[{"data":1,"prerenderedAt":1139},["ShallowReactive",2],{"blog-tri-par-insertion":3},{"id":4,"title":5,"body":6,"coverImage":1126,"description":1127,"extension":1128,"meta":1129,"navigation":362,"path":1130,"published":362,"publishedAt":1131,"readTime":532,"seo":1132,"stem":1133,"tags":1134,"__hash__":1138},"blog\u002Fblog\u002Ftri-par-insertion.md","Le tri par insertion expliqué simplement",{"type":7,"value":8,"toc":1082},"minimark",[9,14,19,23,26,30,33,52,56,59,116,119,123,126,129,144,147,151,154,181,186,192,196,204,207,232,236,246,248,273,277,282,285,310,314,556,560,580,584,641,645,648,651,655,659,671,677,681,699,704,708,737,742,746,750,753,757,760,763,767,771,774,780,790,794,800,804,807,810,824,828,832,835,839,846,850,853,857,860,864,868,1040,1044,1071,1075,1078],[10,11,13],"h1",{"id":12},"le-tri-par-insertion","Le tri par insertion",[15,16,18],"h2",{"id":17},"introduction","Introduction",[20,21,22],"p",{},"Le tri par insertion est un algorithme très utile pour comprendre une logique de tri plus naturelle.",[20,24,25],{},"L'idée est simple : on construit progressivement une partie triée du tableau, en insérant chaque nouvel élément à sa bonne place.",[15,27,29],{"id":28},"ce-que-vous-allez-apprendre","Ce que vous allez apprendre",[20,31,32],{},"À la fin de ce tutoriel, vous saurez :",[34,35,36,40,43,46,49],"ul",{},[37,38,39],"li",{},"comprendre le principe du tri par insertion ;",[37,41,42],{},"suivre l'algorithme pas à pas ;",[37,44,45],{},"l'implémenter en JavaScript ;",[37,47,48],{},"comprendre dans quels cas il est intéressant ;",[37,50,51],{},"voir la différence avec le tri à bulles.",[15,53,55],{"id":54},"_1-le-problème-de-départ","1. Le problème de départ",[20,57,58],{},"Prenons une liste de nombres :",[60,61,66],"pre",{"className":62,"code":63,"language":64,"meta":65,"style":65},"language-js shiki shiki-themes github-light github-dark","const numbers = [7, 4, 5, 2, 9];\n","js","",[67,68,69],"code",{"__ignoreMap":65},[70,71,74,78,82,85,89,92,95,98,100,103,105,108,110,113],"span",{"class":72,"line":73},"line",1,[70,75,77],{"class":76},"szBVR","const",[70,79,81],{"class":80},"sj4cs"," numbers",[70,83,84],{"class":76}," =",[70,86,88],{"class":87},"sVt8B"," [",[70,90,91],{"class":80},"7",[70,93,94],{"class":87},", ",[70,96,97],{"class":80},"4",[70,99,94],{"class":87},[70,101,102],{"class":80},"5",[70,104,94],{"class":87},[70,106,107],{"class":80},"2",[70,109,94],{"class":87},[70,111,112],{"class":80},"9",[70,114,115],{"class":87},"];\n",[20,117,118],{},"Le but est de la trier dans l'ordre croissant.",[15,120,122],{"id":121},"_2-lidée-du-tri-par-insertion","2. L'idée du tri par insertion",[20,124,125],{},"On considère que le premier élément est déjà trié.",[20,127,128],{},"Ensuite :",[130,131,132,135,138,141],"ol",{},[37,133,134],{},"on prend l'élément suivant ;",[37,136,137],{},"on le compare avec les éléments déjà triés ;",[37,139,140],{},"on le place à la bonne position ;",[37,142,143],{},"on recommence avec l'élément suivant.",[20,145,146],{},"C'est une méthode très intuitive.",[15,148,150],{"id":149},"_3-exemple-pas-à-pas","3. Exemple pas à pas",[20,152,153],{},"Avec la liste :",[60,155,157],{"className":62,"code":156,"language":64,"meta":65,"style":65},"[7, 4, 5, 2]\n",[67,158,159],{"__ignoreMap":65},[70,160,161,164,166,168,170,172,174,176,178],{"class":72,"line":73},[70,162,163],{"class":87},"[",[70,165,91],{"class":80},[70,167,94],{"class":87},[70,169,97],{"class":80},[70,171,94],{"class":87},[70,173,102],{"class":80},[70,175,94],{"class":87},[70,177,107],{"class":80},[70,179,180],{"class":87},"]\n",[182,183,185],"h3",{"id":184},"départ","Départ",[20,187,188,189,191],{},"On considère que ",[67,190,91],{}," est déjà trié.",[182,193,195],{"id":194},"insertion-de-4","Insertion de 4",[20,197,198,200,201,203],{},[67,199,97],{}," doit aller avant ",[67,202,91],{},".",[20,205,206],{},"Résultat :",[60,208,210],{"className":62,"code":209,"language":64,"meta":65,"style":65},"[4, 7, 5, 2]\n",[67,211,212],{"__ignoreMap":65},[70,213,214,216,218,220,222,224,226,228,230],{"class":72,"line":73},[70,215,163],{"class":87},[70,217,97],{"class":80},[70,219,94],{"class":87},[70,221,91],{"class":80},[70,223,94],{"class":87},[70,225,102],{"class":80},[70,227,94],{"class":87},[70,229,107],{"class":80},[70,231,180],{"class":87},[182,233,235],{"id":234},"insertion-de-5","Insertion de 5",[20,237,238,240,241,243,244,203],{},[67,239,102],{}," doit se placer entre ",[67,242,97],{}," et ",[67,245,91],{},[20,247,206],{},[60,249,251],{"className":62,"code":250,"language":64,"meta":65,"style":65},"[4, 5, 7, 2]\n",[67,252,253],{"__ignoreMap":65},[70,254,255,257,259,261,263,265,267,269,271],{"class":72,"line":73},[70,256,163],{"class":87},[70,258,97],{"class":80},[70,260,94],{"class":87},[70,262,102],{"class":80},[70,264,94],{"class":87},[70,266,91],{"class":80},[70,268,94],{"class":87},[70,270,107],{"class":80},[70,272,180],{"class":87},[182,274,276],{"id":275},"insertion-de-2","Insertion de 2",[20,278,279,281],{},[67,280,107],{}," doit aller au début.",[20,283,284],{},"Résultat final :",[60,286,288],{"className":62,"code":287,"language":64,"meta":65,"style":65},"[2, 4, 5, 7]\n",[67,289,290],{"__ignoreMap":65},[70,291,292,294,296,298,300,302,304,306,308],{"class":72,"line":73},[70,293,163],{"class":87},[70,295,107],{"class":80},[70,297,94],{"class":87},[70,299,97],{"class":80},[70,301,94],{"class":87},[70,303,102],{"class":80},[70,305,94],{"class":87},[70,307,91],{"class":80},[70,309,180],{"class":87},[15,311,313],{"id":312},"_4-version-javascript","4. Version JavaScript",[60,315,317],{"className":62,"code":316,"language":64,"meta":65,"style":65},"function insertionSort(array) {\n  const result = [...array];\n\n  for (let i = 1; i \u003C result.length; i++) {\n    const current = result[i];\n    let j = i - 1;\n\n    while (j >= 0 && result[j] > current) {\n      result[j + 1] = result[j];\n      j--;\n    }\n\n    result[j + 1] = current;\n  }\n\n  return result;\n}\n",[67,318,319,338,357,364,405,419,440,445,472,491,502,508,513,530,536,541,550],{"__ignoreMap":65},[70,320,321,324,328,331,335],{"class":72,"line":73},[70,322,323],{"class":76},"function",[70,325,327],{"class":326},"sScJk"," insertionSort",[70,329,330],{"class":87},"(",[70,332,334],{"class":333},"s4XuR","array",[70,336,337],{"class":87},") {\n",[70,339,341,344,347,349,351,354],{"class":72,"line":340},2,[70,342,343],{"class":76},"  const",[70,345,346],{"class":80}," result",[70,348,84],{"class":76},[70,350,88],{"class":87},[70,352,353],{"class":76},"...",[70,355,356],{"class":87},"array];\n",[70,358,360],{"class":72,"line":359},3,[70,361,363],{"emptyLinePlaceholder":362},true,"\n",[70,365,367,370,373,376,379,382,385,388,391,394,397,400,403],{"class":72,"line":366},4,[70,368,369],{"class":76},"  for",[70,371,372],{"class":87}," (",[70,374,375],{"class":76},"let",[70,377,378],{"class":87}," i ",[70,380,381],{"class":76},"=",[70,383,384],{"class":80}," 1",[70,386,387],{"class":87},"; i ",[70,389,390],{"class":76},"\u003C",[70,392,393],{"class":87}," result.",[70,395,396],{"class":80},"length",[70,398,399],{"class":87},"; i",[70,401,402],{"class":76},"++",[70,404,337],{"class":87},[70,406,408,411,414,416],{"class":72,"line":407},5,[70,409,410],{"class":76},"    const",[70,412,413],{"class":80}," current",[70,415,84],{"class":76},[70,417,418],{"class":87}," result[i];\n",[70,420,422,425,428,430,432,435,437],{"class":72,"line":421},6,[70,423,424],{"class":76},"    let",[70,426,427],{"class":87}," j ",[70,429,381],{"class":76},[70,431,378],{"class":87},[70,433,434],{"class":76},"-",[70,436,384],{"class":80},[70,438,439],{"class":87},";\n",[70,441,443],{"class":72,"line":442},7,[70,444,363],{"emptyLinePlaceholder":362},[70,446,448,451,454,457,460,463,466,469],{"class":72,"line":447},8,[70,449,450],{"class":76},"    while",[70,452,453],{"class":87}," (j ",[70,455,456],{"class":76},">=",[70,458,459],{"class":80}," 0",[70,461,462],{"class":76}," &&",[70,464,465],{"class":87}," result[j] ",[70,467,468],{"class":76},">",[70,470,471],{"class":87}," current) {\n",[70,473,475,478,481,483,486,488],{"class":72,"line":474},9,[70,476,477],{"class":87},"      result[j ",[70,479,480],{"class":76},"+",[70,482,384],{"class":80},[70,484,485],{"class":87},"] ",[70,487,381],{"class":76},[70,489,490],{"class":87}," result[j];\n",[70,492,494,497,500],{"class":72,"line":493},10,[70,495,496],{"class":87},"      j",[70,498,499],{"class":76},"--",[70,501,439],{"class":87},[70,503,505],{"class":72,"line":504},11,[70,506,507],{"class":87},"    }\n",[70,509,511],{"class":72,"line":510},12,[70,512,363],{"emptyLinePlaceholder":362},[70,514,516,519,521,523,525,527],{"class":72,"line":515},13,[70,517,518],{"class":87},"    result[j ",[70,520,480],{"class":76},[70,522,384],{"class":80},[70,524,485],{"class":87},[70,526,381],{"class":76},[70,528,529],{"class":87}," current;\n",[70,531,533],{"class":72,"line":532},14,[70,534,535],{"class":87},"  }\n",[70,537,539],{"class":72,"line":538},15,[70,540,363],{"emptyLinePlaceholder":362},[70,542,544,547],{"class":72,"line":543},16,[70,545,546],{"class":76},"  return",[70,548,549],{"class":87}," result;\n",[70,551,553],{"class":72,"line":552},17,[70,554,555],{"class":87},"}\n",[182,557,559],{"id":558},"explication","Explication",[34,561,562,568,574,577],{},[37,563,564,567],{},[67,565,566],{},"current"," contient l'élément à insérer ;",[37,569,570,573],{},[67,571,572],{},"j"," permet de remonter dans la partie déjà triée ;",[37,575,576],{},"tant que l'élément courant est plus petit, on décale les éléments vers la droite ;",[37,578,579],{},"dès que la bonne position est trouvée, on insère l'élément.",[15,581,583],{"id":582},"_5-exemple-dutilisation","5. Exemple d'utilisation",[60,585,587],{"className":62,"code":586,"language":64,"meta":65,"style":65},"const numbers = [7, 4, 5, 2, 9];\nconsole.log(insertionSort(numbers));\n\u002F\u002F [2, 4, 5, 7, 9]\n",[67,588,589,619,635],{"__ignoreMap":65},[70,590,591,593,595,597,599,601,603,605,607,609,611,613,615,617],{"class":72,"line":73},[70,592,77],{"class":76},[70,594,81],{"class":80},[70,596,84],{"class":76},[70,598,88],{"class":87},[70,600,91],{"class":80},[70,602,94],{"class":87},[70,604,97],{"class":80},[70,606,94],{"class":87},[70,608,102],{"class":80},[70,610,94],{"class":87},[70,612,107],{"class":80},[70,614,94],{"class":87},[70,616,112],{"class":80},[70,618,115],{"class":87},[70,620,621,624,627,629,632],{"class":72,"line":340},[70,622,623],{"class":87},"console.",[70,625,626],{"class":326},"log",[70,628,330],{"class":87},[70,630,631],{"class":326},"insertionSort",[70,633,634],{"class":87},"(numbers));\n",[70,636,637],{"class":72,"line":359},[70,638,640],{"class":639},"sJ8bj","\u002F\u002F [2, 4, 5, 7, 9]\n",[15,642,644],{"id":643},"_6-pourquoi-cet-algorithme-est-intéressant","6. Pourquoi cet algorithme est intéressant",[20,646,647],{},"Le tri par insertion est souvent plus efficace que le tri à bulles sur de petites listes ou sur des listes déjà presque triées.",[20,649,650],{},"Il est aussi plus proche de la manière dont un humain trie parfois des cartes dans sa main.",[15,652,654],{"id":653},"_7-les-cas-limites","7. Les cas limites",[182,656,658],{"id":657},"tableau-vide","Tableau vide",[60,660,662],{"className":62,"code":661,"language":64,"meta":65,"style":65},"insertionSort([]);\n",[67,663,664],{"__ignoreMap":65},[70,665,666,668],{"class":72,"line":73},[70,667,631],{"class":326},[70,669,670],{"class":87},"([]);\n",[20,672,673,674],{},"Résultat : ",[67,675,676],{},"[]",[182,678,680],{"id":679},"un-seul-élément","Un seul élément",[60,682,684],{"className":62,"code":683,"language":64,"meta":65,"style":65},"insertionSort([10]);\n",[67,685,686],{"__ignoreMap":65},[70,687,688,690,693,696],{"class":72,"line":73},[70,689,631],{"class":326},[70,691,692],{"class":87},"([",[70,694,695],{"class":80},"10",[70,697,698],{"class":87},"]);\n",[20,700,673,701],{},[67,702,703],{},"[10]",[182,705,707],{"id":706},"liste-déjà-triée","Liste déjà triée",[60,709,711],{"className":62,"code":710,"language":64,"meta":65,"style":65},"insertionSort([1, 2, 3, 4]);\n",[67,712,713],{"__ignoreMap":65},[70,714,715,717,719,722,724,726,728,731,733,735],{"class":72,"line":73},[70,716,631],{"class":326},[70,718,692],{"class":87},[70,720,721],{"class":80},"1",[70,723,94],{"class":87},[70,725,107],{"class":80},[70,727,94],{"class":87},[70,729,730],{"class":80},"3",[70,732,94],{"class":87},[70,734,97],{"class":80},[70,736,698],{"class":87},[20,738,673,739],{},[67,740,741],{},"[1, 2, 3, 4]",[15,743,745],{"id":744},"_8-différence-avec-le-tri-à-bulles","8. Différence avec le tri à bulles",[182,747,749],{"id":748},"tri-à-bulles","Tri à bulles",[20,751,752],{},"Il compare des éléments voisins et les échange plusieurs fois.",[182,754,756],{"id":755},"tri-par-insertion","Tri par insertion",[20,758,759],{},"Il construit une partie triée et insère chaque nouvel élément au bon endroit.",[20,761,762],{},"Le tri par insertion est souvent plus naturel à comprendre.",[15,764,766],{"id":765},"_9-erreurs-fréquentes","9. Erreurs fréquentes",[182,768,770],{"id":769},"oublier-de-copier-le-tableau","Oublier de copier le tableau",[20,772,773],{},"Comme pour les autres algorithmes, évitez de modifier directement la donnée d'origine si vous voulez garder une fonction propre.",[182,775,777,778],{"id":776},"mal-gérer-j","Mal gérer ",[67,779,572],{},[20,781,782,783,786,787,789],{},"Le ",[67,784,785],{},"while"," doit s'arrêter quand ",[67,788,572],{}," devient négatif.",[182,791,793],{"id":792},"oublier-la-réinsertion","Oublier la réinsertion",[20,795,796,797,799],{},"À la fin du décalage, il faut bien replacer ",[67,798,566],{}," à la bonne position.",[15,801,803],{"id":802},"_10-résumé","10. Résumé",[20,805,806],{},"Le tri par insertion est un algorithme simple, efficace sur les petites listes et très utile pour apprendre la logique du tri.",[20,808,809],{},"À retenir :",[34,811,812,815,818,821],{},[37,813,814],{},"on construit progressivement une partie triée ;",[37,816,817],{},"on insère chaque élément à sa place ;",[37,819,820],{},"il est souvent plus naturel que le tri à bulles ;",[37,822,823],{},"il est très utile pour comprendre les bases du tri.",[15,825,827],{"id":826},"exercices","Exercices",[182,829,831],{"id":830},"exercice-1","Exercice 1",[20,833,834],{},"Implémentez le tri par insertion en JavaScript.",[182,836,838],{"id":837},"exercice-2","Exercice 2",[20,840,841,842,845],{},"Ajoutez des ",[67,843,844],{},"console.log"," pour afficher l'état du tableau à chaque insertion.",[182,847,849],{"id":848},"exercice-3","Exercice 3",[20,851,852],{},"Modifiez l'algorithme pour trier dans l'ordre décroissant.",[182,854,856],{"id":855},"exercice-4","Exercice 4",[20,858,859],{},"Testez votre fonction avec une liste déjà triée.",[15,861,863],{"id":862},"corrigés","Corrigés",[182,865,867],{"id":866},"correction-exercice-1","Correction exercice 1",[60,869,870],{"className":62,"code":316,"language":64,"meta":65,"style":65},[67,871,872,884,898,902,930,940,956,960,978,992,1000,1004,1008,1022,1026,1030,1036],{"__ignoreMap":65},[70,873,874,876,878,880,882],{"class":72,"line":73},[70,875,323],{"class":76},[70,877,327],{"class":326},[70,879,330],{"class":87},[70,881,334],{"class":333},[70,883,337],{"class":87},[70,885,886,888,890,892,894,896],{"class":72,"line":340},[70,887,343],{"class":76},[70,889,346],{"class":80},[70,891,84],{"class":76},[70,893,88],{"class":87},[70,895,353],{"class":76},[70,897,356],{"class":87},[70,899,900],{"class":72,"line":359},[70,901,363],{"emptyLinePlaceholder":362},[70,903,904,906,908,910,912,914,916,918,920,922,924,926,928],{"class":72,"line":366},[70,905,369],{"class":76},[70,907,372],{"class":87},[70,909,375],{"class":76},[70,911,378],{"class":87},[70,913,381],{"class":76},[70,915,384],{"class":80},[70,917,387],{"class":87},[70,919,390],{"class":76},[70,921,393],{"class":87},[70,923,396],{"class":80},[70,925,399],{"class":87},[70,927,402],{"class":76},[70,929,337],{"class":87},[70,931,932,934,936,938],{"class":72,"line":407},[70,933,410],{"class":76},[70,935,413],{"class":80},[70,937,84],{"class":76},[70,939,418],{"class":87},[70,941,942,944,946,948,950,952,954],{"class":72,"line":421},[70,943,424],{"class":76},[70,945,427],{"class":87},[70,947,381],{"class":76},[70,949,378],{"class":87},[70,951,434],{"class":76},[70,953,384],{"class":80},[70,955,439],{"class":87},[70,957,958],{"class":72,"line":442},[70,959,363],{"emptyLinePlaceholder":362},[70,961,962,964,966,968,970,972,974,976],{"class":72,"line":447},[70,963,450],{"class":76},[70,965,453],{"class":87},[70,967,456],{"class":76},[70,969,459],{"class":80},[70,971,462],{"class":76},[70,973,465],{"class":87},[70,975,468],{"class":76},[70,977,471],{"class":87},[70,979,980,982,984,986,988,990],{"class":72,"line":474},[70,981,477],{"class":87},[70,983,480],{"class":76},[70,985,384],{"class":80},[70,987,485],{"class":87},[70,989,381],{"class":76},[70,991,490],{"class":87},[70,993,994,996,998],{"class":72,"line":493},[70,995,496],{"class":87},[70,997,499],{"class":76},[70,999,439],{"class":87},[70,1001,1002],{"class":72,"line":504},[70,1003,507],{"class":87},[70,1005,1006],{"class":72,"line":510},[70,1007,363],{"emptyLinePlaceholder":362},[70,1009,1010,1012,1014,1016,1018,1020],{"class":72,"line":515},[70,1011,518],{"class":87},[70,1013,480],{"class":76},[70,1015,384],{"class":80},[70,1017,485],{"class":87},[70,1019,381],{"class":76},[70,1021,529],{"class":87},[70,1023,1024],{"class":72,"line":532},[70,1025,535],{"class":87},[70,1027,1028],{"class":72,"line":538},[70,1029,363],{"emptyLinePlaceholder":362},[70,1031,1032,1034],{"class":72,"line":543},[70,1033,546],{"class":76},[70,1035,549],{"class":87},[70,1037,1038],{"class":72,"line":552},[70,1039,555],{"class":87},[182,1041,1043],{"id":1042},"correction-exercice-3","Correction 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