8897],{"encoding":750},[725,12148,12150,12168,12186],{"className":12149,"ariaHidden":755},[754],[725,12151,12153,12156,12159,12162,12165],{"className":12152},[759],[725,12154],{"className":12155,"style":2970},[763],[725,12157,746],{"className":12158},[768,769],[725,12160],{"className":12161,"style":878},[877],[725,12163,3674],{"className":12164},[882],[725,12166],{"className":12167,"style":878},[877],[725,12169,12171,12174,12177,12180,12183],{"className":12170},[759],[725,12172],{"className":12173,"style":2933},[763],[725,12175,794],{"className":12176},[768,769],[725,12178],{"className":12179,"style":1485},[877],[725,12181,1310],{"className":12182},[1489],[725,12184],{"className":12185,"style":1485},[877],[725,12187,12189,12192],{"className":12188},[759],[725,12190],{"className":12191,"style":892},[763],[725,12193,915],{"className":12194},[768],[725,12196,12198,12221],{"className":12197},[728],[725,12199,12201],{"className":12200},[732],[734,12202,12203],{"xmlns":736},[738,12204,12205,12219],{},[741,12206,12207,12209,12215,12217],{},[852,12208,2703],{},[2905,12210,12211,12213],{},[856,12212,1164],{},[744,12214,794],{},[852,12216,1818],{},[856,12218,915],{},[748,12220,8973],{"encoding":750},[725,12222,12224,12236,12280],{"className":12223,"ariaHidden":755},[754],[725,12225,12227,12230,12233],{"className":12226},[759],[725,12228],{"className":12229,"style":2970},[763],[725,12231,2703],{"className":12232},[882],[725,12234],{"className":12235,"style":878},[877],[725,12237,12239,12242,12271,12274,12277],{"className":12238},[759],[725,12240],{"className":12241,"style":2989},[763],[725,12243,12245,12248],{"className":12244},[768],[725,12246,1164],{"className":12247},[768],[725,12249,12251],{"className":12250},[1511],[725,12252,12254],{"className":12253},[1445],[725,12255,12257],{"className":12256},[1450],[725,12258,12260],{"className":12259,"style":3008},[1454],[725,12261,12262,12265],{"style":3011},[725,12263],{"className":12264,"style":1528},[1462],[725,12266,12268],{"className":12267},[1532,1533,1534,1535],[725,12269,794],{"className":12270},[768,769,1535],[725,12272],{"className":12273,"style":1485},[877],[725,12275,1818],{"className":12276},[1489],[725,12278],{"className":12279,"style":1485},[877],[725,12281,12283,12286],{"className":12282},[759],[725,12284],{"className":12285,"style":892},[763],[725,12287,915],{"className":12288},[768],[725,12290,12292,12345],{"className":12291},[728],[725,12293,12295],{"className":12294},[732],[734,12296,12297],{"xmlns":736},[738,12298,12299,12343],{},[741,12300,12301,12303,12305,12307,12309,12311,12313,12319,12321,12323,12325,12327,12339,12341],{},[744,12302,746],{},[852,12304,2703],{},[856,12306,915],{},[852,12308,1310],{},[856,12310,1164],{},[852,12312,1252],{"stretchy":1251},[2905,12314,12315,12317],{},[856,12316,1164],{},[744,12318,794],{},[852,12320,1818],{},[856,12322,915],{},[852,12324,1258],{"stretchy":1251},[852,12326,854],{},[2905,12328,12329,12331],{},[856,12330,1164],{},[741,12332,12333,12335,12337],{},[744,12334,794],{},[852,12336,1310],{},[856,12338,915],{},[852,12340,1818],{},[856,12342,915],{},[748,12344,9099],{"encoding":750},[725,12346,12348,12366,12384,12434,12455,12508],{"className":12347,"ariaHidden":755},[754],[725,12349,12351,12354,12357,12360,12363],{"className":12350},[759],[725,12352],{"className":12353,"style":2970},[763],[725,12355,746],{"className":12356},[768,769],[725,12358],{"className":12359,"style":878},[877],[725,12361,2703],{"className":12362},[882],[725,12364],{"className":12365,"style":878},[877],[725,12367,12369,12372,12375,12378,12381],{"className":12368},[759],[725,12370],{"className":12371,"style":2302},[763],[725,12373,915],{"className":12374},[768],[725,12376],{"className":12377,"style":1485},[877],[725,12379,1310],{"className":12380},[1489],[725,12382],{"className":12383,"style":1485},[877],[725,12385,12387,12390,12393,12396,12425,12428,12431],{"className":12386},[759],[725,12388],{"className":12389,"style":4597},[763],[725,12391,1164],{"className":12392},[768],[725,12394,1252],{"className":12395},[1394],[725,12397,12399,12402],{"className":12398},[768],[725,12400,1164],{"className":12401},[768],[725,12403,12405],{"className":12404},[1511],[725,12406,12408],{"className":12407},[1445],[725,12409,12411],{"className":12410},[1450],[725,12412,12414],{"className":12413,"style":3008},[1454],[725,12415,12416,12419],{"style":3011},[725,12417],{"className":12418,"style":1528},[1462],[725,12420,12422],{"className":12421},[1532,1533,1534,1535],[725,12423,794],{"className":12424},[768,769,1535],[725,12426],{"className":12427,"style":1485},[877],[725,12429,1818],{"className":12430},[1489],[725,12432],{"className":12433,"style":1485},[877],[725,12435,12437,12440,12443,12446,12449,12452],{"className":12436},[759],[725,12438],{"className":12439,"style":1383},[763],[725,12441,915],{"className":12442},[768],[725,12444,1258],{"className":12445},[1401],[725,12447],{"className":12448,"style":878},[877],[725,12450,854],{"className":12451},[882],[725,12453],{"className":12454,"style":878},[877],[725,12456,12458,12461,12499,12502,12505],{"className":12457},[759],[725,12459],{"className":12460,"style":2989},[763],[725,12462,12464,12467],{"className":12463},[768],[725,12465,1164],{"className":12466},[768],[725,12468,12470],{"className":12469},[1511],[725,12471,12473],{"className":12472},[1445],[725,12474,12476],{"className":12475},[1450],[725,12477,12479],{"className":12478,"style":3008},[1454],[725,12480,12481,12484],{"style":3011},[725,12482],{"className":12483,"style":1528},[1462],[725,12485,12487],{"className":12486},[1532,1533,1534,1535],[725,12488,12490,12493,12496],{"className":12489},[768,1535],[725,12491,794],{"className":12492},[768,769,1535],[725,12494,1310],{"className":12495},[1489,1535],[725,12497,915],{"className":12498},[768,1535],[725,12500],{"className":12501,"style":1485},[877],[725,12503,1818],{"className":12504},[1489],[725,12506],{"className":12507,"style":1485},[877],[725,12509,12511,12514],{"className":12510},[759],[725,12512],{"className":12513,"style":892},[763],[725,12515,915],{"className":12516},[768],[7430,12518],{},[7420,12520,9277],{"id":9276},[598,12522,12523],{},[602,12524,9282],{},[5898,12526,7399],{},{"title":968,"searchDepth":989,"depth":989,"links":12528},[],{},{"title":7416,"description":9287},1788035584383]