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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":421,"bo":587,"body":588,"description":3542,"eval":587,"extension":3543,"labo":587,"meta":3544,"navigation":3545,"path":422,"quizzes":3546,"readingTime":946,"seo":3553,"stem":423,"tp":587,"__hash__":3554},"cours\u002F1.nsi-1ere\u002Fph-algorithmique\u002F2.complexite-bases.md",null,{"type":589,"value":590,"toc":3524},"minimark",[591,596,605,609,628,685,689,725,857,861,923,934,979,1027,1063,1126,1219,1286,1390,1518,1541,1545,1666,1958,2119,2234,2238,2581,2596,2850,3045,3049,3056,3093,3191,3210,3214,3383,3387,3520],[592,593,595],"h2",{"id":594},"introduction","Introduction",[597,598,599,600,604],"p",{},"Vous savez maintenant écrire un parcours séquentiel. Mais vous écrirez bientôt\ndes algorithmes plus subtils, et la première question d'un informaticien\ndevant un algorithme n'est pas « est-ce qu'il marche ? » — c'est « combien\ncoûte-t-il ? ». Combien d'opérations effectue-t-il selon la taille des\ndonnées ? Si je double l'entrée, le temps double-t-il, quadruple-t-il, ou\naugmente-t-il à peine ? Ce cours pose le ",[601,602,603],"strong",{},"socle"," de cette analyse. Pas de\nthéorème lourd : juste une intuition claire et une notation simple, qui vous\nserviront dans tout le reste du chapitre.",[592,606,608],{"id":607},"pourquoi-mesurer","Pourquoi mesurer ?",[597,610,611,612,615,616,619,620,623,624,627],{},"Imaginez deux programmes qui font la même chose : chercher un nom dans un\nannuaire de 10 millions d'entrées. Le premier met ",[601,613,614],{},"3 secondes",", le second\nmet ",[601,617,618],{},"3 minutes",". Vous préférerez le premier, évidemment. La complexité,\nc'est l'outil qui permet de ",[601,621,622],{},"prédire"," cette différence ",[601,625,626],{},"avant même\nd'exécuter le code",", en analysant la structure de l'algorithme.",[629,630,631],"tip",{},[597,632,633,634,637,638,684],{},"On ne mesure pas en secondes (cela dépend de la machine, du langage, de la\ncharge système). On compte le ",[601,635,636],{},"nombre d'opérations élémentaires"," effectuées\nen fonction de la taille de l'entrée, notée ",[639,640,643,665],"span",{"className":641},[642],"katex",[639,644,647],{"className":645},[646],"katex-mathml",[648,649,651],"math",{"xmlns":650},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[652,653,654,661],"semantics",{},[655,656,657],"mrow",{},[658,659,660],"mi",{},"n",[662,663,660],"annotation",{"encoding":664},"application\u002Fx-tex",[639,666,670],{"className":667,"ariaHidden":669},[668],"katex-html","true",[639,671,674,679],{"className":672},[673],"base",[639,675],{"className":676,"style":678},[677],"strut","height:0.4306em;",[639,680,660],{"className":681},[682,683],"mord","mathnormal",".",[592,686,688],{"id":687},"taille-de-lentrée","Taille de l'entrée",[597,690,691,692,695,696,724],{},"Avant de compter, il faut décider de ce qu'est la ",[601,693,694],{},"taille"," ",[639,697,699,712],{"className":698},[642],[639,700,702],{"className":701},[646],[648,703,704],{"xmlns":650},[652,705,706,710],{},[655,707,708],{},[658,709,660],{},[662,711,660],{"encoding":664},[639,713,715],{"className":714,"ariaHidden":669},[668],[639,716,718,721],{"className":717},[673],[639,719],{"className":720,"style":678},[677],[639,722,660],{"className":723},[682,683],". C'est en\ngénéral évident :",[726,727,728,761,793],"ul",{},[729,730,731,732,760],"li",{},"pour un tableau ou une liste : ",[639,733,735,748],{"className":734},[642],[639,736,738],{"className":737},[646],[648,739,740],{"xmlns":650},[652,741,742,746],{},[655,743,744],{},[658,745,660],{},[662,747,660],{"encoding":664},[639,749,751],{"className":750,"ariaHidden":669},[668],[639,752,754,757],{"className":753},[673],[639,755],{"className":756,"style":678},[677],[639,758,660],{"className":759},[682,683]," = le nombre d'éléments,",[729,762,763,764,792],{},"pour une chaîne de caractères : ",[639,765,767,780],{"className":766},[642],[639,768,770],{"className":769},[646],[648,771,772],{"xmlns":650},[652,773,774,778],{},[655,775,776],{},[658,777,660],{},[662,779,660],{"encoding":664},[639,781,783],{"className":782,"ariaHidden":669},[668],[639,784,786,789],{"className":785},[673],[639,787],{"className":788,"style":678},[677],[639,790,660],{"className":791},[682,683]," = sa longueur,",[729,794,795,796,827,828,856],{},"pour un entier ",[639,797,799,813],{"className":798},[642],[639,800,802],{"className":801},[646],[648,803,804],{"xmlns":650},[652,805,806,811],{},[655,807,808],{},[658,809,810],{},"k",[662,812,810],{"encoding":664},[639,814,816],{"className":815,"ariaHidden":669},[668],[639,817,819,823],{"className":818},[673],[639,820],{"className":821,"style":822},[677],"height:0.6944em;",[639,824,810],{"className":825,"style":826},[682,683],"margin-right:0.0315em;"," : ",[639,829,831,844],{"className":830},[642],[639,832,834],{"className":833},[646],[648,835,836],{"xmlns":650},[652,837,838,842],{},[655,839,840],{},[658,841,660],{},[662,843,660],{"encoding":664},[639,845,847],{"className":846,"ariaHidden":669},[668],[639,848,850,853],{"className":849},[673],[639,851],{"className":852,"style":678},[677],[639,854,660],{"className":855},[682,683]," = sa valeur (parfois son nombre de chiffres).",[592,858,860],{"id":859},"trois-ordres-de-grandeur-typiques","Trois ordres de grandeur typiques",[862,863,865,866],"h3",{"id":864},"coût-constant-o1mathcalo1o1","Coût constant — ",[639,867,869,897],{"className":868},[642],[639,870,872],{"className":871},[646],[648,873,874],{"xmlns":650},[652,875,876,894],{},[655,877,878,882,887,891],{},[658,879,881],{"mathvariant":880},"script","O",[883,884,886],"mo",{"stretchy":885},"false","(",[888,889,890],"mn",{},"1",[883,892,893],{"stretchy":885},")",[662,895,896],{"encoding":664},"\\mathcal{O}(1)",[639,898,900],{"className":899,"ariaHidden":669},[668],[639,901,903,907,912,916,919],{"className":902},[673],[639,904],{"className":905,"style":906},[677],"height:1em;vertical-align:-0.25em;",[639,908,881],{"className":909,"style":911},[682,910],"mathcal","margin-right:0.0278em;",[639,913,886],{"className":914},[915],"mopen",[639,917,890],{"className":918},[682],[639,920,893],{"className":921},[922],"mclose",[597,924,925,926,930,931,684],{},"Le coût ne dépend pas de la taille. Que ",[927,928,929],"code",{},"tableau"," ait 10 ou 10 millions\nd'éléments, l'opération prend le ",[601,932,933],{},"même temps",[935,936,941],"pre",{"className":937,"code":938,"language":939,"meta":940,"style":940},"language-python shiki shiki-themes github-light github-light github-dark","def premier(tableau):\n    return tableau[0]   # un seul accès, peu importe la taille\n","python","",[927,942,943,959],{"__ignoreMap":940},[639,944,947,951,955],{"class":945,"line":946},"line",1,[639,948,950],{"class":949},"s8jYJ","def",[639,952,954],{"class":953},"snPdu"," premier",[639,956,958],{"class":957},"sxrX7","(tableau):\n",[639,960,962,965,968,972,975],{"class":945,"line":961},2,[639,963,964],{"class":949},"    return",[639,966,967],{"class":957}," tableau[",[639,969,971],{"class":970},"sBjJW","0",[639,973,974],{"class":957},"]   ",[639,976,978],{"class":977},"sCsY4","# un seul accès, peu importe la taille\n",[862,980,982,983],{"id":981},"coût-linéaire-onmathcalonon","Coût linéaire — ",[639,984,986,1006],{"className":985},[642],[639,987,989],{"className":988},[646],[648,990,991],{"xmlns":650},[652,992,993,1003],{},[655,994,995,997,999,1001],{},[658,996,881],{"mathvariant":880},[883,998,886],{"stretchy":885},[658,1000,660],{},[883,1002,893],{"stretchy":885},[662,1004,1005],{"encoding":664},"\\mathcal{O}(n)",[639,1007,1009],{"className":1008,"ariaHidden":669},[668],[639,1010,1012,1015,1018,1021,1024],{"className":1011},[673],[639,1013],{"className":1014,"style":906},[677],[639,1016,881],{"className":1017,"style":911},[682,910],[639,1019,886],{"className":1020},[915],[639,1022,660],{"className":1023},[682,683],[639,1025,893],{"className":1026},[922],[597,1028,1029,1030,1033,1034,1062],{},"Le coût est ",[601,1031,1032],{},"proportionnel"," à ",[639,1035,1037,1050],{"className":1036},[642],[639,1038,1040],{"className":1039},[646],[648,1041,1042],{"xmlns":650},[652,1043,1044,1048],{},[655,1045,1046],{},[658,1047,660],{},[662,1049,660],{"encoding":664},[639,1051,1053],{"className":1052,"ariaHidden":669},[668],[639,1054,1056,1059],{"className":1055},[673],[639,1057],{"className":1058,"style":678},[677],[639,1060,660],{"className":1061},[682,683],". Si on double la taille, le temps double.\nTout parcours séquentiel du cours précédent est dans ce cas.",[935,1064,1066],{"className":937,"code":1065,"language":939,"meta":940,"style":940},"def somme(tableau):\n    total = 0\n    for v in tableau:   # exactement n tours\n        total += v\n    return total\n",[927,1067,1068,1077,1088,1106,1118],{"__ignoreMap":940},[639,1069,1070,1072,1075],{"class":945,"line":946},[639,1071,950],{"class":949},[639,1073,1074],{"class":953}," somme",[639,1076,958],{"class":957},[639,1078,1079,1082,1085],{"class":945,"line":961},[639,1080,1081],{"class":957},"    total ",[639,1083,1084],{"class":949},"=",[639,1086,1087],{"class":970}," 0\n",[639,1089,1091,1094,1097,1100,1103],{"class":945,"line":1090},3,[639,1092,1093],{"class":949},"    for",[639,1095,1096],{"class":957}," v ",[639,1098,1099],{"class":949},"in",[639,1101,1102],{"class":957}," tableau:   ",[639,1104,1105],{"class":977},"# exactement n tours\n",[639,1107,1109,1112,1115],{"class":945,"line":1108},4,[639,1110,1111],{"class":957},"        total ",[639,1113,1114],{"class":949},"+=",[639,1116,1117],{"class":957}," v\n",[639,1119,1121,1123],{"class":945,"line":1120},5,[639,1122,964],{"class":949},[639,1124,1125],{"class":957}," total\n",[862,1127,1129,1130],{"id":1128},"coût-quadratique-on2mathcalon2on2","Coût quadratique — ",[639,1131,1133,1159],{"className":1132},[642],[639,1134,1136],{"className":1135},[646],[648,1137,1138],{"xmlns":650},[652,1139,1140,1156],{},[655,1141,1142,1144,1146,1154],{},[658,1143,881],{"mathvariant":880},[883,1145,886],{"stretchy":885},[1147,1148,1149,1151],"msup",{},[658,1150,660],{},[888,1152,1153],{},"2",[883,1155,893],{"stretchy":885},[662,1157,1158],{"encoding":664},"\\mathcal{O}(n^2)",[639,1160,1162],{"className":1161,"ariaHidden":669},[668],[639,1163,1165,1169,1172,1175,1216],{"className":1164},[673],[639,1166],{"className":1167,"style":1168},[677],"height:1.0641em;vertical-align:-0.25em;",[639,1170,881],{"className":1171,"style":911},[682,910],[639,1173,886],{"className":1174},[915],[639,1176,1178,1181],{"className":1177},[682],[639,1179,660],{"className":1180},[682,683],[639,1182,1185],{"className":1183},[1184],"msupsub",[639,1186,1189],{"className":1187},[1188],"vlist-t",[639,1190,1193],{"className":1191},[1192],"vlist-r",[639,1194,1198],{"className":1195,"style":1197},[1196],"vlist","height:0.8141em;",[639,1199,1201,1206],{"style":1200},"top:-3.063em;margin-right:0.05em;",[639,1202],{"className":1203,"style":1205},[1204],"pstrut","height:2.7em;",[639,1207,1213],{"className":1208},[1209,1210,1211,1212],"sizing","reset-size6","size3","mtight",[639,1214,1153],{"className":1215},[682,1212],[639,1217,893],{"className":1218},[922],[597,1220,1221,1222,1281,1282,1285],{},"Le coût est proportionnel à ",[639,1223,1225,1243],{"className":1224},[642],[639,1226,1228],{"className":1227},[646],[648,1229,1230],{"xmlns":650},[652,1231,1232,1240],{},[655,1233,1234],{},[1147,1235,1236,1238],{},[658,1237,660],{},[888,1239,1153],{},[662,1241,1242],{"encoding":664},"n^2",[639,1244,1246],{"className":1245,"ariaHidden":669},[668],[639,1247,1249,1252],{"className":1248},[673],[639,1250],{"className":1251,"style":1197},[677],[639,1253,1255,1258],{"className":1254},[682],[639,1256,660],{"className":1257},[682,683],[639,1259,1261],{"className":1260},[1184],[639,1262,1264],{"className":1263},[1188],[639,1265,1267],{"className":1266},[1192],[639,1268,1270],{"className":1269,"style":1197},[1196],[639,1271,1272,1275],{"style":1200},[639,1273],{"className":1274,"style":1205},[1204],[639,1276,1278],{"className":1277},[1209,1210,1211,1212],[639,1279,1153],{"className":1280},[682,1212],". Si on double la taille, le temps est\n",[601,1283,1284],{},"multiplié par 4",". On l'obtient typiquement avec deux boucles imbriquées\nqui parcourent chacune le tableau.",[935,1287,1289],{"className":937,"code":1288,"language":939,"meta":940,"style":940},"def doublons(tableau):\n    \"\"\"Renvoie True si tableau contient au moins un doublon.\"\"\"\n    n = len(tableau)\n    for i in range(n):\n        for j in range(i + 1, n):\n            if tableau[i] == tableau[j]:\n                return True\n    return False\n",[927,1290,1291,1300,1306,1319,1334,1358,1373,1382],{"__ignoreMap":940},[639,1292,1293,1295,1298],{"class":945,"line":946},[639,1294,950],{"class":949},[639,1296,1297],{"class":953}," doublons",[639,1299,958],{"class":957},[639,1301,1302],{"class":945,"line":961},[639,1303,1305],{"class":1304},"sIIMD","    \"\"\"Renvoie True si tableau contient au moins un doublon.\"\"\"\n",[639,1307,1308,1311,1313,1316],{"class":945,"line":1090},[639,1309,1310],{"class":957},"    n ",[639,1312,1084],{"class":949},[639,1314,1315],{"class":970}," len",[639,1317,1318],{"class":957},"(tableau)\n",[639,1320,1321,1323,1326,1328,1331],{"class":945,"line":1108},[639,1322,1093],{"class":949},[639,1324,1325],{"class":957}," i ",[639,1327,1099],{"class":949},[639,1329,1330],{"class":970}," range",[639,1332,1333],{"class":957},"(n):\n",[639,1335,1336,1339,1342,1344,1346,1349,1352,1355],{"class":945,"line":1120},[639,1337,1338],{"class":949},"        for",[639,1340,1341],{"class":957}," j ",[639,1343,1099],{"class":949},[639,1345,1330],{"class":970},[639,1347,1348],{"class":957},"(i ",[639,1350,1351],{"class":949},"+",[639,1353,1354],{"class":970}," 1",[639,1356,1357],{"class":957},", n):\n",[639,1359,1361,1364,1367,1370],{"class":945,"line":1360},6,[639,1362,1363],{"class":949},"            if",[639,1365,1366],{"class":957}," tableau[i] ",[639,1368,1369],{"class":949},"==",[639,1371,1372],{"class":957}," tableau[j]:\n",[639,1374,1376,1379],{"class":945,"line":1375},7,[639,1377,1378],{"class":949},"                return",[639,1380,1381],{"class":970}," True\n",[639,1383,1385,1387],{"class":945,"line":1384},8,[639,1386,964],{"class":949},[639,1388,1389],{"class":970}," False\n",[597,1391,1392,1393,1459,1460,684],{},"Le nombre de comparaisons est de l'ordre de ",[639,1394,1396,1421],{"className":1395},[642],[639,1397,1399],{"className":1398},[646],[648,1400,1401],{"xmlns":650},[652,1402,1403,1418],{},[655,1404,1405,1407,1410,1412,1416],{},[658,1406,660],{},[883,1408,1409],{},"×",[658,1411,660],{},[658,1413,1415],{"mathvariant":1414},"normal","\u002F",[888,1417,1153],{},[662,1419,1420],{"encoding":664},"n \\times n \u002F 2",[639,1422,1424,1446],{"className":1423,"ariaHidden":669},[668],[639,1425,1427,1431,1434,1439,1443],{"className":1426},[673],[639,1428],{"className":1429,"style":1430},[677],"height:0.6667em;vertical-align:-0.0833em;",[639,1432,660],{"className":1433},[682,683],[639,1435],{"className":1436,"style":1438},[1437],"mspace","margin-right:0.2222em;",[639,1440,1409],{"className":1441},[1442],"mbin",[639,1444],{"className":1445,"style":1438},[1437],[639,1447,1449,1452,1455],{"className":1448},[673],[639,1450],{"className":1451,"style":906},[677],[639,1453,660],{"className":1454},[682,683],[639,1456,1458],{"className":1457},[682],"\u002F2"," — ce qui reste\nproportionnel à ",[639,1461,1463,1480],{"className":1462},[642],[639,1464,1466],{"className":1465},[646],[648,1467,1468],{"xmlns":650},[652,1469,1470,1478],{},[655,1471,1472],{},[1147,1473,1474,1476],{},[658,1475,660],{},[888,1477,1153],{},[662,1479,1242],{"encoding":664},[639,1481,1483],{"className":1482,"ariaHidden":669},[668],[639,1484,1486,1489],{"className":1485},[673],[639,1487],{"className":1488,"style":1197},[677],[639,1490,1492,1495],{"className":1491},[682],[639,1493,660],{"className":1494},[682,683],[639,1496,1498],{"className":1497},[1184],[639,1499,1501],{"className":1500},[1188],[639,1502,1504],{"className":1503},[1192],[639,1505,1507],{"className":1506,"style":1197},[1196],[639,1508,1509,1512],{"style":1200},[639,1510],{"className":1511,"style":1205},[1204],[639,1513,1515],{"className":1514},[1209,1210,1211,1212],[639,1516,1153],{"className":1517},[682,1212],[1519,1520,1522,1528],"self-eval-qcm",{"correct":890,"slug":1521},"complexite-bases-c1",[1523,1524,1525],"template",{"v-slot:question":940},[597,1526,1527],{},"Si un algo en O(n²) met 1 seconde pour n=1000, combien de temps environ pour n=10000 ?",[1523,1529,1530],{"v-slot:choices":940},[726,1531,1532,1535,1538],{},[729,1533,1534],{},"10 secondes",[729,1536,1537],{},"100 secondes",[729,1539,1540],{},"1000 secondes",[592,1542,1544],{"id":1543},"la-notation-grand-o-en-douceur","La notation grand-O, en douceur",[597,1546,1547,1548,1591,1592,1665],{},"On a écrit ",[639,1549,1551,1570],{"className":1550},[642],[639,1552,1554],{"className":1553},[646],[648,1555,1556],{"xmlns":650},[652,1557,1558,1568],{},[655,1559,1560,1562,1564,1566],{},[658,1561,881],{"mathvariant":880},[883,1563,886],{"stretchy":885},[658,1565,660],{},[883,1567,893],{"stretchy":885},[662,1569,1005],{"encoding":664},[639,1571,1573],{"className":1572,"ariaHidden":669},[668],[639,1574,1576,1579,1582,1585,1588],{"className":1575},[673],[639,1577],{"className":1578,"style":906},[677],[639,1580,881],{"className":1581,"style":911},[682,910],[639,1583,886],{"className":1584},[915],[639,1586,660],{"className":1587},[682,683],[639,1589,893],{"className":1590},[922],", ",[639,1593,1595,1618],{"className":1594},[642],[639,1596,1598],{"className":1597},[646],[648,1599,1600],{"xmlns":650},[652,1601,1602,1616],{},[655,1603,1604,1606,1608,1614],{},[658,1605,881],{"mathvariant":880},[883,1607,886],{"stretchy":885},[1147,1609,1610,1612],{},[658,1611,660],{},[888,1613,1153],{},[883,1615,893],{"stretchy":885},[662,1617,1158],{"encoding":664},[639,1619,1621],{"className":1620,"ariaHidden":669},[668],[639,1622,1624,1627,1630,1633,1662],{"className":1623},[673],[639,1625],{"className":1626,"style":1168},[677],[639,1628,881],{"className":1629,"style":911},[682,910],[639,1631,886],{"className":1632},[915],[639,1634,1636,1639],{"className":1635},[682],[639,1637,660],{"className":1638},[682,683],[639,1640,1642],{"className":1641},[1184],[639,1643,1645],{"className":1644},[1188],[639,1646,1648],{"className":1647},[1192],[639,1649,1651],{"className":1650,"style":1197},[1196],[639,1652,1653,1656],{"style":1200},[639,1654],{"className":1655,"style":1205},[1204],[639,1657,1659],{"className":1658},[1209,1210,1211,1212],[639,1660,1153],{"className":1661},[682,1212],[639,1663,893],{"className":1664},[922],". Que signifie ce symbole ?",[597,1667,1668,1669,1672,1673,1676,1677,1680,1681,1709,1710,1770,1771,1823,1824,1827,1828,1856,1857,1900,1901,1929,1930,684],{},"L'idée : on ",[601,1670,1671],{},"néglige les constantes"," et les ",[601,1674,1675],{},"détails de petite taille","\npour ne garder que l'",[601,1678,1679],{},"ordre de grandeur"," quand ",[639,1682,1684,1697],{"className":1683},[642],[639,1685,1687],{"className":1686},[646],[648,1688,1689],{"xmlns":650},[652,1690,1691,1695],{},[655,1692,1693],{},[658,1694,660],{},[662,1696,660],{"encoding":664},[639,1698,1700],{"className":1699,"ariaHidden":669},[668],[639,1701,1703,1706],{"className":1702},[673],[639,1704],{"className":1705,"style":678},[677],[639,1707,660],{"className":1708},[682,683]," devient grand. Par\nexemple, un algorithme qui fait ",[639,1711,1713,1735],{"className":1712},[642],[639,1714,1716],{"className":1715},[646],[648,1717,1718],{"xmlns":650},[652,1719,1720,1732],{},[655,1721,1722,1725,1727,1729],{},[888,1723,1724],{},"3",[658,1726,660],{},[883,1728,1351],{},[888,1730,1731],{},"7",[662,1733,1734],{"encoding":664},"3n + 7",[639,1736,1738,1760],{"className":1737,"ariaHidden":669},[668],[639,1739,1741,1745,1748,1751,1754,1757],{"className":1740},[673],[639,1742],{"className":1743,"style":1744},[677],"height:0.7278em;vertical-align:-0.0833em;",[639,1746,1724],{"className":1747},[682],[639,1749,660],{"className":1750},[682,683],[639,1752],{"className":1753,"style":1438},[1437],[639,1755,1351],{"className":1756},[1442],[639,1758],{"className":1759,"style":1438},[1437],[639,1761,1763,1767],{"className":1762},[673],[639,1764],{"className":1765,"style":1766},[677],"height:0.6444em;",[639,1768,1731],{"className":1769},[682]," opérations et un autre qui en fait\n",[639,1772,1774,1793],{"className":1773},[642],[639,1775,1777],{"className":1776},[646],[648,1778,1779],{"xmlns":650},[652,1780,1781,1790],{},[655,1782,1783,1785,1788],{},[658,1784,660],{},[883,1786,1787],{},"−",[888,1789,890],{},[662,1791,1792],{"encoding":664},"n - 1",[639,1794,1796,1814],{"className":1795,"ariaHidden":669},[668],[639,1797,1799,1802,1805,1808,1811],{"className":1798},[673],[639,1800],{"className":1801,"style":1430},[677],[639,1803,660],{"className":1804},[682,683],[639,1806],{"className":1807,"style":1438},[1437],[639,1809,1787],{"className":1810},[1442],[639,1812],{"className":1813,"style":1438},[1437],[639,1815,1817,1820],{"className":1816},[673],[639,1818],{"className":1819,"style":1766},[677],[639,1821,890],{"className":1822},[682]," ont le ",[601,1825,1826],{},"même comportement asymptotique"," (c'est-à-dire la même\nallure quand ",[639,1829,1831,1844],{"className":1830},[642],[639,1832,1834],{"className":1833},[646],[648,1835,1836],{"xmlns":650},[652,1837,1838,1842],{},[655,1839,1840],{},[658,1841,660],{},[662,1843,660],{"encoding":664},[639,1845,1847],{"className":1846,"ariaHidden":669},[668],[639,1848,1850,1853],{"className":1849},[673],[639,1851],{"className":1852,"style":678},[677],[639,1854,660],{"className":1855},[682,683]," devient grand) — tous deux sont en ",[639,1858,1860,1879],{"className":1859},[642],[639,1861,1863],{"className":1862},[646],[648,1864,1865],{"xmlns":650},[652,1866,1867,1877],{},[655,1868,1869,1871,1873,1875],{},[658,1870,881],{"mathvariant":880},[883,1872,886],{"stretchy":885},[658,1874,660],{},[883,1876,893],{"stretchy":885},[662,1878,1005],{"encoding":664},[639,1880,1882],{"className":1881,"ariaHidden":669},[668],[639,1883,1885,1888,1891,1894,1897],{"className":1884},[673],[639,1886],{"className":1887,"style":906},[677],[639,1889,881],{"className":1890,"style":911},[682,910],[639,1892,886],{"className":1893},[915],[639,1895,660],{"className":1896},[682,683],[639,1898,893],{"className":1899},[922],".\nQuand ",[639,1902,1904,1917],{"className":1903},[642],[639,1905,1907],{"className":1906},[646],[648,1908,1909],{"xmlns":650},[652,1910,1911,1915],{},[655,1912,1913],{},[658,1914,660],{},[662,1916,660],{"encoding":664},[639,1918,1920],{"className":1919,"ariaHidden":669},[668],[639,1921,1923,1926],{"className":1922},[673],[639,1924],{"className":1925,"style":678},[677],[639,1927,660],{"className":1928},[682,683]," atteint 1 million, le « +7 » et le « ×3 » sont sans importance\nface au grand ",[639,1931,1933,1946],{"className":1932},[642],[639,1934,1936],{"className":1935},[646],[648,1937,1938],{"xmlns":650},[652,1939,1940,1944],{},[655,1941,1942],{},[658,1943,660],{},[662,1945,660],{"encoding":664},[639,1947,1949],{"className":1948,"ariaHidden":669},[668],[639,1950,1952,1955],{"className":1951},[673],[639,1953],{"className":1954,"style":678},[677],[639,1956,660],{"className":1957},[682,683],[1959,1960,1961],"note",{},[597,1962,1963,1966,1967,2026,2027,2074,2075,2118],{},[601,1964,1965],{},"Définition intuitive"," : un algorithme est en ",[639,1968,1970,1997],{"className":1969},[642],[639,1971,1973],{"className":1972},[646],[648,1974,1975],{"xmlns":650},[652,1976,1977,1994],{},[655,1978,1979,1981,1983,1986,1988,1990,1992],{},[658,1980,881],{"mathvariant":880},[883,1982,886],{"stretchy":885},[658,1984,1985],{},"f",[883,1987,886],{"stretchy":885},[658,1989,660],{},[883,1991,893],{"stretchy":885},[883,1993,893],{"stretchy":885},[662,1995,1996],{"encoding":664},"\\mathcal{O}(f(n))",[639,1998,2000],{"className":1999,"ariaHidden":669},[668],[639,2001,2003,2006,2009,2012,2016,2019,2022],{"className":2002},[673],[639,2004],{"className":2005,"style":906},[677],[639,2007,881],{"className":2008,"style":911},[682,910],[639,2010,886],{"className":2011},[915],[639,2013,1985],{"className":2014,"style":2015},[682,683],"margin-right:0.1076em;",[639,2017,886],{"className":2018},[915],[639,2020,660],{"className":2021},[682,683],[639,2023,2025],{"className":2024},[922],"))"," si, à\npartir d'une certaine taille, son nombre d'opérations reste ",[601,2028,2029,2030],{},"borné par un\nmultiple de ",[639,2031,2033,2053],{"className":2032},[642],[639,2034,2036],{"className":2035},[646],[648,2037,2038],{"xmlns":650},[652,2039,2040,2050],{},[655,2041,2042,2044,2046,2048],{},[658,2043,1985],{},[883,2045,886],{"stretchy":885},[658,2047,660],{},[883,2049,893],{"stretchy":885},[662,2051,2052],{"encoding":664},"f(n)",[639,2054,2056],{"className":2055,"ariaHidden":669},[668],[639,2057,2059,2062,2065,2068,2071],{"className":2058},[673],[639,2060],{"className":2061,"style":906},[677],[639,2063,1985],{"className":2064,"style":2015},[682,683],[639,2066,886],{"className":2067},[915],[639,2069,660],{"className":2070},[682,683],[639,2072,893],{"className":2073},[922],". Autrement dit : « il croît au pire comme ",[639,2076,2078,2097],{"className":2077},[642],[639,2079,2081],{"className":2080},[646],[648,2082,2083],{"xmlns":650},[652,2084,2085,2095],{},[655,2086,2087,2089,2091,2093],{},[658,2088,1985],{},[883,2090,886],{"stretchy":885},[658,2092,660],{},[883,2094,893],{"stretchy":885},[662,2096,2052],{"encoding":664},[639,2098,2100],{"className":2099,"ariaHidden":669},[668],[639,2101,2103,2106,2109,2112,2115],{"className":2102},[673],[639,2104],{"className":2105,"style":906},[677],[639,2107,1985],{"className":2108,"style":2015},[682,683],[639,2110,886],{"className":2111},[915],[639,2113,660],{"className":2114},[682,683],[639,2116,893],{"className":2117},[922]," ».",[597,2120,2121,2122,2185,2186,2189,2190,2233],{},"Vous rencontrerez aussi ",[639,2123,2125,2151],{"className":2124},[642],[639,2126,2128],{"className":2127},[646],[648,2129,2130],{"xmlns":650},[652,2131,2132,2148],{},[655,2133,2134,2136,2138,2141,2144,2146],{},[658,2135,881],{"mathvariant":880},[883,2137,886],{"stretchy":885},[658,2139,2140],{},"log",[883,2142,2143],{},"⁡",[658,2145,660],{},[883,2147,893],{"stretchy":885},[662,2149,2150],{"encoding":664},"\\mathcal{O}(\\log n)",[639,2152,2154],{"className":2153,"ariaHidden":669},[668],[639,2155,2157,2160,2163,2166,2175,2179,2182],{"className":2156},[673],[639,2158],{"className":2159,"style":906},[677],[639,2161,881],{"className":2162,"style":911},[682,910],[639,2164,886],{"className":2165},[915],[639,2167,2170,2171],{"className":2168},[2169],"mop","lo",[639,2172,2174],{"style":2173},"margin-right:0.0139em;","g",[639,2176],{"className":2177,"style":2178},[1437],"margin-right:0.1667em;",[639,2180,660],{"className":2181},[682,683],[639,2183,893],{"className":2184},[922]," au cours 4 (dichotomie) — c'est\nun coût ",[601,2187,2188],{},"encore plus petit"," que ",[639,2191,2193,2212],{"className":2192},[642],[639,2194,2196],{"className":2195},[646],[648,2197,2198],{"xmlns":650},[652,2199,2200,2210],{},[655,2201,2202,2204,2206,2208],{},[658,2203,881],{"mathvariant":880},[883,2205,886],{"stretchy":885},[658,2207,660],{},[883,2209,893],{"stretchy":885},[662,2211,1005],{"encoding":664},[639,2213,2215],{"className":2214,"ariaHidden":669},[668],[639,2216,2218,2221,2224,2227,2230],{"className":2217},[673],[639,2219],{"className":2220,"style":906},[677],[639,2222,881],{"className":2223,"style":911},[682,910],[639,2225,886],{"className":2226},[915],[639,2228,660],{"className":2229},[682,683],[639,2231,893],{"className":2232},[922],", qui croît extrêmement\nlentement.",[592,2235,2237],{"id":2236},"comparer-les-ordres-de-grandeur","Comparer les ordres de grandeur",[2239,2240,2241,2462],"table",{},[2242,2243,2244],"thead",{},[2245,2246,2247,2278,2372,2402],"tr",{},[2248,2249,2250],"th",{},[639,2251,2253,2266],{"className":2252},[642],[639,2254,2256],{"className":2255},[646],[648,2257,2258],{"xmlns":650},[652,2259,2260,2264],{},[655,2261,2262],{},[658,2263,660],{},[662,2265,660],{"encoding":664},[639,2267,2269],{"className":2268,"ariaHidden":669},[668],[639,2270,2272,2275],{"className":2271},[673],[639,2273],{"className":2274,"style":678},[677],[639,2276,660],{"className":2277},[682,683],[2248,2279,2280],{},[639,2281,2283,2308],{"className":2282},[642],[639,2284,2286],{"className":2285},[646],[648,2287,2288],{"xmlns":650},[652,2289,2290,2305],{},[655,2291,2292,2303],{},[2293,2294,2295,2301],"msub",{},[655,2296,2297,2299],{},[658,2298,2140],{},[883,2300,2143],{},[888,2302,1153],{},[658,2304,660],{},[662,2306,2307],{"encoding":664},"\\log_2 n",[639,2309,2311],{"className":2310,"ariaHidden":669},[668],[639,2312,2314,2318,2366,2369],{"className":2313},[673],[639,2315],{"className":2316,"style":2317},[677],"height:0.9386em;vertical-align:-0.2441em;",[639,2319,2321,2326],{"className":2320},[2169],[639,2322,2170,2324],{"className":2323},[2169],[639,2325,2174],{"style":2173},[639,2327,2329],{"className":2328},[1184],[639,2330,2333,2357],{"className":2331},[1188,2332],"vlist-t2",[639,2334,2336,2352],{"className":2335},[1192],[639,2337,2340],{"className":2338,"style":2339},[1196],"height:0.207em;",[639,2341,2343,2346],{"style":2342},"top:-2.4559em;margin-right:0.05em;",[639,2344],{"className":2345,"style":1205},[1204],[639,2347,2349],{"className":2348},[1209,1210,1211,1212],[639,2350,1153],{"className":2351},[682,1212],[639,2353,2356],{"className":2354},[2355],"vlist-s","​",[639,2358,2360],{"className":2359},[1192],[639,2361,2364],{"className":2362,"style":2363},[1196],"height:0.2441em;",[639,2365],{},[639,2367],{"className":2368,"style":2178},[1437],[639,2370,660],{"className":2371},[682,683],[2248,2373,2374],{},[639,2375,2377,2390],{"className":2376},[642],[639,2378,2380],{"className":2379},[646],[648,2381,2382],{"xmlns":650},[652,2383,2384,2388],{},[655,2385,2386],{},[658,2387,660],{},[662,2389,660],{"encoding":664},[639,2391,2393],{"className":2392,"ariaHidden":669},[668],[639,2394,2396,2399],{"className":2395},[673],[639,2397],{"className":2398,"style":678},[677],[639,2400,660],{"className":2401},[682,683],[2248,2403,2404],{},[639,2405,2407,2424],{"className":2406},[642],[639,2408,2410],{"className":2409},[646],[648,2411,2412],{"xmlns":650},[652,2413,2414,2422],{},[655,2415,2416],{},[1147,2417,2418,2420],{},[658,2419,660],{},[888,2421,1153],{},[662,2423,1242],{"encoding":664},[639,2425,2427],{"className":2426,"ariaHidden":669},[668],[639,2428,2430,2433],{"className":2429},[673],[639,2431],{"className":2432,"style":1197},[677],[639,2434,2436,2439],{"className":2435},[682],[639,2437,660],{"className":2438},[682,683],[639,2440,2442],{"className":2441},[1184],[639,2443,2445],{"className":2444},[1188],[639,2446,2448],{"className":2447},[1192],[639,2449,2451],{"className":2450,"style":1197},[1196],[639,2452,2453,2456],{"style":1200},[639,2454],{"className":2455,"style":1205},[1204],[639,2457,2459],{"className":2458},[1209,1210,1211,1212],[639,2460,1153],{"className":2461},[682,1212],[2463,2464,2465,2479,2491,2504],"tbody",{},[2245,2466,2467,2471,2474,2476],{},[2468,2469,2470],"td",{},"10",[2468,2472,2473],{},"≈ 3",[2468,2475,2470],{},[2468,2477,2478],{},"100",[2245,2480,2481,2483,2486,2488],{},[2468,2482,2478],{},[2468,2484,2485],{},"≈ 7",[2468,2487,2478],{},[2468,2489,2490],{},"10 000",[2245,2492,2493,2496,2499,2501],{},[2468,2494,2495],{},"1 000",[2468,2497,2498],{},"≈ 10",[2468,2500,2495],{},[2468,2502,2503],{},"1 000 000",[2245,2505,2506,2508,2511,2513],{},[2468,2507,2503],{},[2468,2509,2510],{},"≈ 20",[2468,2512,2503],{},[2468,2514,2515],{},[639,2516,2518,2537],{"className":2517},[642],[639,2519,2521],{"className":2520},[646],[648,2522,2523],{"xmlns":650},[652,2524,2525,2534],{},[655,2526,2527],{},[1147,2528,2529,2531],{},[888,2530,2470],{},[888,2532,2533],{},"12",[662,2535,2536],{"encoding":664},"10^{12}",[639,2538,2540],{"className":2539,"ariaHidden":669},[668],[639,2541,2543,2546,2549],{"className":2542},[673],[639,2544],{"className":2545,"style":1197},[677],[639,2547,890],{"className":2548},[682],[639,2550,2552,2555],{"className":2551},[682],[639,2553,971],{"className":2554},[682],[639,2556,2558],{"className":2557},[1184],[639,2559,2561],{"className":2560},[1188],[639,2562,2564],{"className":2563},[1192],[639,2565,2567],{"className":2566,"style":1197},[1196],[639,2568,2569,2572],{"style":1200},[639,2570],{"className":2571,"style":1205},[1204],[639,2573,2575],{"className":2574},[1209,1210,1211,1212],[639,2576,2578],{"className":2577},[682,1212],[639,2579,2533],{"className":2580},[682,1212],[597,2582,2583,2584,2587,2588,2591,2592,2595],{},"Pour un million d'éléments, un algorithme ",[601,2585,2586],{},"logarithmique"," finit en 20\nétapes ; un algorithme ",[601,2589,2590],{},"linéaire"," en un million ; un algorithme\n",[601,2593,2594],{},"quadratique"," en mille milliards — irréalisable en pratique.",[629,2597,2598,2604,2844],{},[597,2599,2600,2603],{},[601,2601,2602],{},"Hiérarchie à retenir"," :",[639,2605,2608],{"className":2606},[2607],"katex-display",[639,2609,2611,2685],{"className":2610},[642],[639,2612,2614],{"className":2613},[646],[648,2615,2617],{"xmlns":650,"display":2616},"block",[652,2618,2619,2682],{},[655,2620,2621,2623,2625,2627,2629,2633,2636,2638,2640,2642,2644,2646,2648,2650,2652,2654,2656,2658,2660,2662,2664,2666,2668,2670,2672,2674,2680],{},[658,2622,881],{"mathvariant":880},[883,2624,886],{"stretchy":885},[888,2626,890],{},[883,2628,893],{"stretchy":885},[2630,2631,2632],"mtext",{},"  ",[883,2634,2635],{},"\u003C",[2630,2637,2632],{},[658,2639,881],{"mathvariant":880},[883,2641,886],{"stretchy":885},[658,2643,2140],{},[883,2645,2143],{},[658,2647,660],{},[883,2649,893],{"stretchy":885},[2630,2651,2632],{},[883,2653,2635],{},[2630,2655,2632],{},[658,2657,881],{"mathvariant":880},[883,2659,886],{"stretchy":885},[658,2661,660],{},[883,2663,893],{"stretchy":885},[2630,2665,2632],{},[883,2667,2635],{},[2630,2669,2632],{},[658,2671,881],{"mathvariant":880},[883,2673,886],{"stretchy":885},[1147,2675,2676,2678],{},[658,2677,660],{},[888,2679,1153],{},[883,2681,893],{"stretchy":885},[662,2683,2684],{"encoding":664},"\\mathcal{O}(1) \\;\u003C\\; \\mathcal{O}(\\log n) \\;\u003C\\; \\mathcal{O}(n) \\;\u003C\\; \\mathcal{O}(n^2)",[639,2686,2688,2723,2764,2797],{"className":2687,"ariaHidden":669},[668],[639,2689,2691,2694,2697,2700,2703,2706,2710,2713,2717,2720],{"className":2690},[673],[639,2692],{"className":2693,"style":906},[677],[639,2695,881],{"className":2696,"style":911},[682,910],[639,2698,886],{"className":2699},[915],[639,2701,890],{"className":2702},[682],[639,2704,893],{"className":2705},[922],[639,2707],{"className":2708,"style":2709},[1437],"margin-right:0.2778em;",[639,2711],{"className":2712,"style":2709},[1437],[639,2714,2635],{"className":2715},[2716],"mrel",[639,2718],{"className":2719,"style":2709},[1437],[639,2721],{"className":2722,"style":2709},[1437],[639,2724,2726,2729,2732,2735,2740,2743,2746,2749,2752,2755,2758,2761],{"className":2725},[673],[639,2727],{"className":2728,"style":906},[677],[639,2730,881],{"className":2731,"style":911},[682,910],[639,2733,886],{"className":2734},[915],[639,2736,2170,2738],{"className":2737},[2169],[639,2739,2174],{"style":2173},[639,2741],{"className":2742,"style":2178},[1437],[639,2744,660],{"className":2745},[682,683],[639,2747,893],{"className":2748},[922],[639,2750],{"className":2751,"style":2709},[1437],[639,2753],{"className":2754,"style":2709},[1437],[639,2756,2635],{"className":2757},[2716],[639,2759],{"className":2760,"style":2709},[1437],[639,2762],{"className":2763,"style":2709},[1437],[639,2765,2767,2770,2773,2776,2779,2782,2785,2788,2791,2794],{"className":2766},[673],[639,2768],{"className":2769,"style":906},[677],[639,2771,881],{"className":2772,"style":911},[682,910],[639,2774,886],{"className":2775},[915],[639,2777,660],{"className":2778},[682,683],[639,2780,893],{"className":2781},[922],[639,2783],{"className":2784,"style":2709},[1437],[639,2786],{"className":2787,"style":2709},[1437],[639,2789,2635],{"className":2790},[2716],[639,2792],{"className":2793,"style":2709},[1437],[639,2795],{"className":2796,"style":2709},[1437],[639,2798,2800,2804,2807,2810,2841],{"className":2799},[673],[639,2801],{"className":2802,"style":2803},[677],"height:1.1141em;vertical-align:-0.25em;",[639,2805,881],{"className":2806,"style":911},[682,910],[639,2808,886],{"className":2809},[915],[639,2811,2813,2816],{"className":2812},[682],[639,2814,660],{"className":2815},[682,683],[639,2817,2819],{"className":2818},[1184],[639,2820,2822],{"className":2821},[1188],[639,2823,2825],{"className":2824},[1192],[639,2826,2829],{"className":2827,"style":2828},[1196],"height:0.8641em;",[639,2830,2832,2835],{"style":2831},"top:-3.113em;margin-right:0.05em;",[639,2833],{"className":2834,"style":1205},[1204],[639,2836,2838],{"className":2837},[1209,1210,1211,1212],[639,2839,1153],{"className":2840},[682,1212],[639,2842,893],{"className":2843},[922],[597,2845,2846,2847,684],{},"Plus on est à gauche, mieux on ",[601,2848,2849],{},"passe à l'échelle",[2851,2852,2853],"python-snippet",{},[935,2854,2856],{"className":937,"code":2855,"language":939,"meta":940,"style":940},"# Comparer les trois croissances pour quelques valeurs de n\nimport math\nprint(f\"{'n':>10} | {'log2(n)':>10} | {'n':>10} | {'n^2':>15}\")\nprint(\"-\" * 55)\nfor n in [10, 100, 1000, 10000]:\n    print(f\"{n:>10} | {math.log2(n):>10.2f} | {n:>10} | {n * n:>15}\")\n",[927,2857,2858,2863,2871,2934,2951,2983],{"__ignoreMap":940},[639,2859,2860],{"class":945,"line":946},[639,2861,2862],{"class":977},"# Comparer les trois croissances pour quelques valeurs de n\n",[639,2864,2865,2868],{"class":945,"line":961},[639,2866,2867],{"class":949},"import",[639,2869,2870],{"class":957}," math\n",[639,2872,2873,2876,2878,2880,2883,2886,2889,2892,2895,2898,2900,2903,2905,2907,2909,2911,2913,2915,2917,2919,2921,2924,2927,2929,2931],{"class":945,"line":1090},[639,2874,2875],{"class":970},"print",[639,2877,886],{"class":957},[639,2879,1985],{"class":949},[639,2881,2882],{"class":1304},"\"",[639,2884,2885],{"class":970},"{",[639,2887,2888],{"class":1304},"'n'",[639,2890,2891],{"class":949},":>10",[639,2893,2894],{"class":970},"}",[639,2896,2897],{"class":1304}," | ",[639,2899,2885],{"class":970},[639,2901,2902],{"class":1304},"'log2(n)'",[639,2904,2891],{"class":949},[639,2906,2894],{"class":970},[639,2908,2897],{"class":1304},[639,2910,2885],{"class":970},[639,2912,2888],{"class":1304},[639,2914,2891],{"class":949},[639,2916,2894],{"class":970},[639,2918,2897],{"class":1304},[639,2920,2885],{"class":970},[639,2922,2923],{"class":1304},"'n^2'",[639,2925,2926],{"class":949},":>15",[639,2928,2894],{"class":970},[639,2930,2882],{"class":1304},[639,2932,2933],{"class":957},")\n",[639,2935,2936,2938,2940,2943,2946,2949],{"class":945,"line":1108},[639,2937,2875],{"class":970},[639,2939,886],{"class":957},[639,2941,2942],{"class":1304},"\"-\"",[639,2944,2945],{"class":949}," *",[639,2947,2948],{"class":970}," 55",[639,2950,2933],{"class":957},[639,2952,2953,2956,2959,2961,2964,2966,2968,2970,2972,2975,2977,2980],{"class":945,"line":1120},[639,2954,2955],{"class":949},"for",[639,2957,2958],{"class":957}," n ",[639,2960,1099],{"class":949},[639,2962,2963],{"class":957}," [",[639,2965,2470],{"class":970},[639,2967,1591],{"class":957},[639,2969,2478],{"class":970},[639,2971,1591],{"class":957},[639,2973,2974],{"class":970},"1000",[639,2976,1591],{"class":957},[639,2978,2979],{"class":970},"10000",[639,2981,2982],{"class":957},"]:\n",[639,2984,2985,2988,2990,2992,2994,2996,2998,3000,3002,3004,3006,3009,3012,3014,3016,3018,3020,3022,3024,3026,3028,3031,3034,3037,3039,3041,3043],{"class":945,"line":1360},[639,2986,2987],{"class":970},"    print",[639,2989,886],{"class":957},[639,2991,1985],{"class":949},[639,2993,2882],{"class":1304},[639,2995,2885],{"class":970},[639,2997,660],{"class":957},[639,2999,2891],{"class":949},[639,3001,2894],{"class":970},[639,3003,2897],{"class":1304},[639,3005,2885],{"class":970},[639,3007,3008],{"class":957},"math.log2(n)",[639,3010,3011],{"class":949},":>10.2f",[639,3013,2894],{"class":970},[639,3015,2897],{"class":1304},[639,3017,2885],{"class":970},[639,3019,660],{"class":957},[639,3021,2891],{"class":949},[639,3023,2894],{"class":970},[639,3025,2897],{"class":1304},[639,3027,2885],{"class":970},[639,3029,3030],{"class":957},"n ",[639,3032,3033],{"class":949},"*",[639,3035,3036],{"class":957}," n",[639,3038,2926],{"class":949},[639,3040,2894],{"class":970},[639,3042,2882],{"class":1304},[639,3044,2933],{"class":957},[592,3046,3048],{"id":3047},"cas-pire-cas-moyen","Cas pire, cas moyen",[597,3050,3051,3052,3055],{},"Tous les algorithmes n'effectuent pas le même nombre d'opérations sur toutes\nles entrées de même taille. La ",[601,3053,3054],{},"recherche linéaire"," peut :",[726,3057,3058,3061],{},[729,3059,3060],{},"trouver dès la 1ère case (cas favorable, 1 comparaison) ;",[729,3062,3063,3064,3092],{},"trouver à la dernière case ou ne rien trouver (cas pire, ",[639,3065,3067,3080],{"className":3066},[642],[639,3068,3070],{"className":3069},[646],[648,3071,3072],{"xmlns":650},[652,3073,3074,3078],{},[655,3075,3076],{},[658,3077,660],{},[662,3079,660],{"encoding":664},[639,3081,3083],{"className":3082,"ariaHidden":669},[668],[639,3084,3086,3089],{"className":3085},[673],[639,3087],{"className":3088,"style":678},[677],[639,3090,660],{"className":3091},[682,683]," comparaisons).",[597,3094,3095,3096,3099,3100,3103,3104,3147,3148,684],{},"On parle souvent du ",[601,3097,3098],{},"cas pire"," car c'est la ",[601,3101,3102],{},"garantie maximale"," offerte\npar l'algorithme. Quand on dit « la recherche linéaire est en\n",[639,3105,3107,3126],{"className":3106},[642],[639,3108,3110],{"className":3109},[646],[648,3111,3112],{"xmlns":650},[652,3113,3114,3124],{},[655,3115,3116,3118,3120,3122],{},[658,3117,881],{"mathvariant":880},[883,3119,886],{"stretchy":885},[658,3121,660],{},[883,3123,893],{"stretchy":885},[662,3125,1005],{"encoding":664},[639,3127,3129],{"className":3128,"ariaHidden":669},[668],[639,3130,3132,3135,3138,3141,3144],{"className":3131},[673],[639,3133],{"className":3134,"style":906},[677],[639,3136,881],{"className":3137,"style":911},[682,910],[639,3139,886],{"className":3140},[915],[639,3142,660],{"className":3143},[682,683],[639,3145,893],{"className":3146},[922]," », c'est au pire — au mieux, elle est en ",[639,3149,3151,3170],{"className":3150},[642],[639,3152,3154],{"className":3153},[646],[648,3155,3156],{"xmlns":650},[652,3157,3158,3168],{},[655,3159,3160,3162,3164,3166],{},[658,3161,881],{"mathvariant":880},[883,3163,886],{"stretchy":885},[888,3165,890],{},[883,3167,893],{"stretchy":885},[662,3169,896],{"encoding":664},[639,3171,3173],{"className":3172,"ariaHidden":669},[668],[639,3174,3176,3179,3182,3185,3188],{"className":3175},[673],[639,3177],{"className":3178,"style":906},[677],[639,3180,881],{"className":3181,"style":911},[682,910],[639,3183,886],{"className":3184},[915],[639,3186,890],{"className":3187},[682],[639,3189,893],{"className":3190},[922],[1519,3192,3194,3199],{"correct":890,"slug":3193},"complexite-bases-c2",[1523,3195,3196],{"v-slot:question":940},[597,3197,3198],{},"Au mieux, combien d'opérations effectue une recherche linéaire qui trouve sa cible ?",[1523,3200,3201],{"v-slot:choices":940},[726,3202,3203,3205,3208],{},[729,3204,890],{},[729,3206,3207],{},"log n",[729,3209,660],{},[592,3211,3213],{"id":3212},"pièges-courants","Pièges courants",[726,3215,3216,3222,3377],{},[729,3217,3218,3221],{},[601,3219,3220],{},"Compter en secondes"," au lieu de compter des opérations : trompeur, car\ndépendant de la machine.",[729,3223,3224,3227,3228,3258,3259,1591,3302,695,3305,684],{},[601,3225,3226],{},"Garder les constantes"," dans la notation ",[639,3229,3231,3245],{"className":3230},[642],[639,3232,3234],{"className":3233},[646],[648,3235,3236],{"xmlns":650},[652,3237,3238,3242],{},[655,3239,3240],{},[658,3241,881],{"mathvariant":880},[662,3243,3244],{"encoding":664},"\\mathcal{O}",[639,3246,3248],{"className":3247,"ariaHidden":669},[668],[639,3249,3251,3255],{"className":3250},[673],[639,3252],{"className":3253,"style":3254},[677],"height:0.6833em;",[639,3256,881],{"className":3257,"style":911},[682,910]," : on écrit\n",[639,3260,3262,3281],{"className":3261},[642],[639,3263,3265],{"className":3264},[646],[648,3266,3267],{"xmlns":650},[652,3268,3269,3279],{},[655,3270,3271,3273,3275,3277],{},[658,3272,881],{"mathvariant":880},[883,3274,886],{"stretchy":885},[658,3276,660],{},[883,3278,893],{"stretchy":885},[662,3280,1005],{"encoding":664},[639,3282,3284],{"className":3283,"ariaHidden":669},[668],[639,3285,3287,3290,3293,3296,3299],{"className":3286},[673],[639,3288],{"className":3289,"style":906},[677],[639,3291,881],{"className":3292,"style":911},[682,910],[639,3294,886],{"className":3295},[915],[639,3297,660],{"className":3298},[682,683],[639,3300,893],{"className":3301},[922],[601,3303,3304],{},"jamais",[639,3306,3308,3335],{"className":3307},[642],[639,3309,3311],{"className":3310},[646],[648,3312,3313],{"xmlns":650},[652,3314,3315,3332],{},[655,3316,3317,3319,3321,3323,3325,3327,3330],{},[658,3318,881],{"mathvariant":880},[883,3320,886],{"stretchy":885},[888,3322,1724],{},[658,3324,660],{},[883,3326,1351],{},[888,3328,3329],{},"5",[883,3331,893],{"stretchy":885},[662,3333,3334],{"encoding":664},"\\mathcal{O}(3n + 5)",[639,3336,3338,3365],{"className":3337,"ariaHidden":669},[668],[639,3339,3341,3344,3347,3350,3353,3356,3359,3362],{"className":3340},[673],[639,3342],{"className":3343,"style":906},[677],[639,3345,881],{"className":3346,"style":911},[682,910],[639,3348,886],{"className":3349},[915],[639,3351,1724],{"className":3352},[682],[639,3354,660],{"className":3355},[682,683],[639,3357],{"className":3358,"style":1438},[1437],[639,3360,1351],{"className":3361},[1442],[639,3363],{"className":3364,"style":1438},[1437],[639,3366,3368,3371,3374],{"className":3367},[673],[639,3369],{"className":3370,"style":906},[677],[639,3372,3329],{"className":3373},[682],[639,3375,893],{"className":3376},[922],[729,3378,3379,3382],{},[601,3380,3381],{},"Confondre cas pire et cas moyen"," : à l'oral, préciser quand c'est ambigu.",[592,3384,3386],{"id":3385},"pour-aller-plus-loin","Pour aller plus loin",[597,3388,3389,3390,3463,3464,3519],{},"Vous allez vérifier ces ordres de grandeur dans les cours suivants : les tris\ndu cours 3 sont en ",[639,3391,3393,3416],{"className":3392},[642],[639,3394,3396],{"className":3395},[646],[648,3397,3398],{"xmlns":650},[652,3399,3400,3414],{},[655,3401,3402,3404,3406,3412],{},[658,3403,881],{"mathvariant":880},[883,3405,886],{"stretchy":885},[1147,3407,3408,3410],{},[658,3409,660],{},[888,3411,1153],{},[883,3413,893],{"stretchy":885},[662,3415,1158],{"encoding":664},[639,3417,3419],{"className":3418,"ariaHidden":669},[668],[639,3420,3422,3425,3428,3431,3460],{"className":3421},[673],[639,3423],{"className":3424,"style":1168},[677],[639,3426,881],{"className":3427,"style":911},[682,910],[639,3429,886],{"className":3430},[915],[639,3432,3434,3437],{"className":3433},[682],[639,3435,660],{"className":3436},[682,683],[639,3438,3440],{"className":3439},[1184],[639,3441,3443],{"className":3442},[1188],[639,3444,3446],{"className":3445},[1192],[639,3447,3449],{"className":3448,"style":1197},[1196],[639,3450,3451,3454],{"style":1200},[639,3452],{"className":3453,"style":1205},[1204],[639,3455,3457],{"className":3456},[1209,1210,1211,1212],[639,3458,1153],{"className":3459},[682,1212],[639,3461,893],{"className":3462},[922],", la dichotomie du cours 4 est en\n",[639,3465,3467,3490],{"className":3466},[642],[639,3468,3470],{"className":3469},[646],[648,3471,3472],{"xmlns":650},[652,3473,3474,3488],{},[655,3475,3476,3478,3480,3482,3484,3486],{},[658,3477,881],{"mathvariant":880},[883,3479,886],{"stretchy":885},[658,3481,2140],{},[883,3483,2143],{},[658,3485,660],{},[883,3487,893],{"stretchy":885},[662,3489,2150],{"encoding":664},[639,3491,3493],{"className":3492,"ariaHidden":669},[668],[639,3494,3496,3499,3502,3505,3510,3513,3516],{"className":3495},[673],[639,3497],{"className":3498,"style":906},[677],[639,3500,881],{"className":3501,"style":911},[682,910],[639,3503,886],{"className":3504},[915],[639,3506,2170,3508],{"className":3507},[2169],[639,3509,2174],{"style":2173},[639,3511],{"className":3512,"style":2178},[1437],[639,3514,660],{"className":3515},[682,683],[639,3517,893],{"className":3518},[922],". La différence de performance entre les deux dernières\nest colossale — un algorithme dichotomique sur un milliard d'éléments tient en\n30 étapes seulement.",[3521,3522,3523],"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 .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}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 .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}",{"title":940,"searchDepth":961,"depth":961,"links":3525},[3526,3527,3528,3529,3537,3538,3539,3540,3541],{"id":594,"depth":961,"text":595},{"id":607,"depth":961,"text":608},{"id":687,"depth":961,"text":688},{"id":859,"depth":961,"text":860,"children":3530},[3531,3533,3535],{"id":864,"depth":1090,"text":3532},"Coût constant — O(1)\\mathcal{O}(1)O(1)",{"id":981,"depth":1090,"text":3534},"Coût linéaire — O(n)\\mathcal{O}(n)O(n)",{"id":1128,"depth":1090,"text":3536},"Coût quadratique — O(n2)\\mathcal{O}(n^2)O(n2)",{"id":1543,"depth":961,"text":1544},{"id":2236,"depth":961,"text":2237},{"id":3047,"depth":961,"text":3048},{"id":3212,"depth":961,"text":3213},{"id":3385,"depth":961,"text":3386},"Combien coûte un algorithme ? Premier contact avec la notation grand-O, sans dramatiser les maths.","md",{},true,[3547,3551],{"slug":1521,"kind":3548,"question":1527,"choices":3549,"correct":890,"multi":3550,"explanation":940},"qcm",[1534,1537,1540],false,{"slug":3193,"kind":3548,"question":3198,"choices":3552,"correct":890,"multi":3550,"explanation":940},[890,3207,660],{"title":421,"description":3542},"WlEeOnXTHztMfuEDmwjyHJ1smTjMJp3RMIYBKuQetYM",{"id":3556,"title":3557,"bo":587,"body":3558,"description":5114,"eval":587,"extension":3543,"labo":587,"meta":5115,"navigation":3550,"path":5116,"quizzes":5117,"readingTime":946,"seo":5118,"stem":5119,"tp":587,"__hash__":5120},"coursMemo\u002F1.nsi-1ere\u002Fph-algorithmique\u002F2.complexite-bases.memo.md","Bases de la complexité — l'essentiel",{"type":589,"value":3559,"toc":5105},[3560,3564,3603,3607,4261,4265,4578,4667,4935,4937,4976,4980,5102],[592,3561,3563],{"id":3562},"en-une-phrase","En une phrase",[597,3565,3566,3567,3570,3571,3602],{},"La complexité ",[601,3568,3569],{},"mesure le coût"," d'un algorithme en nombre d'opérations\n",[601,3572,3573,3574],{},"en fonction de la taille de l'entrée ",[639,3575,3577,3590],{"className":3576},[642],[639,3578,3580],{"className":3579},[646],[648,3581,3582],{"xmlns":650},[652,3583,3584,3588],{},[655,3585,3586],{},[658,3587,660],{},[662,3589,660],{"encoding":664},[639,3591,3593],{"className":3592,"ariaHidden":669},[668],[639,3594,3596,3599],{"className":3595},[673],[639,3597],{"className":3598,"style":678},[677],[639,3600,660],{"className":3601},[682,683],", en négligeant constantes et\ndétails de petite taille.",[592,3604,3606],{"id":3605},"à-mémoriser","À mémoriser",[726,3608,3609,3643,3933,4135,4255],{},[729,3610,3611,3642],{},[601,3612,3613,3614],{},"Taille ",[639,3615,3617,3630],{"className":3616},[642],[639,3618,3620],{"className":3619},[646],[648,3621,3622],{"xmlns":650},[652,3623,3624,3628],{},[655,3625,3626],{},[658,3627,660],{},[662,3629,660],{"encoding":664},[639,3631,3633],{"className":3632,"ariaHidden":669},[668],[639,3634,3636,3639],{"className":3635},[673],[639,3637],{"className":3638,"style":678},[677],[639,3640,660],{"className":3641},[682,683]," : nombre d'éléments d'un tableau, longueur d'une chaîne, …",[729,3644,3645,3648,3649],{},[601,3646,3647],{},"Trois ordres de grandeur clés"," :\n",[726,3650,3651,3725,3799],{},[729,3652,3653,3696,3697,684],{},[639,3654,3656,3675],{"className":3655},[642],[639,3657,3659],{"className":3658},[646],[648,3660,3661],{"xmlns":650},[652,3662,3663,3673],{},[655,3664,3665,3667,3669,3671],{},[658,3666,881],{"mathvariant":880},[883,3668,886],{"stretchy":885},[888,3670,890],{},[883,3672,893],{"stretchy":885},[662,3674,896],{"encoding":664},[639,3676,3678],{"className":3677,"ariaHidden":669},[668],[639,3679,3681,3684,3687,3690,3693],{"className":3680},[673],[639,3682],{"className":3683,"style":906},[677],[639,3685,881],{"className":3686,"style":911},[682,910],[639,3688,886],{"className":3689},[915],[639,3691,890],{"className":3692},[682],[639,3694,893],{"className":3695},[922]," : constant — indépendant de ",[639,3698,3700,3713],{"className":3699},[642],[639,3701,3703],{"className":3702},[646],[648,3704,3705],{"xmlns":650},[652,3706,3707,3711],{},[655,3708,3709],{},[658,3710,660],{},[662,3712,660],{"encoding":664},[639,3714,3716],{"className":3715,"ariaHidden":669},[668],[639,3717,3719,3722],{"className":3718},[673],[639,3720],{"className":3721,"style":678},[677],[639,3723,660],{"className":3724},[682,683],[729,3726,3727,3770,3771,684],{},[639,3728,3730,3749],{"className":3729},[642],[639,3731,3733],{"className":3732},[646],[648,3734,3735],{"xmlns":650},[652,3736,3737,3747],{},[655,3738,3739,3741,3743,3745],{},[658,3740,881],{"mathvariant":880},[883,3742,886],{"stretchy":885},[658,3744,660],{},[883,3746,893],{"stretchy":885},[662,3748,1005],{"encoding":664},[639,3750,3752],{"className":3751,"ariaHidden":669},[668],[639,3753,3755,3758,3761,3764,3767],{"className":3754},[673],[639,3756],{"className":3757,"style":906},[677],[639,3759,881],{"className":3760,"style":911},[682,910],[639,3762,886],{"className":3763},[915],[639,3765,660],{"className":3766},[682,683],[639,3768,893],{"className":3769},[922]," : linéaire — proportionnel à ",[639,3772,3774,3787],{"className":3773},[642],[639,3775,3777],{"className":3776},[646],[648,3778,3779],{"xmlns":650},[652,3780,3781,3785],{},[655,3782,3783],{},[658,3784,660],{},[662,3786,660],{"encoding":664},[639,3788,3790],{"className":3789,"ariaHidden":669},[668],[639,3791,3793,3796],{"className":3792},[673],[639,3794],{"className":3795,"style":678},[677],[639,3797,660],{"className":3798},[682,683],[729,3800,3801,3874,3875,684],{},[639,3802,3804,3827],{"className":3803},[642],[639,3805,3807],{"className":3806},[646],[648,3808,3809],{"xmlns":650},[652,3810,3811,3825],{},[655,3812,3813,3815,3817,3823],{},[658,3814,881],{"mathvariant":880},[883,3816,886],{"stretchy":885},[1147,3818,3819,3821],{},[658,3820,660],{},[888,3822,1153],{},[883,3824,893],{"stretchy":885},[662,3826,1158],{"encoding":664},[639,3828,3830],{"className":3829,"ariaHidden":669},[668],[639,3831,3833,3836,3839,3842,3871],{"className":3832},[673],[639,3834],{"className":3835,"style":1168},[677],[639,3837,881],{"className":3838,"style":911},[682,910],[639,3840,886],{"className":3841},[915],[639,3843,3845,3848],{"className":3844},[682],[639,3846,660],{"className":3847},[682,683],[639,3849,3851],{"className":3850},[1184],[639,3852,3854],{"className":3853},[1188],[639,3855,3857],{"className":3856},[1192],[639,3858,3860],{"className":3859,"style":1197},[1196],[639,3861,3862,3865],{"style":1200},[639,3863],{"className":3864,"style":1205},[1204],[639,3866,3868],{"className":3867},[1209,1210,1211,1212],[639,3869,1153],{"className":3870},[682,1212],[639,3872,893],{"className":3873},[922]," : quadratique — proportionnel à 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\u003C \\mathcal{O}(\\log n) \u003C \\mathcal{O}(n) \u003C \\mathcal{O}(n^2)",[639,4000,4002,4029,4064,4091],{"className":4001,"ariaHidden":669},[668],[639,4003,4005,4008,4011,4014,4017,4020,4023,4026],{"className":4004},[673],[639,4006],{"className":4007,"style":906},[677],[639,4009,881],{"className":4010,"style":911},[682,910],[639,4012,886],{"className":4013},[915],[639,4015,890],{"className":4016},[682],[639,4018,893],{"className":4019},[922],[639,4021],{"className":4022,"style":2709},[1437],[639,4024,2635],{"className":4025},[2716],[639,4027],{"className":4028,"style":2709},[1437],[639,4030,4032,4035,4038,4041,4046,4049,4052,4055,4058,4061],{"className":4031},[673],[639,4033],{"className":4034,"style":906},[677],[639,4036,881],{"className":4037,"style":911},[682,910],[639,4039,886],{"className":4040},[915],[639,4042,2170,4044],{"className":4043},[2169],[639,4045,2174],{"style":2173},[639,4047],{"className":4048,"style":2178},[1437],[639,4050,660],{"className":4051},[682,683],[639,4053,893],{"className":4054},[922],[639,4056],{"className":4057,"style":2709},[1437],[639,4059,2635],{"className":4060},[2716],[639,4062],{"className":4063,"style":2709},[1437],[639,4065,4067,4070,4073,4076,4079,4082,4085,4088],{"className":4066},[673],[639,4068],{"className":4069,"style":906},[677],[639,4071,881],{"className":4072,"style":911},[682,910],[639,4074,886],{"className":4075},[915],[639,4077,660],{"className":4078},[682,683],[639,4080,893],{"className":4081},[922],[639,4083],{"className":4084,"style":2709},[1437],[639,4086,2635],{"className":4087},[2716],[639,4089],{"className":4090,"style":2709},[1437],[639,4092,4094,4097,4100,4103,4132],{"className":4093},[673],[639,4095],{"className":4096,"style":1168},[677],[639,4098,881],{"className":4099,"style":911},[682,910],[639,4101,886],{"className":4102},[915],[639,4104,4106,4109],{"className":4105},[682],[639,4107,660],{"className":4108},[682,683],[639,4110,4112],{"className":4111},[1184],[639,4113,4115],{"className":4114},[1188],[639,4116,4118],{"className":4117},[1192],[639,4119,4121],{"className":4120,"style":1197},[1196],[639,4122,4123,4126],{"style":1200},[639,4124],{"className":4125,"style":1205},[1204],[639,4127,4129],{"className":4128},[1209,1210,1211,1212],[639,4130,1153],{"className":4131},[682,1212],[639,4133,893],{"className":4134},[922],[729,4136,4137,4140,4141,4211,4212,684],{},[601,4138,4139],{},"Grand-O ignore"," : constantes multiplicatives et termes d'ordre inférieur.\n",[639,4142,4144,4169],{"className":4143},[642],[639,4145,4147],{"className":4146},[646],[648,4148,4149],{"xmlns":650},[652,4150,4151,4167],{},[655,4152,4153,4155,4157,4159,4161,4163,4165],{},[658,4154,881],{"mathvariant":880},[883,4156,886],{"stretchy":885},[888,4158,1724],{},[658,4160,660],{},[883,4162,1351],{},[888,4164,3329],{},[883,4166,893],{"stretchy":885},[662,4168,3334],{"encoding":664},[639,4170,4172,4199],{"className":4171,"ariaHidden":669},[668],[639,4173,4175,4178,4181,4184,4187,4190,4193,4196],{"className":4174},[673],[639,4176],{"className":4177,"style":906},[677],[639,4179,881],{"className":4180,"style":911},[682,910],[639,4182,886],{"className":4183},[915],[639,4185,1724],{"className":4186},[682],[639,4188,660],{"className":4189},[682,683],[639,4191],{"className":4192,"style":1438},[1437],[639,4194,1351],{"className":4195},[1442],[639,4197],{"className":4198,"style":1438},[1437],[639,4200,4202,4205,4208],{"className":4201},[673],[639,4203],{"className":4204,"style":906},[677],[639,4206,3329],{"className":4207},[682],[639,4209,893],{"className":4210},[922]," s'écrit ",[639,4213,4215,4234],{"className":4214},[642],[639,4216,4218],{"className":4217},[646],[648,4219,4220],{"xmlns":650},[652,4221,4222,4232],{},[655,4223,4224,4226,4228,4230],{},[658,4225,881],{"mathvariant":880},[883,4227,886],{"stretchy":885},[658,4229,660],{},[883,4231,893],{"stretchy":885},[662,4233,1005],{"encoding":664},[639,4235,4237],{"className":4236,"ariaHidden":669},[668],[639,4238,4240,4243,4246,4249,4252],{"className":4239},[673],[639,4241],{"className":4242,"style":906},[677],[639,4244,881],{"className":4245,"style":911},[682,910],[639,4247,886],{"className":4248},[915],[639,4250,660],{"className":4251},[682,683],[639,4253,893],{"className":4254},[922],[729,4256,4257,4260],{},[601,4258,4259],{},"Cas pire"," : borne maximale — c'est ce qu'on annonce par défaut.",[592,4262,4264],{"id":4263},"à-savoir-reconnaître","À savoir reconnaître",[2239,4266,4267,4277],{},[2242,4268,4269],{},[2245,4270,4271,4274],{},[2248,4272,4273],{},"Structure du code",[2248,4275,4276],{},"Complexité typique",[2463,4278,4279,4329,4408,4516],{},[2245,4280,4281,4284],{},[2468,4282,4283],{},"Accès direct, opération unique",[2468,4285,4286],{},[639,4287,4289,4308],{"className":4288},[642],[639,4290,4292],{"className":4291},[646],[648,4293,4294],{"xmlns":650},[652,4295,4296,4306],{},[655,4297,4298,4300,4302,4304],{},[658,4299,881],{"mathvariant":880},[883,4301,886],{"stretchy":885},[888,4303,890],{},[883,4305,893],{"stretchy":885},[662,4307,896],{"encoding":664},[639,4309,4311],{"className":4310,"ariaHidden":669},[668],[639,4312,4314,4317,4320,4323,4326],{"className":4313},[673],[639,4315],{"className":4316,"style":906},[677],[639,4318,881],{"className":4319,"style":911},[682,910],[639,4321,886],{"className":4322},[915],[639,4324,890],{"className":4325},[682],[639,4327,893],{"className":4328},[922],[2245,4330,4331,4363],{},[2468,4332,4333,4334,4362],{},"Une boucle qui parcourt ",[639,4335,4337,4350],{"className":4336},[642],[639,4338,4340],{"className":4339},[646],[648,4341,4342],{"xmlns":650},[652,4343,4344,4348],{},[655,4345,4346],{},[658,4347,660],{},[662,4349,660],{"encoding":664},[639,4351,4353],{"className":4352,"ariaHidden":669},[668],[639,4354,4356,4359],{"className":4355},[673],[639,4357],{"className":4358,"style":678},[677],[639,4360,660],{"className":4361},[682,683]," éléments",[2468,4364,4365],{},[639,4366,4368,4387],{"className":4367},[642],[639,4369,4371],{"className":4370},[646],[648,4372,4373],{"xmlns":650},[652,4374,4375,4385],{},[655,4376,4377,4379,4381,4383],{},[658,4378,881],{"mathvariant":880},[883,4380,886],{"stretchy":885},[658,4382,660],{},[883,4384,893],{"stretchy":885},[662,4386,1005],{"encoding":664},[639,4388,4390],{"className":4389,"ariaHidden":669},[668],[639,4391,4393,4396,4399,4402,4405],{"className":4392},[673],[639,4394],{"className":4395,"style":906},[677],[639,4397,881],{"className":4398,"style":911},[682,910],[639,4400,886],{"className":4401},[915],[639,4403,660],{"className":4404},[682,683],[639,4406,893],{"className":4407},[922],[2245,4409,4410,4441],{},[2468,4411,4412,4413],{},"Deux boucles imbriquées sur ",[639,4414,4416,4429],{"className":4415},[642],[639,4417,4419],{"className":4418},[646],[648,4420,4421],{"xmlns":650},[652,4422,4423,4427],{},[655,4424,4425],{},[658,4426,660],{},[662,4428,660],{"encoding":664},[639,4430,4432],{"className":4431,"ariaHidden":669},[668],[639,4433,4435,4438],{"className":4434},[673],[639,4436],{"className":4437,"style":678},[677],[639,4439,660],{"className":4440},[682,683],[2468,4442,4443],{},[639,4444,4446,4469],{"className":4445},[642],[639,4447,4449],{"className":4448},[646],[648,4450,4451],{"xmlns":650},[652,4452,4453,4467],{},[655,4454,4455,4457,4459,4465],{},[658,4456,881],{"mathvariant":880},[883,4458,886],{"stretchy":885},[1147,4460,4461,4463],{},[658,4462,660],{},[888,4464,1153],{},[883,4466,893],{"stretchy":885},[662,4468,1158],{"encoding":664},[639,4470,4472],{"className":4471,"ariaHidden":669},[668],[639,4473,4475,4478,4481,4484,4513],{"className":4474},[673],[639,4476],{"className":4477,"style":1168},[677],[639,4479,881],{"className":4480,"style":911},[682,910],[639,4482,886],{"className":4483},[915],[639,4485,4487,4490],{"className":4486},[682],[639,4488,660],{"className":4489},[682,683],[639,4491,4493],{"className":4492},[1184],[639,4494,4496],{"className":4495},[1188],[639,4497,4499],{"className":4498},[1192],[639,4500,4502],{"className":4501,"style":1197},[1196],[639,4503,4504,4507],{"style":1200},[639,4505],{"className":4506,"style":1205},[1204],[639,4508,4510],{"className":4509},[1209,1210,1211,1212],[639,4511,1153],{"className":4512},[682,1212],[639,4514,893],{"className":4515},[922],[2245,4517,4518,4521],{},[2468,4519,4520],{},"Division par 2 à chaque tour",[2468,4522,4523],{},[639,4524,4526,4549],{"className":4525},[642],[639,4527,4529],{"className":4528},[646],[648,4530,4531],{"xmlns":650},[652,4532,4533,4547],{},[655,4534,4535,4537,4539,4541,4543,4545],{},[658,4536,881],{"mathvariant":880},[883,4538,886],{"stretchy":885},[658,4540,2140],{},[883,4542,2143],{},[658,4544,660],{},[883,4546,893],{"stretchy":885},[662,4548,2150],{"encoding":664},[639,4550,4552],{"className":4551,"ariaHidden":669},[668],[639,4553,4555,4558,4561,4564,4569,4572,4575],{"className":4554},[673],[639,4556],{"className":4557,"style":906},[677],[639,4559,881],{"className":4560,"style":911},[682,910],[639,4562,886],{"className":4563},[915],[639,4565,2170,4567],{"className":4566},[2169],[639,4568,2174],{"style":2173},[639,4570],{"className":4571,"style":2178},[1437],[639,4573,660],{"className":4574},[682,683],[639,4576,893],{"className":4577},[922],[592,4579,4581,4582],{"id":4580},"ordres-de-grandeur-pour-n106n-106n106","Ordres de grandeur pour ",[639,4583,4585,4608],{"className":4584},[642],[639,4586,4588],{"className":4587},[646],[648,4589,4590],{"xmlns":650},[652,4591,4592,4605],{},[655,4593,4594,4596,4598],{},[658,4595,660],{},[883,4597,1084],{},[1147,4599,4600,4602],{},[888,4601,2470],{},[888,4603,4604],{},"6",[662,4606,4607],{"encoding":664},"n = 10^6",[639,4609,4611,4629],{"className":4610,"ariaHidden":669},[668],[639,4612,4614,4617,4620,4623,4626],{"className":4613},[673],[639,4615],{"className":4616,"style":678},[677],[639,4618,660],{"className":4619},[682,683],[639,4621],{"className":4622,"style":2709},[1437],[639,4624,1084],{"className":4625},[2716],[639,4627],{"className":4628,"style":2709},[1437],[639,4630,4632,4635,4638],{"className":4631},[673],[639,4633],{"className":4634,"style":1197},[677],[639,4636,890],{"className":4637},[682],[639,4639,4641,4644],{"className":4640},[682],[639,4642,971],{"className":4643},[682],[639,4645,4647],{"className":4646},[1184],[639,4648,4650],{"className":4649},[1188],[639,4651,4653],{"className":4652},[1192],[639,4654,4656],{"className":4655,"style":1197},[1196],[639,4657,4658,4661],{"style":1200},[639,4659],{"className":4660,"style":1205},[1204],[639,4662,4664],{"className":4663},[1209,1210,1211,1212],[639,4665,4604],{"className":4666},[682,1212],[2239,4668,4669,4679],{},[2242,4670,4671],{},[2245,4672,4673,4676],{},[2248,4674,4675],{},"Complexité",[2248,4677,4678],{},"Étapes",[2463,4680,4681,4742,4791],{},[2245,4682,4683,4740],{},[2468,4684,4685],{},[639,4686,4688,4711],{"className":4687},[642],[639,4689,4691],{"className":4690},[646],[648,4692,4693],{"xmlns":650},[652,4694,4695,4709],{},[655,4696,4697,4699,4701,4703,4705,4707],{},[658,4698,881],{"mathvariant":880},[883,4700,886],{"stretchy":885},[658,4702,2140],{},[883,4704,2143],{},[658,4706,660],{},[883,4708,893],{"stretchy":885},[662,4710,2150],{"encoding":664},[639,4712,4714],{"className":4713,"ariaHidden":669},[668],[639,4715,4717,4720,4723,4726,4731,4734,4737],{"className":4716},[673],[639,4718],{"className":4719,"style":906},[677],[639,4721,881],{"className":4722,"style":911},[682,910],[639,4724,886],{"className":4725},[915],[639,4727,2170,4729],{"className":4728},[2169],[639,4730,2174],{"style":2173},[639,4732],{"className":4733,"style":2178},[1437],[639,4735,660],{"className":4736},[682,683],[639,4738,893],{"className":4739},[922],[2468,4741,2510],{},[2245,4743,4744,4789],{},[2468,4745,4746],{},[639,4747,4749,4768],{"className":4748},[642],[639,4750,4752],{"className":4751},[646],[648,4753,4754],{"xmlns":650},[652,4755,4756,4766],{},[655,4757,4758,4760,4762,4764],{},[658,4759,881],{"mathvariant":880},[883,4761,886],{"stretchy":885},[658,4763,660],{},[883,4765,893],{"stretchy":885},[662,4767,1005],{"encoding":664},[639,4769,4771],{"className":4770,"ariaHidden":669},[668],[639,4772,4774,4777,4780,4783,4786],{"className":4773},[673],[639,4775],{"className":4776,"style":906},[677],[639,4778,881],{"className":4779,"style":911},[682,910],[639,4781,886],{"className":4782},[915],[639,4784,660],{"className":4785},[682,683],[639,4787,893],{"className":4788},[922],[2468,4790,2503],{},[2245,4792,4793,4868],{},[2468,4794,4795],{},[639,4796,4798,4821],{"className":4797},[642],[639,4799,4801],{"className":4800},[646],[648,4802,4803],{"xmlns":650},[652,4804,4805,4819],{},[655,4806,4807,4809,4811,4817],{},[658,4808,881],{"mathvariant":880},[883,4810,886],{"stretchy":885},[1147,4812,4813,4815],{},[658,4814,660],{},[888,4816,1153],{},[883,4818,893],{"stretchy":885},[662,4820,1158],{"encoding":664},[639,4822,4824],{"className":4823,"ariaHidden":669},[668],[639,4825,4827,4830,4833,4836,4865],{"className":4826},[673],[639,4828],{"className":4829,"style":1168},[677],[639,4831,881],{"className":4832,"style":911},[682,910],[639,4834,886],{"className":4835},[915],[639,4837,4839,4842],{"className":4838},[682],[639,4840,660],{"className":4841},[682,683],[639,4843,4845],{"className":4844},[1184],[639,4846,4848],{"className":4847},[1188],[639,4849,4851],{"className":4850},[1192],[639,4852,4854],{"className":4853,"style":1197},[1196],[639,4855,4856,4859],{"style":1200},[639,4857],{"className":4858,"style":1205},[1204],[639,4860,4862],{"className":4861},[1209,1210,1211,1212],[639,4863,1153],{"className":4864},[682,1212],[639,4866,893],{"className":4867},[922],[2468,4869,4870,4934],{},[639,4871,4873,4890],{"className":4872},[642],[639,4874,4876],{"className":4875},[646],[648,4877,4878],{"xmlns":650},[652,4879,4880,4888],{},[655,4881,4882],{},[1147,4883,4884,4886],{},[888,4885,2470],{},[888,4887,2533],{},[662,4889,2536],{"encoding":664},[639,4891,4893],{"className":4892,"ariaHidden":669},[668],[639,4894,4896,4899,4902],{"className":4895},[673],[639,4897],{"className":4898,"style":1197},[677],[639,4900,890],{"className":4901},[682],[639,4903,4905,4908],{"className":4904},[682],[639,4906,971],{"className":4907},[682],[639,4909,4911],{"className":4910},[1184],[639,4912,4914],{"className":4913},[1188],[639,4915,4917],{"className":4916},[1192],[639,4918,4920],{"className":4919,"style":1197},[1196],[639,4921,4922,4925],{"style":1200},[639,4923],{"className":4924,"style":1205},[1204],[639,4926,4928],{"className":4927},[1209,1210,1211,1212],[639,4929,4931],{"className":4930},[682,1212],[639,4932,2533],{"className":4933},[682,1212]," — irréalisable",[592,4936,3213],{"id":3212},[726,4938,4939,4942,4973],{},[729,4940,4941],{},"Mesurer en secondes (dépend de la machine).",[729,4943,4944,4945,684],{},"Garder les constantes dans le ",[639,4946,4948,4961],{"className":4947},[642],[639,4949,4951],{"className":4950},[646],[648,4952,4953],{"xmlns":650},[652,4954,4955,4959],{},[655,4956,4957],{},[658,4958,881],{"mathvariant":880},[662,4960,3244],{"encoding":664},[639,4962,4964],{"className":4963,"ariaHidden":669},[668],[639,4965,4967,4970],{"className":4966},[673],[639,4968],{"className":4969,"style":3254},[677],[639,4971,881],{"className":4972,"style":911},[682,910],[729,4974,4975],{},"Confondre cas pire et cas moyen.",[592,4977,4979],{"id":4978},"syntaxe-python","Syntaxe Python",[935,4981,4983],{"className":937,"code":4982,"language":939,"meta":940,"style":940},"def constant(t):       # O(1)\n    return t[0]\n\ndef lineaire(t):       # O(n)\n    for v in t:\n        ...\n\ndef quadratique(t):    # O(n^2)\n    for i in range(len(t)):\n        for j in range(len(t)):\n            ...\n",[927,4984,4985,4998,5010,5015,5027,5038,5043,5047,5060,5079,5096],{"__ignoreMap":940},[639,4986,4987,4989,4992,4995],{"class":945,"line":946},[639,4988,950],{"class":949},[639,4990,4991],{"class":953}," constant",[639,4993,4994],{"class":957},"(t):       ",[639,4996,4997],{"class":977},"# O(1)\n",[639,4999,5000,5002,5005,5007],{"class":945,"line":961},[639,5001,964],{"class":949},[639,5003,5004],{"class":957}," t[",[639,5006,971],{"class":970},[639,5008,5009],{"class":957},"]\n",[639,5011,5012],{"class":945,"line":1090},[639,5013,5014],{"emptyLinePlaceholder":3545},"\n",[639,5016,5017,5019,5022,5024],{"class":945,"line":1108},[639,5018,950],{"class":949},[639,5020,5021],{"class":953}," lineaire",[639,5023,4994],{"class":957},[639,5025,5026],{"class":977},"# O(n)\n",[639,5028,5029,5031,5033,5035],{"class":945,"line":1120},[639,5030,1093],{"class":949},[639,5032,1096],{"class":957},[639,5034,1099],{"class":949},[639,5036,5037],{"class":957}," t:\n",[639,5039,5040],{"class":945,"line":1360},[639,5041,5042],{"class":970},"        ...\n",[639,5044,5045],{"class":945,"line":1375},[639,5046,5014],{"emptyLinePlaceholder":3545},[639,5048,5049,5051,5054,5057],{"class":945,"line":1384},[639,5050,950],{"class":949},[639,5052,5053],{"class":953}," quadratique",[639,5055,5056],{"class":957},"(t):    ",[639,5058,5059],{"class":977},"# O(n^2)\n",[639,5061,5063,5065,5067,5069,5071,5073,5076],{"class":945,"line":5062},9,[639,5064,1093],{"class":949},[639,5066,1325],{"class":957},[639,5068,1099],{"class":949},[639,5070,1330],{"class":970},[639,5072,886],{"class":957},[639,5074,5075],{"class":970},"len",[639,5077,5078],{"class":957},"(t)):\n",[639,5080,5082,5084,5086,5088,5090,5092,5094],{"class":945,"line":5081},10,[639,5083,1338],{"class":949},[639,5085,1341],{"class":957},[639,5087,1099],{"class":949},[639,5089,1330],{"class":970},[639,5091,886],{"class":957},[639,5093,5075],{"class":970},[639,5095,5078],{"class":957},[639,5097,5099],{"class":945,"line":5098},11,[639,5100,5101],{"class":970},"            ...\n",[3521,5103,5104],{},"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 .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}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":940,"searchDepth":961,"depth":961,"links":5106},[5107,5108,5109,5110,5112,5113],{"id":3562,"depth":961,"text":3563},{"id":3605,"depth":961,"text":3606},{"id":4263,"depth":961,"text":4264},{"id":4580,"depth":961,"text":5111},"Ordres de grandeur pour n=106n = 10^6n=106",{"id":3212,"depth":961,"text":3213},{"id":4978,"depth":961,"text":4979},"Mémo de révision sur la notation grand-O et les trois ordres de grandeur classiques.",{},"\u002Fnsi-1ere\u002Fph-algorithmique\u002Fcomplexite-bases.memo",[],{"title":3557,"description":5114},"1.nsi-1ere\u002Fph-algorithmique\u002F2.complexite-bases.memo","4xteAkJ58uzNRuqkgAr7aDbFMKFDXhtAd-yKgQXjpJY",{"id":5122,"title":5123,"body":5124,"description":6567,"extension":3543,"meta":6568,"navigation":3550,"path":6569,"seo":6570,"stem":6571,"__hash__":6572},"coursSlides\u002F1.nsi-1ere\u002Fph-algorithmique\u002F2.complexite-bases.slides.md","Bases de la complexité — diapositives",{"type":589,"value":5125,"toc":6565},[5126,5131,5134,5137,5139,5185,5187,5219,5259,5261,5306,5330,5333,5335,5380,5425,5457,5459,5534,5567,5598,5600,5632,5775,5777,5780,6009,6012,6014,6101,6367,6369,6372,6420,6422,6426,6562],[5127,5128,5130],"h1",{"id":5129},"combien-ça-coûte","Combien ça coûte ?",[597,5132,5133],{},"Mesurer un algorithme avant même de l'exécuter.",[5135,5136],"hr",{},[5127,5138,608],{"id":607},[726,5140,5141,5144,5147,5150],{},[729,5142,5143],{},"Comparer deux algorithmes qui font la même chose",[729,5145,5146],{},"Prévoir le comportement à grande échelle",[729,5148,5149],{},"Pas en secondes (machine-dépendant)",[729,5151,5152,5153,5156,5157],{},"En ",[601,5154,5155],{},"nombre d'opérations"," selon ",[639,5158,5160,5173],{"className":5159},[642],[639,5161,5163],{"className":5162},[646],[648,5164,5165],{"xmlns":650},[652,5166,5167,5171],{},[655,5168,5169],{},[658,5170,660],{},[662,5172,660],{"encoding":664},[639,5174,5176],{"className":5175,"ariaHidden":669},[668],[639,5177,5179,5182],{"className":5178},[673],[639,5180],{"className":5181,"style":678},[677],[639,5183,660],{"className":5184},[682,683],[5135,5186],{},[5127,5188,5190,5191],{"id":5189},"la-taille-de-lentrée-nnn","La taille de l'entrée ",[639,5192,5194,5207],{"className":5193},[642],[639,5195,5197],{"className":5196},[646],[648,5198,5199],{"xmlns":650},[652,5200,5201,5205],{},[655,5202,5203],{},[658,5204,660],{},[662,5206,660],{"encoding":664},[639,5208,5210],{"className":5209,"ariaHidden":669},[668],[639,5211,5213,5216],{"className":5212},[673],[639,5214],{"className":5215,"style":678},[677],[639,5217,660],{"className":5218},[682,683],[726,5220,5221,5224,5227],{},[729,5222,5223],{},"Tableau : nombre d'éléments",[729,5225,5226],{},"Chaîne : longueur",[729,5228,5229,5230,5258],{},"Entier ",[639,5231,5233,5246],{"className":5232},[642],[639,5234,5236],{"className":5235},[646],[648,5237,5238],{"xmlns":650},[652,5239,5240,5244],{},[655,5241,5242],{},[658,5243,810],{},[662,5245,810],{"encoding":664},[639,5247,5249],{"className":5248,"ariaHidden":669},[668],[639,5250,5252,5255],{"className":5251},[673],[639,5253],{"className":5254,"style":822},[677],[639,5256,810],{"className":5257,"style":826},[682,683]," : sa valeur, parfois son nombre de chiffres",[5135,5260],{},[5127,5262,865,5263],{"id":864},[639,5264,5266,5285],{"className":5265},[642],[639,5267,5269],{"className":5268},[646],[648,5270,5271],{"xmlns":650},[652,5272,5273,5283],{},[655,5274,5275,5277,5279,5281],{},[658,5276,881],{"mathvariant":880},[883,5278,886],{"stretchy":885},[888,5280,890],{},[883,5282,893],{"stretchy":885},[662,5284,896],{"encoding":664},[639,5286,5288],{"className":5287,"ariaHidden":669},[668],[639,5289,5291,5294,5297,5300,5303],{"className":5290},[673],[639,5292],{"className":5293,"style":906},[677],[639,5295,881],{"className":5296,"style":911},[682,910],[639,5298,886],{"className":5299},[915],[639,5301,890],{"className":5302},[682],[639,5304,893],{"className":5305},[922],[935,5307,5309],{"className":937,"code":5308,"language":939,"meta":940,"style":940},"def premier(t):\n    return t[0]\n",[927,5310,5311,5320],{"__ignoreMap":940},[639,5312,5313,5315,5317],{"class":945,"line":946},[639,5314,950],{"class":949},[639,5316,954],{"class":953},[639,5318,5319],{"class":957},"(t):\n",[639,5321,5322,5324,5326,5328],{"class":945,"line":961},[639,5323,964],{"class":949},[639,5325,5004],{"class":957},[639,5327,971],{"class":970},[639,5329,5009],{"class":957},[597,5331,5332],{},"Une opération. Indépendant de la taille.",[5135,5334],{},[5127,5336,982,5337],{"id":981},[639,5338,5340,5359],{"className":5339},[642],[639,5341,5343],{"className":5342},[646],[648,5344,5345],{"xmlns":650},[652,5346,5347,5357],{},[655,5348,5349,5351,5353,5355],{},[658,5350,881],{"mathvariant":880},[883,5352,886],{"stretchy":885},[658,5354,660],{},[883,5356,893],{"stretchy":885},[662,5358,1005],{"encoding":664},[639,5360,5362],{"className":5361,"ariaHidden":669},[668],[639,5363,5365,5368,5371,5374,5377],{"className":5364},[673],[639,5366],{"className":5367,"style":906},[677],[639,5369,881],{"className":5370,"style":911},[682,910],[639,5372,886],{"className":5373},[915],[639,5375,660],{"className":5376},[682,683],[639,5378,893],{"className":5379},[922],[935,5381,5383],{"className":937,"code":5382,"language":939,"meta":940,"style":940},"def somme(t):\n    total = 0\n    for v in t:\n        total += v\n    return total\n",[927,5384,5385,5393,5401,5411,5419],{"__ignoreMap":940},[639,5386,5387,5389,5391],{"class":945,"line":946},[639,5388,950],{"class":949},[639,5390,1074],{"class":953},[639,5392,5319],{"class":957},[639,5394,5395,5397,5399],{"class":945,"line":961},[639,5396,1081],{"class":957},[639,5398,1084],{"class":949},[639,5400,1087],{"class":970},[639,5402,5403,5405,5407,5409],{"class":945,"line":1090},[639,5404,1093],{"class":949},[639,5406,1096],{"class":957},[639,5408,1099],{"class":949},[639,5410,5037],{"class":957},[639,5412,5413,5415,5417],{"class":945,"line":1108},[639,5414,1111],{"class":957},[639,5416,1114],{"class":949},[639,5418,1117],{"class":957},[639,5420,5421,5423],{"class":945,"line":1120},[639,5422,964],{"class":949},[639,5424,1125],{"class":957},[597,5426,5427,5428,5456],{},"Si ",[639,5429,5431,5444],{"className":5430},[642],[639,5432,5434],{"className":5433},[646],[648,5435,5436],{"xmlns":650},[652,5437,5438,5442],{},[655,5439,5440],{},[658,5441,660],{},[662,5443,660],{"encoding":664},[639,5445,5447],{"className":5446,"ariaHidden":669},[668],[639,5448,5450,5453],{"className":5449},[673],[639,5451],{"className":5452,"style":678},[677],[639,5454,660],{"className":5455},[682,683]," double → temps double.",[5135,5458],{},[5127,5460,1129,5461],{"id":1128},[639,5462,5464,5487],{"className":5463},[642],[639,5465,5467],{"className":5466},[646],[648,5468,5469],{"xmlns":650},[652,5470,5471,5485],{},[655,5472,5473,5475,5477,5483],{},[658,5474,881],{"mathvariant":880},[883,5476,886],{"stretchy":885},[1147,5478,5479,5481],{},[658,5480,660],{},[888,5482,1153],{},[883,5484,893],{"stretchy":885},[662,5486,1158],{"encoding":664},[639,5488,5490],{"className":5489,"ariaHidden":669},[668],[639,5491,5493,5496,5499,5502,5531],{"className":5492},[673],[639,5494],{"className":5495,"style":1168},[677],[639,5497,881],{"className":5498,"style":911},[682,910],[639,5500,886],{"className":5501},[915],[639,5503,5505,5508],{"className":5504},[682],[639,5506,660],{"className":5507},[682,683],[639,5509,5511],{"className":5510},[1184],[639,5512,5514],{"className":5513},[1188],[639,5515,5517],{"className":5516},[1192],[639,5518,5520],{"className":5519,"style":1197},[1196],[639,5521,5522,5525],{"style":1200},[639,5523],{"className":5524,"style":1205},[1204],[639,5526,5528],{"className":5527},[1209,1210,1211,1212],[639,5529,1153],{"className":5530},[682,1212],[639,5532,893],{"className":5533},[922],[935,5535,5537],{"className":937,"code":5536,"language":939,"meta":940,"style":940},"for i in range(n):\n    for j in range(n):\n        ...\n",[927,5538,5539,5551,5563],{"__ignoreMap":940},[639,5540,5541,5543,5545,5547,5549],{"class":945,"line":946},[639,5542,2955],{"class":949},[639,5544,1325],{"class":957},[639,5546,1099],{"class":949},[639,5548,1330],{"class":970},[639,5550,1333],{"class":957},[639,5552,5553,5555,5557,5559,5561],{"class":945,"line":961},[639,5554,1093],{"class":949},[639,5556,1341],{"class":957},[639,5558,1099],{"class":949},[639,5560,1330],{"class":970},[639,5562,1333],{"class":957},[639,5564,5565],{"class":945,"line":1090},[639,5566,5042],{"class":970},[597,5568,5427,5569,5597],{},[639,5570,5572,5585],{"className":5571},[642],[639,5573,5575],{"className":5574},[646],[648,5576,5577],{"xmlns":650},[652,5578,5579,5583],{},[655,5580,5581],{},[658,5582,660],{},[662,5584,660],{"encoding":664},[639,5586,5588],{"className":5587,"ariaHidden":669},[668],[639,5589,5591,5594],{"className":5590},[673],[639,5592],{"className":5593,"style":678},[677],[639,5595,660],{"className":5596},[682,683]," double → temps × 4.",[5135,5599],{},[5127,5601,5603,5604],{"id":5602},"la-notation-omathcaloo","La notation ",[639,5605,5607,5620],{"className":5606},[642],[639,5608,5610],{"className":5609},[646],[648,5611,5612],{"xmlns":650},[652,5613,5614,5618],{},[655,5615,5616],{},[658,5617,881],{"mathvariant":880},[662,5619,3244],{"encoding":664},[639,5621,5623],{"className":5622,"ariaHidden":669},[668],[639,5624,5626,5629],{"className":5625},[673],[639,5627],{"className":5628,"style":3254},[677],[639,5630,881],{"className":5631,"style":911},[682,910],[726,5633,5634,5737,5743],{},[729,5635,5636,5637,827,5639,4211,5694],{},"On ",[601,5638,1671],{},[639,5640,5642,5661],{"className":5641},[642],[639,5643,5645],{"className":5644},[646],[648,5646,5647],{"xmlns":650},[652,5648,5649,5659],{},[655,5650,5651,5653,5655,5657],{},[888,5652,1724],{},[658,5654,660],{},[883,5656,1351],{},[888,5658,1731],{},[662,5660,1734],{"encoding":664},[639,5662,5664,5685],{"className":5663,"ariaHidden":669},[668],[639,5665,5667,5670,5673,5676,5679,5682],{"className":5666},[673],[639,5668],{"className":5669,"style":1744},[677],[639,5671,1724],{"className":5672},[682],[639,5674,660],{"className":5675},[682,683],[639,5677],{"className":5678,"style":1438},[1437],[639,5680,1351],{"className":5681},[1442],[639,5683],{"className":5684,"style":1438},[1437],[639,5686,5688,5691],{"className":5687},[673],[639,5689],{"className":5690,"style":1766},[677],[639,5692,1731],{"className":5693},[682],[639,5695,5697,5716],{"className":5696},[642],[639,5698,5700],{"className":5699},[646],[648,5701,5702],{"xmlns":650},[652,5703,5704,5714],{},[655,5705,5706,5708,5710,5712],{},[658,5707,881],{"mathvariant":880},[883,5709,886],{"stretchy":885},[658,5711,660],{},[883,5713,893],{"stretchy":885},[662,5715,1005],{"encoding":664},[639,5717,5719],{"className":5718,"ariaHidden":669},[668],[639,5720,5722,5725,5728,5731,5734],{"className":5721},[673],[639,5723],{"className":5724,"style":906},[677],[639,5726,881],{"className":5727,"style":911},[682,910],[639,5729,886],{"className":5730},[915],[639,5732,660],{"className":5733},[682,683],[639,5735,893],{"className":5736},[922],[729,5738,5739,5740],{},"On garde l'",[601,5741,5742],{},"ordre de grandeur dominant",[729,5744,5745,5746,5774],{},"Bornes asymptotiques — quand ",[639,5747,5749,5762],{"className":5748},[642],[639,5750,5752],{"className":5751},[646],[648,5753,5754],{"xmlns":650},[652,5755,5756,5760],{},[655,5757,5758],{},[658,5759,660],{},[662,5761,660],{"encoding":664},[639,5763,5765],{"className":5764,"ariaHidden":669},[668],[639,5766,5768,5771],{"className":5767},[673],[639,5769],{"className":5770,"style":678},[677],[639,5772,660],{"className":5773},[682,683]," devient grand",[5135,5776],{},[5127,5778,3937],{"id":5779},"hiérarchie",[639,5781,5783],{"className":5782},[2607],[639,5784,5786,5855],{"className":5785},[642],[639,5787,5789],{"className":5788},[646],[648,5790,5791],{"xmlns":650,"display":2616},[652,5792,5793,5853],{},[655,5794,5795,5797,5799,5801,5803,5805,5807,5809,5811,5813,5815,5817,5819,5821,5823,5825,5827,5829,5831,5833,5835,5837,5839,5841,5843,5845,5851],{},[658,5796,881],{"mathvariant":880},[883,5798,886],{"stretchy":885},[888,5800,890],{},[883,5802,893],{"stretchy":885},[2630,5804,2632],{},[883,5806,2635],{},[2630,5808,2632],{},[658,5810,881],{"mathvariant":880},[883,5812,886],{"stretchy":885},[658,5814,2140],{},[883,5816,2143],{},[658,5818,660],{},[883,5820,893],{"stretchy":885},[2630,5822,2632],{},[883,5824,2635],{},[2630,5826,2632],{},[658,5828,881],{"mathvariant":880},[883,5830,886],{"stretchy":885},[658,5832,660],{},[883,5834,893],{"stretchy":885},[2630,5836,2632],{},[883,5838,2635],{},[2630,5840,2632],{},[658,5842,881],{"mathvariant":880},[883,5844,886],{"stretchy":885},[1147,5846,5847,5849],{},[658,5848,660],{},[888,5850,1153],{},[883,5852,893],{"stretchy":885},[662,5854,2684],{"encoding":664},[639,5856,5858,5891,5932,5965],{"className":5857,"ariaHidden":669},[668],[639,5859,5861,5864,5867,5870,5873,5876,5879,5882,5885,5888],{"className":5860},[673],[639,5862],{"className":5863,"style":906},[677],[639,5865,881],{"className":5866,"style":911},[682,910],[639,5868,886],{"className":5869},[915],[639,5871,890],{"className":5872},[682],[639,5874,893],{"className":5875},[922],[639,5877],{"className":5878,"style":2709},[1437],[639,5880],{"className":5881,"style":2709},[1437],[639,5883,2635],{"className":5884},[2716],[639,5886],{"className":5887,"style":2709},[1437],[639,5889],{"className":5890,"style":2709},[1437],[639,5892,5894,5897,5900,5903,5908,5911,5914,5917,5920,5923,5926,5929],{"className":5893},[673],[639,5895],{"className":5896,"style":906},[677],[639,5898,881],{"className":5899,"style":911},[682,910],[639,5901,886],{"className":5902},[915],[639,5904,2170,5906],{"className":5905},[2169],[639,5907,2174],{"style":2173},[639,5909],{"className":5910,"style":2178},[1437],[639,5912,660],{"className":5913},[682,683],[639,5915,893],{"className":5916},[922],[639,5918],{"className":5919,"style":2709},[1437],[639,5921],{"className":5922,"style":2709},[1437],[639,5924,2635],{"className":5925},[2716],[639,5927],{"className":5928,"style":2709},[1437],[639,5930],{"className":5931,"style":2709},[1437],[639,5933,5935,5938,5941,5944,5947,5950,5953,5956,5959,5962],{"className":5934},[673],[639,5936],{"className":5937,"style":906},[677],[639,5939,881],{"className":5940,"style":911},[682,910],[639,5942,886],{"className":5943},[915],[639,5945,660],{"className":5946},[682,683],[639,5948,893],{"className":5949},[922],[639,5951],{"className":5952,"style":2709},[1437],[639,5954],{"className":5955,"style":2709},[1437],[639,5957,2635],{"className":5958},[2716],[639,5960],{"className":5961,"style":2709},[1437],[639,5963],{"className":5964,"style":2709},[1437],[639,5966,5968,5971,5974,5977,6006],{"className":5967},[673],[639,5969],{"className":5970,"style":2803},[677],[639,5972,881],{"className":5973,"style":911},[682,910],[639,5975,886],{"className":5976},[915],[639,5978,5980,5983],{"className":5979},[682],[639,5981,660],{"className":5982},[682,683],[639,5984,5986],{"className":5985},[1184],[639,5987,5989],{"className":5988},[1188],[639,5990,5992],{"className":5991},[1192],[639,5993,5995],{"className":5994,"style":2828},[1196],[639,5996,5997,6000],{"style":2831},[639,5998],{"className":5999,"style":1205},[1204],[639,6001,6003],{"className":6002},[1209,1210,1211,1212],[639,6004,1153],{"className":6005},[682,1212],[639,6007,893],{"className":6008},[922],[597,6010,6011],{},"Plus on est à gauche, mieux on passe à l'échelle.",[5135,6013],{},[5127,6015,6017,6018],{"id":6016},"comparaison-pour-n106n-106n106","Comparaison pour 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