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hypertexte","\u002Fsnt-2nde\u002Fsb-web\u002Furl-hypertexte","0.snt-2nde\u002Fsb-web\u002F2.url-hypertexte",{"title":51,"path":52,"stem":53},"HTML et CSS — le contenu et la présentation","\u002Fsnt-2nde\u002Fsb-web\u002Fhtml-css","0.snt-2nde\u002Fsb-web\u002F3.html-css",{"title":55,"path":56,"stem":57},"Client-serveur et requêtes HTTP","\u002Fsnt-2nde\u002Fsb-web\u002Fclient-serveur-http","0.snt-2nde\u002Fsb-web\u002F4.client-serveur-http",{"title":59,"path":60,"stem":61},"Moteurs de recherche","\u002Fsnt-2nde\u002Fsb-web\u002Fmoteurs-recherche","0.snt-2nde\u002Fsb-web\u002F5.moteurs-recherche",{"title":63,"path":64,"stem":65},"Sécurité du navigateur et notions juridiques","\u002Fsnt-2nde\u002Fsb-web\u002Fsecurite-droits","0.snt-2nde\u002Fsb-web\u002F6.securite-droits",{"title":67,"path":68,"stem":69,"children":70},"Les réseaux 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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 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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 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Là où un arbre\nimpose une hiérarchie stricte avec une racine unique, le graphe autorise des\ncycles, des relations multiples, des composantes disjointes.",[598,611,612,613,616,617,620,621,624],{},"L'exemple le plus parlant reste le ",[602,614,615],{},"plan du métro parisien"," : les ",[602,618,619],{},"stations","\nsont les sommets, les ",[602,622,623],{},"liaisons directes"," entre stations voisines sont les\narêtes. On peut tourner en rond (cycle), bifurquer, traverser des composantes\nséparées (les terminus d'une ligne disjointe).",[598,626,627,628,631],{},"L'item ",[629,630],"bo-ref",{"code":588}," demande deux choses :",[633,634,635,643],"ol",{},[636,637,638,639,642],"li",{},"savoir ",[602,640,641],{},"modéliser"," une situation par un graphe ;",[636,644,638,645,648,649,652],{},[602,646,647],{},"implémenter"," un graphe de deux manières (matrice d'adjacence, liste\nde successeurs) et ",[602,650,651],{},"passer de l'une à l'autre",".",[593,654,656],{"id":655},"vocabulaire","Vocabulaire",[658,659,660,673],"table",{},[661,662,663],"thead",{},[664,665,666,670],"tr",{},[667,668,669],"th",{},"Terme",[667,671,672],{},"Définition",[674,675,676,688,784,851,861,871,991,1108,1226,1265],"tbody",{},[664,677,678,685],{},[679,680,681,684],"td",{},[602,682,683],{},"Sommet"," (ou nœud)",[679,686,687],{},"Élément du 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d'arcs — la relation a un sens.",[664,872,873,908],{},[679,874,875,878,879],{},[602,876,877],{},"Successeur"," de ",[703,880,882,895],{"className":881},[706],[703,883,885],{"className":884},[710],[712,886,887],{"xmlns":714},[716,888,889,893],{},[719,890,891],{},[727,892,729],{},[741,894,729],{"encoding":743},[703,896,898],{"className":897,"ariaHidden":732},[748],[703,899,901,905],{"className":900},[752],[703,902],{"className":903,"style":904},[756],"height:0.4306em;",[703,906,729],{"className":907},[765,766],[679,909,910,911,939,940,652],{},"Sommet ",[703,912,914,927],{"className":913},[706],[703,915,917],{"className":916},[710],[712,918,919],{"xmlns":714},[716,920,921,925],{},[719,922,923],{},[727,924,736],{},[741,926,736],{"encoding":743},[703,928,930],{"className":929,"ariaHidden":732},[748],[703,931,933,936],{"className":932},[752],[703,934],{"className":935,"style":904},[756],[703,937,736],{"className":938,"style":779},[765,766]," tel qu'il existe un arc ",[703,941,943,964],{"className":942},[706],[703,944,946],{"className":945},[710],[712,947,948],{"xmlns":714},[716,949,950,962],{},[719,951,952,954,956,958,960],{},[722,953,811],{"stretchy":724},[727,955,729],{},[722,957,733],{"separator":732},[727,959,736],{},[722,961,820],{"stretchy":724},[741,963,823],{"encoding":743},[703,965,967],{"className":966,"ariaHidden":732},[748],[703,968,970,973,976,979,982,985,988],{"className":969},[752],[703,971],{"className":972,"style":757},[756],[703,974,811],{"className":975},[761],[703,977,729],{"className":978},[765,766],[703,980,733],{"className":981},[770],[703,983],{"className":984,"style":775},[774],[703,986,736],{"className":987,"style":779},[765,766],[703,989,820],{"className":990},[783],[664,992,993,1026],{},[679,994,995,878,998],{},[602,996,997],{},"Prédécesseur",[703,999,1001,1014],{"className":1000},[706],[703,1002,1004],{"className":1003},[710],[712,1005,1006],{"xmlns":714},[716,1007,1008,1012],{},[719,1009,1010],{},[727,1011,729],{},[741,1013,729],{"encoding":743},[703,1015,1017],{"className":1016,"ariaHidden":732},[748],[703,1018,1020,1023],{"className":1019},[752],[703,1021],{"className":1022,"style":904},[756],[703,1024,729],{"className":1025},[765,766],[679,1027,910,1028,939,1056,652],{},[703,1029,1031,1044],{"className":1030},[706],[703,1032,1034],{"className":1033},[710],[712,1035,1036],{"xmlns":714},[716,1037,1038,1042],{},[719,1039,1040],{},[727,1041,736],{},[741,1043,736],{"encoding":743},[703,1045,1047],{"className":1046,"ariaHidden":732},[748],[703,1048,1050,1053],{"className":1049},[752],[703,1051],{"className":1052,"style":904},[756],[703,1054,736],{"className":1055,"style":779},[765,766],[703,1057,1059,1081],{"className":1058},[706],[703,1060,1062],{"className":1061},[710],[712,1063,1064],{"xmlns":714},[716,1065,1066,1078],{},[719,1067,1068,1070,1072,1074,1076],{},[722,1069,811],{"stretchy":724},[727,1071,736],{},[722,1073,733],{"separator":732},[727,1075,729],{},[722,1077,820],{"stretchy":724},[741,1079,1080],{"encoding":743},"(v, u)",[703,1082,1084],{"className":1083,"ariaHidden":732},[748],[703,1085,1087,1090,1093,1096,1099,1102,1105],{"className":1086},[752],[703,1088],{"className":1089,"style":757},[756],[703,1091,811],{"className":1092},[761],[703,1094,736],{"className":1095,"style":779},[765,766],[703,1097,733],{"className":1098},[770],[703,1100],{"className":1101,"style":775},[774],[703,1103,729],{"className":1104},[765,766],[703,1106,820],{"className":1107},[783],[664,1109,1110,1144],{},[679,1111,1112,878,1115,1143],{},[602,1113,1114],{},"Voisin",[703,1116,1118,1131],{"className":1117},[706],[703,1119,1121],{"className":1120},[710],[712,1122,1123],{"xmlns":714},[716,1124,1125,1129],{},[719,1126,1127],{},[727,1128,729],{},[741,1130,729],{"encoding":743},[703,1132,1134],{"className":1133,"ariaHidden":732},[748],[703,1135,1137,1140],{"className":1136},[752],[703,1138],{"className":1139,"style":904},[756],[703,1141,729],{"className":1142},[765,766]," (non orienté)",[679,1145,910,1146,1174,1175,652],{},[703,1147,1149,1162],{"className":1148},[706],[703,1150,1152],{"className":1151},[710],[712,1153,1154],{"xmlns":714},[716,1155,1156,1160],{},[719,1157,1158],{},[727,1159,736],{},[741,1161,736],{"encoding":743},[703,1163,1165],{"className":1164,"ariaHidden":732},[748],[703,1166,1168,1171],{"className":1167},[752],[703,1169],{"className":1170,"style":904},[756],[703,1172,736],{"className":1173,"style":779},[765,766]," tel qu'il existe une arête ",[703,1176,1178,1199],{"className":1177},[706],[703,1179,1181],{"className":1180},[710],[712,1182,1183],{"xmlns":714},[716,1184,1185,1197],{},[719,1186,1187,1189,1191,1193,1195],{},[722,1188,725],{"stretchy":724},[727,1190,729],{},[722,1192,733],{"separator":732},[727,1194,736],{},[722,1196,739],{"stretchy":724},[741,1198,744],{"encoding":743},[703,1200,1202],{"className":1201,"ariaHidden":732},[748],[703,1203,1205,1208,1211,1214,1217,1220,1223],{"className":1204},[752],[703,1206],{"className":1207,"style":757},[756],[703,1209,725],{"className":1210},[761],[703,1212,729],{"className":1213},[765,766],[703,1215,733],{"className":1216},[770],[703,1218],{"className":1219,"style":775},[774],[703,1221,736],{"className":1222,"style":779},[765,766],[703,1224,739],{"className":1225},[783],[664,1227,1228,1233],{},[679,1229,1230],{},[602,1231,1232],{},"Ordre",[679,1234,1235,1236,652],{},"Nombre de sommets, noté ",[703,1237,1239,1253],{"className":1238},[706],[703,1240,1242],{"className":1241},[710],[712,1243,1244],{"xmlns":714},[716,1245,1246,1251],{},[719,1247,1248],{},[727,1249,1250],{},"n",[741,1252,1250],{"encoding":743},[703,1254,1256],{"className":1255,"ariaHidden":732},[748],[703,1257,1259,1262],{"className":1258},[752],[703,1260],{"className":1261,"style":904},[756],[703,1263,1250],{"className":1264},[765,766],[664,1266,1267,1272],{},[679,1268,1269],{},[602,1270,1271],{},"Taille",[679,1273,1274,1275,652],{},"Nombre d'arêtes ou d'arcs, noté ",[703,1276,1278,1292],{"className":1277},[706],[703,1279,1281],{"className":1280},[710],[712,1282,1283],{"xmlns":714},[716,1284,1285,1290],{},[719,1286,1287],{},[727,1288,1289],{},"m",[741,1291,1289],{"encoding":743},[703,1293,1295],{"className":1294,"ariaHidden":732},[748],[703,1296,1298,1301],{"className":1297},[752],[703,1299],{"className":1300,"style":904},[756],[703,1302,1289],{"className":1303},[765,766],[1305,1306,1307],"note",{},[598,1308,1309,1312,1313,1316],{},[602,1310,1311],{},"Routier ↔ non orienté"," (une route va dans les deux sens), ",[602,1314,1315],{},"Internet ↔\norienté"," (un lien hypertexte d'une page A vers B ne crée pas le lien réciproque).\nLe choix orienté\u002Fnon orienté découle de la situation modélisée.",[1318,1319,1322,1433],"self-eval-qcm",{"correct":1320,"slug":1321},"1","graphes-c1",[1323,1324,1326],"template",{"v-slot:question":1325},"",[598,1327,1328,1329,1380,1381,1432],{},"Dans un graphe orienté, ",[703,1330,1332,1353],{"className":1331},[706],[703,1333,1335],{"className":1334},[710],[712,1336,1337],{"xmlns":714},[716,1338,1339,1351],{},[719,1340,1341,1343,1345,1347,1349],{},[722,1342,811],{"stretchy":724},[727,1344,729],{},[722,1346,733],{"separator":732},[727,1348,736],{},[722,1350,820],{"stretchy":724},[741,1352,823],{"encoding":743},[703,1354,1356],{"className":1355,"ariaHidden":732},[748],[703,1357,1359,1362,1365,1368,1371,1374,1377],{"className":1358},[752],[703,1360],{"className":1361,"style":757},[756],[703,1363,811],{"className":1364},[761],[703,1366,729],{"className":1367},[765,766],[703,1369,733],{"className":1370},[770],[703,1372],{"className":1373,"style":775},[774],[703,1375,736],{"className":1376,"style":779},[765,766],[703,1378,820],{"className":1379},[783]," et ",[703,1382,1384,1405],{"className":1383},[706],[703,1385,1387],{"className":1386},[710],[712,1388,1389],{"xmlns":714},[716,1390,1391,1403],{},[719,1392,1393,1395,1397,1399,1401],{},[722,1394,811],{"stretchy":724},[727,1396,736],{},[722,1398,733],{"separator":732},[727,1400,729],{},[722,1402,820],{"stretchy":724},[741,1404,1080],{"encoding":743},[703,1406,1408],{"className":1407,"ariaHidden":732},[748],[703,1409,1411,1414,1417,1420,1423,1426,1429],{"className":1410},[752],[703,1412],{"className":1413,"style":757},[756],[703,1415,811],{"className":1416},[761],[703,1418,736],{"className":1419,"style":779},[765,766],[703,1421,733],{"className":1422},[770],[703,1424],{"className":1425,"style":775},[774],[703,1427,729],{"className":1428},[765,766],[703,1430,820],{"className":1431},[783]," représentent…",[1323,1434,1435],{"v-slot:choices":1325},[1436,1437,1438,1441,1444],"ul",{},[636,1439,1440],{},"le même arc",[636,1442,1443],{},"deux arcs distincts",[636,1445,1446],{},"une seule arête",[593,1448,1450],{"id":1449},"représentation-1-matrice-dadjacence","Représentation 1 — matrice d'adjacence",[598,1452,1453,1454,1485,1486,1541,1542,1545,1546,1577,1578,1630],{},"On numérote les sommets de ",[703,1455,1457,1472],{"className":1456},[706],[703,1458,1460],{"className":1459},[710],[712,1461,1462],{"xmlns":714},[716,1463,1464,1470],{},[719,1465,1466],{},[1467,1468,1469],"mn",{},"0",[741,1471,1469],{"encoding":743},[703,1473,1475],{"className":1474,"ariaHidden":732},[748],[703,1476,1478,1482],{"className":1477},[752],[703,1479],{"className":1480,"style":1481},[756],"height:0.6444em;",[703,1483,1469],{"className":1484},[765]," à ",[703,1487,1489,1508],{"className":1488},[706],[703,1490,1492],{"className":1491},[710],[712,1493,1494],{"xmlns":714},[716,1495,1496,1505],{},[719,1497,1498,1500,1503],{},[727,1499,1250],{},[722,1501,1502],{},"−",[1467,1504,1320],{},[741,1506,1507],{"encoding":743},"n - 1",[703,1509,1511,1532],{"className":1510,"ariaHidden":732},[748],[703,1512,1514,1518,1521,1525,1529],{"className":1513},[752],[703,1515],{"className":1516,"style":1517},[756],"height:0.6667em;vertical-align:-0.0833em;",[703,1519,1250],{"className":1520},[765,766],[703,1522],{"className":1523,"style":1524},[774],"margin-right:0.2222em;",[703,1526,1502],{"className":1527},[1528],"mbin",[703,1530],{"className":1531,"style":1524},[774],[703,1533,1535,1538],{"className":1534},[752],[703,1536],{"className":1537,"style":1481},[756],[703,1539,1320],{"className":1540},[765],". La ",[602,1543,1544],{},"matrice d'adjacence"," ",[703,1547,1549,1563],{"className":1548},[706],[703,1550,1552],{"className":1551},[710],[712,1553,1554],{"xmlns":714},[716,1555,1556,1561],{},[719,1557,1558],{},[727,1559,1560],{},"M",[741,1562,1560],{"encoding":743},[703,1564,1566],{"className":1565,"ariaHidden":732},[748],[703,1567,1569,1573],{"className":1568},[752],[703,1570],{"className":1571,"style":1572},[756],"height:0.6833em;",[703,1574,1560],{"className":1575,"style":1576},[765,766],"margin-right:0.109em;"," est un\ntableau carré ",[703,1579,1581,1600],{"className":1580},[706],[703,1582,1584],{"className":1583},[710],[712,1585,1586],{"xmlns":714},[716,1587,1588,1597],{},[719,1589,1590,1592,1595],{},[727,1591,1250],{},[722,1593,1594],{},"×",[727,1596,1250],{},[741,1598,1599],{"encoding":743},"n \\times n",[703,1601,1603,1621],{"className":1602,"ariaHidden":732},[748],[703,1604,1606,1609,1612,1615,1618],{"className":1605},[752],[703,1607],{"className":1608,"style":1517},[756],[703,1610,1250],{"className":1611},[765,766],[703,1613],{"className":1614,"style":1524},[774],[703,1616,1594],{"className":1617},[1528],[703,1619],{"className":1620,"style":1524},[774],[703,1622,1624,1627],{"className":1623},[752],[703,1625],{"className":1626,"style":904},[756],[703,1628,1250],{"className":1629},[765,766]," où :",[598,1632,1633],{},[703,1634,1636,1736],{"className":1635},[706],[703,1637,1639],{"className":1638},[710],[712,1640,1641],{"xmlns":714},[716,1642,1643,1733],{},[719,1644,1645,1647,1650,1653,1656,1658,1661,1663,1666],{},[727,1646,1560],{},[722,1648,1649],{"stretchy":724},"[",[727,1651,1652],{},"i",[722,1654,1655],{"stretchy":724},"]",[722,1657,1649],{"stretchy":724},[727,1659,1660],{},"j",[722,1662,1655],{"stretchy":724},[722,1664,1665],{},"=",[719,1667,1668,1670],{},[722,1669,725],{"fence":732},[1671,1672,1676,1718],"mtable",{"rowspacing":1673,"columnalign":1674,"columnspacing":1675},"0.36em","left left","1em",[1677,1678,1679,1687],"mtr",{},[1680,1681,1682],"mtd",{},[1683,1684,1685],"mstyle",{"scriptlevel":1469,"displaystyle":724},[1467,1686,1320],{},[1680,1688,1689],{},[1683,1690,1691],{"scriptlevel":1469,"displaystyle":724},[719,1692,1693,1711,1713,1716],{},[719,1694,1695,1699,1708],{},[1696,1697,1698],"mtext",{},"s’il existe un arc (ou une ar",[1700,1701,1702,1705],"mover",{"accent":732},[1696,1703,1704],{},"e",[722,1706,1707],{},"ˆ",[1696,1709,1710],{},"te) de ",[727,1712,1652],{},[1696,1714,1715],{}," vers ",[727,1717,1660],{},[1677,1719,1720,1726],{},[1680,1721,1722],{},[1683,1723,1724],{"scriptlevel":1469,"displaystyle":724},[1467,1725,1469],{},[1680,1727,1728],{},[1683,1729,1730],{"scriptlevel":1469,"displaystyle":724},[1696,1731,1732],{},"sinon",[741,1734,1735],{"encoding":743},"M[i][j] = \\begin{cases} 1 & \\text{s'il existe un arc (ou une arête) de } i \\text{ vers } j \\\\ 0 & \\text{sinon} \\end{cases}",[703,1737,1739,1778],{"className":1738,"ariaHidden":732},[748],[703,1740,1742,1745,1748,1751,1754,1757,1760,1764,1767,1771,1775],{"className":1741},[752],[703,1743],{"className":1744,"style":757},[756],[703,1746,1560],{"className":1747,"style":1576},[765,766],[703,1749,1649],{"className":1750},[761],[703,1752,1652],{"className":1753},[765,766],[703,1755,1655],{"className":1756},[783],[703,1758,1649],{"className":1759},[761],[703,1761,1660],{"className":1762,"style":1763},[765,766],"margin-right:0.0572em;",[703,1765,1655],{"className":1766},[783],[703,1768],{"className":1769,"style":1770},[774],"margin-right:0.2778em;",[703,1772,1665],{"className":1773},[1774],"mrel",[703,1776],{"className":1777,"style":1770},[774],[703,1779,1781,1785],{"className":1780},[752],[703,1782],{"className":1783,"style":1784},[756],"height:3em;vertical-align:-1.25em;",[703,1786,1789,1799,1972],{"className":1787},[1788],"minner",[703,1790,1794],{"className":1791,"style":1793},[761,1792],"delimcenter","top:0em;",[703,1795,725],{"className":1796},[1797,1798],"delimsizing","size4",[703,1800,1802],{"className":1801},[765],[703,1803,1805,1863,1868],{"className":1804},[1671],[703,1806,1809],{"className":1807},[1808],"col-align-l",[703,1810,1814,1854],{"className":1811},[1812,1813],"vlist-t","vlist-t2",[703,1815,1818,1849],{"className":1816},[1817],"vlist-r",[703,1819,1823,1837],{"className":1820,"style":1822},[1821],"vlist","height:1.69em;",[703,1824,1826,1831],{"style":1825},"top:-3.69em;",[703,1827],{"className":1828,"style":1830},[1829],"pstrut","height:3.008em;",[703,1832,1834],{"className":1833},[765],[703,1835,1320],{"className":1836},[765],[703,1838,1840,1843],{"style":1839},"top:-2.25em;",[703,1841],{"className":1842,"style":1830},[1829],[703,1844,1846],{"className":1845},[765],[703,1847,1469],{"className":1848},[765],[703,1850,1853],{"className":1851},[1852],"vlist-s","​",[703,1855,1857],{"className":1856},[1817],[703,1858,1861],{"className":1859,"style":1860},[1821],"height:1.19em;",[703,1862],{},[703,1864],{"className":1865,"style":1867},[1866],"arraycolsep","width:1em;",[703,1869,1871],{"className":1870},[1808],[703,1872,1874,1964],{"className":1873},[1812,1813],[703,1875,1877,1961],{"className":1876},[1817],[703,1878,1880,1947],{"className":1879,"style":1822},[1821],[703,1881,1882,1885],{"style":1825},[703,1883],{"className":1884,"style":1830},[1829],[703,1886,1888,1935,1938,1944],{"className":1887},[765],[703,1889,1892,1895,1932],{"className":1890},[765,1891],"text",[703,1893,1698],{"className":1894},[765],[703,1896,1899],{"className":1897},[765,1898],"accent",[703,1900,1902],{"className":1901},[1812],[703,1903,1905],{"className":1904},[1817],[703,1906,1909,1919],{"className":1907,"style":1908},[1821],"height:0.6944em;",[703,1910,1912,1916],{"style":1911},"top:-3em;",[703,1913],{"className":1914,"style":1915},[1829],"height:3em;",[703,1917,1704],{"className":1918},[765],[703,1920,1921,1924],{"style":1911},[703,1922],{"className":1923,"style":1915},[1829],[703,1925,1929],{"className":1926,"style":1928},[1927],"accent-body","left:-0.25em;",[703,1930,1707],{"className":1931},[765],[703,1933,1710],{"className":1934},[765],[703,1936,1652],{"className":1937},[765,766],[703,1939,1941],{"className":1940},[765,1891],[703,1942,1715],{"className":1943},[765],[703,1945,1660],{"className":1946,"style":1763},[765,766],[703,1948,1949,1952],{"style":1839},[703,1950],{"className":1951,"style":1830},[1829],[703,1953,1955],{"className":1954},[765],[703,1956,1958],{"className":1957},[765,1891],[703,1959,1732],{"className":1960},[765],[703,1962,1853],{"className":1963},[1852],[703,1965,1967],{"className":1966},[1817],[703,1968,1970],{"className":1969,"style":1860},[1821],[703,1971],{},[703,1973],{"className":1974},[783,1975],"nulldelimiter",[598,1977,1978,1979,1981,1982,1985,1986,652],{},"Pour un graphe ",[602,1980,700],{},", la matrice est ",[602,1983,1984],{},"symétrique"," :\n",[703,1987,1989,2031],{"className":1988},[706],[703,1990,1992],{"className":1991},[710],[712,1993,1994],{"xmlns":714},[716,1995,1996,2028],{},[719,1997,1998,2000,2002,2004,2006,2008,2010,2012,2014,2016,2018,2020,2022,2024,2026],{},[727,1999,1560],{},[722,2001,1649],{"stretchy":724},[727,2003,1652],{},[722,2005,1655],{"stretchy":724},[722,2007,1649],{"stretchy":724},[727,2009,1660],{},[722,2011,1655],{"stretchy":724},[722,2013,1665],{},[727,2015,1560],{},[722,2017,1649],{"stretchy":724},[727,2019,1660],{},[722,2021,1655],{"stretchy":724},[722,2023,1649],{"stretchy":724},[727,2025,1652],{},[722,2027,1655],{"stretchy":724},[741,2029,2030],{"encoding":743},"M[i][j] = M[j][i]",[703,2032,2034,2070],{"className":2033,"ariaHidden":732},[748],[703,2035,2037,2040,2043,2046,2049,2052,2055,2058,2061,2064,2067],{"className":2036},[752],[703,2038],{"className":2039,"style":757},[756],[703,2041,1560],{"className":2042,"style":1576},[765,766],[703,2044,1649],{"className":2045},[761],[703,2047,1652],{"className":2048},[765,766],[703,2050,1655],{"className":2051},[783],[703,2053,1649],{"className":2054},[761],[703,2056,1660],{"className":2057,"style":1763},[765,766],[703,2059,1655],{"className":2060},[783],[703,2062],{"className":2063,"style":1770},[774],[703,2065,1665],{"className":2066},[1774],[703,2068],{"className":2069,"style":1770},[774],[703,2071,2073,2076,2079,2082,2085,2088,2091,2094],{"className":2072},[752],[703,2074],{"className":2075,"style":757},[756],[703,2077,1560],{"className":2078,"style":1576},[765,766],[703,2080,1649],{"className":2081},[761],[703,2083,1660],{"className":2084,"style":1763},[765,766],[703,2086,1655],{"className":2087},[783],[703,2089,1649],{"className":2090},[761],[703,2092,1652],{"className":2093},[765,766],[703,2095,1655],{"className":2096},[783],[2098,2099,2103],"pre",{"className":2100,"code":2101,"language":2102,"meta":1325,"style":1325},"language-python shiki shiki-themes github-light github-light github-dark","class GrapheMatrice:\n    \"\"\"Graphe à n sommets numérotés 0..n-1, représenté par matrice d'adjacence.\"\"\"\n\n    def __init__(self, n, oriente=False):\n        self.n = n\n        self.oriente = oriente\n        self.M = [[0] * n for _ in range(n)]\n\n    def ajouter_arete(self, u, v):\n        self.M[u][v] = 1\n        if not self.oriente:\n            self.M[v][u] = 1\n\n    def sont_adjacents(self, u, v):\n        return self.M[u][v] == 1\n\n    def voisins(self, u):\n        return [v for v in range(self.n) if self.M[u][v] == 1]\n","python",[2104,2105,2106,2122,2129,2136,2157,2171,2184,2223,2228,2239,2252,2267,2280,2285,2295,2310,2315,2326],"code",{"__ignoreMap":1325},[703,2107,2110,2114,2118],{"class":2108,"line":2109},"line",1,[703,2111,2113],{"class":2112},"s8jYJ","class",[703,2115,2117],{"class":2116},"snPdu"," GrapheMatrice",[703,2119,2121],{"class":2120},"sxrX7",":\n",[703,2123,2125],{"class":2108,"line":2124},2,[703,2126,2128],{"class":2127},"sIIMD","    \"\"\"Graphe à n sommets numérotés 0..n-1, représenté par matrice d'adjacence.\"\"\"\n",[703,2130,2132],{"class":2108,"line":2131},3,[703,2133,2135],{"emptyLinePlaceholder":2134},true,"\n",[703,2137,2139,2142,2146,2149,2151,2154],{"class":2108,"line":2138},4,[703,2140,2141],{"class":2112},"    def",[703,2143,2145],{"class":2144},"sBjJW"," __init__",[703,2147,2148],{"class":2120},"(self, n, oriente",[703,2150,1665],{"class":2112},[703,2152,2153],{"class":2144},"False",[703,2155,2156],{"class":2120},"):\n",[703,2158,2160,2163,2166,2168],{"class":2108,"line":2159},5,[703,2161,2162],{"class":2144},"        self",[703,2164,2165],{"class":2120},".n ",[703,2167,1665],{"class":2112},[703,2169,2170],{"class":2120}," n\n",[703,2172,2174,2176,2179,2181],{"class":2108,"line":2173},6,[703,2175,2162],{"class":2144},[703,2177,2178],{"class":2120},".oriente ",[703,2180,1665],{"class":2112},[703,2182,2183],{"class":2120}," oriente\n",[703,2185,2187,2189,2192,2194,2197,2199,2202,2205,2208,2211,2214,2217,2220],{"class":2108,"line":2186},7,[703,2188,2162],{"class":2144},[703,2190,2191],{"class":2120},".M ",[703,2193,1665],{"class":2112},[703,2195,2196],{"class":2120}," [[",[703,2198,1469],{"class":2144},[703,2200,2201],{"class":2120},"] ",[703,2203,2204],{"class":2112},"*",[703,2206,2207],{"class":2120}," n ",[703,2209,2210],{"class":2112},"for",[703,2212,2213],{"class":2120}," _ ",[703,2215,2216],{"class":2112},"in",[703,2218,2219],{"class":2144}," range",[703,2221,2222],{"class":2120},"(n)]\n",[703,2224,2226],{"class":2108,"line":2225},8,[703,2227,2135],{"emptyLinePlaceholder":2134},[703,2229,2231,2233,2236],{"class":2108,"line":2230},9,[703,2232,2141],{"class":2112},[703,2234,2235],{"class":2116}," ajouter_arete",[703,2237,2238],{"class":2120},"(self, u, v):\n",[703,2240,2242,2244,2247,2249],{"class":2108,"line":2241},10,[703,2243,2162],{"class":2144},[703,2245,2246],{"class":2120},".M[u][v] ",[703,2248,1665],{"class":2112},[703,2250,2251],{"class":2144}," 1\n",[703,2253,2255,2258,2261,2264],{"class":2108,"line":2254},11,[703,2256,2257],{"class":2112},"        if",[703,2259,2260],{"class":2112}," not",[703,2262,2263],{"class":2144}," self",[703,2265,2266],{"class":2120},".oriente:\n",[703,2268,2270,2273,2276,2278],{"class":2108,"line":2269},12,[703,2271,2272],{"class":2144},"            self",[703,2274,2275],{"class":2120},".M[v][u] ",[703,2277,1665],{"class":2112},[703,2279,2251],{"class":2144},[703,2281,2283],{"class":2108,"line":2282},13,[703,2284,2135],{"emptyLinePlaceholder":2134},[703,2286,2288,2290,2293],{"class":2108,"line":2287},14,[703,2289,2141],{"class":2112},[703,2291,2292],{"class":2116}," sont_adjacents",[703,2294,2238],{"class":2120},[703,2296,2298,2301,2303,2305,2308],{"class":2108,"line":2297},15,[703,2299,2300],{"class":2112},"        return",[703,2302,2263],{"class":2144},[703,2304,2246],{"class":2120},[703,2306,2307],{"class":2112},"==",[703,2309,2251],{"class":2144},[703,2311,2313],{"class":2108,"line":2312},16,[703,2314,2135],{"emptyLinePlaceholder":2134},[703,2316,2318,2320,2323],{"class":2108,"line":2317},17,[703,2319,2141],{"class":2112},[703,2321,2322],{"class":2116}," voisins",[703,2324,2325],{"class":2120},"(self, u):\n",[703,2327,2329,2331,2334,2336,2339,2341,2343,2345,2348,2351,2354,2356,2358,2360,2363],{"class":2108,"line":2328},18,[703,2330,2300],{"class":2112},[703,2332,2333],{"class":2120}," [v ",[703,2335,2210],{"class":2112},[703,2337,2338],{"class":2120}," v ",[703,2340,2216],{"class":2112},[703,2342,2219],{"class":2144},[703,2344,811],{"class":2120},[703,2346,2347],{"class":2144},"self",[703,2349,2350],{"class":2120},".n) ",[703,2352,2353],{"class":2112},"if",[703,2355,2263],{"class":2144},[703,2357,2246],{"class":2120},[703,2359,2307],{"class":2112},[703,2361,2362],{"class":2144}," 1",[703,2364,2365],{"class":2120},"]\n",[598,2367,2368,2371],{},[602,2369,2370],{},"Coûts"," :",[1436,2373,2374,2467,2518],{},[636,2375,2376,2377,2466],{},"Espace : ",[703,2378,2380,2408],{"className":2379},[706],[703,2381,2383],{"className":2382},[710],[712,2384,2385],{"xmlns":714},[716,2386,2387,2405],{},[719,2388,2389,2393,2395,2403],{},[727,2390,2392],{"mathvariant":2391},"script","O",[722,2394,811],{"stretchy":724},[2396,2397,2398,2400],"msup",{},[727,2399,1250],{},[1467,2401,2402],{},"2",[722,2404,820],{"stretchy":724},[741,2406,2407],{"encoding":743},"\\mathcal{O}(n^2)",[703,2409,2411],{"className":2410,"ariaHidden":732},[748],[703,2412,2414,2418,2423,2426,2463],{"className":2413},[752],[703,2415],{"className":2416,"style":2417},[756],"height:1.0641em;vertical-align:-0.25em;",[703,2419,2392],{"className":2420,"style":2422},[765,2421],"mathcal","margin-right:0.0278em;",[703,2424,811],{"className":2425},[761],[703,2427,2429,2432],{"className":2428},[765],[703,2430,1250],{"className":2431},[765,766],[703,2433,2436],{"className":2434},[2435],"msupsub",[703,2437,2439],{"className":2438},[1812],[703,2440,2442],{"className":2441},[1817],[703,2443,2446],{"className":2444,"style":2445},[1821],"height:0.8141em;",[703,2447,2449,2453],{"style":2448},"top:-3.063em;margin-right:0.05em;",[703,2450],{"className":2451,"style":2452},[1829],"height:2.7em;",[703,2454,2460],{"className":2455},[2456,2457,2458,2459],"sizing","reset-size6","size3","mtight",[703,2461,2402],{"className":2462},[765,2459],[703,2464,820],{"className":2465},[783]," — quel que soit le nombre d'arêtes.",[636,2468,2469,2470,2473,2474,652],{},"Test d'adjacence ",[2104,2471,2472],{},"sont_adjacents"," : ",[703,2475,2477,2497],{"className":2476},[706],[703,2478,2480],{"className":2479},[710],[712,2481,2482],{"xmlns":714},[716,2483,2484,2494],{},[719,2485,2486,2488,2490,2492],{},[727,2487,2392],{"mathvariant":2391},[722,2489,811],{"stretchy":724},[1467,2491,1320],{},[722,2493,820],{"stretchy":724},[741,2495,2496],{"encoding":743},"\\mathcal{O}(1)",[703,2498,2500],{"className":2499,"ariaHidden":732},[748],[703,2501,2503,2506,2509,2512,2515],{"className":2502},[752],[703,2504],{"className":2505,"style":757},[756],[703,2507,2392],{"className":2508,"style":2422},[765,2421],[703,2510,811],{"className":2511},[761],[703,2513,1320],{"className":2514},[765],[703,2516,820],{"className":2517},[783],[636,2519,2520,2521,2565],{},"Liste des voisins : ",[703,2522,2524,2544],{"className":2523},[706],[703,2525,2527],{"className":2526},[710],[712,2528,2529],{"xmlns":714},[716,2530,2531,2541],{},[719,2532,2533,2535,2537,2539],{},[727,2534,2392],{"mathvariant":2391},[722,2536,811],{"stretchy":724},[727,2538,1250],{},[722,2540,820],{"stretchy":724},[741,2542,2543],{"encoding":743},"\\mathcal{O}(n)",[703,2545,2547],{"className":2546,"ariaHidden":732},[748],[703,2548,2550,2553,2556,2559,2562],{"className":2549},[752],[703,2551],{"className":2552,"style":757},[756],[703,2554,2392],{"className":2555,"style":2422},[765,2421],[703,2557,811],{"className":2558},[761],[703,2560,1250],{"className":2561},[765,766],[703,2563,820],{"className":2564},[783]," (parcours d'une ligne).",[593,2567,2569],{"id":2568},"représentation-2-liste-de-successeurs","Représentation 2 — liste de successeurs",[598,2571,2572,2573,2601,2602,2605],{},"Pour chaque sommet ",[703,2574,2576,2589],{"className":2575},[706],[703,2577,2579],{"className":2578},[710],[712,2580,2581],{"xmlns":714},[716,2582,2583,2587],{},[719,2584,2585],{},[727,2586,729],{},[741,2588,729],{"encoding":743},[703,2590,2592],{"className":2591,"ariaHidden":732},[748],[703,2593,2595,2598],{"className":2594},[752],[703,2596],{"className":2597,"style":904},[756],[703,2599,729],{"className":2600},[765,766],", on stocke la ",[602,2603,2604],{},"liste de ses successeurs"," (ou voisins,\npour un graphe non orienté). En Python, on utilise un dictionnaire dont les clés\nsont les sommets et les valeurs sont des listes.",[2098,2607,2609],{"className":2100,"code":2608,"language":2102,"meta":1325,"style":1325},"class GrapheListe:\n    \"\"\"Graphe représenté par une liste de successeurs (dictionnaire).\"\"\"\n\n    def __init__(self, sommets, oriente=False):\n        self.oriente = oriente\n        self.succ = {s: [] for s in sommets}\n\n    def ajouter_arete(self, u, v):\n        self.succ[u].append(v)\n        if not self.oriente:\n            self.succ[v].append(u)\n\n    def sont_adjacents(self, u, v):\n        return v in self.succ[u]\n\n    def voisins(self, u):\n        return list(self.succ[u])\n",[2104,2610,2611,2620,2625,2629,2644,2654,2676,2680,2688,2695,2705,2712,2716,2724,2737,2741,2749],{"__ignoreMap":1325},[703,2612,2613,2615,2618],{"class":2108,"line":2109},[703,2614,2113],{"class":2112},[703,2616,2617],{"class":2116}," GrapheListe",[703,2619,2121],{"class":2120},[703,2621,2622],{"class":2108,"line":2124},[703,2623,2624],{"class":2127},"    \"\"\"Graphe représenté par une liste de successeurs (dictionnaire).\"\"\"\n",[703,2626,2627],{"class":2108,"line":2131},[703,2628,2135],{"emptyLinePlaceholder":2134},[703,2630,2631,2633,2635,2638,2640,2642],{"class":2108,"line":2138},[703,2632,2141],{"class":2112},[703,2634,2145],{"class":2144},[703,2636,2637],{"class":2120},"(self, sommets, oriente",[703,2639,1665],{"class":2112},[703,2641,2153],{"class":2144},[703,2643,2156],{"class":2120},[703,2645,2646,2648,2650,2652],{"class":2108,"line":2159},[703,2647,2162],{"class":2144},[703,2649,2178],{"class":2120},[703,2651,1665],{"class":2112},[703,2653,2183],{"class":2120},[703,2655,2656,2658,2661,2663,2666,2668,2671,2673],{"class":2108,"line":2173},[703,2657,2162],{"class":2144},[703,2659,2660],{"class":2120},".succ ",[703,2662,1665],{"class":2112},[703,2664,2665],{"class":2120}," {s: [] ",[703,2667,2210],{"class":2112},[703,2669,2670],{"class":2120}," s ",[703,2672,2216],{"class":2112},[703,2674,2675],{"class":2120}," sommets}\n",[703,2677,2678],{"class":2108,"line":2186},[703,2679,2135],{"emptyLinePlaceholder":2134},[703,2681,2682,2684,2686],{"class":2108,"line":2225},[703,2683,2141],{"class":2112},[703,2685,2235],{"class":2116},[703,2687,2238],{"class":2120},[703,2689,2690,2692],{"class":2108,"line":2230},[703,2691,2162],{"class":2144},[703,2693,2694],{"class":2120},".succ[u].append(v)\n",[703,2696,2697,2699,2701,2703],{"class":2108,"line":2241},[703,2698,2257],{"class":2112},[703,2700,2260],{"class":2112},[703,2702,2263],{"class":2144},[703,2704,2266],{"class":2120},[703,2706,2707,2709],{"class":2108,"line":2254},[703,2708,2272],{"class":2144},[703,2710,2711],{"class":2120},".succ[v].append(u)\n",[703,2713,2714],{"class":2108,"line":2269},[703,2715,2135],{"emptyLinePlaceholder":2134},[703,2717,2718,2720,2722],{"class":2108,"line":2282},[703,2719,2141],{"class":2112},[703,2721,2292],{"class":2116},[703,2723,2238],{"class":2120},[703,2725,2726,2728,2730,2732,2734],{"class":2108,"line":2287},[703,2727,2300],{"class":2112},[703,2729,2338],{"class":2120},[703,2731,2216],{"class":2112},[703,2733,2263],{"class":2144},[703,2735,2736],{"class":2120},".succ[u]\n",[703,2738,2739],{"class":2108,"line":2297},[703,2740,2135],{"emptyLinePlaceholder":2134},[703,2742,2743,2745,2747],{"class":2108,"line":2312},[703,2744,2141],{"class":2112},[703,2746,2322],{"class":2116},[703,2748,2325],{"class":2120},[703,2750,2751,2753,2756,2758,2760],{"class":2108,"line":2317},[703,2752,2300],{"class":2112},[703,2754,2755],{"class":2144}," list",[703,2757,811],{"class":2120},[703,2759,2347],{"class":2144},[703,2761,2762],{"class":2120},".succ[u])\n",[598,2764,2765,2767,2768,2813,2814,878,2817,2845],{},[602,2766,2370],{}," (où ",[703,2769,2771,2792],{"className":2770},[706],[703,2772,2774],{"className":2773},[710],[712,2775,2776],{"xmlns":714},[716,2777,2778,2789],{},[719,2779,2780,2783,2785,2787],{},[727,2781,2782],{},"d",[722,2784,811],{"stretchy":724},[727,2786,729],{},[722,2788,820],{"stretchy":724},[741,2790,2791],{"encoding":743},"d(u)",[703,2793,2795],{"className":2794,"ariaHidden":732},[748],[703,2796,2798,2801,2804,2807,2810],{"className":2797},[752],[703,2799],{"className":2800,"style":757},[756],[703,2802,2782],{"className":2803},[765,766],[703,2805,811],{"className":2806},[761],[703,2808,729],{"className":2809},[765,766],[703,2811,820],{"className":2812},[783]," est le ",[602,2815,2816],{},"degré",[703,2818,2820,2833],{"className":2819},[706],[703,2821,2823],{"className":2822},[710],[712,2824,2825],{"xmlns":714},[716,2826,2827,2831],{},[719,2828,2829],{},[727,2830,729],{},[741,2832,729],{"encoding":743},[703,2834,2836],{"className":2835,"ariaHidden":732},[748],[703,2837,2839,2842],{"className":2838},[752],[703,2840],{"className":2841,"style":904},[756],[703,2843,729],{"className":2844},[765,766],", c'est-à-dire son nombre de\nvoisins) :",[1436,2847,2848,2921,2981],{},[636,2849,2376,2850,2917,2918,652],{},[703,2851,2853,2878],{"className":2852},[706],[703,2854,2856],{"className":2855},[710],[712,2857,2858],{"xmlns":714},[716,2859,2860,2875],{},[719,2861,2862,2864,2866,2868,2871,2873],{},[727,2863,2392],{"mathvariant":2391},[722,2865,811],{"stretchy":724},[727,2867,1250],{},[722,2869,2870],{},"+",[727,2872,1289],{},[722,2874,820],{"stretchy":724},[741,2876,2877],{"encoding":743},"\\mathcal{O}(n + m)",[703,2879,2881,2905],{"className":2880,"ariaHidden":732},[748],[703,2882,2884,2887,2890,2893,2896,2899,2902],{"className":2883},[752],[703,2885],{"className":2886,"style":757},[756],[703,2888,2392],{"className":2889,"style":2422},[765,2421],[703,2891,811],{"className":2892},[761],[703,2894,1250],{"className":2895},[765,766],[703,2897],{"className":2898,"style":1524},[774],[703,2900,2870],{"className":2901},[1528],[703,2903],{"className":2904,"style":1524},[774],[703,2906,2908,2911,2914],{"className":2907},[752],[703,2909],{"className":2910,"style":757},[756],[703,2912,1289],{"className":2913},[765,766],[703,2915,820],{"className":2916},[783]," — économique pour les graphes ",[602,2919,2920],{},"creux",[636,2922,2923,2924,652],{},"Test d'adjacence : ",[703,2925,2927,2953],{"className":2926},[706],[703,2928,2930],{"className":2929},[710],[712,2931,2932],{"xmlns":714},[716,2933,2934,2950],{},[719,2935,2936,2938,2940,2942,2944,2946,2948],{},[727,2937,2392],{"mathvariant":2391},[722,2939,811],{"stretchy":724},[727,2941,2782],{},[722,2943,811],{"stretchy":724},[727,2945,729],{},[722,2947,820],{"stretchy":724},[722,2949,820],{"stretchy":724},[741,2951,2952],{"encoding":743},"\\mathcal{O}(d(u))",[703,2954,2956],{"className":2955,"ariaHidden":732},[748],[703,2957,2959,2962,2965,2968,2971,2974,2977],{"className":2958},[752],[703,2960],{"className":2961,"style":757},[756],[703,2963,2392],{"className":2964,"style":2422},[765,2421],[703,2966,811],{"className":2967},[761],[703,2969,2782],{"className":2970},[765,766],[703,2972,811],{"className":2973},[761],[703,2975,729],{"className":2976},[765,766],[703,2978,2980],{"className":2979},[783],"))",[636,2982,2520,2983,652],{},[703,2984,2986,3011],{"className":2985},[706],[703,2987,2989],{"className":2988},[710],[712,2990,2991],{"xmlns":714},[716,2992,2993,3009],{},[719,2994,2995,2997,2999,3001,3003,3005,3007],{},[727,2996,2392],{"mathvariant":2391},[722,2998,811],{"stretchy":724},[727,3000,2782],{},[722,3002,811],{"stretchy":724},[727,3004,729],{},[722,3006,820],{"stretchy":724},[722,3008,820],{"stretchy":724},[741,3010,2952],{"encoding":743},[703,3012,3014],{"className":3013,"ariaHidden":732},[748],[703,3015,3017,3020,3023,3026,3029,3032,3035],{"className":3016},[752],[703,3018],{"className":3019,"style":757},[756],[703,3021,2392],{"className":3022,"style":2422},[765,2421],[703,3024,811],{"className":3025},[761],[703,3027,2782],{"className":3028},[765,766],[703,3030,811],{"className":3031},[761],[703,3033,729],{"className":3034},[765,766],[703,3036,2980],{"className":3037},[783],[3039,3040,3041],"tip",{},[598,3042,3043,3046,3047,3050,3051,3134,3135,3050,3137,3220],{},[602,3044,3045],{},"Règle pratique"," : matrice d'adjacence si le graphe est ",[602,3048,3049],{},"dense"," (",[703,3052,3054,3077],{"className":3053},[706],[703,3055,3057],{"className":3056},[710],[712,3058,3059],{"xmlns":714},[716,3060,3061,3074],{},[719,3062,3063,3065,3068],{},[727,3064,1289],{},[722,3066,3067],{},"≈",[2396,3069,3070,3072],{},[727,3071,1250],{},[1467,3073,2402],{},[741,3075,3076],{"encoding":743},"m \\approx n^2",[703,3078,3080,3099],{"className":3079,"ariaHidden":732},[748],[703,3081,3083,3087,3090,3093,3096],{"className":3082},[752],[703,3084],{"className":3085,"style":3086},[756],"height:0.4831em;",[703,3088,1289],{"className":3089},[765,766],[703,3091],{"className":3092,"style":1770},[774],[703,3094,3067],{"className":3095},[1774],[703,3097],{"className":3098,"style":1770},[774],[703,3100,3102,3105],{"className":3101},[752],[703,3103],{"className":3104,"style":2445},[756],[703,3106,3108,3111],{"className":3107},[765],[703,3109,1250],{"className":3110},[765,766],[703,3112,3114],{"className":3113},[2435],[703,3115,3117],{"className":3116},[1812],[703,3118,3120],{"className":3119},[1817],[703,3121,3123],{"className":3122,"style":2445},[1821],[703,3124,3125,3128],{"style":2448},[703,3126],{"className":3127,"style":2452},[1829],[703,3129,3131],{"className":3130},[2456,2457,2458,2459],[703,3132,2402],{"className":3133},[765,2459],")\nou si les tests d'adjacence sont fréquents ; liste de successeurs si le graphe\nest ",[602,3136,2920],{},[703,3138,3140,3163],{"className":3139},[706],[703,3141,3143],{"className":3142},[710],[712,3144,3145],{"xmlns":714},[716,3146,3147,3160],{},[719,3148,3149,3151,3154],{},[727,3150,1289],{},[722,3152,3153],{},"≪",[2396,3155,3156,3158],{},[727,3157,1250],{},[1467,3159,2402],{},[741,3161,3162],{"encoding":743},"m \\ll n^2",[703,3164,3166,3185],{"className":3165,"ariaHidden":732},[748],[703,3167,3169,3173,3176,3179,3182],{"className":3168},[752],[703,3170],{"className":3171,"style":3172},[756],"height:0.5782em;vertical-align:-0.0391em;",[703,3174,1289],{"className":3175},[765,766],[703,3177],{"className":3178,"style":1770},[774],[703,3180,3153],{"className":3181},[1774],[703,3183],{"className":3184,"style":1770},[774],[703,3186,3188,3191],{"className":3187},[752],[703,3189],{"className":3190,"style":2445},[756],[703,3192,3194,3197],{"className":3193},[765],[703,3195,1250],{"className":3196},[765,766],[703,3198,3200],{"className":3199},[2435],[703,3201,3203],{"className":3202},[1812],[703,3204,3206],{"className":3205},[1817],[703,3207,3209],{"className":3208,"style":2445},[1821],[703,3210,3211,3214],{"style":2448},[703,3212],{"className":3213,"style":2452},[1829],[703,3215,3217],{"className":3216},[2456,2457,2458,2459],[703,3218,2402],{"className":3219},[765,2459],") ou si l'on parcourt souvent les voisins.",[1318,3222,3224,3229],{"correct":1320,"slug":3223},"graphes-c2",[1323,3225,3226],{"v-slot:question":1325},[598,3227,3228],{},"Pour un réseau social avec 1 million d'utilisateurs et 100 amis moyens, quelle représentation est viable ?",[1323,3230,3231],{"v-slot:choices":1325},[1436,3232,3233,3236,3239],{},[636,3234,3235],{},"matrice d’adjacence",[636,3237,3238],{},"liste de successeurs",[636,3240,3241],{},"les deux à coût égal",[593,3243,3245],{"id":3244},"passer-dune-représentation-à-lautre","Passer d'une représentation à l'autre",[598,3247,3248],{},"Le BO demande explicitement de savoir convertir. Voici les deux sens, en\nPython :",[2098,3250,3252],{"className":2100,"code":3251,"language":2102,"meta":1325,"style":1325},"def matrice_vers_liste(M):\n    \"\"\"De matrice d'adjacence vers liste de successeurs.\"\"\"\n    n = len(M)\n    succ = {i: [] for i in range(n)}\n    for i in range(n):\n        for j in range(n):\n            if M[i][j] == 1:\n                succ[i].append(j)\n    return succ\n\ndef liste_vers_matrice(succ):\n    \"\"\"De liste de successeurs vers matrice d'adjacence.\"\"\"\n    n = len(succ)\n    M = [[0] * n for _ in range(n)]\n    for u, vs in succ.items():\n        for v in vs:\n            M[u][v] = 1\n    return M\n",[2104,3253,3254,3265,3270,3283,3305,3319,3333,3347,3352,3360,3364,3374,3379,3390,3417,3429,3440,3449],{"__ignoreMap":1325},[703,3255,3256,3259,3262],{"class":2108,"line":2109},[703,3257,3258],{"class":2112},"def",[703,3260,3261],{"class":2116}," matrice_vers_liste",[703,3263,3264],{"class":2120},"(M):\n",[703,3266,3267],{"class":2108,"line":2124},[703,3268,3269],{"class":2127},"    \"\"\"De matrice d'adjacence vers liste de successeurs.\"\"\"\n",[703,3271,3272,3275,3277,3280],{"class":2108,"line":2131},[703,3273,3274],{"class":2120},"    n ",[703,3276,1665],{"class":2112},[703,3278,3279],{"class":2144}," len",[703,3281,3282],{"class":2120},"(M)\n",[703,3284,3285,3288,3290,3293,3295,3298,3300,3302],{"class":2108,"line":2138},[703,3286,3287],{"class":2120},"    succ ",[703,3289,1665],{"class":2112},[703,3291,3292],{"class":2120}," {i: [] ",[703,3294,2210],{"class":2112},[703,3296,3297],{"class":2120}," i ",[703,3299,2216],{"class":2112},[703,3301,2219],{"class":2144},[703,3303,3304],{"class":2120},"(n)}\n",[703,3306,3307,3310,3312,3314,3316],{"class":2108,"line":2159},[703,3308,3309],{"class":2112},"    for",[703,3311,3297],{"class":2120},[703,3313,2216],{"class":2112},[703,3315,2219],{"class":2144},[703,3317,3318],{"class":2120},"(n):\n",[703,3320,3321,3324,3327,3329,3331],{"class":2108,"line":2173},[703,3322,3323],{"class":2112},"        for",[703,3325,3326],{"class":2120}," j ",[703,3328,2216],{"class":2112},[703,3330,2219],{"class":2144},[703,3332,3318],{"class":2120},[703,3334,3335,3338,3341,3343,3345],{"class":2108,"line":2186},[703,3336,3337],{"class":2112},"            if",[703,3339,3340],{"class":2120}," M[i][j] ",[703,3342,2307],{"class":2112},[703,3344,2362],{"class":2144},[703,3346,2121],{"class":2120},[703,3348,3349],{"class":2108,"line":2225},[703,3350,3351],{"class":2120},"                succ[i].append(j)\n",[703,3353,3354,3357],{"class":2108,"line":2230},[703,3355,3356],{"class":2112},"    return",[703,3358,3359],{"class":2120}," succ\n",[703,3361,3362],{"class":2108,"line":2241},[703,3363,2135],{"emptyLinePlaceholder":2134},[703,3365,3366,3368,3371],{"class":2108,"line":2254},[703,3367,3258],{"class":2112},[703,3369,3370],{"class":2116}," liste_vers_matrice",[703,3372,3373],{"class":2120},"(succ):\n",[703,3375,3376],{"class":2108,"line":2269},[703,3377,3378],{"class":2127},"    \"\"\"De liste de successeurs vers matrice d'adjacence.\"\"\"\n",[703,3380,3381,3383,3385,3387],{"class":2108,"line":2282},[703,3382,3274],{"class":2120},[703,3384,1665],{"class":2112},[703,3386,3279],{"class":2144},[703,3388,3389],{"class":2120},"(succ)\n",[703,3391,3392,3395,3397,3399,3401,3403,3405,3407,3409,3411,3413,3415],{"class":2108,"line":2287},[703,3393,3394],{"class":2120},"    M ",[703,3396,1665],{"class":2112},[703,3398,2196],{"class":2120},[703,3400,1469],{"class":2144},[703,3402,2201],{"class":2120},[703,3404,2204],{"class":2112},[703,3406,2207],{"class":2120},[703,3408,2210],{"class":2112},[703,3410,2213],{"class":2120},[703,3412,2216],{"class":2112},[703,3414,2219],{"class":2144},[703,3416,2222],{"class":2120},[703,3418,3419,3421,3424,3426],{"class":2108,"line":2297},[703,3420,3309],{"class":2112},[703,3422,3423],{"class":2120}," u, vs ",[703,3425,2216],{"class":2112},[703,3427,3428],{"class":2120}," succ.items():\n",[703,3430,3431,3433,3435,3437],{"class":2108,"line":2312},[703,3432,3323],{"class":2112},[703,3434,2338],{"class":2120},[703,3436,2216],{"class":2112},[703,3438,3439],{"class":2120}," vs:\n",[703,3441,3442,3445,3447],{"class":2108,"line":2317},[703,3443,3444],{"class":2120},"            M[u][v] ",[703,3446,1665],{"class":2112},[703,3448,2251],{"class":2144},[703,3450,3451,3453],{"class":2108,"line":2328},[703,3452,3356],{"class":2112},[703,3454,3455],{"class":2120}," M\n",[598,3457,3458,2371],{},[602,3459,3460],{},"Complexités",[1436,3462,3463,3542],{},[636,3464,3465,2473,3468,3541],{},[2104,3466,3467],{},"matrice_vers_liste",[703,3469,3471,3494],{"className":3470},[706],[703,3472,3474],{"className":3473},[710],[712,3475,3476],{"xmlns":714},[716,3477,3478,3492],{},[719,3479,3480,3482,3484,3490],{},[727,3481,2392],{"mathvariant":2391},[722,3483,811],{"stretchy":724},[2396,3485,3486,3488],{},[727,3487,1250],{},[1467,3489,2402],{},[722,3491,820],{"stretchy":724},[741,3493,2407],{"encoding":743},[703,3495,3497],{"className":3496,"ariaHidden":732},[748],[703,3498,3500,3503,3506,3509,3538],{"className":3499},[752],[703,3501],{"className":3502,"style":2417},[756],[703,3504,2392],{"className":3505,"style":2422},[765,2421],[703,3507,811],{"className":3508},[761],[703,3510,3512,3515],{"className":3511},[765],[703,3513,1250],{"className":3514},[765,766],[703,3516,3518],{"className":3517},[2435],[703,3519,3521],{"className":3520},[1812],[703,3522,3524],{"className":3523},[1817],[703,3525,3527],{"className":3526,"style":2445},[1821],[703,3528,3529,3532],{"style":2448},[703,3530],{"className":3531,"style":2452},[1829],[703,3533,3535],{"className":3534},[2456,2457,2458,2459],[703,3536,2402],{"className":3537},[765,2459],[703,3539,820],{"className":3540},[783]," — on lit toute la matrice.",[636,3543,3544,2473,3547,3612],{},[2104,3545,3546],{},"liste_vers_matrice",[703,3548,3550,3573],{"className":3549},[706],[703,3551,3553],{"className":3552},[710],[712,3554,3555],{"xmlns":714},[716,3556,3557,3571],{},[719,3558,3559,3561,3563,3565,3567,3569],{},[727,3560,2392],{"mathvariant":2391},[722,3562,811],{"stretchy":724},[727,3564,1250],{},[722,3566,2870],{},[727,3568,1289],{},[722,3570,820],{"stretchy":724},[741,3572,2877],{"encoding":743},[703,3574,3576,3600],{"className":3575,"ariaHidden":732},[748],[703,3577,3579,3582,3585,3588,3591,3594,3597],{"className":3578},[752],[703,3580],{"className":3581,"style":757},[756],[703,3583,2392],{"className":3584,"style":2422},[765,2421],[703,3586,811],{"className":3587},[761],[703,3589,1250],{"className":3590},[765,766],[703,3592],{"className":3593,"style":1524},[774],[703,3595,2870],{"className":3596},[1528],[703,3598],{"className":3599,"style":1524},[774],[703,3601,3603,3606,3609],{"className":3602},[752],[703,3604],{"className":3605,"style":757},[756],[703,3607,1289],{"className":3608},[765,766],[703,3610,820],{"className":3611},[783]," — on alloue la matrice, on parcourt\nles arêtes.",[593,3614,3616],{"id":3615},"liste-de-prédécesseurs-cas-orienté","Liste de prédécesseurs (cas orienté)",[598,3618,3619,3620,3623],{},"Pour un graphe orienté, on peut symétriquement vouloir, pour chaque sommet, la\n",[602,3621,3622],{},"liste de ses prédécesseurs",". Elle se construit à partir des successeurs en\ninversant les arcs :",[2098,3625,3627],{"className":2100,"code":3626,"language":2102,"meta":1325,"style":1325},"def predecesseurs(succ):\n    pred = {u: [] for u in succ}\n    for u, vs in succ.items():\n        for v in vs:\n            pred[v].append(u)\n    return pred\n",[2104,3628,3629,3638,3658,3668,3678,3683],{"__ignoreMap":1325},[703,3630,3631,3633,3636],{"class":2108,"line":2109},[703,3632,3258],{"class":2112},[703,3634,3635],{"class":2116}," predecesseurs",[703,3637,3373],{"class":2120},[703,3639,3640,3643,3645,3648,3650,3653,3655],{"class":2108,"line":2124},[703,3641,3642],{"class":2120},"    pred ",[703,3644,1665],{"class":2112},[703,3646,3647],{"class":2120}," {u: [] ",[703,3649,2210],{"class":2112},[703,3651,3652],{"class":2120}," u ",[703,3654,2216],{"class":2112},[703,3656,3657],{"class":2120}," succ}\n",[703,3659,3660,3662,3664,3666],{"class":2108,"line":2131},[703,3661,3309],{"class":2112},[703,3663,3423],{"class":2120},[703,3665,2216],{"class":2112},[703,3667,3428],{"class":2120},[703,3669,3670,3672,3674,3676],{"class":2108,"line":2138},[703,3671,3323],{"class":2112},[703,3673,2338],{"class":2120},[703,3675,2216],{"class":2112},[703,3677,3439],{"class":2120},[703,3679,3680],{"class":2108,"line":2159},[703,3681,3682],{"class":2120},"            pred[v].append(u)\n",[703,3684,3685,3687],{"class":2108,"line":2173},[703,3686,3356],{"class":2112},[703,3688,3689],{"class":2120}," pred\n",[598,3691,1978,3692,3694],{},[602,3693,700],{},", successeurs et prédécesseurs coïncident — c'est\nla liste des voisins.",[593,3696,3698],{"id":3697},"pour-aller-plus-loin","Pour aller plus loin",[598,3700,3701],{},"Le chapitre TE exploite ces représentations pour les parcours (BFS, DFS) et les\nalgorithmes de plus court chemin (Dijkstra). Le choix de la représentation\ninfluence directement la complexité de ces algorithmes — vous y reviendrez.",[629,3703],{"code":588},[3705,3706,3707],"style",{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span 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var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":1325,"searchDepth":2124,"depth":2124,"links":3709},[3710,3711,3712,3713,3714,3715,3716],{"id":595,"depth":2124,"text":596},{"id":655,"depth":2124,"text":656},{"id":1449,"depth":2124,"text":1450},{"id":2568,"depth":2124,"text":2569},{"id":3244,"depth":2124,"text":3245},{"id":3615,"depth":2124,"text":3616},{"id":3697,"depth":2124,"text":3698},"Sommets et arêtes, orientés ou non — matrice d'adjacence et liste de successeurs, et le passage de l'une à l'autre.",null,"md",{},[3722,3727],{"slug":1321,"kind":3723,"question":3724,"choices":3725,"correct":1320,"multi":3726,"explanation":1325},"qcm","Dans un graphe orienté, (u,v)(u, v)(u,v) et (v,u)(v, u)(v,u) représentent…",[1440,1443,1446],false,{"slug":3223,"kind":3723,"question":3228,"choices":3728,"correct":1320,"multi":3726,"explanation":1325},[3235,3238,3241],{"title":473,"description":3717},"hHlZmC5Km2YR9HloYwvbGT97fkoOtdRk34TrNeKUcSs",{"id":3732,"title":3733,"bo":3734,"body":3735,"description":4630,"eval":3718,"extension":3719,"labo":3718,"meta":4631,"navigation":3726,"path":4632,"quizzes":4633,"readingTime":2109,"seo":4634,"stem":4635,"tp":3718,"__hash__":4636},"coursMemo\u002F2.nsi-tale\u002Fta-structures-donnees\u002F5.graphes.memo.md","Graphes — l'essentiel",[588],{"type":590,"value":3736,"toc":4623},[3737,3741,3887,3891,4278,4282,4462,4466,4477,4481,4620],[593,3738,3740],{"id":3739},"en-une-phrase","En une phrase",[598,3742,3743],{},[602,3744,3745,3746,3819,3820,3886],{},"Un graphe modélise des relations entre sommets ; il se représente soit par une matrice d'adjacence (",[703,3747,3749,3772],{"className":3748},[706],[703,3750,3752],{"className":3751},[710],[712,3753,3754],{"xmlns":714},[716,3755,3756,3770],{},[719,3757,3758,3760,3762,3768],{},[727,3759,2392],{"mathvariant":2391},[722,3761,811],{"stretchy":724},[2396,3763,3764,3766],{},[727,3765,1250],{},[1467,3767,2402],{},[722,3769,820],{"stretchy":724},[741,3771,2407],{"encoding":743},[703,3773,3775],{"className":3774,"ariaHidden":732},[748],[703,3776,3778,3781,3784,3787,3816],{"className":3777},[752],[703,3779],{"className":3780,"style":2417},[756],[703,3782,2392],{"className":3783,"style":2422},[765,2421],[703,3785,811],{"className":3786},[761],[703,3788,3790,3793],{"className":3789},[765],[703,3791,1250],{"className":3792},[765,766],[703,3794,3796],{"className":3795},[2435],[703,3797,3799],{"className":3798},[1812],[703,3800,3802],{"className":3801},[1817],[703,3803,3805],{"className":3804,"style":2445},[1821],[703,3806,3807,3810],{"style":2448},[703,3808],{"className":3809,"style":2452},[1829],[703,3811,3813],{"className":3812},[2456,2457,2458,2459],[703,3814,2402],{"className":3815},[765,2459],[703,3817,820],{"className":3818},[783]," d'espace), soit par une liste de successeurs (",[703,3821,3823,3847],{"className":3822},[706],[703,3824,3826],{"className":3825},[710],[712,3827,3828],{"xmlns":714},[716,3829,3830,3844],{},[719,3831,3832,3834,3836,3838,3840,3842],{},[727,3833,2392],{"mathvariant":2391},[722,3835,811],{"stretchy":724},[727,3837,1250],{},[722,3839,2870],{},[727,3841,1289],{},[722,3843,820],{"stretchy":724},[741,3845,3846],{"encoding":743},"\\mathcal{O}(n+m)",[703,3848,3850,3874],{"className":3849,"ariaHidden":732},[748],[703,3851,3853,3856,3859,3862,3865,3868,3871],{"className":3852},[752],[703,3854],{"className":3855,"style":757},[756],[703,3857,2392],{"className":3858,"style":2422},[765,2421],[703,3860,811],{"className":3861},[761],[703,3863,1250],{"className":3864},[765,766],[703,3866],{"className":3867,"style":1524},[774],[703,3869,2870],{"className":3870},[1528],[703,3872],{"className":3873,"style":1524},[774],[703,3875,3877,3880,3883],{"className":3876},[752],[703,3878],{"className":3879,"style":757},[756],[703,3881,1289],{"className":3882},[765,766],[703,3884,820],{"className":3885},[783],").",[593,3888,3890],{"id":3889},"à-mémoriser","À mémoriser",[1436,3892,3893,4011,4126,4210,4275],{},[636,3894,3895,3897,3898,3901,3902,3954,3955,3958,3959,3886],{},[602,3896,683],{}," (nœud), ",[602,3899,3900],{},"arête"," (non orientée, ",[703,3903,3905,3927],{"className":3904},[706],[703,3906,3908],{"className":3907},[710],[712,3909,3910],{"xmlns":714},[716,3911,3912,3924],{},[719,3913,3914,3916,3918,3920,3922],{},[722,3915,725],{"stretchy":724},[727,3917,729],{},[722,3919,733],{"separator":732},[727,3921,736],{},[722,3923,739],{"stretchy":724},[741,3925,3926],{"encoding":743},"\\{u,v\\}",[703,3928,3930],{"className":3929,"ariaHidden":732},[748],[703,3931,3933,3936,3939,3942,3945,3948,3951],{"className":3932},[752],[703,3934],{"className":3935,"style":757},[756],[703,3937,725],{"className":3938},[761],[703,3940,729],{"className":3941},[765,766],[703,3943,733],{"className":3944},[770],[703,3946],{"className":3947,"style":775},[774],[703,3949,736],{"className":3950,"style":779},[765,766],[703,3952,739],{"className":3953},[783],"), ",[602,3956,3957],{},"arc"," (orienté, ",[703,3960,3962,3984],{"className":3961},[706],[703,3963,3965],{"className":3964},[710],[712,3966,3967],{"xmlns":714},[716,3968,3969,3981],{},[719,3970,3971,3973,3975,3977,3979],{},[722,3972,811],{"stretchy":724},[727,3974,729],{},[722,3976,733],{"separator":732},[727,3978,736],{},[722,3980,820],{"stretchy":724},[741,3982,3983],{"encoding":743},"(u,v)",[703,3985,3987],{"className":3986,"ariaHidden":732},[748],[703,3988,3990,3993,3996,3999,4002,4005,4008],{"className":3989},[752],[703,3991],{"className":3992,"style":757},[756],[703,3994,811],{"className":3995},[761],[703,3997,729],{"className":3998},[765,766],[703,4000,733],{"className":4001},[770],[703,4003],{"className":4004,"style":775},[774],[703,4006,736],{"className":4007,"style":779},[765,766],[703,4009,820],{"className":4010},[783],[636,4012,4013,878,4016,4044,4045,4073,4074,4125],{},[602,4014,4015],{},"Successeurs",[703,4017,4019,4032],{"className":4018},[706],[703,4020,4022],{"className":4021},[710],[712,4023,4024],{"xmlns":714},[716,4025,4026,4030],{},[719,4027,4028],{},[727,4029,729],{},[741,4031,729],{"encoding":743},[703,4033,4035],{"className":4034,"ariaHidden":732},[748],[703,4036,4038,4041],{"className":4037},[752],[703,4039],{"className":4040,"style":904},[756],[703,4042,729],{"className":4043},[765,766]," = sommets ",[703,4046,4048,4061],{"className":4047},[706],[703,4049,4051],{"className":4050},[710],[712,4052,4053],{"xmlns":714},[716,4054,4055,4059],{},[719,4056,4057],{},[727,4058,736],{},[741,4060,736],{"encoding":743},[703,4062,4064],{"className":4063,"ariaHidden":732},[748],[703,4065,4067,4070],{"className":4066},[752],[703,4068],{"className":4069,"style":904},[756],[703,4071,736],{"className":4072,"style":779},[765,766]," tels que ",[703,4075,4077,4098],{"className":4076},[706],[703,4078,4080],{"className":4079},[710],[712,4081,4082],{"xmlns":714},[716,4083,4084,4096],{},[719,4085,4086,4088,4090,4092,4094],{},[722,4087,811],{"stretchy":724},[727,4089,729],{},[722,4091,733],{"separator":732},[727,4093,736],{},[722,4095,820],{"stretchy":724},[741,4097,823],{"encoding":743},[703,4099,4101],{"className":4100,"ariaHidden":732},[748],[703,4102,4104,4107,4110,4113,4116,4119,4122],{"className":4103},[752],[703,4105],{"className":4106,"style":757},[756],[703,4108,811],{"className":4109},[761],[703,4111,729],{"className":4112},[765,766],[703,4114,733],{"className":4115},[770],[703,4117],{"className":4118,"style":775},[774],[703,4120,736],{"className":4121,"style":779},[765,766],[703,4123,820],{"className":4124},[783]," existe.",[636,4127,4128,4044,4131,4073,4159,4125],{},[602,4129,4130],{},"Prédécesseurs",[703,4132,4134,4147],{"className":4133},[706],[703,4135,4137],{"className":4136},[710],[712,4138,4139],{"xmlns":714},[716,4140,4141,4145],{},[719,4142,4143],{},[727,4144,736],{},[741,4146,736],{"encoding":743},[703,4148,4150],{"className":4149,"ariaHidden":732},[748],[703,4151,4153,4156],{"className":4152},[752],[703,4154],{"className":4155,"style":904},[756],[703,4157,736],{"className":4158,"style":779},[765,766],[703,4160,4162,4183],{"className":4161},[706],[703,4163,4165],{"className":4164},[710],[712,4166,4167],{"xmlns":714},[716,4168,4169,4181],{},[719,4170,4171,4173,4175,4177,4179],{},[722,4172,811],{"stretchy":724},[727,4174,736],{},[722,4176,733],{"separator":732},[727,4178,729],{},[722,4180,820],{"stretchy":724},[741,4182,1080],{"encoding":743},[703,4184,4186],{"className":4185,"ariaHidden":732},[748],[703,4187,4189,4192,4195,4198,4201,4204,4207],{"className":4188},[752],[703,4190],{"className":4191,"style":757},[756],[703,4193,811],{"className":4194},[761],[703,4196,736],{"className":4197,"style":779},[765,766],[703,4199,733],{"className":4200},[770],[703,4202],{"className":4203,"style":775},[774],[703,4205,729],{"className":4206},[765,766],[703,4208,820],{"className":4209},[783],[636,4211,4212,1545,4214,4242,4243,1545,4246,4274],{},[602,4213,1232],{},[703,4215,4217,4230],{"className":4216},[706],[703,4218,4220],{"className":4219},[710],[712,4221,4222],{"xmlns":714},[716,4223,4224,4228],{},[719,4225,4226],{},[727,4227,1250],{},[741,4229,1250],{"encoding":743},[703,4231,4233],{"className":4232,"ariaHidden":732},[748],[703,4234,4236,4239],{"className":4235},[752],[703,4237],{"className":4238,"style":904},[756],[703,4240,1250],{"className":4241},[765,766]," = nombre de sommets ; ",[602,4244,4245],{},"taille",[703,4247,4249,4262],{"className":4248},[706],[703,4250,4252],{"className":4251},[710],[712,4253,4254],{"xmlns":714},[716,4255,4256,4260],{},[719,4257,4258],{},[727,4259,1289],{},[741,4261,1289],{"encoding":743},[703,4263,4265],{"className":4264,"ariaHidden":732},[748],[703,4266,4268,4271],{"className":4267},[752],[703,4269],{"className":4270,"style":904},[756],[703,4272,1289],{"className":4273},[765,766]," = nombre d'arêtes\u002Farcs.",[636,4276,4277],{},"Matrice symétrique ⇔ graphe non orienté.",[593,4279,4281],{"id":4280},"à-savoir-reconnaître","À savoir reconnaître",[658,4283,4284,4294],{},[661,4285,4286],{},[664,4287,4288,4291],{},[667,4289,4290],{},"Choix",[667,4292,4293],{},"Représentation adaptée",[674,4295,4296,4303,4310,4390],{},[664,4297,4298,4301],{},[679,4299,4300],{},"Graphe dense, tests d'adjacence",[679,4302,1544],{},[664,4304,4305,4308],{},[679,4306,4307],{},"Graphe creux, parcours de voisins",[679,4309,3238],{},[664,4311,4312,4315],{},[679,4313,4314],{},"Conversion matrice → liste",[679,4316,4317],{},[703,4318,4320,4343],{"className":4319},[706],[703,4321,4323],{"className":4322},[710],[712,4324,4325],{"xmlns":714},[716,4326,4327,4341],{},[719,4328,4329,4331,4333,4339],{},[727,4330,2392],{"mathvariant":2391},[722,4332,811],{"stretchy":724},[2396,4334,4335,4337],{},[727,4336,1250],{},[1467,4338,2402],{},[722,4340,820],{"stretchy":724},[741,4342,2407],{"encoding":743},[703,4344,4346],{"className":4345,"ariaHidden":732},[748],[703,4347,4349,4352,4355,4358,4387],{"className":4348},[752],[703,4350],{"className":4351,"style":2417},[756],[703,4353,2392],{"className":4354,"style":2422},[765,2421],[703,4356,811],{"className":4357},[761],[703,4359,4361,4364],{"className":4360},[765],[703,4362,1250],{"className":4363},[765,766],[703,4365,4367],{"className":4366},[2435],[703,4368,4370],{"className":4369},[1812],[703,4371,4373],{"className":4372},[1817],[703,4374,4376],{"className":4375,"style":2445},[1821],[703,4377,4378,4381],{"style":2448},[703,4379],{"className":4380,"style":2452},[1829],[703,4382,4384],{"className":4383},[2456,2457,2458,2459],[703,4385,2402],{"className":4386},[765,2459],[703,4388,820],{"className":4389},[783],[664,4391,4392,4395],{},[679,4393,4394],{},"Conversion liste → matrice",[679,4396,4397],{},[703,4398,4400,4423],{"className":4399},[706],[703,4401,4403],{"className":4402},[710],[712,4404,4405],{"xmlns":714},[716,4406,4407,4421],{},[719,4408,4409,4411,4413,4415,4417,4419],{},[727,4410,2392],{"mathvariant":2391},[722,4412,811],{"stretchy":724},[727,4414,1250],{},[722,4416,2870],{},[727,4418,1289],{},[722,4420,820],{"stretchy":724},[741,4422,2877],{"encoding":743},[703,4424,4426,4450],{"className":4425,"ariaHidden":732},[748],[703,4427,4429,4432,4435,4438,4441,4444,4447],{"className":4428},[752],[703,4430],{"className":4431,"style":757},[756],[703,4433,2392],{"className":4434,"style":2422},[765,2421],[703,4436,811],{"className":4437},[761],[703,4439,1250],{"className":4440},[765,766],[703,4442],{"className":4443,"style":1524},[774],[703,4445,2870],{"className":4446},[1528],[703,4448],{"className":4449,"style":1524},[774],[703,4451,4453,4456,4459],{"className":4452},[752],[703,4454],{"className":4455,"style":757},[756],[703,4457,1289],{"className":4458},[765,766],[703,4460,820],{"className":4461},[783],[593,4463,4465],{"id":4464},"pièges-courants","Pièges courants",[1436,4467,4468,4471,4474],{},[636,4469,4470],{},"Oublier la symétrie de la matrice pour un graphe non orienté.",[636,4472,4473],{},"Coder un graphe creux en matrice — gaspillage mémoire.",[636,4475,4476],{},"Confondre arête (non orientée) et arc (orienté).",[593,4478,4480],{"id":4479},"syntaxe-python","Syntaxe Python",[2098,4482,4484],{"className":2100,"code":4483,"language":2102,"meta":1325,"style":1325},"# Matrice\nM = [[0]*n for _ in range(n)]\nM[u][v] = M[v][u] = 1   # non orienté\n\n# Liste de successeurs\nsucc = {s: [] for s in sommets}\nsucc[u].append(v)\nsucc[v].append(u)       # non orienté\n\n# Conversion\nsucc = {i: [j for j in range(n) if M[i][j]] for i in range(n)}\n",[2104,4485,4486,4492,4520,4537,4541,4546,4563,4568,4576,4580,4585],{"__ignoreMap":1325},[703,4487,4488],{"class":2108,"line":2109},[703,4489,4491],{"class":4490},"sCsY4","# Matrice\n",[703,4493,4494,4497,4499,4501,4503,4505,4507,4510,4512,4514,4516,4518],{"class":2108,"line":2124},[703,4495,4496],{"class":2120},"M ",[703,4498,1665],{"class":2112},[703,4500,2196],{"class":2120},[703,4502,1469],{"class":2144},[703,4504,1655],{"class":2120},[703,4506,2204],{"class":2112},[703,4508,4509],{"class":2120},"n ",[703,4511,2210],{"class":2112},[703,4513,2213],{"class":2120},[703,4515,2216],{"class":2112},[703,4517,2219],{"class":2144},[703,4519,2222],{"class":2120},[703,4521,4522,4525,4527,4530,4532,4534],{"class":2108,"line":2131},[703,4523,4524],{"class":2120},"M[u][v] ",[703,4526,1665],{"class":2112},[703,4528,4529],{"class":2120}," M[v][u] ",[703,4531,1665],{"class":2112},[703,4533,2362],{"class":2144},[703,4535,4536],{"class":4490},"   # non orienté\n",[703,4538,4539],{"class":2108,"line":2138},[703,4540,2135],{"emptyLinePlaceholder":2134},[703,4542,4543],{"class":2108,"line":2159},[703,4544,4545],{"class":4490},"# Liste de successeurs\n",[703,4547,4548,4551,4553,4555,4557,4559,4561],{"class":2108,"line":2173},[703,4549,4550],{"class":2120},"succ ",[703,4552,1665],{"class":2112},[703,4554,2665],{"class":2120},[703,4556,2210],{"class":2112},[703,4558,2670],{"class":2120},[703,4560,2216],{"class":2112},[703,4562,2675],{"class":2120},[703,4564,4565],{"class":2108,"line":2186},[703,4566,4567],{"class":2120},"succ[u].append(v)\n",[703,4569,4570,4573],{"class":2108,"line":2225},[703,4571,4572],{"class":2120},"succ[v].append(u)       ",[703,4574,4575],{"class":4490},"# non orienté\n",[703,4577,4578],{"class":2108,"line":2230},[703,4579,2135],{"emptyLinePlaceholder":2134},[703,4581,4582],{"class":2108,"line":2241},[703,4583,4584],{"class":4490},"# Conversion\n",[703,4586,4587,4589,4591,4594,4596,4598,4600,4602,4605,4607,4610,4612,4614,4616,4618],{"class":2108,"line":2254},[703,4588,4550],{"class":2120},[703,4590,1665],{"class":2112},[703,4592,4593],{"class":2120}," {i: [j ",[703,4595,2210],{"class":2112},[703,4597,3326],{"class":2120},[703,4599,2216],{"class":2112},[703,4601,2219],{"class":2144},[703,4603,4604],{"class":2120},"(n) ",[703,4606,2353],{"class":2112},[703,4608,4609],{"class":2120}," M[i][j]] ",[703,4611,2210],{"class":2112},[703,4613,3297],{"class":2120},[703,4615,2216],{"class":2112},[703,4617,2219],{"class":2144},[703,4619,3304],{"class":2120},[3705,4621,4622],{},"html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}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":1325,"searchDepth":2124,"depth":2124,"links":4624},[4625,4626,4627,4628,4629],{"id":3739,"depth":2124,"text":3740},{"id":3889,"depth":2124,"text":3890},{"id":4280,"depth":2124,"text":4281},{"id":4464,"depth":2124,"text":4465},{"id":4479,"depth":2124,"text":4480},"Mémo de révision sur les graphes, leurs représentations et leur conversion.",{},"\u002Fnsi-tale\u002Fta-structures-donnees\u002Fgraphes.memo",[],{"title":3733,"description":4630},"2.nsi-tale\u002Fta-structures-donnees\u002F5.graphes.memo","kCeb76GP__kYpSEvnw7j5nDLf-tCypKYRbrVy9PkxbI",{"id":4638,"title":4639,"body":4640,"description":5651,"extension":3719,"meta":5652,"navigation":3726,"path":5653,"seo":5654,"stem":5655,"__hash__":5656},"coursSlides\u002F2.nsi-tale\u002Fta-structures-donnees\u002F5.graphes.slides.md","Graphes — diapositives",{"type":590,"value":4641,"toc":5649},[4642,4646,4652,4655,4657,4839,4841,4845,4887,4889,4891,5041,5080,5199,5201,5203,5228,5350,5352,5356,5363,5365,5368,5427,5503,5505,5508,5568,5635,5637,5641,5646],[4643,4644,473],"h1",{"id":4645},"graphes",[598,4647,4648,4649,4651],{},"Item ",[629,4650],{"code":588}," — Sommets, arcs, arêtes, orientés ou non.",[4653,4654],"hr",{},[4643,4656,656],{"id":655},[1436,4658,4659,4664,4720,4776],{},[636,4660,4661,4663],{},[602,4662,683],{}," : élément.",[636,4665,4666,1545,4668,4719],{},[602,4667,694],{},[703,4669,4671,4692],{"className":4670},[706],[703,4672,4674],{"className":4673},[710],[712,4675,4676],{"xmlns":714},[716,4677,4678,4690],{},[719,4679,4680,4682,4684,4686,4688],{},[722,4681,725],{"stretchy":724},[727,4683,729],{},[722,4685,733],{"separator":732},[727,4687,736],{},[722,4689,739],{"stretchy":724},[741,4691,744],{"encoding":743},[703,4693,4695],{"className":4694,"ariaHidden":732},[748],[703,4696,4698,4701,4704,4707,4710,4713,4716],{"className":4697},[752],[703,4699],{"className":4700,"style":757},[756],[703,4702,725],{"className":4703},[761],[703,4705,729],{"className":4706},[765,766],[703,4708,733],{"className":4709},[770],[703,4711],{"className":4712,"style":775},[774],[703,4714,736],{"className":4715,"style":779},[765,766],[703,4717,739],{"className":4718},[783]," : lien non orienté.",[636,4721,4722,1545,4724,4775],{},[602,4723,790],{},[703,4725,4727,4748],{"className":4726},[706],[703,4728,4730],{"className":4729},[710],[712,4731,4732],{"xmlns":714},[716,4733,4734,4746],{},[719,4735,4736,4738,4740,4742,4744],{},[722,4737,811],{"stretchy":724},[727,4739,729],{},[722,4741,733],{"separator":732},[727,4743,736],{},[722,4745,820],{"stretchy":724},[741,4747,823],{"encoding":743},[703,4749,4751],{"className":4750,"ariaHidden":732},[748],[703,4752,4754,4757,4760,4763,4766,4769,4772],{"className":4753},[752],[703,4755],{"className":4756,"style":757},[756],[703,4758,811],{"className":4759},[761],[703,4761,729],{"className":4762},[765,766],[703,4764,733],{"className":4765},[770],[703,4767],{"className":4768,"style":775},[774],[703,4770,736],{"className":4771,"style":779},[765,766],[703,4773,820],{"className":4774},[783]," : lien orienté.",[636,4777,4778,1545,4780,4808,4809,1545,4811,652],{},[602,4779,1232],{},[703,4781,4783,4796],{"className":4782},[706],[703,4784,4786],{"className":4785},[710],[712,4787,4788],{"xmlns":714},[716,4789,4790,4794],{},[719,4791,4792],{},[727,4793,1250],{},[741,4795,1250],{"encoding":743},[703,4797,4799],{"className":4798,"ariaHidden":732},[748],[703,4800,4802,4805],{"className":4801},[752],[703,4803],{"className":4804,"style":904},[756],[703,4806,1250],{"className":4807},[765,766],", ",[602,4810,4245],{},[703,4812,4814,4827],{"className":4813},[706],[703,4815,4817],{"className":4816},[710],[712,4818,4819],{"xmlns":714},[716,4820,4821,4825],{},[719,4822,4823],{},[727,4824,1289],{},[741,4826,1289],{"encoding":743},[703,4828,4830],{"className":4829,"ariaHidden":732},[748],[703,4831,4833,4836],{"className":4832},[752],[703,4834],{"className":4835,"style":904},[756],[703,4837,1289],{"className":4838},[765,766],[4653,4840],{},[4643,4842,4844],{"id":4843},"exemples-de-modélisation","Exemples de modélisation",[658,4846,4847,4857],{},[661,4848,4849],{},[664,4850,4851,4854],{},[667,4852,4853],{},"Situation",[667,4855,4856],{},"Graphe",[674,4858,4859,4866,4873,4880],{},[664,4860,4861,4864],{},[679,4862,4863],{},"Réseau routier",[679,4865,700],{},[664,4867,4868,4871],{},[679,4869,4870],{},"Réseau social (amitiés)",[679,4872,700],{},[664,4874,4875,4878],{},[679,4876,4877],{},"Web (liens)",[679,4879,795],{},[664,4881,4882,4885],{},[679,4883,4884],{},"Hiérarchie d'appels",[679,4886,795],{},[4653,4888],{},[4643,4890,1450],{"id":1449},[598,4892,4893],{},[703,4894,4896,4947],{"className":4895},[706],[703,4897,4899],{"className":4898},[710],[712,4900,4901],{"xmlns":714},[716,4902,4903,4944],{},[719,4904,4905,4907,4909,4911,4913,4915,4917,4919,4921,4923,4926,4929,4931,4933,4935,4937,4939,4941],{},[727,4906,1560],{},[722,4908,1649],{"stretchy":724},[727,4910,1652],{},[722,4912,1655],{"stretchy":724},[722,4914,1649],{"stretchy":724},[727,4916,1660],{},[722,4918,1655],{"stretchy":724},[722,4920,1665],{},[1467,4922,1320],{},[1696,4924,4925],{},"  ",[722,4927,4928],{},"⟺",[1696,4930,4925],{},[722,4932,811],{"stretchy":724},[727,4934,1652],{},[722,4936,733],{"separator":732},[727,4938,1660],{},[722,4940,820],{"stretchy":724},[1696,4942,4943],{}," est un arc",[741,4945,4946],{"encoding":743},"M[i][j] = 1 \\iff (i, j) \\text{ est un arc}",[703,4948,4950,4986,5011],{"className":4949,"ariaHidden":732},[748],[703,4951,4953,4956,4959,4962,4965,4968,4971,4974,4977,4980,4983],{"className":4952},[752],[703,4954],{"className":4955,"style":757},[756],[703,4957,1560],{"className":4958,"style":1576},[765,766],[703,4960,1649],{"className":4961},[761],[703,4963,1652],{"className":4964},[765,766],[703,4966,1655],{"className":4967},[783],[703,4969,1649],{"className":4970},[761],[703,4972,1660],{"className":4973,"style":1763},[765,766],[703,4975,1655],{"className":4976},[783],[703,4978],{"className":4979,"style":1770},[774],[703,4981,1665],{"className":4982},[1774],[703,4984],{"className":4985,"style":1770},[774],[703,4987,4989,4993,4996,4999,5002,5005,5008],{"className":4988},[752],[703,4990],{"className":4991,"style":4992},[756],"height:0.6684em;vertical-align:-0.024em;",[703,4994,1320],{"className":4995},[765],[703,4997],{"className":4998,"style":1770},[774],[703,5000],{"className":5001,"style":1770},[774],[703,5003,4928],{"className":5004},[1774],[703,5006],{"className":5007,"style":1770},[774],[703,5009],{"className":5010,"style":1770},[774],[703,5012,5014,5017,5020,5023,5026,5029,5032,5035],{"className":5013},[752],[703,5015],{"className":5016,"style":757},[756],[703,5018,811],{"className":5019},[761],[703,5021,1652],{"className":5022},[765,766],[703,5024,733],{"className":5025},[770],[703,5027],{"className":5028,"style":775},[774],[703,5030,1660],{"className":5031,"style":1763},[765,766],[703,5033,820],{"className":5034},[783],[703,5036,5038],{"className":5037},[765,1891],[703,5039,4943],{"className":5040},[765],[2098,5042,5044],{"className":2100,"code":5043,"language":2102,"meta":1325,"style":1325},"M = [[0]*n for _ in range(n)]\nM[u][v] = 1\n",[2104,5045,5046,5072],{"__ignoreMap":1325},[703,5047,5048,5050,5052,5054,5056,5058,5060,5062,5064,5066,5068,5070],{"class":2108,"line":2109},[703,5049,4496],{"class":2120},[703,5051,1665],{"class":2112},[703,5053,2196],{"class":2120},[703,5055,1469],{"class":2144},[703,5057,1655],{"class":2120},[703,5059,2204],{"class":2112},[703,5061,4509],{"class":2120},[703,5063,2210],{"class":2112},[703,5065,2213],{"class":2120},[703,5067,2216],{"class":2112},[703,5069,2219],{"class":2144},[703,5071,2222],{"class":2120},[703,5073,5074,5076,5078],{"class":2108,"line":2124},[703,5075,4524],{"class":2120},[703,5077,1665],{"class":2112},[703,5079,2251],{"class":2144},[598,5081,2376,5082,5155,5156,652],{},[703,5083,5085,5108],{"className":5084},[706],[703,5086,5088],{"className":5087},[710],[712,5089,5090],{"xmlns":714},[716,5091,5092,5106],{},[719,5093,5094,5096,5098,5104],{},[727,5095,2392],{"mathvariant":2391},[722,5097,811],{"stretchy":724},[2396,5099,5100,5102],{},[727,5101,1250],{},[1467,5103,2402],{},[722,5105,820],{"stretchy":724},[741,5107,2407],{"encoding":743},[703,5109,5111],{"className":5110,"ariaHidden":732},[748],[703,5112,5114,5117,5120,5123,5152],{"className":5113},[752],[703,5115],{"className":5116,"style":2417},[756],[703,5118,2392],{"className":5119,"style":2422},[765,2421],[703,5121,811],{"className":5122},[761],[703,5124,5126,5129],{"className":5125},[765],[703,5127,1250],{"className":5128},[765,766],[703,5130,5132],{"className":5131},[2435],[703,5133,5135],{"className":5134},[1812],[703,5136,5138],{"className":5137},[1817],[703,5139,5141],{"className":5140,"style":2445},[1821],[703,5142,5143,5146],{"style":2448},[703,5144],{"className":5145,"style":2452},[1829],[703,5147,5149],{"className":5148},[2456,2457,2458,2459],[703,5150,2402],{"className":5151},[765,2459],[703,5153,820],{"className":5154},[783],". Test adjacence : ",[703,5157,5159,5178],{"className":5158},[706],[703,5160,5162],{"className":5161},[710],[712,5163,5164],{"xmlns":714},[716,5165,5166,5176],{},[719,5167,5168,5170,5172,5174],{},[727,5169,2392],{"mathvariant":2391},[722,5171,811],{"stretchy":724},[1467,5173,1320],{},[722,5175,820],{"stretchy":724},[741,5177,2496],{"encoding":743},[703,5179,5181],{"className":5180,"ariaHidden":732},[748],[703,5182,5184,5187,5190,5193,5196],{"className":5183},[752],[703,5185],{"className":5186,"style":757},[756],[703,5188,2392],{"className":5189,"style":2422},[765,2421],[703,5191,811],{"className":5192},[761],[703,5194,1320],{"className":5195},[765],[703,5197,820],{"className":5198},[783],[4653,5200],{},[4643,5202,2569],{"id":2568},[2098,5204,5206],{"className":2100,"code":5205,"language":2102,"meta":1325,"style":1325},"succ = {s: [] for s in sommets}\nsucc[u].append(v)\n",[2104,5207,5208,5224],{"__ignoreMap":1325},[703,5209,5210,5212,5214,5216,5218,5220,5222],{"class":2108,"line":2109},[703,5211,4550],{"class":2120},[703,5213,1665],{"class":2112},[703,5215,2665],{"class":2120},[703,5217,2210],{"class":2112},[703,5219,2670],{"class":2120},[703,5221,2216],{"class":2112},[703,5223,2675],{"class":2120},[703,5225,5226],{"class":2108,"line":2124},[703,5227,4567],{"class":2120},[598,5229,2376,5230,5155,5295,652],{},[703,5231,5233,5256],{"className":5232},[706],[703,5234,5236],{"className":5235},[710],[712,5237,5238],{"xmlns":714},[716,5239,5240,5254],{},[719,5241,5242,5244,5246,5248,5250,5252],{},[727,5243,2392],{"mathvariant":2391},[722,5245,811],{"stretchy":724},[727,5247,1250],{},[722,5249,2870],{},[727,5251,1289],{},[722,5253,820],{"stretchy":724},[741,5255,2877],{"encoding":743},[703,5257,5259,5283],{"className":5258,"ariaHidden":732},[748],[703,5260,5262,5265,5268,5271,5274,5277,5280],{"className":5261},[752],[703,5263],{"className":5264,"style":757},[756],[703,5266,2392],{"className":5267,"style":2422},[765,2421],[703,5269,811],{"className":5270},[761],[703,5272,1250],{"className":5273},[765,766],[703,5275],{"className":5276,"style":1524},[774],[703,5278,2870],{"className":5279},[1528],[703,5281],{"className":5282,"style":1524},[774],[703,5284,5286,5289,5292],{"className":5285},[752],[703,5287],{"className":5288,"style":757},[756],[703,5290,1289],{"className":5291},[765,766],[703,5293,820],{"className":5294},[783],[703,5296,5298,5323],{"className":5297},[706],[703,5299,5301],{"className":5300},[710],[712,5302,5303],{"xmlns":714},[716,5304,5305,5321],{},[719,5306,5307,5309,5311,5313,5315,5317,5319],{},[727,5308,2392],{"mathvariant":2391},[722,5310,811],{"stretchy":724},[727,5312,2782],{},[722,5314,811],{"stretchy":724},[727,5316,729],{},[722,5318,820],{"stretchy":724},[722,5320,820],{"stretchy":724},[741,5322,2952],{"encoding":743},[703,5324,5326],{"className":5325,"ariaHidden":732},[748],[703,5327,5329,5332,5335,5338,5341,5344,5347],{"className":5328},[752],[703,5330],{"className":5331,"style":757},[756],[703,5333,2392],{"className":5334,"style":2422},[765,2421],[703,5336,811],{"className":5337},[761],[703,5339,2782],{"className":5340},[765,766],[703,5342,811],{"className":5343},[761],[703,5345,729],{"className":5346},[765,766],[703,5348,2980],{"className":5349},[783],[4653,5351],{},[4643,5353,5355],{"id":5354},"choisir-sa-représentation","Choisir sa représentation",[5357,5358],"illustration",{"alt":5359,"kind":5360,"src":5361,"svg":5362},"Tableau de décision : graphe dense ou tests d'adjacence fréquents → matrice d'adjacence ; graphe creux ou parcours de voisins → liste de successeurs.","schema","\u002Fillustrations\u002F2.nsi-tale\u002Fta-structures-donnees\u002Fchoix-representation-graphe.svg","\u003Csvg class=\"illustration-svg\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 480 220\" role=\"img\" aria-label=\"Tableau de décision pour représenter un graphe : si graphe dense ou tests d'adjacence fréquents, choisir la matrice d'adjacence ; si graphe creux ou parcours des voisins, choisir la liste de successeurs\">\n  \u003Ctitle>Choisir la représentation d'un graphe\u003C\u002Ftitle>\n  \u003Cstyle>\n    .cg-svg { font-family: Geist, Inter, system-ui, sans-serif; }\n    .cg-head    { fill: var(--diagram-surface-alt); stroke: var(--diagram-border); stroke-width: 1.5; }\n    .cg-cell    { fill: var(--diagram-surface); stroke: var(--diagram-border); stroke-width: 1.5; }\n    .cg-pick    { fill: var(--diagram-node-bg); stroke: var(--diagram-node-border); stroke-width: 1.5; }\n    .cg-heademph{ fill: var(--diagram-text); font-size: 12px; font-weight: 600; letter-spacing: 0.5px; }\n    .cg-cond    { fill: var(--diagram-text); font-size: 12px; }\n    .cg-choice  { fill: var(--diagram-text); font-family: 'JetBrains Mono', monospace; font-size: 12px; font-weight: 600; }\n  \u003C\u002Fstyle>\n\n  \u003Cg class=\"cg-svg\">\n    \u003C!-- en-têtes de colonnes -->\n    \u003Crect x=\"20\"  y=\"24\" width=\"250\" height=\"34\" rx=\"4\" class=\"cg-head\"\u002F>\n    \u003Ctext x=\"36\" y=\"46\" class=\"cg-heademph\">SI…\u003C\u002Ftext>\n    \u003Crect x=\"278\" y=\"24\" width=\"182\" height=\"34\" rx=\"4\" class=\"cg-head\"\u002F>\n    \u003Ctext x=\"294\" y=\"46\" class=\"cg-heademph\">ALORS\u003C\u002Ftext>\n\n    \u003C!-- ligne 1 : matrice -->\n    \u003Crect x=\"20\"  y=\"66\" width=\"250\" height=\"58\" rx=\"4\" class=\"cg-cell\"\u002F>\n    \u003Ctext x=\"36\" y=\"90\"  class=\"cg-cond\">graphe dense, ou\u003C\u002Ftext>\n    \u003Ctext x=\"36\" y=\"110\" class=\"cg-cond\">tests d'adjacence fréquents\u003C\u002Ftext>\n    \u003Crect x=\"278\" y=\"66\" width=\"182\" height=\"58\" rx=\"4\" class=\"cg-pick\"\u002F>\n    \u003Ctext x=\"294\" y=\"100\" class=\"cg-choice\">matrice d'adjacence\u003C\u002Ftext>\n\n    \u003C!-- ligne 2 : liste de successeurs -->\n    \u003Crect x=\"20\"  y=\"132\" width=\"250\" height=\"58\" rx=\"4\" class=\"cg-cell\"\u002F>\n    \u003Ctext x=\"36\" y=\"156\" class=\"cg-cond\">graphe creux, ou\u003C\u002Ftext>\n    \u003Ctext x=\"36\" y=\"176\" class=\"cg-cond\">parcours des voisins\u003C\u002Ftext>\n    \u003Crect x=\"278\" y=\"132\" width=\"182\" height=\"58\" rx=\"4\" class=\"cg-pick\"\u002F>\n    \u003Ctext x=\"294\" y=\"166\" class=\"cg-choice\">liste de successeurs\u003C\u002Ftext>\n  \u003C\u002Fg>\n\u003C\u002Fsvg>\n",[4653,5364],{},[4643,5366,4314],{"id":5367},"conversion-matrice-liste",[2098,5369,5371],{"className":2100,"code":5370,"language":2102,"meta":1325,"style":1325},"succ = {i: [] for i in range(n)}\nfor i in range(n):\n    for j in range(n):\n        if M[i][j]:\n            succ[i].append(j)\n",[2104,5372,5373,5391,5403,5415,5422],{"__ignoreMap":1325},[703,5374,5375,5377,5379,5381,5383,5385,5387,5389],{"class":2108,"line":2109},[703,5376,4550],{"class":2120},[703,5378,1665],{"class":2112},[703,5380,3292],{"class":2120},[703,5382,2210],{"class":2112},[703,5384,3297],{"class":2120},[703,5386,2216],{"class":2112},[703,5388,2219],{"class":2144},[703,5390,3304],{"class":2120},[703,5392,5393,5395,5397,5399,5401],{"class":2108,"line":2124},[703,5394,2210],{"class":2112},[703,5396,3297],{"class":2120},[703,5398,2216],{"class":2112},[703,5400,2219],{"class":2144},[703,5402,3318],{"class":2120},[703,5404,5405,5407,5409,5411,5413],{"class":2108,"line":2131},[703,5406,3309],{"class":2112},[703,5408,3326],{"class":2120},[703,5410,2216],{"class":2112},[703,5412,2219],{"class":2144},[703,5414,3318],{"class":2120},[703,5416,5417,5419],{"class":2108,"line":2138},[703,5418,2257],{"class":2112},[703,5420,5421],{"class":2120}," M[i][j]:\n",[703,5423,5424],{"class":2108,"line":2159},[703,5425,5426],{"class":2120},"            succ[i].append(j)\n",[598,5428,5429,5430,652],{},"Coût : ",[703,5431,5433,5456],{"className":5432},[706],[703,5434,5436],{"className":5435},[710],[712,5437,5438],{"xmlns":714},[716,5439,5440,5454],{},[719,5441,5442,5444,5446,5452],{},[727,5443,2392],{"mathvariant":2391},[722,5445,811],{"stretchy":724},[2396,5447,5448,5450],{},[727,5449,1250],{},[1467,5451,2402],{},[722,5453,820],{"stretchy":724},[741,5455,2407],{"encoding":743},[703,5457,5459],{"className":5458,"ariaHidden":732},[748],[703,5460,5462,5465,5468,5471,5500],{"className":5461},[752],[703,5463],{"className":5464,"style":2417},[756],[703,5466,2392],{"className":5467,"style":2422},[765,2421],[703,5469,811],{"className":5470},[761],[703,5472,5474,5477],{"className":5473},[765],[703,5475,1250],{"className":5476},[765,766],[703,5478,5480],{"className":5479},[2435],[703,5481,5483],{"className":5482},[1812],[703,5484,5486],{"className":5485},[1817],[703,5487,5489],{"className":5488,"style":2445},[1821],[703,5490,5491,5494],{"style":2448},[703,5492],{"className":5493,"style":2452},[1829],[703,5495,5497],{"className":5496},[2456,2457,2458,2459],[703,5498,2402],{"className":5499},[765,2459],[703,5501,820],{"className":5502},[783],[4653,5504],{},[4643,5506,4394],{"id":5507},"conversion-liste-matrice",[2098,5509,5511],{"className":2100,"code":5510,"language":2102,"meta":1325,"style":1325},"M = [[0]*n for _ in range(n)]\nfor u, vs in succ.items():\n    for v in vs:\n        M[u][v] = 1\n",[2104,5512,5513,5539,5549,5559],{"__ignoreMap":1325},[703,5514,5515,5517,5519,5521,5523,5525,5527,5529,5531,5533,5535,5537],{"class":2108,"line":2109},[703,5516,4496],{"class":2120},[703,5518,1665],{"class":2112},[703,5520,2196],{"class":2120},[703,5522,1469],{"class":2144},[703,5524,1655],{"class":2120},[703,5526,2204],{"class":2112},[703,5528,4509],{"class":2120},[703,5530,2210],{"class":2112},[703,5532,2213],{"class":2120},[703,5534,2216],{"class":2112},[703,5536,2219],{"class":2144},[703,5538,2222],{"class":2120},[703,5540,5541,5543,5545,5547],{"class":2108,"line":2124},[703,5542,2210],{"class":2112},[703,5544,3423],{"class":2120},[703,5546,2216],{"class":2112},[703,5548,3428],{"class":2120},[703,5550,5551,5553,5555,5557],{"class":2108,"line":2131},[703,5552,3309],{"class":2112},[703,5554,2338],{"class":2120},[703,5556,2216],{"class":2112},[703,5558,3439],{"class":2120},[703,5560,5561,5564,5566],{"class":2108,"line":2138},[703,5562,5563],{"class":2120},"        M[u][v] ",[703,5565,1665],{"class":2112},[703,5567,2251],{"class":2144},[598,5569,5429,5570,652],{},[703,5571,5573,5596],{"className":5572},[706],[703,5574,5576],{"className":5575},[710],[712,5577,5578],{"xmlns":714},[716,5579,5580,5594],{},[719,5581,5582,5584,5586,5588,5590,5592],{},[727,5583,2392],{"mathvariant":2391},[722,5585,811],{"stretchy":724},[727,5587,1250],{},[722,5589,2870],{},[727,5591,1289],{},[722,5593,820],{"stretchy":724},[741,5595,2877],{"encoding":743},[703,5597,5599,5623],{"className":5598,"ariaHidden":732},[748],[703,5600,5602,5605,5608,5611,5614,5617,5620],{"className":5601},[752],[703,5603],{"className":5604,"style":757},[756],[703,5606,2392],{"className":5607,"style":2422},[765,2421],[703,5609,811],{"className":5610},[761],[703,5612,1250],{"className":5613},[765,766],[703,5615],{"className":5616,"style":1524},[774],[703,5618,2870],{"className":5619},[1528],[703,5621],{"className":5622,"style":1524},[774],[703,5624,5626,5629,5632],{"className":5625},[752],[703,5627],{"className":5628,"style":757},[756],[703,5630,1289],{"className":5631},[765,766],[703,5633,820],{"className":5634},[783],[4653,5636],{},[4643,5638,5640],{"id":5639},"à-retenir","À retenir",[598,5642,5643],{},[602,5644,5645],{},"Le choix de la représentation découle du graphe (densité) et des opérations dominantes (test d'adjacence vs parcours de voisins).",[3705,5647,5648],{},"html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}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: 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