[{"data":1,"prerenderedAt":1149},["ShallowReactive",2],{"blog-tri-rapide":3},{"id":4,"title":5,"body":6,"coverImage":1136,"description":1137,"extension":1138,"meta":1139,"navigation":260,"path":1140,"published":260,"publishedAt":1141,"readTime":423,"seo":1142,"stem":1143,"tags":1144,"__hash__":1148},"blog\u002Fblog\u002Ftri-rapide.md","Le tri rapide expliqué simplement",{"type":7,"value":8,"toc":1095},"minimark",[9,14,19,23,26,29,33,36,58,62,65,137,140,144,147,162,166,172,186,189,193,196,482,487,522,526,594,598,601,604,608,611,614,617,621,624,627,631,661,665,669,681,687,691,709,714,718,745,750,754,758,769,773,784,787,791,795,798,802,805,809,812,816,819,822,836,840,844,847,851,854,858,861,865,868,872,876,1084,1088,1091],[10,11,13],"h1",{"id":12},"le-tri-rapide","Le tri rapide",[15,16,18],"h2",{"id":17},"introduction","Introduction",[20,21,22],"p",{},"Le tri rapide est l'un des algorithmes de tri les plus connus.",[20,24,25],{},"Il est souvent très performant en pratique, même si son fonctionnement demande un peu plus d'attention au début.",[20,27,28],{},"Son idée principale repose sur un pivot : on choisit une valeur, on sépare les éléments plus petits et plus grands, puis on recommence sur chaque partie.",[15,30,32],{"id":31},"ce-que-vous-allez-apprendre","Ce que vous allez apprendre",[20,34,35],{},"À la fin de ce tutoriel, vous saurez :",[37,38,39,43,46,49,52,55],"ul",{},[40,41,42],"li",{},"comprendre le principe du tri rapide ;",[40,44,45],{},"savoir ce qu'est un pivot ;",[40,47,48],{},"comprendre le partitionnement ;",[40,50,51],{},"écrire une version simple en JavaScript ;",[40,53,54],{},"voir les limites de l'algorithme ;",[40,56,57],{},"le comparer au tri fusion.",[15,59,61],{"id":60},"_1-le-problème-de-départ","1. Le problème de départ",[20,63,64],{},"Prenons cette liste :",[66,67,72],"pre",{"className":68,"code":69,"language":70,"meta":71,"style":71},"language-js shiki shiki-themes github-light github-dark","const numbers = [7, 2, 1, 6, 8, 5, 3, 4];\n","js","",[73,74,75],"code",{"__ignoreMap":71},[76,77,80,84,88,91,95,98,101,104,106,109,111,114,116,119,121,124,126,129,131,134],"span",{"class":78,"line":79},"line",1,[76,81,83],{"class":82},"szBVR","const",[76,85,87],{"class":86},"sj4cs"," numbers",[76,89,90],{"class":82}," =",[76,92,94],{"class":93},"sVt8B"," [",[76,96,97],{"class":86},"7",[76,99,100],{"class":93},", ",[76,102,103],{"class":86},"2",[76,105,100],{"class":93},[76,107,108],{"class":86},"1",[76,110,100],{"class":93},[76,112,113],{"class":86},"6",[76,115,100],{"class":93},[76,117,118],{"class":86},"8",[76,120,100],{"class":93},[76,122,123],{"class":86},"5",[76,125,100],{"class":93},[76,127,128],{"class":86},"3",[76,130,100],{"class":93},[76,132,133],{"class":86},"4",[76,135,136],{"class":93},"];\n",[20,138,139],{},"Le but est de la trier dans l'ordre croissant.",[15,141,143],{"id":142},"_2-lidée-du-tri-rapide","2. L'idée du tri rapide",[20,145,146],{},"Le tri rapide fonctionne ainsi :",[148,149,150,153,156,159],"ol",{},[40,151,152],{},"choisir un pivot ;",[40,154,155],{},"placer les nombres plus petits à gauche ;",[40,157,158],{},"placer les nombres plus grands à droite ;",[40,160,161],{},"recommencer sur chaque sous-liste.",[15,163,165],{"id":164},"_3-exemple-intuitif","3. Exemple intuitif",[20,167,168,169,171],{},"Si le pivot est ",[73,170,123],{},", on peut séparer la liste en deux groupes :",[37,173,174,180],{},[40,175,176,177,179],{},"à gauche : les nombres plus petits que ",[73,178,123],{}," ;",[40,181,182,183,185],{},"à droite : les nombres plus grands que ",[73,184,123],{},".",[20,187,188],{},"Ensuite, on trie chaque partie de la même manière.",[15,190,192],{"id":191},"_4-version-javascript-simple","4. Version JavaScript simple",[20,194,195],{},"Voici une version lisible et pédagogique :",[66,197,199],{"className":68,"code":198,"language":70,"meta":71,"style":71},"function quickSort(array) {\n  if (array.length \u003C= 1) {\n    return array;\n  }\n\n  const pivot = array[Math.floor(array.length \u002F 2)];\n  const left = [];\n  const middle = [];\n  const right = [];\n\n  for (const value of array) {\n    if (value \u003C pivot) {\n      left.push(value);\n    } else if (value > pivot) {\n      right.push(value);\n    } else {\n      middle.push(value);\n    }\n  }\n\n  return [...quickSort(left), ...middle, ...quickSort(right)];\n}\n",[73,200,201,220,240,249,255,262,293,306,318,330,335,355,370,382,401,411,421,431,437,442,447,476],{"__ignoreMap":71},[76,202,203,206,210,213,217],{"class":78,"line":79},[76,204,205],{"class":82},"function",[76,207,209],{"class":208},"sScJk"," quickSort",[76,211,212],{"class":93},"(",[76,214,216],{"class":215},"s4XuR","array",[76,218,219],{"class":93},") {\n",[76,221,223,226,229,232,235,238],{"class":78,"line":222},2,[76,224,225],{"class":82},"  if",[76,227,228],{"class":93}," (array.",[76,230,231],{"class":86},"length",[76,233,234],{"class":82}," \u003C=",[76,236,237],{"class":86}," 1",[76,239,219],{"class":93},[76,241,243,246],{"class":78,"line":242},3,[76,244,245],{"class":82},"    return",[76,247,248],{"class":93}," array;\n",[76,250,252],{"class":78,"line":251},4,[76,253,254],{"class":93},"  }\n",[76,256,258],{"class":78,"line":257},5,[76,259,261],{"emptyLinePlaceholder":260},true,"\n",[76,263,265,268,271,273,276,279,282,284,287,290],{"class":78,"line":264},6,[76,266,267],{"class":82},"  const",[76,269,270],{"class":86}," pivot",[76,272,90],{"class":82},[76,274,275],{"class":93}," array[Math.",[76,277,278],{"class":208},"floor",[76,280,281],{"class":93},"(array.",[76,283,231],{"class":86},[76,285,286],{"class":82}," \u002F",[76,288,289],{"class":86}," 2",[76,291,292],{"class":93},")];\n",[76,294,296,298,301,303],{"class":78,"line":295},7,[76,297,267],{"class":82},[76,299,300],{"class":86}," left",[76,302,90],{"class":82},[76,304,305],{"class":93}," [];\n",[76,307,309,311,314,316],{"class":78,"line":308},8,[76,310,267],{"class":82},[76,312,313],{"class":86}," middle",[76,315,90],{"class":82},[76,317,305],{"class":93},[76,319,321,323,326,328],{"class":78,"line":320},9,[76,322,267],{"class":82},[76,324,325],{"class":86}," right",[76,327,90],{"class":82},[76,329,305],{"class":93},[76,331,333],{"class":78,"line":332},10,[76,334,261],{"emptyLinePlaceholder":260},[76,336,338,341,344,346,349,352],{"class":78,"line":337},11,[76,339,340],{"class":82},"  for",[76,342,343],{"class":93}," (",[76,345,83],{"class":82},[76,347,348],{"class":86}," value",[76,350,351],{"class":82}," of",[76,353,354],{"class":93}," array) {\n",[76,356,358,361,364,367],{"class":78,"line":357},12,[76,359,360],{"class":82},"    if",[76,362,363],{"class":93}," (value ",[76,365,366],{"class":82},"\u003C",[76,368,369],{"class":93}," pivot) {\n",[76,371,373,376,379],{"class":78,"line":372},13,[76,374,375],{"class":93},"      left.",[76,377,378],{"class":208},"push",[76,380,381],{"class":93},"(value);\n",[76,383,385,388,391,394,396,399],{"class":78,"line":384},14,[76,386,387],{"class":93},"    } ",[76,389,390],{"class":82},"else",[76,392,393],{"class":82}," if",[76,395,363],{"class":93},[76,397,398],{"class":82},">",[76,400,369],{"class":93},[76,402,404,407,409],{"class":78,"line":403},15,[76,405,406],{"class":93},"      right.",[76,408,378],{"class":208},[76,410,381],{"class":93},[76,412,414,416,418],{"class":78,"line":413},16,[76,415,387],{"class":93},[76,417,390],{"class":82},[76,419,420],{"class":93}," {\n",[76,422,424,427,429],{"class":78,"line":423},17,[76,425,426],{"class":93},"      middle.",[76,428,378],{"class":208},[76,430,381],{"class":93},[76,432,434],{"class":78,"line":433},18,[76,435,436],{"class":93},"    }\n",[76,438,440],{"class":78,"line":439},19,[76,441,254],{"class":93},[76,443,445],{"class":78,"line":444},20,[76,446,261],{"emptyLinePlaceholder":260},[76,448,450,453,455,458,461,464,466,469,471,473],{"class":78,"line":449},21,[76,451,452],{"class":82},"  return",[76,454,94],{"class":93},[76,456,457],{"class":82},"...",[76,459,460],{"class":208},"quickSort",[76,462,463],{"class":93},"(left), ",[76,465,457],{"class":82},[76,467,468],{"class":93},"middle, ",[76,470,457],{"class":82},[76,472,460],{"class":208},[76,474,475],{"class":93},"(right)];\n",[76,477,479],{"class":78,"line":478},22,[76,480,481],{"class":93},"}\n",[483,484,486],"h3",{"id":485},"explication","Explication",[37,488,489,495,501,507,513],{},[40,490,491,494],{},[73,492,493],{},"pivot"," est la valeur de référence ;",[40,496,497,500],{},[73,498,499],{},"left"," contient les valeurs plus petites ;",[40,502,503,506],{},[73,504,505],{},"middle"," contient les valeurs égales au pivot ;",[40,508,509,512],{},[73,510,511],{},"right"," contient les valeurs plus grandes ;",[40,514,515,516,518,519,521],{},"on trie ensuite ",[73,517,499],{}," et ",[73,520,511],{}," récursivement.",[15,523,525],{"id":524},"_5-exemple-dutilisation","5. Exemple d'utilisation",[66,527,529],{"className":68,"code":528,"language":70,"meta":71,"style":71},"const numbers = [7, 2, 1, 6, 8, 5, 3, 4];\nconsole.log(quickSort(numbers));\n\u002F\u002F [1, 2, 3, 4, 5, 6, 7, 8]\n",[73,530,531,573,588],{"__ignoreMap":71},[76,532,533,535,537,539,541,543,545,547,549,551,553,555,557,559,561,563,565,567,569,571],{"class":78,"line":79},[76,534,83],{"class":82},[76,536,87],{"class":86},[76,538,90],{"class":82},[76,540,94],{"class":93},[76,542,97],{"class":86},[76,544,100],{"class":93},[76,546,103],{"class":86},[76,548,100],{"class":93},[76,550,108],{"class":86},[76,552,100],{"class":93},[76,554,113],{"class":86},[76,556,100],{"class":93},[76,558,118],{"class":86},[76,560,100],{"class":93},[76,562,123],{"class":86},[76,564,100],{"class":93},[76,566,128],{"class":86},[76,568,100],{"class":93},[76,570,133],{"class":86},[76,572,136],{"class":93},[76,574,575,578,581,583,585],{"class":78,"line":222},[76,576,577],{"class":93},"console.",[76,579,580],{"class":208},"log",[76,582,212],{"class":93},[76,584,460],{"class":208},[76,586,587],{"class":93},"(numbers));\n",[76,589,590],{"class":78,"line":242},[76,591,593],{"class":592},"sJ8bj","\u002F\u002F [1, 2, 3, 4, 5, 6, 7, 8]\n",[15,595,597],{"id":596},"_6-pourquoi-cet-algorithme-est-intéressant","6. Pourquoi cet algorithme est intéressant",[20,599,600],{},"Le tri rapide est souvent très efficace en pratique.",[20,602,603],{},"Il est apprécié parce qu'il trie rapidement de grandes listes dans beaucoup de situations réelles.",[15,605,607],{"id":606},"_7-le-rôle-du-pivot","7. Le rôle du pivot",[20,609,610],{},"Le pivot est le point central de l'algorithme.",[20,612,613],{},"Un bon choix de pivot peut améliorer le comportement du tri.",[20,615,616],{},"Si le pivot est mal choisi de manière répétée, l'algorithme peut devenir moins performant.",[15,618,620],{"id":619},"_8-la-récursion","8. La récursion",[20,622,623],{},"Comme le tri fusion, le tri rapide utilise la récursion.",[20,625,626],{},"On trie une sous-liste, puis une autre, jusqu'à arriver à des listes très petites.",[483,628,630],{"id":629},"cas-de-base","Cas de base",[66,632,634],{"className":68,"code":633,"language":70,"meta":71,"style":71},"if (array.length \u003C= 1) {\n  return array;\n}\n",[73,635,636,651,657],{"__ignoreMap":71},[76,637,638,641,643,645,647,649],{"class":78,"line":79},[76,639,640],{"class":82},"if",[76,642,228],{"class":93},[76,644,231],{"class":86},[76,646,234],{"class":82},[76,648,237],{"class":86},[76,650,219],{"class":93},[76,652,653,655],{"class":78,"line":222},[76,654,452],{"class":82},[76,656,248],{"class":93},[76,658,659],{"class":78,"line":242},[76,660,481],{"class":93},[15,662,664],{"id":663},"_9-les-cas-limites","9. Les cas limites",[483,666,668],{"id":667},"tableau-vide","Tableau vide",[66,670,672],{"className":68,"code":671,"language":70,"meta":71,"style":71},"quickSort([]);\n",[73,673,674],{"__ignoreMap":71},[76,675,676,678],{"class":78,"line":79},[76,677,460],{"class":208},[76,679,680],{"class":93},"([]);\n",[20,682,683,684],{},"Résultat : ",[73,685,686],{},"[]",[483,688,690],{"id":689},"un-seul-élément","Un seul élément",[66,692,694],{"className":68,"code":693,"language":70,"meta":71,"style":71},"quickSort([10]);\n",[73,695,696],{"__ignoreMap":71},[76,697,698,700,703,706],{"class":78,"line":79},[76,699,460],{"class":208},[76,701,702],{"class":93},"([",[76,704,705],{"class":86},"10",[76,707,708],{"class":93},"]);\n",[20,710,683,711],{},[73,712,713],{},"[10]",[483,715,717],{"id":716},"liste-déjà-triée","Liste déjà triée",[66,719,721],{"className":68,"code":720,"language":70,"meta":71,"style":71},"quickSort([1, 2, 3, 4]);\n",[73,722,723],{"__ignoreMap":71},[76,724,725,727,729,731,733,735,737,739,741,743],{"class":78,"line":79},[76,726,460],{"class":208},[76,728,702],{"class":93},[76,730,108],{"class":86},[76,732,100],{"class":93},[76,734,103],{"class":86},[76,736,100],{"class":93},[76,738,128],{"class":86},[76,740,100],{"class":93},[76,742,133],{"class":86},[76,744,708],{"class":93},[20,746,683,747],{},[73,748,749],{},"[1, 2, 3, 4]",[15,751,753],{"id":752},"_10-tri-rapide-ou-tri-fusion","10. Tri rapide ou tri fusion ?",[483,755,757],{"id":756},"tri-rapide","Tri rapide",[37,759,760,763,766],{},[40,761,762],{},"souvent très performant en pratique ;",[40,764,765],{},"repose sur le pivot et le partitionnement ;",[40,767,768],{},"peut être sensible au choix du pivot.",[483,770,772],{"id":771},"tri-fusion","Tri fusion",[37,774,775,778,781],{},[40,776,777],{},"très régulier ;",[40,779,780],{},"repose sur la division en deux parties égales ;",[40,782,783],{},"utilise une étape de fusion très claire.",[20,785,786],{},"Les deux sont importants à connaître.",[15,788,790],{"id":789},"_11-erreurs-fréquentes","11. Erreurs fréquentes",[483,792,794],{"id":793},"oublier-le-cas-de-base","Oublier le cas de base",[20,796,797],{},"La récursion doit toujours avoir une condition d'arrêt.",[483,799,801],{"id":800},"mal-gérer-le-pivot","Mal gérer le pivot",[20,803,804],{},"Il faut bien séparer les valeurs plus petites, égales et plus grandes.",[483,806,808],{"id":807},"modifier-la-même-liste-partout","Modifier la même liste partout",[20,810,811],{},"Pour apprendre plus facilement, il est souvent plus clair de retourner une nouvelle liste.",[15,813,815],{"id":814},"_12-résumé","12. Résumé",[20,817,818],{},"Le tri rapide est un algorithme puissant qui repose sur le pivot et le partitionnement.",[20,820,821],{},"À retenir :",[37,823,824,827,830,833],{},[40,825,826],{},"on choisit un pivot ;",[40,828,829],{},"on sépare les valeurs en plusieurs groupes ;",[40,831,832],{},"on trie récursivement les sous-listes ;",[40,834,835],{},"il est souvent très efficace en pratique.",[15,837,839],{"id":838},"exercices","Exercices",[483,841,843],{"id":842},"exercice-1","Exercice 1",[20,845,846],{},"Implémentez le tri rapide en JavaScript.",[483,848,850],{"id":849},"exercice-2","Exercice 2",[20,852,853],{},"Testez votre fonction avec une liste vide.",[483,855,857],{"id":856},"exercice-3","Exercice 3",[20,859,860],{},"Testez votre fonction avec une liste déjà triée.",[483,862,864],{"id":863},"exercice-4","Exercice 4",[20,866,867],{},"Essayez de modifier le pivot pour prendre le premier élément.",[15,869,871],{"id":870},"corrigés","Corrigés",[483,873,875],{"id":874},"correction-exercice-1","Correction exercice 1",[66,877,878],{"className":68,"code":198,"language":70,"meta":71,"style":71},[73,879,880,892,906,912,916,920,942,952,962,972,976,990,1000,1008,1022,1030,1038,1046,1050,1054,1058,1080],{"__ignoreMap":71},[76,881,882,884,886,888,890],{"class":78,"line":79},[76,883,205],{"class":82},[76,885,209],{"class":208},[76,887,212],{"class":93},[76,889,216],{"class":215},[76,891,219],{"class":93},[76,893,894,896,898,900,902,904],{"class":78,"line":222},[76,895,225],{"class":82},[76,897,228],{"class":93},[76,899,231],{"class":86},[76,901,234],{"class":82},[76,903,237],{"class":86},[76,905,219],{"class":93},[76,907,908,910],{"class":78,"line":242},[76,909,245],{"class":82},[76,911,248],{"class":93},[76,913,914],{"class":78,"line":251},[76,915,254],{"class":93},[76,917,918],{"class":78,"line":257},[76,919,261],{"emptyLinePlaceholder":260},[76,921,922,924,926,928,930,932,934,936,938,940],{"class":78,"line":264},[76,923,267],{"class":82},[76,925,270],{"class":86},[76,927,90],{"class":82},[76,929,275],{"class":93},[76,931,278],{"class":208},[76,933,281],{"class":93},[76,935,231],{"class":86},[76,937,286],{"class":82},[76,939,289],{"class":86},[76,941,292],{"class":93},[76,943,944,946,948,950],{"class":78,"line":295},[76,945,267],{"class":82},[76,947,300],{"class":86},[76,949,90],{"class":82},[76,951,305],{"class":93},[76,953,954,956,958,960],{"class":78,"line":308},[76,955,267],{"class":82},[76,957,313],{"class":86},[76,959,90],{"class":82},[76,961,305],{"class":93},[76,963,964,966,968,970],{"class":78,"line":320},[76,965,267],{"class":82},[76,967,325],{"class":86},[76,969,90],{"class":82},[76,971,305],{"class":93},[76,973,974],{"class":78,"line":332},[76,975,261],{"emptyLinePlaceholder":260},[76,977,978,980,982,984,986,988],{"class":78,"line":337},[76,979,340],{"class":82},[76,981,343],{"class":93},[76,983,83],{"class":82},[76,985,348],{"class":86},[76,987,351],{"class":82},[76,989,354],{"class":93},[76,991,992,994,996,998],{"class":78,"line":357},[76,993,360],{"class":82},[76,995,363],{"class":93},[76,997,366],{"class":82},[76,999,369],{"class":93},[76,1001,1002,1004,1006],{"class":78,"line":372},[76,1003,375],{"class":93},[76,1005,378],{"class":208},[76,1007,381],{"class":93},[76,1009,1010,1012,1014,1016,1018,1020],{"class":78,"line":384},[76,1011,387],{"class":93},[76,1013,390],{"class":82},[76,1015,393],{"class":82},[76,1017,363],{"class":93},[76,1019,398],{"class":82},[76,1021,369],{"class":93},[76,1023,1024,1026,1028],{"class":78,"line":403},[76,1025,406],{"class":93},[76,1027,378],{"class":208},[76,1029,381],{"class":93},[76,1031,1032,1034,1036],{"class":78,"line":413},[76,1033,387],{"class":93},[76,1035,390],{"class":82},[76,1037,420],{"class":93},[76,1039,1040,1042,1044],{"class":78,"line":423},[76,1041,426],{"class":93},[76,1043,378],{"class":208},[76,1045,381],{"class":93},[76,1047,1048],{"class":78,"line":433},[76,1049,436],{"class":93},[76,1051,1052],{"class":78,"line":439},[76,1053,254],{"class":93},[76,1055,1056],{"class":78,"line":444},[76,1057,261],{"emptyLinePlaceholder":260},[76,1059,1060,1062,1064,1066,1068,1070,1072,1074,1076,1078],{"class":78,"line":449},[76,1061,452],{"class":82},[76,1063,94],{"class":93},[76,1065,457],{"class":82},[76,1067,460],{"class":208},[76,1069,463],{"class":93},[76,1071,457],{"class":82},[76,1073,468],{"class":93},[76,1075,457],{"class":82},[76,1077,460],{"class":208},[76,1079,475],{"class":93},[76,1081,1082],{"class":78,"line":478},[76,1083,481],{"class":93},[15,1085,1087],{"id":1086},"prochaine-étape","Prochaine étape",[20,1089,1090],{},"Une fois le tri rapide compris, vous avez déjà une bonne base pour lire et écrire la plupart des algorithmes de tri classiques.",[1092,1093,1094],"style",{},"html pre.shiki code .szBVR, html code.shiki .szBVR{--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sj4cs, html code.shiki .sj4cs{--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sVt8B, html code.shiki .sVt8B{--shiki-default:#24292E;--shiki-dark:#E1E4E8}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: 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