[{"data":1,"prerenderedAt":8451},["ShallowReactive",2],{"dsa-sorteren":3,"dsa-nav-sorteren":4110},{"id":4,"title":5,"body":6,"description":4101,"extension":4102,"icon":4103,"meta":4104,"navigation":3209,"order":303,"path":4105,"seo":4106,"stem":4107,"topic":4108,"__hash__":4109},"practicelyDsa\u002Fpracticely-dsa\u002Fsorteren.md","Sorteeralgoritmes uitgelegd: van insertion sort tot quicksort",{"type":7,"value":8,"toc":4089},"minimark",[9,18,32,37,40,143,149,152,157,257,263,702,720,723,728,848,869,1308,1318,1321,1326,1405,1433,1440,1815,1819,1839,1978,1985,2748,2766,2770,2786,2794,2803,2813,2996,3011,3739,3759,3763,3766,3793,3796,3944,3958,3962,4030,4034,4085],[10,11,12,13,17],"p",{},"Sorteren is het bekendste probleem uit de informatica: zet een rij getallen van klein naar groot. Je\ngebruikt in de praktijk bijna altijd de ingebouwde ",[14,15,16],"code",{},"sort()",", maar op het tentamen moet je laten zien\ndat je snapt wat er onder de motorkap gebeurt. De klassieke vraag is: \"hoe ziet de array eruit na\nronde 2?\" En in sollicitatiegesprekken is \"waarom is quicksort in het slechtste geval kwadratisch?\"\neen vaste kandidaat.",[10,19,20,21,25,26,31],{},"Op deze pagina behandelen we vijf algoritmes. Bij elk staat een uitgewerkt voorbeeld met de toestand\n",[22,23,24],"strong",{},"na elke ronde",", precies zoals de oefeningen eronder het vragen. Ken je Big-O nog niet goed, lees\ndan eerst ",[27,28,30],"a",{"href":29},"\u002Fpracticely\u002Fdsa\u002Fcomplexiteit","complexiteit",".",[33,34,36],"h2",{"id":35},"wat-betekent-na-ronde-k","Wat betekent \"na ronde k\"?",[10,38,39],{},"Een traceervraag heeft alleen één goed antwoord als iedereen dezelfde variant bedoelt. Op Practicely\ngelden deze afspraken (rondes tellen vanaf 1, arrays zijn 0-geïndexeerd):",[41,42,43,59],"table",{},[44,45,46],"thead",{},[47,48,49,53,56],"tr",{},[50,51,52],"th",{},"Algoritme",[50,54,55],{},"Eén ronde",[50,57,58],{},"Toestand na ronde k",[60,61,62,80,107,124],"tbody",{},[47,63,64,68,74],{},[65,66,67],"td",{},"Insertion sort",[65,69,70,73],{},[14,71,72],{},"a[k]"," wordt ingevoegd in het gesorteerde deel links ervan",[65,75,76,79],{},[14,77,78],{},"a[0..k]"," gesorteerd, de rest onveranderd",[47,81,82,85,100],{},[65,83,84],{},"Selection sort",[65,86,87,88,91,92,95,96,99],{},"zoek het minimum in ",[14,89,90],{},"a[k-1..n-1]"," en ",[22,93,94],{},"wissel"," het met ",[14,97,98],{},"a[k-1]",", ook als dat hetzelfde element is",[65,101,102,103,106],{},"de ",[14,104,105],{},"k"," kleinste staan gesorteerd vooraan",[47,108,109,112,119],{},[65,110,111],{},"Bubble sort",[65,113,114,115,118],{},"één volledige doorloop van links naar rechts, wissel buren als ",[14,116,117],{},"a[j] > a[j+1]",", geen vroegtijdige stop",[65,120,102,121,123],{},[14,122,105],{}," grootste staan gesorteerd achteraan",[47,125,126,129,136],{},[65,127,128],{},"Quicksort",[65,130,131,132,135],{},"Lomuto-partitie met het ",[22,133,134],{},"laatste"," element als pivot",[65,137,138,139,142],{},"de vraag gaat over de array na de ",[22,140,141],{},"eerste"," partitie",[10,144,145,146,31],{},"In alle voorbeelden hieronder sorteren we dezelfde array: ",[14,147,148],{},"[5, 2, 4, 6, 1, 3]",[33,150,67],{"id":151},"insertion-sort",[10,153,154,156],{},[22,155,67],{}," (invoegend sorteren) werkt zoals je kaarten in je hand sorteert: je pakt de\nvolgende kaart en schuift hem naar links tot hij op zijn plek zit. Het deel links van de huidige\npositie is steeds al gesorteerd.",[41,158,159,172],{},[44,160,161],{},[47,162,163,166,169],{},[50,164,165],{},"Ronde",[50,167,168],{},"Ingevoegd element",[50,170,171],{},"Array na de ronde",[60,173,174,187,202,216,230,243],{},[47,175,176,179,182],{},[65,177,178],{},"start",[65,180,181],{},"–",[65,183,184],{},[14,185,186],{},"5, 2, 4, 6, 1, 3",[47,188,189,192,197],{},[65,190,191],{},"1",[65,193,194],{},[14,195,196],{},"2",[65,198,199],{},[14,200,201],{},"2, 5, 4, 6, 1, 3",[47,203,204,206,211],{},[65,205,196],{},[65,207,208],{},[14,209,210],{},"4",[65,212,213],{},[14,214,215],{},"2, 4, 5, 6, 1, 3",[47,217,218,221,226],{},[65,219,220],{},"3",[65,222,223],{},[14,224,225],{},"6",[65,227,228],{},[14,229,215],{},[47,231,232,234,238],{},[65,233,210],{},[65,235,236],{},[14,237,191],{},[65,239,240],{},[14,241,242],{},"1, 2, 4, 5, 6, 3",[47,244,245,248,252],{},[65,246,247],{},"5",[65,249,250],{},[14,251,220],{},[65,253,254],{},[14,255,256],{},"1, 2, 3, 4, 5, 6",[10,258,259,260,262],{},"Let op ronde 3: ",[14,261,225],{}," is groter dan alles links ervan, dus er verandert niets. Dat telt wél als ronde.",[264,265,266,481],"code-tabs",{},[267,268,270],"template",{"v-slot:python":269},"",[271,272,276],"pre",{"className":273,"code":274,"language":275,"meta":269,"style":269},"language-python shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","def insertion_sort(a):\n    for k in range(1, len(a)):\n        x = a[k]\n        j = k - 1\n        # schuif grotere elementen één plek naar rechts\n        while j >= 0 and a[j] > x:\n            a[j + 1] = a[j]\n            j -= 1\n        a[j + 1] = x  # na ronde k is a[0..k] gesorteerd\n","python",[14,277,278,301,336,356,372,379,416,446,457],{"__ignoreMap":269},[279,280,283,287,291,295,298],"span",{"class":281,"line":282},"line",1,[279,284,286],{"class":285},"spNyl","def",[279,288,290],{"class":289},"s2Zo4"," insertion_sort",[279,292,294],{"class":293},"sMK4o","(",[279,296,27],{"class":297},"sHdIc",[279,299,300],{"class":293},"):\n",[279,302,304,308,312,315,318,320,323,326,329,331,333],{"class":281,"line":303},2,[279,305,307],{"class":306},"s7zQu","    for",[279,309,311],{"class":310},"sTEyZ"," k ",[279,313,314],{"class":306},"in",[279,316,317],{"class":289}," range",[279,319,294],{"class":293},[279,321,191],{"class":322},"sbssI",[279,324,325],{"class":293},",",[279,327,328],{"class":289}," len",[279,330,294],{"class":293},[279,332,27],{"class":289},[279,334,335],{"class":293},")):\n",[279,337,339,342,345,348,351,353],{"class":281,"line":338},3,[279,340,341],{"class":310},"        x ",[279,343,344],{"class":293},"=",[279,346,347],{"class":310}," a",[279,349,350],{"class":293},"[",[279,352,105],{"class":310},[279,354,355],{"class":293},"]\n",[279,357,359,362,364,366,369],{"class":281,"line":358},4,[279,360,361],{"class":310},"        j ",[279,363,344],{"class":293},[279,365,311],{"class":310},[279,367,368],{"class":293},"-",[279,370,371],{"class":322}," 1\n",[279,373,375],{"class":281,"line":374},5,[279,376,378],{"class":377},"sHwdD","        # schuif grotere elementen één plek naar rechts\n",[279,380,382,385,388,391,394,397,399,401,404,407,410,413],{"class":281,"line":381},6,[279,383,384],{"class":306},"        while",[279,386,387],{"class":310}," j ",[279,389,390],{"class":293},">=",[279,392,393],{"class":322}," 0",[279,395,396],{"class":293}," and",[279,398,347],{"class":310},[279,400,350],{"class":293},[279,402,403],{"class":310},"j",[279,405,406],{"class":293},"]",[279,408,409],{"class":293}," >",[279,411,412],{"class":310}," x",[279,414,415],{"class":293},":\n",[279,417,419,422,424,427,430,433,435,438,440,442,444],{"class":281,"line":418},7,[279,420,421],{"class":310},"            a",[279,423,350],{"class":293},[279,425,426],{"class":310},"j ",[279,428,429],{"class":293},"+",[279,431,432],{"class":322}," 1",[279,434,406],{"class":293},[279,436,437],{"class":293}," =",[279,439,347],{"class":310},[279,441,350],{"class":293},[279,443,403],{"class":310},[279,445,355],{"class":293},[279,447,449,452,455],{"class":281,"line":448},8,[279,450,451],{"class":310},"            j ",[279,453,454],{"class":293},"-=",[279,456,371],{"class":322},[279,458,460,463,465,467,469,471,473,475,478],{"class":281,"line":459},9,[279,461,462],{"class":310},"        a",[279,464,350],{"class":293},[279,466,426],{"class":310},[279,468,429],{"class":293},[279,470,432],{"class":322},[279,472,406],{"class":293},[279,474,437],{"class":293},[279,476,477],{"class":310}," x  ",[279,479,480],{"class":377},"# na ronde k is a[0..k] gesorteerd\n",[267,482,483],{"v-slot:java":269},[271,484,488],{"className":485,"code":486,"language":487,"meta":269,"style":269},"language-java shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","static void insertionSort(int[] a) {\n    for (int k = 1; k \u003C a.length; k++) {\n        int x = a[k];\n        int j = k - 1;\n        \u002F\u002F schuif grotere elementen één plek naar rechts\n        while (j >= 0 && a[j] > x) {\n            a[j + 1] = a[j];\n            j--;\n        }\n        a[j + 1] = x; \u002F\u002F na ronde k is a[0..k] gesorteerd\n    }\n}\n","java",[14,489,490,517,557,576,593,598,629,653,661,666,690,696],{"__ignoreMap":269},[279,491,492,495,498,501,503,506,509,511,514],{"class":281,"line":282},[279,493,494],{"class":285},"static",[279,496,497],{"class":285}," void",[279,499,500],{"class":289}," insertionSort",[279,502,294],{"class":293},[279,504,505],{"class":285},"int",[279,507,508],{"class":293},"[]",[279,510,347],{"class":310},[279,512,513],{"class":293},")",[279,515,516],{"class":293}," {\n",[279,518,519,521,524,526,528,530,532,535,537,540,542,544,547,549,552,555],{"class":281,"line":303},[279,520,307],{"class":306},[279,522,523],{"class":293}," (",[279,525,505],{"class":285},[279,527,311],{"class":310},[279,529,344],{"class":293},[279,531,432],{"class":322},[279,533,534],{"class":293},";",[279,536,311],{"class":310},[279,538,539],{"class":293},"\u003C",[279,541,347],{"class":310},[279,543,31],{"class":293},[279,545,546],{"class":310},"length",[279,548,534],{"class":293},[279,550,551],{"class":310}," k",[279,553,554],{"class":293},"++)",[279,556,516],{"class":293},[279,558,559,562,565,567,569,571,573],{"class":281,"line":338},[279,560,561],{"class":285},"        int",[279,563,564],{"class":310}," x ",[279,566,344],{"class":293},[279,568,347],{"class":310},[279,570,350],{"class":293},[279,572,105],{"class":310},[279,574,575],{"class":293},"];\n",[279,577,578,580,582,584,586,588,590],{"class":281,"line":358},[279,579,561],{"class":285},[279,581,387],{"class":310},[279,583,344],{"class":293},[279,585,311],{"class":310},[279,587,368],{"class":293},[279,589,432],{"class":322},[279,591,592],{"class":293},";\n",[279,594,595],{"class":281,"line":374},[279,596,597],{"class":377},"        \u002F\u002F schuif grotere elementen één plek naar rechts\n",[279,599,600,602,604,606,608,610,613,615,617,619,621,623,625,627],{"class":281,"line":381},[279,601,384],{"class":306},[279,603,523],{"class":293},[279,605,426],{"class":310},[279,607,390],{"class":293},[279,609,393],{"class":322},[279,611,612],{"class":293}," &&",[279,614,347],{"class":310},[279,616,350],{"class":293},[279,618,403],{"class":310},[279,620,406],{"class":293},[279,622,409],{"class":293},[279,624,412],{"class":310},[279,626,513],{"class":293},[279,628,516],{"class":293},[279,630,631,633,635,637,639,641,643,645,647,649,651],{"class":281,"line":418},[279,632,421],{"class":310},[279,634,350],{"class":293},[279,636,426],{"class":310},[279,638,429],{"class":293},[279,640,432],{"class":322},[279,642,406],{"class":293},[279,644,437],{"class":293},[279,646,347],{"class":310},[279,648,350],{"class":293},[279,650,403],{"class":310},[279,652,575],{"class":293},[279,654,655,658],{"class":281,"line":448},[279,656,657],{"class":310},"            j",[279,659,660],{"class":293},"--;\n",[279,662,663],{"class":281,"line":459},[279,664,665],{"class":293},"        }\n",[279,667,669,671,673,675,677,679,681,683,685,687],{"class":281,"line":668},10,[279,670,462],{"class":310},[279,672,350],{"class":293},[279,674,426],{"class":310},[279,676,429],{"class":293},[279,678,432],{"class":322},[279,680,406],{"class":293},[279,682,437],{"class":293},[279,684,412],{"class":310},[279,686,534],{"class":293},[279,688,689],{"class":377}," \u002F\u002F na ronde k is a[0..k] gesorteerd\n",[279,691,693],{"class":281,"line":692},11,[279,694,695],{"class":293},"    }\n",[279,697,699],{"class":281,"line":698},12,[279,700,701],{"class":293},"}\n",[10,703,704,705,708,709,712,713,716,717,31],{},"Omdat de ",[14,706,707],{},"while"," stopt zodra ",[14,710,711],{},"a[j] > x"," niet meer geldt, schuiven gelijke elementen nooit langs\nelkaar. Daardoor is insertion sort ",[22,714,715],{},"stabiel",". Op een al gesorteerde array doet de binnenlus niets:\ndan is het ",[14,718,719],{},"O(n)",[33,721,84],{"id":722},"selection-sort",[10,724,725,727],{},[22,726,84],{}," (selecterend sorteren) zoekt in elke ronde het kleinste element van het\nongesorteerde deel en wisselt het naar voren.",[41,729,730,744],{},[44,731,732],{},[47,733,734,736,739,742],{},[50,735,165],{},[50,737,738],{},"Zoekgebied",[50,740,741],{},"Minimum (index)",[50,743,171],{},[60,745,746,758,777,795,814,831],{},[47,747,748,750,752,754],{},[65,749,178],{},[65,751,181],{},[65,753,181],{},[65,755,756],{},[14,757,186],{},[47,759,760,762,767,772],{},[65,761,191],{},[65,763,764],{},[14,765,766],{},"a[0..5]",[65,768,769,771],{},[14,770,191],{}," (4)",[65,773,774],{},[14,775,776],{},"1, 2, 4, 6, 5, 3",[47,778,779,781,786,791],{},[65,780,196],{},[65,782,783],{},[14,784,785],{},"a[1..5]",[65,787,788,790],{},[14,789,196],{}," (1)",[65,792,793],{},[14,794,776],{},[47,796,797,799,804,809],{},[65,798,220],{},[65,800,801],{},[14,802,803],{},"a[2..5]",[65,805,806,808],{},[14,807,220],{}," (5)",[65,810,811],{},[14,812,813],{},"1, 2, 3, 6, 5, 4",[47,815,816,818,823,827],{},[65,817,210],{},[65,819,820],{},[14,821,822],{},"a[3..5]",[65,824,825,808],{},[14,826,210],{},[65,828,829],{},[14,830,256],{},[47,832,833,835,840,844],{},[65,834,247],{},[65,836,837],{},[14,838,839],{},"a[4..5]",[65,841,842,771],{},[14,843,247],{},[65,845,846],{},[14,847,256],{},[10,849,850,851,854,855,858,859,861,862,865,866,31],{},"In ronde 2 staat het minimum al op zijn plek; de \"wissel\" van ",[14,852,853],{},"a[1]"," met zichzelf verandert niets.\nIn ronde 1 zie je ook waarom selection sort ",[22,856,857],{},"niet stabiel"," is: de ",[14,860,247],{}," springt in één keer van\nvoren naar index 4, over andere elementen heen. Bij gelijke waarden kan zo'n sprong hun volgorde\nomdraaien: ",[14,863,864],{},"[3a, 3b, 1]"," wordt na ronde 1 ",[14,867,868],{},"[1, 3b, 3a]",[264,870,871,1054],{},[267,872,873],{"v-slot:python":269},[271,874,876],{"className":273,"code":875,"language":275,"meta":269,"style":269},"def selection_sort(a):\n    n = len(a)\n    for k in range(1, n):\n        # zoek het minimum in a[k-1..n-1]\n        m = k - 1\n        for j in range(k, n):\n            if a[j] \u003C a[m]:\n                m = j\n        # wissel altijd, ook als m == k-1\n        a[k - 1], a[m] = a[m], a[k - 1]\n",[14,877,878,891,907,928,933,946,967,993,1003,1008],{"__ignoreMap":269},[279,879,880,882,885,887,889],{"class":281,"line":282},[279,881,286],{"class":285},[279,883,884],{"class":289}," selection_sort",[279,886,294],{"class":293},[279,888,27],{"class":297},[279,890,300],{"class":293},[279,892,893,896,898,900,902,904],{"class":281,"line":303},[279,894,895],{"class":310},"    n ",[279,897,344],{"class":293},[279,899,328],{"class":289},[279,901,294],{"class":293},[279,903,27],{"class":289},[279,905,906],{"class":293},")\n",[279,908,909,911,913,915,917,919,921,923,926],{"class":281,"line":338},[279,910,307],{"class":306},[279,912,311],{"class":310},[279,914,314],{"class":306},[279,916,317],{"class":289},[279,918,294],{"class":293},[279,920,191],{"class":322},[279,922,325],{"class":293},[279,924,925],{"class":289}," n",[279,927,300],{"class":293},[279,929,930],{"class":281,"line":358},[279,931,932],{"class":377},"        # zoek het minimum in a[k-1..n-1]\n",[279,934,935,938,940,942,944],{"class":281,"line":374},[279,936,937],{"class":310},"        m ",[279,939,344],{"class":293},[279,941,311],{"class":310},[279,943,368],{"class":293},[279,945,371],{"class":322},[279,947,948,951,953,955,957,959,961,963,965],{"class":281,"line":381},[279,949,950],{"class":306},"        for",[279,952,387],{"class":310},[279,954,314],{"class":306},[279,956,317],{"class":289},[279,958,294],{"class":293},[279,960,105],{"class":289},[279,962,325],{"class":293},[279,964,925],{"class":289},[279,966,300],{"class":293},[279,968,969,972,974,976,978,980,983,985,987,990],{"class":281,"line":418},[279,970,971],{"class":306},"            if",[279,973,347],{"class":310},[279,975,350],{"class":293},[279,977,403],{"class":310},[279,979,406],{"class":293},[279,981,982],{"class":293}," \u003C",[279,984,347],{"class":310},[279,986,350],{"class":293},[279,988,989],{"class":310},"m",[279,991,992],{"class":293},"]:\n",[279,994,995,998,1000],{"class":281,"line":448},[279,996,997],{"class":310},"                m ",[279,999,344],{"class":293},[279,1001,1002],{"class":310}," j\n",[279,1004,1005],{"class":281,"line":459},[279,1006,1007],{"class":377},"        # wissel altijd, ook als m == k-1\n",[279,1009,1010,1012,1014,1017,1019,1021,1024,1026,1028,1030,1032,1034,1036,1038,1040,1042,1044,1046,1048,1050,1052],{"class":281,"line":668},[279,1011,462],{"class":310},[279,1013,350],{"class":293},[279,1015,1016],{"class":310},"k ",[279,1018,368],{"class":293},[279,1020,432],{"class":322},[279,1022,1023],{"class":293},"],",[279,1025,347],{"class":310},[279,1027,350],{"class":293},[279,1029,989],{"class":310},[279,1031,406],{"class":293},[279,1033,437],{"class":293},[279,1035,347],{"class":310},[279,1037,350],{"class":293},[279,1039,989],{"class":310},[279,1041,1023],{"class":293},[279,1043,347],{"class":310},[279,1045,350],{"class":293},[279,1047,1016],{"class":310},[279,1049,368],{"class":293},[279,1051,432],{"class":322},[279,1053,355],{"class":293},[267,1055,1056],{"v-slot:java":269},[271,1057,1059],{"className":485,"code":1058,"language":487,"meta":269,"style":269},"static void selectionSort(int[] a) {\n    int n = a.length;\n    for (int k = 1; k \u003C n; k++) {\n        \u002F\u002F zoek het minimum in a[k-1..n-1]\n        int m = k - 1;\n        for (int j = k; j \u003C n; j++) {\n            if (a[j] \u003C a[m]) {\n                m = j;\n            }\n        }\n        \u002F\u002F wissel altijd, ook als m == k-1\n        int tmp = a[k - 1];\n        a[k - 1] = a[m];\n        a[m] = tmp;\n    }\n}\n",[14,1060,1061,1082,1100,1130,1135,1152,1183,1210,1220,1225,1229,1234,1255,1280,1298,1303],{"__ignoreMap":269},[279,1062,1063,1065,1067,1070,1072,1074,1076,1078,1080],{"class":281,"line":282},[279,1064,494],{"class":285},[279,1066,497],{"class":285},[279,1068,1069],{"class":289}," selectionSort",[279,1071,294],{"class":293},[279,1073,505],{"class":285},[279,1075,508],{"class":293},[279,1077,347],{"class":310},[279,1079,513],{"class":293},[279,1081,516],{"class":293},[279,1083,1084,1087,1090,1092,1094,1096,1098],{"class":281,"line":303},[279,1085,1086],{"class":285},"    int",[279,1088,1089],{"class":310}," n ",[279,1091,344],{"class":293},[279,1093,347],{"class":310},[279,1095,31],{"class":293},[279,1097,546],{"class":310},[279,1099,592],{"class":293},[279,1101,1102,1104,1106,1108,1110,1112,1114,1116,1118,1120,1122,1124,1126,1128],{"class":281,"line":338},[279,1103,307],{"class":306},[279,1105,523],{"class":293},[279,1107,505],{"class":285},[279,1109,311],{"class":310},[279,1111,344],{"class":293},[279,1113,432],{"class":322},[279,1115,534],{"class":293},[279,1117,311],{"class":310},[279,1119,539],{"class":293},[279,1121,925],{"class":310},[279,1123,534],{"class":293},[279,1125,551],{"class":310},[279,1127,554],{"class":293},[279,1129,516],{"class":293},[279,1131,1132],{"class":281,"line":358},[279,1133,1134],{"class":377},"        \u002F\u002F zoek het minimum in a[k-1..n-1]\n",[279,1136,1137,1139,1142,1144,1146,1148,1150],{"class":281,"line":374},[279,1138,561],{"class":285},[279,1140,1141],{"class":310}," m ",[279,1143,344],{"class":293},[279,1145,311],{"class":310},[279,1147,368],{"class":293},[279,1149,432],{"class":322},[279,1151,592],{"class":293},[279,1153,1154,1156,1158,1160,1162,1164,1166,1168,1170,1172,1174,1176,1179,1181],{"class":281,"line":381},[279,1155,950],{"class":306},[279,1157,523],{"class":293},[279,1159,505],{"class":285},[279,1161,387],{"class":310},[279,1163,344],{"class":293},[279,1165,551],{"class":310},[279,1167,534],{"class":293},[279,1169,387],{"class":310},[279,1171,539],{"class":293},[279,1173,925],{"class":310},[279,1175,534],{"class":293},[279,1177,1178],{"class":310}," j",[279,1180,554],{"class":293},[279,1182,516],{"class":293},[279,1184,1185,1187,1189,1191,1193,1195,1197,1199,1201,1203,1205,1208],{"class":281,"line":418},[279,1186,971],{"class":306},[279,1188,523],{"class":293},[279,1190,27],{"class":310},[279,1192,350],{"class":293},[279,1194,403],{"class":310},[279,1196,406],{"class":293},[279,1198,982],{"class":293},[279,1200,347],{"class":310},[279,1202,350],{"class":293},[279,1204,989],{"class":310},[279,1206,1207],{"class":293},"])",[279,1209,516],{"class":293},[279,1211,1212,1214,1216,1218],{"class":281,"line":448},[279,1213,997],{"class":310},[279,1215,344],{"class":293},[279,1217,1178],{"class":310},[279,1219,592],{"class":293},[279,1221,1222],{"class":281,"line":459},[279,1223,1224],{"class":293},"            }\n",[279,1226,1227],{"class":281,"line":668},[279,1228,665],{"class":293},[279,1230,1231],{"class":281,"line":692},[279,1232,1233],{"class":377},"        \u002F\u002F wissel altijd, ook als m == k-1\n",[279,1235,1236,1238,1241,1243,1245,1247,1249,1251,1253],{"class":281,"line":698},[279,1237,561],{"class":285},[279,1239,1240],{"class":310}," tmp ",[279,1242,344],{"class":293},[279,1244,347],{"class":310},[279,1246,350],{"class":293},[279,1248,1016],{"class":310},[279,1250,368],{"class":293},[279,1252,432],{"class":322},[279,1254,575],{"class":293},[279,1256,1258,1260,1262,1264,1266,1268,1270,1272,1274,1276,1278],{"class":281,"line":1257},13,[279,1259,462],{"class":310},[279,1261,350],{"class":293},[279,1263,1016],{"class":310},[279,1265,368],{"class":293},[279,1267,432],{"class":322},[279,1269,406],{"class":293},[279,1271,437],{"class":293},[279,1273,347],{"class":310},[279,1275,350],{"class":293},[279,1277,989],{"class":310},[279,1279,575],{"class":293},[279,1281,1283,1285,1287,1289,1291,1293,1296],{"class":281,"line":1282},14,[279,1284,462],{"class":310},[279,1286,350],{"class":293},[279,1288,989],{"class":310},[279,1290,406],{"class":293},[279,1292,437],{"class":293},[279,1294,1295],{"class":310}," tmp",[279,1297,592],{"class":293},[279,1299,1301],{"class":281,"line":1300},15,[279,1302,695],{"class":293},[279,1304,1306],{"class":281,"line":1305},16,[279,1307,701],{"class":293},[10,1309,1310,1311,1314,1315,31],{},"Selection sort doet altijd evenveel vergelijkingen, ongeacht de invoer: ",[14,1312,1313],{},"n(n-1)\u002F2",". Ook een al\ngesorteerde array kost dus ",[14,1316,1317],{},"O(n²)",[33,1319,111],{"id":1320},"bubble-sort",[10,1322,1323,1325],{},[22,1324,111],{}," loopt van links naar rechts en wisselt twee buren als de linker groter is. Het\ngrootste element \"borrelt\" zo in één doorloop naar het einde.",[41,1327,1328,1339],{},[44,1329,1330],{},[47,1331,1332,1334,1337],{},[50,1333,165],{},[50,1335,1336],{},"Aantal wissels",[50,1338,171],{},[60,1340,1341,1351,1362,1373,1384,1394],{},[47,1342,1343,1345,1347],{},[65,1344,178],{},[65,1346,181],{},[65,1348,1349],{},[14,1350,186],{},[47,1352,1353,1355,1357],{},[65,1354,191],{},[65,1356,210],{},[65,1358,1359],{},[14,1360,1361],{},"2, 4, 5, 1, 3, 6",[47,1363,1364,1366,1368],{},[65,1365,196],{},[65,1367,196],{},[65,1369,1370],{},[14,1371,1372],{},"2, 4, 1, 3, 5, 6",[47,1374,1375,1377,1379],{},[65,1376,220],{},[65,1378,196],{},[65,1380,1381],{},[14,1382,1383],{},"2, 1, 3, 4, 5, 6",[47,1385,1386,1388,1390],{},[65,1387,210],{},[65,1389,191],{},[65,1391,1392],{},[14,1393,256],{},[47,1395,1396,1398,1401],{},[65,1397,247],{},[65,1399,1400],{},"0",[65,1402,1403],{},[14,1404,256],{},[10,1406,1407,1408,1411,1412,1411,1415,1418,1419,1411,1422,1425,1426,1428,1429,1432],{},"Ronde 1 in detail: ",[14,1409,1410],{},"5>2"," wissel, ",[14,1413,1414],{},"5>4",[14,1416,1417],{},"5\u003C6"," niets, ",[14,1420,1421],{},"6>1",[14,1423,1424],{},"6>3"," wissel. Na ronde 1\nstaat ",[14,1427,225],{}," achteraan, na ronde 2 staan ",[14,1430,1431],{},"5, 6"," achteraan, enzovoort.",[10,1434,1435,1436,1439],{},"Na ronde 4 is de array al gesorteerd. Er bestaat een variant die dan stopt (als een ronde geen enkele\nwissel deed), maar volgens onze afspraak loopt bubble sort altijd alle ",[14,1437,1438],{},"n-1"," rondes door.",[264,1441,1442,1595],{},[267,1443,1444],{"v-slot:python":269},[271,1445,1447],{"className":273,"code":1446,"language":275,"meta":269,"style":269},"def bubble_sort(a):\n    n = len(a)\n    for r in range(1, n):\n        # na ronde r staan de r grootste achteraan, die slaan we over\n        for j in range(n - r):\n            if a[j] > a[j + 1]:\n                a[j], a[j + 1] = a[j + 1], a[j]\n",[14,1448,1449,1462,1476,1497,1502,1524,1550],{"__ignoreMap":269},[279,1450,1451,1453,1456,1458,1460],{"class":281,"line":282},[279,1452,286],{"class":285},[279,1454,1455],{"class":289}," bubble_sort",[279,1457,294],{"class":293},[279,1459,27],{"class":297},[279,1461,300],{"class":293},[279,1463,1464,1466,1468,1470,1472,1474],{"class":281,"line":303},[279,1465,895],{"class":310},[279,1467,344],{"class":293},[279,1469,328],{"class":289},[279,1471,294],{"class":293},[279,1473,27],{"class":289},[279,1475,906],{"class":293},[279,1477,1478,1480,1483,1485,1487,1489,1491,1493,1495],{"class":281,"line":338},[279,1479,307],{"class":306},[279,1481,1482],{"class":310}," r ",[279,1484,314],{"class":306},[279,1486,317],{"class":289},[279,1488,294],{"class":293},[279,1490,191],{"class":322},[279,1492,325],{"class":293},[279,1494,925],{"class":289},[279,1496,300],{"class":293},[279,1498,1499],{"class":281,"line":358},[279,1500,1501],{"class":377},"        # na ronde r staan de r grootste achteraan, die slaan we over\n",[279,1503,1504,1506,1508,1510,1512,1514,1517,1519,1522],{"class":281,"line":374},[279,1505,950],{"class":306},[279,1507,387],{"class":310},[279,1509,314],{"class":306},[279,1511,317],{"class":289},[279,1513,294],{"class":293},[279,1515,1516],{"class":289},"n ",[279,1518,368],{"class":293},[279,1520,1521],{"class":289}," r",[279,1523,300],{"class":293},[279,1525,1526,1528,1530,1532,1534,1536,1538,1540,1542,1544,1546,1548],{"class":281,"line":381},[279,1527,971],{"class":306},[279,1529,347],{"class":310},[279,1531,350],{"class":293},[279,1533,403],{"class":310},[279,1535,406],{"class":293},[279,1537,409],{"class":293},[279,1539,347],{"class":310},[279,1541,350],{"class":293},[279,1543,426],{"class":310},[279,1545,429],{"class":293},[279,1547,432],{"class":322},[279,1549,992],{"class":293},[279,1551,1552,1555,1557,1559,1561,1563,1565,1567,1569,1571,1573,1575,1577,1579,1581,1583,1585,1587,1589,1591,1593],{"class":281,"line":418},[279,1553,1554],{"class":310},"                a",[279,1556,350],{"class":293},[279,1558,403],{"class":310},[279,1560,1023],{"class":293},[279,1562,347],{"class":310},[279,1564,350],{"class":293},[279,1566,426],{"class":310},[279,1568,429],{"class":293},[279,1570,432],{"class":322},[279,1572,406],{"class":293},[279,1574,437],{"class":293},[279,1576,347],{"class":310},[279,1578,350],{"class":293},[279,1580,426],{"class":310},[279,1582,429],{"class":293},[279,1584,432],{"class":322},[279,1586,1023],{"class":293},[279,1588,347],{"class":310},[279,1590,350],{"class":293},[279,1592,403],{"class":310},[279,1594,355],{"class":293},[267,1596,1597],{"v-slot:java":269},[271,1598,1600],{"className":485,"code":1599,"language":487,"meta":269,"style":269},"static void bubbleSort(int[] a) {\n    int n = a.length;\n    for (int r = 1; r \u003C n; r++) {\n        \u002F\u002F na ronde r staan de r grootste achteraan, die slaan we over\n        for (int j = 0; j \u003C n - r; j++) {\n            if (a[j] > a[j + 1]) {\n                int tmp = a[j];\n                a[j] = a[j + 1];\n                a[j + 1] = tmp;\n            }\n        }\n    }\n}\n",[14,1601,1602,1623,1639,1669,1674,1708,1738,1755,1779,1799,1803,1807,1811],{"__ignoreMap":269},[279,1603,1604,1606,1608,1611,1613,1615,1617,1619,1621],{"class":281,"line":282},[279,1605,494],{"class":285},[279,1607,497],{"class":285},[279,1609,1610],{"class":289}," bubbleSort",[279,1612,294],{"class":293},[279,1614,505],{"class":285},[279,1616,508],{"class":293},[279,1618,347],{"class":310},[279,1620,513],{"class":293},[279,1622,516],{"class":293},[279,1624,1625,1627,1629,1631,1633,1635,1637],{"class":281,"line":303},[279,1626,1086],{"class":285},[279,1628,1089],{"class":310},[279,1630,344],{"class":293},[279,1632,347],{"class":310},[279,1634,31],{"class":293},[279,1636,546],{"class":310},[279,1638,592],{"class":293},[279,1640,1641,1643,1645,1647,1649,1651,1653,1655,1657,1659,1661,1663,1665,1667],{"class":281,"line":338},[279,1642,307],{"class":306},[279,1644,523],{"class":293},[279,1646,505],{"class":285},[279,1648,1482],{"class":310},[279,1650,344],{"class":293},[279,1652,432],{"class":322},[279,1654,534],{"class":293},[279,1656,1482],{"class":310},[279,1658,539],{"class":293},[279,1660,925],{"class":310},[279,1662,534],{"class":293},[279,1664,1521],{"class":310},[279,1666,554],{"class":293},[279,1668,516],{"class":293},[279,1670,1671],{"class":281,"line":358},[279,1672,1673],{"class":377},"        \u002F\u002F na ronde r staan de r grootste achteraan, die slaan we over\n",[279,1675,1676,1678,1680,1682,1684,1686,1688,1690,1692,1694,1696,1698,1700,1702,1704,1706],{"class":281,"line":374},[279,1677,950],{"class":306},[279,1679,523],{"class":293},[279,1681,505],{"class":285},[279,1683,387],{"class":310},[279,1685,344],{"class":293},[279,1687,393],{"class":322},[279,1689,534],{"class":293},[279,1691,387],{"class":310},[279,1693,539],{"class":293},[279,1695,1089],{"class":310},[279,1697,368],{"class":293},[279,1699,1521],{"class":310},[279,1701,534],{"class":293},[279,1703,1178],{"class":310},[279,1705,554],{"class":293},[279,1707,516],{"class":293},[279,1709,1710,1712,1714,1716,1718,1720,1722,1724,1726,1728,1730,1732,1734,1736],{"class":281,"line":381},[279,1711,971],{"class":306},[279,1713,523],{"class":293},[279,1715,27],{"class":310},[279,1717,350],{"class":293},[279,1719,403],{"class":310},[279,1721,406],{"class":293},[279,1723,409],{"class":293},[279,1725,347],{"class":310},[279,1727,350],{"class":293},[279,1729,426],{"class":310},[279,1731,429],{"class":293},[279,1733,432],{"class":322},[279,1735,1207],{"class":293},[279,1737,516],{"class":293},[279,1739,1740,1743,1745,1747,1749,1751,1753],{"class":281,"line":418},[279,1741,1742],{"class":285},"                int",[279,1744,1240],{"class":310},[279,1746,344],{"class":293},[279,1748,347],{"class":310},[279,1750,350],{"class":293},[279,1752,403],{"class":310},[279,1754,575],{"class":293},[279,1756,1757,1759,1761,1763,1765,1767,1769,1771,1773,1775,1777],{"class":281,"line":448},[279,1758,1554],{"class":310},[279,1760,350],{"class":293},[279,1762,403],{"class":310},[279,1764,406],{"class":293},[279,1766,437],{"class":293},[279,1768,347],{"class":310},[279,1770,350],{"class":293},[279,1772,426],{"class":310},[279,1774,429],{"class":293},[279,1776,432],{"class":322},[279,1778,575],{"class":293},[279,1780,1781,1783,1785,1787,1789,1791,1793,1795,1797],{"class":281,"line":459},[279,1782,1554],{"class":310},[279,1784,350],{"class":293},[279,1786,426],{"class":310},[279,1788,429],{"class":293},[279,1790,432],{"class":322},[279,1792,406],{"class":293},[279,1794,437],{"class":293},[279,1796,1295],{"class":310},[279,1798,592],{"class":293},[279,1800,1801],{"class":281,"line":668},[279,1802,1224],{"class":293},[279,1804,1805],{"class":281,"line":692},[279,1806,665],{"class":293},[279,1808,1809],{"class":281,"line":698},[279,1810,695],{"class":293},[279,1812,1813],{"class":281,"line":1257},[279,1814,701],{"class":293},[33,1816,1818],{"id":1817},"merge-sort","Merge sort",[10,1820,1821,1823,1824,1828,1829,91,1832,1835,1836,31],{},[22,1822,1818],{}," (samenvoegend sorteren) is verdeel-en-heers (",[1825,1826,1827],"em",{},"divide and conquer","): splits de array\nin twee helften, sorteer elke helft recursief en voeg de twee gesorteerde helften samen. We splitsen\nin ",[14,1830,1831],{},"a[0..mid-1]",[14,1833,1834],{},"a[mid..n-1]"," met ",[14,1837,1838],{},"mid = ⌊n\u002F2⌋",[41,1840,1841,1854],{},[44,1842,1843],{},[47,1844,1845,1848,1851],{},[50,1846,1847],{},"Stap",[50,1849,1850],{},"Wat gebeurt er",[50,1852,1853],{},"Resultaat",[60,1855,1856,1874,1890,1903,1920,1935,1947,1963],{},[47,1857,1858,1860,1866],{},[65,1859,191],{},[65,1861,1862,1863,1865],{},"splits ",[14,1864,186],{}," (mid = 3)",[65,1867,1868,91,1871],{},[14,1869,1870],{},"5, 2, 4",[14,1872,1873],{},"6, 1, 3",[47,1875,1876,1878,1883],{},[65,1877,196],{},[65,1879,1862,1880,1882],{},[14,1881,1870],{}," (mid = 1)",[65,1884,1885,91,1887],{},[14,1886,247],{},[14,1888,1889],{},"2, 4",[47,1891,1892,1894,1899],{},[65,1893,220],{},[65,1895,1862,1896,1898],{},[14,1897,1889],{},", voeg samen",[65,1900,1901],{},[14,1902,1889],{},[47,1904,1905,1907,1915],{},[65,1906,210],{},[65,1908,1909,1910,91,1912,1914],{},"voeg ",[14,1911,247],{},[14,1913,1889],{}," samen",[65,1916,1917],{},[14,1918,1919],{},"2, 4, 5",[47,1921,1922,1924,1928],{},[65,1923,247],{},[65,1925,1862,1926,1882],{},[14,1927,1873],{},[65,1929,1930,91,1932],{},[14,1931,225],{},[14,1933,1934],{},"1, 3",[47,1936,1937,1939,1943],{},[65,1938,225],{},[65,1940,1862,1941,1898],{},[14,1942,1934],{},[65,1944,1945],{},[14,1946,1934],{},[47,1948,1949,1952,1958],{},[65,1950,1951],{},"7",[65,1953,1909,1954,91,1956,1914],{},[14,1955,225],{},[14,1957,1934],{},[65,1959,1960],{},[14,1961,1962],{},"1, 3, 6",[47,1964,1965,1968,1974],{},[65,1966,1967],{},"8",[65,1969,1909,1970,91,1972,1914],{},[14,1971,1919],{},[14,1973,1962],{},[65,1975,1976],{},[14,1977,256],{},[10,1979,1980,1981,1984],{},"Bij het samenvoegen vergelijk je steeds de voorste elementen van beide helften en pak je de\nkleinste. Bij gelijke waarden pak je ",[22,1982,1983],{},"eerst links",": daardoor is merge sort stabiel.",[264,1986,1987,2299],{},[267,1988,1989],{"v-slot:python":269},[271,1990,1992],{"className":273,"code":1991,"language":275,"meta":269,"style":269},"def merge_sort(a):\n    if len(a) \u003C= 1:\n        return a\n    mid = len(a) \u002F\u002F 2\n    links = merge_sort(a[:mid])\n    rechts = merge_sort(a[mid:])\n    # samenvoegen: bij gelijke waarden eerst links (stabiel)\n    res = []\n    i = j = 0\n    while i \u003C len(links) and j \u003C len(rechts):\n        if links[i] \u003C= rechts[j]:\n            res.append(links[i])\n            i += 1\n        else:\n            res.append(rechts[j])\n            j += 1\n    res.extend(links[i:])\n    res.extend(rechts[j:])\n    return res\n",[14,1993,1994,2007,2027,2035,2056,2078,2098,2103,2113,2127,2161,2187,2207,2217,2224,2242,2250,2271,2290],{"__ignoreMap":269},[279,1995,1996,1998,2001,2003,2005],{"class":281,"line":282},[279,1997,286],{"class":285},[279,1999,2000],{"class":289}," merge_sort",[279,2002,294],{"class":293},[279,2004,27],{"class":297},[279,2006,300],{"class":293},[279,2008,2009,2012,2014,2016,2018,2020,2023,2025],{"class":281,"line":303},[279,2010,2011],{"class":306},"    if",[279,2013,328],{"class":289},[279,2015,294],{"class":293},[279,2017,27],{"class":289},[279,2019,513],{"class":293},[279,2021,2022],{"class":293}," \u003C=",[279,2024,432],{"class":322},[279,2026,415],{"class":293},[279,2028,2029,2032],{"class":281,"line":338},[279,2030,2031],{"class":306},"        return",[279,2033,2034],{"class":310}," a\n",[279,2036,2037,2040,2042,2044,2046,2048,2050,2053],{"class":281,"line":358},[279,2038,2039],{"class":310},"    mid ",[279,2041,344],{"class":293},[279,2043,328],{"class":289},[279,2045,294],{"class":293},[279,2047,27],{"class":289},[279,2049,513],{"class":293},[279,2051,2052],{"class":293}," \u002F\u002F",[279,2054,2055],{"class":322}," 2\n",[279,2057,2058,2061,2063,2065,2067,2069,2072,2075],{"class":281,"line":374},[279,2059,2060],{"class":310},"    links ",[279,2062,344],{"class":293},[279,2064,2000],{"class":289},[279,2066,294],{"class":293},[279,2068,27],{"class":289},[279,2070,2071],{"class":293},"[:",[279,2073,2074],{"class":289},"mid",[279,2076,2077],{"class":293},"])\n",[279,2079,2080,2083,2085,2087,2089,2091,2093,2095],{"class":281,"line":381},[279,2081,2082],{"class":310},"    rechts ",[279,2084,344],{"class":293},[279,2086,2000],{"class":289},[279,2088,294],{"class":293},[279,2090,27],{"class":289},[279,2092,350],{"class":293},[279,2094,2074],{"class":289},[279,2096,2097],{"class":293},":])\n",[279,2099,2100],{"class":281,"line":418},[279,2101,2102],{"class":377},"    # samenvoegen: bij gelijke waarden eerst links (stabiel)\n",[279,2104,2105,2108,2110],{"class":281,"line":448},[279,2106,2107],{"class":310},"    res ",[279,2109,344],{"class":293},[279,2111,2112],{"class":293}," []\n",[279,2114,2115,2118,2120,2122,2124],{"class":281,"line":459},[279,2116,2117],{"class":310},"    i ",[279,2119,344],{"class":293},[279,2121,387],{"class":310},[279,2123,344],{"class":293},[279,2125,2126],{"class":322}," 0\n",[279,2128,2129,2132,2135,2137,2139,2141,2144,2146,2148,2150,2152,2154,2156,2159],{"class":281,"line":668},[279,2130,2131],{"class":306},"    while",[279,2133,2134],{"class":310}," i ",[279,2136,539],{"class":293},[279,2138,328],{"class":289},[279,2140,294],{"class":293},[279,2142,2143],{"class":289},"links",[279,2145,513],{"class":293},[279,2147,396],{"class":293},[279,2149,387],{"class":310},[279,2151,539],{"class":293},[279,2153,328],{"class":289},[279,2155,294],{"class":293},[279,2157,2158],{"class":289},"rechts",[279,2160,300],{"class":293},[279,2162,2163,2166,2169,2171,2174,2176,2178,2181,2183,2185],{"class":281,"line":692},[279,2164,2165],{"class":306},"        if",[279,2167,2168],{"class":310}," links",[279,2170,350],{"class":293},[279,2172,2173],{"class":310},"i",[279,2175,406],{"class":293},[279,2177,2022],{"class":293},[279,2179,2180],{"class":310}," rechts",[279,2182,350],{"class":293},[279,2184,403],{"class":310},[279,2186,992],{"class":293},[279,2188,2189,2192,2194,2197,2199,2201,2203,2205],{"class":281,"line":698},[279,2190,2191],{"class":310},"            res",[279,2193,31],{"class":293},[279,2195,2196],{"class":289},"append",[279,2198,294],{"class":293},[279,2200,2143],{"class":289},[279,2202,350],{"class":293},[279,2204,2173],{"class":289},[279,2206,2077],{"class":293},[279,2208,2209,2212,2215],{"class":281,"line":1257},[279,2210,2211],{"class":310},"            i ",[279,2213,2214],{"class":293},"+=",[279,2216,371],{"class":322},[279,2218,2219,2222],{"class":281,"line":1282},[279,2220,2221],{"class":306},"        else",[279,2223,415],{"class":293},[279,2225,2226,2228,2230,2232,2234,2236,2238,2240],{"class":281,"line":1300},[279,2227,2191],{"class":310},[279,2229,31],{"class":293},[279,2231,2196],{"class":289},[279,2233,294],{"class":293},[279,2235,2158],{"class":289},[279,2237,350],{"class":293},[279,2239,403],{"class":289},[279,2241,2077],{"class":293},[279,2243,2244,2246,2248],{"class":281,"line":1305},[279,2245,451],{"class":310},[279,2247,2214],{"class":293},[279,2249,371],{"class":322},[279,2251,2253,2256,2258,2261,2263,2265,2267,2269],{"class":281,"line":2252},17,[279,2254,2255],{"class":310},"    res",[279,2257,31],{"class":293},[279,2259,2260],{"class":289},"extend",[279,2262,294],{"class":293},[279,2264,2143],{"class":289},[279,2266,350],{"class":293},[279,2268,2173],{"class":289},[279,2270,2097],{"class":293},[279,2272,2274,2276,2278,2280,2282,2284,2286,2288],{"class":281,"line":2273},18,[279,2275,2255],{"class":310},[279,2277,31],{"class":293},[279,2279,2260],{"class":289},[279,2281,294],{"class":293},[279,2283,2158],{"class":289},[279,2285,350],{"class":293},[279,2287,403],{"class":289},[279,2289,2097],{"class":293},[279,2291,2293,2296],{"class":281,"line":2292},19,[279,2294,2295],{"class":306},"    return",[279,2297,2298],{"class":310}," res\n",[267,2300,2301],{"v-slot:java":269},[271,2302,2304],{"className":485,"code":2303,"language":487,"meta":269,"style":269},"static int[] mergeSort(int[] a) {\n    if (a.length \u003C= 1) {\n        return a;\n    }\n    int mid = a.length \u002F 2;\n    int[] links = mergeSort(java.util.Arrays.copyOfRange(a, 0, mid));\n    int[] rechts = mergeSort(java.util.Arrays.copyOfRange(a, mid, a.length));\n    \u002F\u002F samenvoegen: bij gelijke waarden eerst links (stabiel)\n    int[] res = new int[a.length];\n    int i = 0, j = 0, k = 0;\n    while (i \u003C links.length && j \u003C rechts.length) {\n        if (links[i] \u003C= rechts[j]) {\n            res[k++] = links[i++];\n        } else {\n            res[k++] = rechts[j++];\n        }\n    }\n    while (i \u003C links.length) res[k++] = links[i++];\n    while (j \u003C rechts.length) res[k++] = rechts[j++];\n    return res;\n}\n",[14,2305,2306,2330,2352,2360,2364,2387,2435,2482,2487,2513,2541,2575,2601,2623,2633,2653,2657,2661,2698,2734,2743],{"__ignoreMap":269},[279,2307,2308,2310,2313,2315,2318,2320,2322,2324,2326,2328],{"class":281,"line":282},[279,2309,494],{"class":285},[279,2311,2312],{"class":285}," int",[279,2314,508],{"class":293},[279,2316,2317],{"class":289}," mergeSort",[279,2319,294],{"class":293},[279,2321,505],{"class":285},[279,2323,508],{"class":293},[279,2325,347],{"class":310},[279,2327,513],{"class":293},[279,2329,516],{"class":293},[279,2331,2332,2334,2336,2338,2340,2343,2346,2348,2350],{"class":281,"line":303},[279,2333,2011],{"class":306},[279,2335,523],{"class":293},[279,2337,27],{"class":310},[279,2339,31],{"class":293},[279,2341,2342],{"class":310},"length ",[279,2344,2345],{"class":293},"\u003C=",[279,2347,432],{"class":322},[279,2349,513],{"class":293},[279,2351,516],{"class":293},[279,2353,2354,2356,2358],{"class":281,"line":338},[279,2355,2031],{"class":306},[279,2357,347],{"class":310},[279,2359,592],{"class":293},[279,2361,2362],{"class":281,"line":358},[279,2363,695],{"class":293},[279,2365,2366,2368,2371,2373,2375,2377,2379,2382,2385],{"class":281,"line":374},[279,2367,1086],{"class":285},[279,2369,2370],{"class":310}," mid ",[279,2372,344],{"class":293},[279,2374,347],{"class":310},[279,2376,31],{"class":293},[279,2378,2342],{"class":310},[279,2380,2381],{"class":293},"\u002F",[279,2383,2384],{"class":322}," 2",[279,2386,592],{"class":293},[279,2388,2389,2391,2393,2396,2398,2400,2402,2404,2406,2409,2411,2414,2416,2419,2421,2423,2425,2427,2429,2432],{"class":281,"line":381},[279,2390,1086],{"class":285},[279,2392,508],{"class":293},[279,2394,2395],{"class":310}," links ",[279,2397,344],{"class":293},[279,2399,2317],{"class":289},[279,2401,294],{"class":293},[279,2403,487],{"class":310},[279,2405,31],{"class":293},[279,2407,2408],{"class":310},"util",[279,2410,31],{"class":293},[279,2412,2413],{"class":310},"Arrays",[279,2415,31],{"class":293},[279,2417,2418],{"class":289},"copyOfRange",[279,2420,294],{"class":293},[279,2422,27],{"class":310},[279,2424,325],{"class":293},[279,2426,393],{"class":322},[279,2428,325],{"class":293},[279,2430,2431],{"class":310}," mid",[279,2433,2434],{"class":293},"));\n",[279,2436,2437,2439,2441,2444,2446,2448,2450,2452,2454,2456,2458,2460,2462,2464,2466,2468,2470,2472,2474,2476,2478,2480],{"class":281,"line":418},[279,2438,1086],{"class":285},[279,2440,508],{"class":293},[279,2442,2443],{"class":310}," rechts ",[279,2445,344],{"class":293},[279,2447,2317],{"class":289},[279,2449,294],{"class":293},[279,2451,487],{"class":310},[279,2453,31],{"class":293},[279,2455,2408],{"class":310},[279,2457,31],{"class":293},[279,2459,2413],{"class":310},[279,2461,31],{"class":293},[279,2463,2418],{"class":289},[279,2465,294],{"class":293},[279,2467,27],{"class":310},[279,2469,325],{"class":293},[279,2471,2431],{"class":310},[279,2473,325],{"class":293},[279,2475,347],{"class":310},[279,2477,31],{"class":293},[279,2479,546],{"class":310},[279,2481,2434],{"class":293},[279,2483,2484],{"class":281,"line":448},[279,2485,2486],{"class":377},"    \u002F\u002F samenvoegen: bij gelijke waarden eerst links (stabiel)\n",[279,2488,2489,2491,2493,2496,2498,2501,2503,2505,2507,2509,2511],{"class":281,"line":459},[279,2490,1086],{"class":285},[279,2492,508],{"class":293},[279,2494,2495],{"class":310}," res ",[279,2497,344],{"class":293},[279,2499,2500],{"class":306}," new",[279,2502,2312],{"class":285},[279,2504,350],{"class":293},[279,2506,27],{"class":310},[279,2508,31],{"class":293},[279,2510,546],{"class":310},[279,2512,575],{"class":293},[279,2514,2515,2517,2519,2521,2523,2525,2527,2529,2531,2533,2535,2537,2539],{"class":281,"line":668},[279,2516,1086],{"class":285},[279,2518,2134],{"class":310},[279,2520,344],{"class":293},[279,2522,393],{"class":322},[279,2524,325],{"class":293},[279,2526,387],{"class":310},[279,2528,344],{"class":293},[279,2530,393],{"class":322},[279,2532,325],{"class":293},[279,2534,311],{"class":310},[279,2536,344],{"class":293},[279,2538,393],{"class":322},[279,2540,592],{"class":293},[279,2542,2543,2545,2547,2550,2552,2554,2556,2558,2561,2563,2565,2567,2569,2571,2573],{"class":281,"line":692},[279,2544,2131],{"class":306},[279,2546,523],{"class":293},[279,2548,2549],{"class":310},"i ",[279,2551,539],{"class":293},[279,2553,2168],{"class":310},[279,2555,31],{"class":293},[279,2557,2342],{"class":310},[279,2559,2560],{"class":293},"&&",[279,2562,387],{"class":310},[279,2564,539],{"class":293},[279,2566,2180],{"class":310},[279,2568,31],{"class":293},[279,2570,546],{"class":310},[279,2572,513],{"class":293},[279,2574,516],{"class":293},[279,2576,2577,2579,2581,2583,2585,2587,2589,2591,2593,2595,2597,2599],{"class":281,"line":698},[279,2578,2165],{"class":306},[279,2580,523],{"class":293},[279,2582,2143],{"class":310},[279,2584,350],{"class":293},[279,2586,2173],{"class":310},[279,2588,406],{"class":293},[279,2590,2022],{"class":293},[279,2592,2180],{"class":310},[279,2594,350],{"class":293},[279,2596,403],{"class":310},[279,2598,1207],{"class":293},[279,2600,516],{"class":293},[279,2602,2603,2605,2607,2609,2612,2614,2616,2618,2620],{"class":281,"line":1257},[279,2604,2191],{"class":310},[279,2606,350],{"class":293},[279,2608,105],{"class":310},[279,2610,2611],{"class":293},"++]",[279,2613,437],{"class":293},[279,2615,2168],{"class":310},[279,2617,350],{"class":293},[279,2619,2173],{"class":310},[279,2621,2622],{"class":293},"++];\n",[279,2624,2625,2628,2631],{"class":281,"line":1282},[279,2626,2627],{"class":293},"        }",[279,2629,2630],{"class":306}," else",[279,2632,516],{"class":293},[279,2634,2635,2637,2639,2641,2643,2645,2647,2649,2651],{"class":281,"line":1300},[279,2636,2191],{"class":310},[279,2638,350],{"class":293},[279,2640,105],{"class":310},[279,2642,2611],{"class":293},[279,2644,437],{"class":293},[279,2646,2180],{"class":310},[279,2648,350],{"class":293},[279,2650,403],{"class":310},[279,2652,2622],{"class":293},[279,2654,2655],{"class":281,"line":1305},[279,2656,665],{"class":293},[279,2658,2659],{"class":281,"line":2252},[279,2660,695],{"class":293},[279,2662,2663,2665,2667,2669,2671,2673,2675,2677,2679,2682,2684,2686,2688,2690,2692,2694,2696],{"class":281,"line":2273},[279,2664,2131],{"class":306},[279,2666,523],{"class":293},[279,2668,2549],{"class":310},[279,2670,539],{"class":293},[279,2672,2168],{"class":310},[279,2674,31],{"class":293},[279,2676,546],{"class":310},[279,2678,513],{"class":293},[279,2680,2681],{"class":310}," res",[279,2683,350],{"class":293},[279,2685,105],{"class":310},[279,2687,2611],{"class":293},[279,2689,437],{"class":293},[279,2691,2168],{"class":310},[279,2693,350],{"class":293},[279,2695,2173],{"class":310},[279,2697,2622],{"class":293},[279,2699,2700,2702,2704,2706,2708,2710,2712,2714,2716,2718,2720,2722,2724,2726,2728,2730,2732],{"class":281,"line":2292},[279,2701,2131],{"class":306},[279,2703,523],{"class":293},[279,2705,426],{"class":310},[279,2707,539],{"class":293},[279,2709,2180],{"class":310},[279,2711,31],{"class":293},[279,2713,546],{"class":310},[279,2715,513],{"class":293},[279,2717,2681],{"class":310},[279,2719,350],{"class":293},[279,2721,105],{"class":310},[279,2723,2611],{"class":293},[279,2725,437],{"class":293},[279,2727,2180],{"class":310},[279,2729,350],{"class":293},[279,2731,403],{"class":310},[279,2733,2622],{"class":293},[279,2735,2737,2739,2741],{"class":281,"line":2736},20,[279,2738,2295],{"class":306},[279,2740,2681],{"class":310},[279,2742,592],{"class":293},[279,2744,2746],{"class":281,"line":2745},21,[279,2747,701],{"class":293},[10,2749,2750,2751,2754,2755,2757,2758,2761,2762,2765],{},"Er zijn ",[14,2752,2753],{},"log n"," niveaus van splitsen, en op elk niveau kost samenvoegen samen ",[14,2756,719],{},". Totaal:\n",[14,2759,2760],{},"O(n log n)",", altijd. Het nadeel: je hebt een extra array van grootte ",[14,2763,2764],{},"n"," nodig.",[33,2767,2769],{"id":2768},"quicksort-met-lomuto-partitie","Quicksort met Lomuto-partitie",[10,2771,2772,2774,2775,2778,2779,2782,2783,2785],{},[22,2773,128],{}," kiest een spil (",[1825,2776,2777],{},"pivot","), zet alles wat kleiner is links ervan en de rest rechts, en\nsorteert daarna beide kanten recursief. Het hart is de partitie. Wij gebruiken de\n",[22,2780,2781],{},"Lomuto-partitie"," met het ",[22,2784,134],{}," element als pivot:",[271,2787,2792],{"className":2788,"code":2790,"language":2791},[2789],"language-text","pivot = a[hi]; i = lo\nfor j = lo .. hi-1:\n    if a[j] \u003C pivot: swap(a[i], a[j]); i++\nswap(a[i], a[hi]); return i\n","text",[14,2793,2790],{"__ignoreMap":269},[10,2795,2796,2798,2799,2802],{},[14,2797,2173],{}," wijst naar de eerste plek waar het volgende \"kleine\" element moet komen. Elementen die\n",[22,2800,2801],{},"strikt kleiner"," zijn dan de pivot gaan naar links; gelijke elementen blijven rechts.",[10,2804,2805,2806,2809,2810,2812],{},"Uitgewerkt op ",[14,2807,2808],{},"[7, 2, 9, 4, 1, 8, 5]",", pivot = ",[14,2811,247],{},":",[41,2814,2815,2839],{},[44,2816,2817],{},[47,2818,2819,2821,2825,2830,2833,2836],{},[50,2820,403],{},[50,2822,27,2823],{},[279,2824,403],{},[50,2826,27,2827,2829],{},[279,2828,403],{}," \u003C 5?",[50,2831,2832],{},"Actie",[50,2834,2835],{},"i daarna",[50,2837,2838],{},"Array",[60,2840,2841,2858,2875,2899,2916,2937,2958,2974],{},[47,2842,2843,2845,2847,2849,2851,2853],{},[65,2844,178],{},[65,2846,181],{},[65,2848,181],{},[65,2850,181],{},[65,2852,1400],{},[65,2854,2855],{},[14,2856,2857],{},"7, 2, 9, 4, 1, 8, 5",[47,2859,2860,2862,2864,2867,2869,2871],{},[65,2861,1400],{},[65,2863,1951],{},[65,2865,2866],{},"nee",[65,2868,181],{},[65,2870,1400],{},[65,2872,2873],{},[14,2874,2857],{},[47,2876,2877,2879,2881,2884,2892,2894],{},[65,2878,191],{},[65,2880,196],{},[65,2882,2883],{},"ja",[65,2885,2886,2887,2889,2890],{},"wissel a",[279,2888,1400],{},", a",[279,2891,191],{},[65,2893,191],{},[65,2895,2896],{},[14,2897,2898],{},"2, 7, 9, 4, 1, 8, 5",[47,2900,2901,2903,2906,2908,2910,2912],{},[65,2902,196],{},[65,2904,2905],{},"9",[65,2907,2866],{},[65,2909,181],{},[65,2911,191],{},[65,2913,2914],{},[14,2915,2898],{},[47,2917,2918,2920,2922,2924,2930,2932],{},[65,2919,220],{},[65,2921,210],{},[65,2923,2883],{},[65,2925,2886,2926,2889,2928],{},[279,2927,191],{},[279,2929,220],{},[65,2931,196],{},[65,2933,2934],{},[14,2935,2936],{},"2, 4, 9, 7, 1, 8, 5",[47,2938,2939,2941,2943,2945,2951,2953],{},[65,2940,210],{},[65,2942,191],{},[65,2944,2883],{},[65,2946,2886,2947,2889,2949],{},[279,2948,196],{},[279,2950,210],{},[65,2952,220],{},[65,2954,2955],{},[14,2956,2957],{},"2, 4, 1, 7, 9, 8, 5",[47,2959,2960,2962,2964,2966,2968,2970],{},[65,2961,247],{},[65,2963,1967],{},[65,2965,2866],{},[65,2967,181],{},[65,2969,220],{},[65,2971,2972],{},[14,2973,2957],{},[47,2975,2976,2979,2981,2983,2989,2991],{},[65,2977,2978],{},"eind",[65,2980,181],{},[65,2982,181],{},[65,2984,2886,2985,2889,2987],{},[279,2986,220],{},[279,2988,225],{},[65,2990,220],{},[65,2992,2993],{},[14,2994,2995],{},"2, 4, 1, 5, 9, 8, 7",[10,2997,2998,2999,3001,3002,3004,3005,91,3008,31],{},"Na de eerste partitie is de array ",[14,3000,2995],{}," en staat de pivot ",[14,3003,247],{}," op index 3, zijn\ndefinitieve plek. Links staan alleen kleinere getallen, rechts alleen grotere, maar beide kanten zijn\nnog niet gesorteerd. Quicksort gaat nu verder met ",[14,3006,3007],{},"a[0..2]",[14,3009,3010],{},"a[4..6]",[264,3012,3013,3352],{},[267,3014,3015],{"v-slot:python":269},[271,3016,3018],{"className":273,"code":3017,"language":275,"meta":269,"style":269},"def partition(a, lo, hi):\n    pivot = a[hi]  # laatste element is de pivot\n    i = lo\n    for j in range(lo, hi):\n        if a[j] \u003C pivot:  # strikt kleiner gaat naar links\n            a[i], a[j] = a[j], a[i]\n            i += 1\n    a[i], a[hi] = a[hi], a[i]  # pivot op zijn definitieve plek\n    return i\n\ndef quicksort(a, lo=0, hi=None):\n    if hi is None:\n        hi = len(a) - 1\n    if lo \u003C hi:\n        p = partition(a, lo, hi)\n        quicksort(a, lo, p - 1)\n        quicksort(a, p + 1, hi)\n",[14,3019,3020,3043,3062,3071,3092,3114,3150,3158,3198,3205,3211,3237,3250,3270,3283,3306,3330],{"__ignoreMap":269},[279,3021,3022,3024,3027,3029,3031,3033,3036,3038,3041],{"class":281,"line":282},[279,3023,286],{"class":285},[279,3025,3026],{"class":289}," partition",[279,3028,294],{"class":293},[279,3030,27],{"class":297},[279,3032,325],{"class":293},[279,3034,3035],{"class":297}," lo",[279,3037,325],{"class":293},[279,3039,3040],{"class":297}," hi",[279,3042,300],{"class":293},[279,3044,3045,3048,3050,3052,3054,3057,3059],{"class":281,"line":303},[279,3046,3047],{"class":310},"    pivot ",[279,3049,344],{"class":293},[279,3051,347],{"class":310},[279,3053,350],{"class":293},[279,3055,3056],{"class":310},"hi",[279,3058,406],{"class":293},[279,3060,3061],{"class":377},"  # laatste element is de pivot\n",[279,3063,3064,3066,3068],{"class":281,"line":338},[279,3065,2117],{"class":310},[279,3067,344],{"class":293},[279,3069,3070],{"class":310}," lo\n",[279,3072,3073,3075,3077,3079,3081,3083,3086,3088,3090],{"class":281,"line":358},[279,3074,307],{"class":306},[279,3076,387],{"class":310},[279,3078,314],{"class":306},[279,3080,317],{"class":289},[279,3082,294],{"class":293},[279,3084,3085],{"class":289},"lo",[279,3087,325],{"class":293},[279,3089,3040],{"class":289},[279,3091,300],{"class":293},[279,3093,3094,3096,3098,3100,3102,3104,3106,3109,3111],{"class":281,"line":374},[279,3095,2165],{"class":306},[279,3097,347],{"class":310},[279,3099,350],{"class":293},[279,3101,403],{"class":310},[279,3103,406],{"class":293},[279,3105,982],{"class":293},[279,3107,3108],{"class":310}," pivot",[279,3110,2812],{"class":293},[279,3112,3113],{"class":377},"  # strikt kleiner gaat naar links\n",[279,3115,3116,3118,3120,3122,3124,3126,3128,3130,3132,3134,3136,3138,3140,3142,3144,3146,3148],{"class":281,"line":381},[279,3117,421],{"class":310},[279,3119,350],{"class":293},[279,3121,2173],{"class":310},[279,3123,1023],{"class":293},[279,3125,347],{"class":310},[279,3127,350],{"class":293},[279,3129,403],{"class":310},[279,3131,406],{"class":293},[279,3133,437],{"class":293},[279,3135,347],{"class":310},[279,3137,350],{"class":293},[279,3139,403],{"class":310},[279,3141,1023],{"class":293},[279,3143,347],{"class":310},[279,3145,350],{"class":293},[279,3147,2173],{"class":310},[279,3149,355],{"class":293},[279,3151,3152,3154,3156],{"class":281,"line":418},[279,3153,2211],{"class":310},[279,3155,2214],{"class":293},[279,3157,371],{"class":322},[279,3159,3160,3163,3165,3167,3169,3171,3173,3175,3177,3179,3181,3183,3185,3187,3189,3191,3193,3195],{"class":281,"line":448},[279,3161,3162],{"class":310},"    a",[279,3164,350],{"class":293},[279,3166,2173],{"class":310},[279,3168,1023],{"class":293},[279,3170,347],{"class":310},[279,3172,350],{"class":293},[279,3174,3056],{"class":310},[279,3176,406],{"class":293},[279,3178,437],{"class":293},[279,3180,347],{"class":310},[279,3182,350],{"class":293},[279,3184,3056],{"class":310},[279,3186,1023],{"class":293},[279,3188,347],{"class":310},[279,3190,350],{"class":293},[279,3192,2173],{"class":310},[279,3194,406],{"class":293},[279,3196,3197],{"class":377},"  # pivot op zijn definitieve plek\n",[279,3199,3200,3202],{"class":281,"line":459},[279,3201,2295],{"class":306},[279,3203,3204],{"class":310}," i\n",[279,3206,3207],{"class":281,"line":668},[279,3208,3210],{"emptyLinePlaceholder":3209},true,"\n",[279,3212,3213,3215,3218,3220,3222,3224,3226,3228,3230,3232,3234],{"class":281,"line":692},[279,3214,286],{"class":285},[279,3216,3217],{"class":289}," quicksort",[279,3219,294],{"class":293},[279,3221,27],{"class":297},[279,3223,325],{"class":293},[279,3225,3035],{"class":297},[279,3227,344],{"class":293},[279,3229,1400],{"class":322},[279,3231,325],{"class":293},[279,3233,3040],{"class":297},[279,3235,3236],{"class":293},"=None):\n",[279,3238,3239,3241,3244,3247],{"class":281,"line":698},[279,3240,2011],{"class":306},[279,3242,3243],{"class":310}," hi ",[279,3245,3246],{"class":293},"is",[279,3248,3249],{"class":293}," None:\n",[279,3251,3252,3255,3257,3259,3261,3263,3265,3268],{"class":281,"line":1257},[279,3253,3254],{"class":310},"        hi ",[279,3256,344],{"class":293},[279,3258,328],{"class":289},[279,3260,294],{"class":293},[279,3262,27],{"class":289},[279,3264,513],{"class":293},[279,3266,3267],{"class":293}," -",[279,3269,371],{"class":322},[279,3271,3272,3274,3277,3279,3281],{"class":281,"line":1282},[279,3273,2011],{"class":306},[279,3275,3276],{"class":310}," lo ",[279,3278,539],{"class":293},[279,3280,3040],{"class":310},[279,3282,415],{"class":293},[279,3284,3285,3288,3290,3292,3294,3296,3298,3300,3302,3304],{"class":281,"line":1300},[279,3286,3287],{"class":310},"        p ",[279,3289,344],{"class":293},[279,3291,3026],{"class":289},[279,3293,294],{"class":293},[279,3295,27],{"class":289},[279,3297,325],{"class":293},[279,3299,3035],{"class":289},[279,3301,325],{"class":293},[279,3303,3040],{"class":289},[279,3305,906],{"class":293},[279,3307,3308,3311,3313,3315,3317,3319,3321,3324,3326,3328],{"class":281,"line":1305},[279,3309,3310],{"class":289},"        quicksort",[279,3312,294],{"class":293},[279,3314,27],{"class":289},[279,3316,325],{"class":293},[279,3318,3035],{"class":289},[279,3320,325],{"class":293},[279,3322,3323],{"class":289}," p ",[279,3325,368],{"class":293},[279,3327,432],{"class":322},[279,3329,906],{"class":293},[279,3331,3332,3334,3336,3338,3340,3342,3344,3346,3348,3350],{"class":281,"line":2252},[279,3333,3310],{"class":289},[279,3335,294],{"class":293},[279,3337,27],{"class":289},[279,3339,325],{"class":293},[279,3341,3323],{"class":289},[279,3343,429],{"class":293},[279,3345,432],{"class":322},[279,3347,325],{"class":293},[279,3349,3040],{"class":289},[279,3351,906],{"class":293},[267,3353,3354],{"v-slot:java":269},[271,3355,3357],{"className":485,"code":3356,"language":487,"meta":269,"style":269},"static int partition(int[] a, int lo, int hi) {\n    int pivot = a[hi]; \u002F\u002F laatste element is de pivot\n    int i = lo;\n    for (int j = lo; j \u003C hi; j++) {\n        if (a[j] \u003C pivot) { \u002F\u002F strikt kleiner gaat naar links\n            int tmp = a[i]; a[i] = a[j]; a[j] = tmp;\n            i++;\n        }\n    }\n    int tmp = a[i]; a[i] = a[hi]; a[hi] = tmp; \u002F\u002F pivot op zijn definitieve plek\n    return i;\n}\n\nstatic void quicksort(int[] a, int lo, int hi) {\n    if (lo \u003C hi) {\n        int p = partition(a, lo, hi);\n        quicksort(a, lo, p - 1);\n        quicksort(a, p + 1, hi);\n    }\n}\n",[14,3358,3359,3391,3412,3424,3454,3480,3529,3537,3541,3545,3596,3605,3609,3613,3645,3662,3687,3709,3731,3735],{"__ignoreMap":269},[279,3360,3361,3363,3365,3367,3369,3371,3373,3375,3377,3379,3381,3383,3385,3387,3389],{"class":281,"line":282},[279,3362,494],{"class":285},[279,3364,2312],{"class":285},[279,3366,3026],{"class":289},[279,3368,294],{"class":293},[279,3370,505],{"class":285},[279,3372,508],{"class":293},[279,3374,347],{"class":310},[279,3376,325],{"class":293},[279,3378,2312],{"class":285},[279,3380,3035],{"class":310},[279,3382,325],{"class":293},[279,3384,2312],{"class":285},[279,3386,3040],{"class":310},[279,3388,513],{"class":293},[279,3390,516],{"class":293},[279,3392,3393,3395,3398,3400,3402,3404,3406,3409],{"class":281,"line":303},[279,3394,1086],{"class":285},[279,3396,3397],{"class":310}," pivot ",[279,3399,344],{"class":293},[279,3401,347],{"class":310},[279,3403,350],{"class":293},[279,3405,3056],{"class":310},[279,3407,3408],{"class":293},"];",[279,3410,3411],{"class":377}," \u002F\u002F laatste element is de pivot\n",[279,3413,3414,3416,3418,3420,3422],{"class":281,"line":338},[279,3415,1086],{"class":285},[279,3417,2134],{"class":310},[279,3419,344],{"class":293},[279,3421,3035],{"class":310},[279,3423,592],{"class":293},[279,3425,3426,3428,3430,3432,3434,3436,3438,3440,3442,3444,3446,3448,3450,3452],{"class":281,"line":358},[279,3427,307],{"class":306},[279,3429,523],{"class":293},[279,3431,505],{"class":285},[279,3433,387],{"class":310},[279,3435,344],{"class":293},[279,3437,3035],{"class":310},[279,3439,534],{"class":293},[279,3441,387],{"class":310},[279,3443,539],{"class":293},[279,3445,3040],{"class":310},[279,3447,534],{"class":293},[279,3449,1178],{"class":310},[279,3451,554],{"class":293},[279,3453,516],{"class":293},[279,3455,3456,3458,3460,3462,3464,3466,3468,3470,3472,3474,3477],{"class":281,"line":374},[279,3457,2165],{"class":306},[279,3459,523],{"class":293},[279,3461,27],{"class":310},[279,3463,350],{"class":293},[279,3465,403],{"class":310},[279,3467,406],{"class":293},[279,3469,982],{"class":293},[279,3471,3108],{"class":310},[279,3473,513],{"class":293},[279,3475,3476],{"class":293}," {",[279,3478,3479],{"class":377}," \u002F\u002F strikt kleiner gaat naar links\n",[279,3481,3482,3485,3487,3489,3491,3493,3495,3497,3499,3501,3503,3505,3507,3509,3511,3513,3515,3517,3519,3521,3523,3525,3527],{"class":281,"line":381},[279,3483,3484],{"class":285},"            int",[279,3486,1240],{"class":310},[279,3488,344],{"class":293},[279,3490,347],{"class":310},[279,3492,350],{"class":293},[279,3494,2173],{"class":310},[279,3496,3408],{"class":293},[279,3498,347],{"class":310},[279,3500,350],{"class":293},[279,3502,2173],{"class":310},[279,3504,406],{"class":293},[279,3506,437],{"class":293},[279,3508,347],{"class":310},[279,3510,350],{"class":293},[279,3512,403],{"class":310},[279,3514,3408],{"class":293},[279,3516,347],{"class":310},[279,3518,350],{"class":293},[279,3520,403],{"class":310},[279,3522,406],{"class":293},[279,3524,437],{"class":293},[279,3526,1295],{"class":310},[279,3528,592],{"class":293},[279,3530,3531,3534],{"class":281,"line":418},[279,3532,3533],{"class":310},"            i",[279,3535,3536],{"class":293},"++;\n",[279,3538,3539],{"class":281,"line":448},[279,3540,665],{"class":293},[279,3542,3543],{"class":281,"line":459},[279,3544,695],{"class":293},[279,3546,3547,3549,3551,3553,3555,3557,3559,3561,3563,3565,3567,3569,3571,3573,3575,3577,3579,3581,3583,3585,3587,3589,3591,3593],{"class":281,"line":668},[279,3548,1086],{"class":285},[279,3550,1240],{"class":310},[279,3552,344],{"class":293},[279,3554,347],{"class":310},[279,3556,350],{"class":293},[279,3558,2173],{"class":310},[279,3560,3408],{"class":293},[279,3562,347],{"class":310},[279,3564,350],{"class":293},[279,3566,2173],{"class":310},[279,3568,406],{"class":293},[279,3570,437],{"class":293},[279,3572,347],{"class":310},[279,3574,350],{"class":293},[279,3576,3056],{"class":310},[279,3578,3408],{"class":293},[279,3580,347],{"class":310},[279,3582,350],{"class":293},[279,3584,3056],{"class":310},[279,3586,406],{"class":293},[279,3588,437],{"class":293},[279,3590,1295],{"class":310},[279,3592,534],{"class":293},[279,3594,3595],{"class":377}," \u002F\u002F pivot op zijn definitieve plek\n",[279,3597,3598,3600,3603],{"class":281,"line":692},[279,3599,2295],{"class":306},[279,3601,3602],{"class":310}," i",[279,3604,592],{"class":293},[279,3606,3607],{"class":281,"line":698},[279,3608,701],{"class":293},[279,3610,3611],{"class":281,"line":1257},[279,3612,3210],{"emptyLinePlaceholder":3209},[279,3614,3615,3617,3619,3621,3623,3625,3627,3629,3631,3633,3635,3637,3639,3641,3643],{"class":281,"line":1282},[279,3616,494],{"class":285},[279,3618,497],{"class":285},[279,3620,3217],{"class":289},[279,3622,294],{"class":293},[279,3624,505],{"class":285},[279,3626,508],{"class":293},[279,3628,347],{"class":310},[279,3630,325],{"class":293},[279,3632,2312],{"class":285},[279,3634,3035],{"class":310},[279,3636,325],{"class":293},[279,3638,2312],{"class":285},[279,3640,3040],{"class":310},[279,3642,513],{"class":293},[279,3644,516],{"class":293},[279,3646,3647,3649,3651,3654,3656,3658,3660],{"class":281,"line":1300},[279,3648,2011],{"class":306},[279,3650,523],{"class":293},[279,3652,3653],{"class":310},"lo ",[279,3655,539],{"class":293},[279,3657,3040],{"class":310},[279,3659,513],{"class":293},[279,3661,516],{"class":293},[279,3663,3664,3666,3668,3670,3672,3674,3676,3678,3680,3682,3684],{"class":281,"line":1305},[279,3665,561],{"class":285},[279,3667,3323],{"class":310},[279,3669,344],{"class":293},[279,3671,3026],{"class":289},[279,3673,294],{"class":293},[279,3675,27],{"class":310},[279,3677,325],{"class":293},[279,3679,3035],{"class":310},[279,3681,325],{"class":293},[279,3683,3040],{"class":310},[279,3685,3686],{"class":293},");\n",[279,3688,3689,3691,3693,3695,3697,3699,3701,3703,3705,3707],{"class":281,"line":2252},[279,3690,3310],{"class":289},[279,3692,294],{"class":293},[279,3694,27],{"class":310},[279,3696,325],{"class":293},[279,3698,3035],{"class":310},[279,3700,325],{"class":293},[279,3702,3323],{"class":310},[279,3704,368],{"class":293},[279,3706,432],{"class":322},[279,3708,3686],{"class":293},[279,3710,3711,3713,3715,3717,3719,3721,3723,3725,3727,3729],{"class":281,"line":2273},[279,3712,3310],{"class":289},[279,3714,294],{"class":293},[279,3716,27],{"class":310},[279,3718,325],{"class":293},[279,3720,3323],{"class":310},[279,3722,429],{"class":293},[279,3724,432],{"class":322},[279,3726,325],{"class":293},[279,3728,3040],{"class":310},[279,3730,3686],{"class":293},[279,3732,3733],{"class":281,"line":2292},[279,3734,695],{"class":293},[279,3736,3737],{"class":281,"line":2736},[279,3738,701],{"class":293},[10,3740,3741,3742,3744,3745,3748,3749,3751,3752,3755,3756,3758],{},"Valt de pivot steeds ongeveer in het midden, dan halveer je het probleem en kom je op\n",[14,3743,2760],{},". Maar is de array ",[22,3746,3747],{},"al gesorteerd",", dan is het laatste element steeds het grootste. De\npartitie levert dan een linkerdeel van ",[14,3750,1438],{}," elementen en een leeg rechterdeel op. Dat geeft\n",[14,3753,3754],{},"T(n) = T(n-1) + n",", en dus ",[14,3757,1317],{},". In de praktijk kies je daarom vaak een willekeurige pivot.",[33,3760,3762],{"id":3761},"stabiel-en-in-place","Stabiel en in-place",[10,3764,3765],{},"Twee eigenschappen die op het tentamen vaak gevraagd worden:",[3767,3768,3769,3779],"ul",{},[3770,3771,3772,523,3775,3778],"li",{},[22,3773,3774],{},"Stabiel",[1825,3776,3777],{},"stable","): gelijke elementen behouden hun onderlinge volgorde. Belangrijk als je\neerst op naam en daarna op leeftijd sorteert: binnen dezelfde leeftijd blijft de naamvolgorde\ndan staan.",[3770,3780,3781,3784,3785,3788,3789,3792],{},[22,3782,3783],{},"In-place",": het algoritme gebruikt maar ",[14,3786,3787],{},"O(1)"," (of hooguit ",[14,3790,3791],{},"O(log n)",") extra geheugen naast de\narray zelf.",[33,3794,3795],{"id":30},"Complexiteit",[41,3797,3798,3820],{},[44,3799,3800],{},[47,3801,3802,3804,3807,3810,3813,3816,3818],{},[50,3803,52],{},[50,3805,3806],{},"Best",[50,3808,3809],{},"Gemiddeld",[50,3811,3812],{},"Slechtst",[50,3814,3815],{},"Extra geheugen",[50,3817,3774],{},[50,3819,3783],{},[60,3821,3822,3846,3870,3894,3918],{},[47,3823,3824,3826,3830,3834,3838,3842,3844],{},[65,3825,67],{},[65,3827,3828],{},[14,3829,719],{},[65,3831,3832],{},[14,3833,1317],{},[65,3835,3836],{},[14,3837,1317],{},[65,3839,3840],{},[14,3841,3787],{},[65,3843,2883],{},[65,3845,2883],{},[47,3847,3848,3850,3854,3858,3862,3866,3868],{},[65,3849,84],{},[65,3851,3852],{},[14,3853,1317],{},[65,3855,3856],{},[14,3857,1317],{},[65,3859,3860],{},[14,3861,1317],{},[65,3863,3864],{},[14,3865,3787],{},[65,3867,2866],{},[65,3869,2883],{},[47,3871,3872,3874,3878,3882,3886,3890,3892],{},[65,3873,111],{},[65,3875,3876],{},[14,3877,1317],{},[65,3879,3880],{},[14,3881,1317],{},[65,3883,3884],{},[14,3885,1317],{},[65,3887,3888],{},[14,3889,3787],{},[65,3891,2883],{},[65,3893,2883],{},[47,3895,3896,3898,3902,3906,3910,3914,3916],{},[65,3897,1818],{},[65,3899,3900],{},[14,3901,2760],{},[65,3903,3904],{},[14,3905,2760],{},[65,3907,3908],{},[14,3909,2760],{},[65,3911,3912],{},[14,3913,719],{},[65,3915,2883],{},[65,3917,2866],{},[47,3919,3920,3923,3927,3931,3935,3940,3942],{},[65,3921,3922],{},"Quicksort (Lomuto)",[65,3924,3925],{},[14,3926,2760],{},[65,3928,3929],{},[14,3930,2760],{},[65,3932,3933],{},[14,3934,1317],{},[65,3936,3937,3939],{},[14,3938,3791],{}," gemiddeld",[65,3941,2866],{},[65,3943,2883],{},[10,3945,3946,3947,3949,3950,3952,3953,3955,3956,31],{},"Bubble sort met vroegtijdige stop heeft een best case van ",[14,3948,719],{},"; zonder stop, zoals wij hem\ndefiniëren, is ook de best case ",[14,3951,1317],{},". Het geheugen van quicksort is de recursiestapel: gemiddeld\n",[14,3954,3791],{},", in het slechtste geval ",[14,3957,719],{},[33,3959,3961],{"id":3960},"veelgemaakte-fouten-op-het-tentamen","Veelgemaakte fouten op het tentamen",[3963,3964,3965,3987,3993,4002,4019],"ol",{},[3770,3966,3967,3970,3971,3974,3975,3978,3979,3981,3982,3984,3985,31],{},[22,3968,3969],{},"Insertion en selection sort verwisselen."," Insertion sort pakt het ",[1825,3972,3973],{},"volgende"," element en schuift\nhet op zijn plek; het gesorteerde deel bevat dan nog niet per se de kleinste. Selection sort\n",[1825,3976,3977],{},"zoekt"," het kleinste in de rest. Na ronde 1 van ",[14,3980,186],{}," geeft insertion\n",[14,3983,201],{},", selection ",[14,3986,776],{},[3770,3988,3989,3992],{},[22,3990,3991],{},"Een ronde overslaan omdat er niets verandert."," Bij insertion sort telt ronde 3 hierboven\ngewoon mee, ook al blijft de array gelijk.",[3770,3994,3995,3998,3999,4001],{},[22,3996,3997],{},"Bubble sort vroegtijdig stoppen."," Volgens de afspraak loop je alle ",[14,4000,1438],{}," rondes door. Bij een\nvraag als \"hoeveel vergelijkingen?\" maakt dat uit.",[3770,4003,4004,4007,4008,4011,4012,4014,4015,4018],{},[22,4005,4006],{},"De laatste wissel van Lomuto vergeten."," Na de lus staat de pivot nog achteraan; pas de\n",[14,4009,4010],{},"swap(a[i], a[hi])"," zet hem op index ",[14,4013,2173],{},". Ook: gelijke waarden aan de pivot gaan ",[1825,4016,4017],{},"niet"," naar\nlinks, alleen strikt kleinere.",[3770,4020,4021,4027,4028,31],{},[22,4022,4023,4024,4026],{},"Denken dat quicksort altijd ",[14,4025,2760],{}," is."," Met het laatste element als pivot is een\ngesorteerde invoer het slechtste geval: ",[14,4029,1317],{},[33,4031,4033],{"id":4032},"samenvatting","Samenvatting",[3767,4035,4036,4045,4057,4068,4077],{},[3770,4037,4038,4039,4041,4042,4044],{},"Insertion sort: na ronde ",[14,4040,105],{}," is ",[14,4043,78],{}," gesorteerd; snel op bijna gesorteerde data, stabiel.",[3770,4046,4047,4048,4050,4051,4053,4054,4056],{},"Selection sort: na ronde ",[14,4049,105],{}," staan de ",[14,4052,105],{}," kleinsten vooraan; altijd ",[14,4055,1317],{},", niet stabiel.",[3770,4058,4059,4060,4050,4062,4064,4065,4067],{},"Bubble sort: na ronde ",[14,4061,105],{},[14,4063,105],{}," grootsten achteraan; ",[14,4066,1317],{},", stabiel.",[3770,4069,4070,4071,4073,4074,4076],{},"Merge sort: altijd ",[14,4072,2760],{}," en stabiel, maar kost ",[14,4075,719],{}," extra geheugen.",[3770,4078,4079,4080,4082,4083,31],{},"Quicksort (Lomuto, laatste element als pivot): gemiddeld ",[14,4081,2760],{}," en in-place, slechtst ",[14,4084,1317],{},[4086,4087,4088],"style",{},"html pre.shiki code .spNyl, html code.shiki .spNyl{--shiki-light:#9C3EDA;--shiki-default:#C792EA;--shiki-dark:#C792EA}html pre.shiki code .s2Zo4, html code.shiki .s2Zo4{--shiki-light:#6182B8;--shiki-default:#82AAFF;--shiki-dark:#82AAFF}html pre.shiki code .sMK4o, html code.shiki .sMK4o{--shiki-light:#39ADB5;--shiki-default:#89DDFF;--shiki-dark:#89DDFF}html pre.shiki code .sHdIc, html code.shiki .sHdIc{--shiki-light:#90A4AE;--shiki-light-font-style:italic;--shiki-default:#EEFFFF;--shiki-default-font-style:italic;--shiki-dark:#BABED8;--shiki-dark-font-style:italic}html pre.shiki code .s7zQu, html code.shiki .s7zQu{--shiki-light:#39ADB5;--shiki-light-font-style:italic;--shiki-default:#89DDFF;--shiki-default-font-style:italic;--shiki-dark:#89DDFF;--shiki-dark-font-style:italic}html pre.shiki code .sTEyZ, html code.shiki .sTEyZ{--shiki-light:#90A4AE;--shiki-default:#EEFFFF;--shiki-dark:#BABED8}html pre.shiki code .sbssI, html code.shiki .sbssI{--shiki-light:#F76D47;--shiki-default:#F78C6C;--shiki-dark:#F78C6C}html pre.shiki code .sHwdD, html code.shiki .sHwdD{--shiki-light:#90A4AE;--shiki-light-font-style:italic;--shiki-default:#546E7A;--shiki-default-font-style:italic;--shiki-dark:#676E95;--shiki-dark-font-style:italic}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: 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var(--shiki-dark-text-decoration);}",{"title":269,"searchDepth":303,"depth":303,"links":4090},[4091,4092,4093,4094,4095,4096,4097,4098,4099,4100],{"id":35,"depth":303,"text":36},{"id":151,"depth":303,"text":67},{"id":722,"depth":303,"text":84},{"id":1320,"depth":303,"text":111},{"id":1817,"depth":303,"text":1818},{"id":2768,"depth":303,"text":2769},{"id":3761,"depth":303,"text":3762},{"id":30,"depth":303,"text":3795},{"id":3960,"depth":303,"text":3961},{"id":4032,"depth":303,"text":4033},"Insertion, selection, bubble, merge sort en quicksort stap voor stap: tabellen per ronde, Python- en Java-code, stabiliteit en complexiteit voor je tentamen.","md","i-lucide-arrow-down-wide-narrow",{},"\u002Fpracticely-dsa\u002Fsorteren",{"title":5,"description":4101},"practicely-dsa\u002Fsorteren","sorteren","UIA63XLS5o3aeifdip2qZtjYjc5fIIaub0fKqIQnEWs",{"prev":4111,"next":6369},{"id":4112,"title":4113,"body":4114,"description":6362,"extension":4102,"icon":6363,"meta":6364,"navigation":3209,"order":282,"path":6365,"seo":6366,"stem":6367,"topic":30,"__hash__":6368},"practicelyDsa\u002Fpracticely-dsa\u002Fcomplexiteit.md","Complexiteit en Big-O: zo schat je de looptijd van een algoritme",{"type":7,"value":4115,"toc":6345},[4116,4125,4137,4141,4151,4196,4212,4216,4219,4253,4270,4285,4289,4292,4308,4424,4432,4436,4439,4444,4540,4550,4554,4754,4771,4776,4794,4798,4894,4908,4911,5004,5058,5076,5080,5083,5306,5319,5323,5460,5472,5476,5494,5497,5594,5597,5840,5854,5858,5868,5873,5893,5963,5966,6102,6114,6120,6132,6136,6221,6223,6287,6289,6342],[10,4117,4118,4119,523,4121,4124],{},"Twee programma's kunnen precies hetzelfde antwoord geven en toch totaal verschillend presteren. Het\nene sorteert een miljoen getallen in een fractie van een seconde, het andere is na een uur nog bezig.\n",[22,4120,3795],{},[1825,4122,4123],{},"complexity",") is de taal waarmee je dat verschil beschrijft zonder een stopwatch:\nje telt hoe het aantal stappen groeit als de invoer groter wordt.",[10,4126,4127,4128,4131,4132,4136],{},"Je hebt dit nodig op elk tentamen algoritmen, in vrijwel elk technisch sollicitatiegesprek (\"wat is\nde complexiteit van jouw oplossing?\") en in de praktijk, zodra je data groter wordt dan je testset.\nAlle andere onderwerpen hier, van ",[27,4129,4108],{"href":4130},"\u002Fpracticely\u002Fdsa\u002Fsorteren"," tot\n",[27,4133,4135],{"href":4134},"\u002Fpracticely\u002Fdsa\u002Fgrafen","grafen",", gebruiken deze notatie.",[33,4138,4140],{"id":4139},"big-o-en-θ-het-idee","Big-O en Θ: het idee",[10,4142,4143,4144,4146,4147,4150],{},"Noem de grootte van de invoer ",[14,4145,2764],{}," (het aantal elementen in een lijst, het aantal knopen in een graaf).\nDe looptijd ",[14,4148,4149],{},"T(n)"," is het aantal basisstappen: een vergelijking, een toekenning, een optelling.",[3767,4152,4153,4179],{},[3770,4154,4155,523,4158,4161,4162,4165,4166,4169,4170,4172,4173,4175,4176,4026],{},[22,4156,4157],{},"Big-O",[14,4159,4160],{},"O",") is een ",[22,4163,4164],{},"bovengrens",": ",[14,4167,4168],{},"T(n) = O(f(n))"," betekent dat ",[14,4171,4149],{}," voor grote ",[14,4174,2764],{}," hooguit\neen constante keer ",[14,4177,4178],{},"f(n)",[3770,4180,4181,523,4184,4161,4187,4165,4190,4192,4193,4195],{},[22,4182,4183],{},"Theta",[14,4185,4186],{},"Θ",[22,4188,4189],{},"strakke grens",[14,4191,4149],{}," groeit precies zo snel als ",[14,4194,4178],{},", op een\nconstante factor na. Zowel boven- als ondergrens.",[10,4197,4198,4199,4201,4202,4205,4206,4208,4209,4211],{},"Strikt genomen is een enkele lus ook ",[14,4200,1317],{},", want ",[14,4203,4204],{},"n²"," is óók een bovengrens. Maar dat is een\nnutteloos antwoord. Op Practicely en op de meeste tentamens bedoelen we met Big-O de ",[22,4207,4189],{},":\neen enkele lus is ",[14,4210,719],{},", punt.",[33,4213,4215],{"id":4214},"rekenregels","Rekenregels",[10,4217,4218],{},"Je hoeft nooit precies te tellen. Twee regels doen het meeste werk:",[3963,4220,4221,4239],{},[3770,4222,4223,4226,4227,4041,4230,4232,4233,4236,4237,31],{},[22,4224,4225],{},"Constanten vallen weg."," ",[14,4228,4229],{},"3n + 7",[14,4231,719],{},". ",[14,4234,4235],{},"n\u002F2"," is ook ",[14,4238,719],{},[3770,4240,4241,4226,4244,4041,4247,4249,4250,4252],{},[22,4242,4243],{},"Alleen de dominante term telt.",[14,4245,4246],{},"n² + 100n + 5000",[14,4248,1317],{},", want voor grote ",[14,4251,2764],{}," maakt de\nrest niets meer uit.",[10,4254,4255,4256,4041,4259,4261,4262,4265,4266,4269],{},"Zie het zo: bij ",[14,4257,4258],{},"n = 1000",[14,4260,4204],{}," een miljoen en ",[14,4263,4264],{},"100n"," maar honderdduizend. Bij ",[14,4267,4268],{},"n = 1.000.000"," is\nhet verschil een factor tienduizend.",[10,4271,4272,4273,91,4276,4279,4280,4282,4283,31],{},"Verder geldt: het grondtal van een logaritme maakt in Big-O niet uit, omdat ",[14,4274,4275],{},"log₁₀ n",[14,4277,4278],{},"log₂ n","\neen constante factor van elkaar verschillen. Staat er ",[14,4281,2753],{},", dan bedoelen we ",[14,4284,4278],{},[33,4286,4288],{"id":4287},"de-veelvoorkomende-klassen","De veelvoorkomende klassen",[10,4290,4291],{},"Van snel naar traag:",[10,4293,4294,4296,4297,4296,4299,4296,4301,4296,4303,4296,4305],{},[14,4295,3787],{}," \u003C ",[14,4298,3791],{},[14,4300,719],{},[14,4302,2760],{},[14,4304,1317],{},[14,4306,4307],{},"O(2ⁿ)",[41,4309,4310,4326],{},[44,4311,4312],{},[47,4313,4314,4317,4320,4323],{},[50,4315,4316],{},"Klasse",[50,4318,4319],{},"Naam",[50,4321,4322],{},"Voorbeeld",[50,4324,4325],{},"Stappen bij n = 1000 (orde)",[60,4327,4328,4346,4364,4379,4394,4409],{},[47,4329,4330,4334,4337,4344],{},[65,4331,4332],{},[14,4333,3787],{},[65,4335,4336],{},"constant",[65,4338,4339,4340,4343],{},"element ",[14,4341,4342],{},"a[i]"," opvragen",[65,4345,191],{},[47,4347,4348,4352,4355,4361],{},[65,4349,4350],{},[14,4351,3791],{},[65,4353,4354],{},"logaritmisch",[65,4356,4357],{},[27,4358,4360],{"href":4359},"\u002Fpracticely\u002Fdsa\u002Fzoeken","binair zoeken",[65,4362,4363],{},"10",[47,4365,4366,4370,4373,4376],{},[65,4367,4368],{},[14,4369,719],{},[65,4371,4372],{},"lineair",[65,4374,4375],{},"maximum van een lijst zoeken",[65,4377,4378],{},"1.000",[47,4380,4381,4385,4388,4391],{},[65,4382,4383],{},[14,4384,2760],{},[65,4386,4387],{},"n-log-n",[65,4389,4390],{},"merge sort",[65,4392,4393],{},"10.000",[47,4395,4396,4400,4403,4406],{},[65,4397,4398],{},[14,4399,1317],{},[65,4401,4402],{},"kwadratisch",[65,4404,4405],{},"insertion sort, alle paren bekijken",[65,4407,4408],{},"1.000.000",[47,4410,4411,4415,4418,4421],{},[65,4412,4413],{},[14,4414,4307],{},[65,4416,4417],{},"exponentieel",[65,4419,4420],{},"alle deelverzamelingen opsommen",[65,4422,4423],{},"meer dan atomen in het heelal",[10,4425,4426,4427,91,4429,4431],{},"Het verschil tussen ",[14,4428,2760],{},[14,4430,1317],{}," is bij duizend elementen al een factor honderd. Daarom\nloont het om de klasse van je algoritme te kennen.",[33,4433,4435],{"id":4434},"lussen-tellen","Lussen tellen",[10,4437,4438],{},"Het meeste werk bij het bepalen van de complexiteit is: kijk hoe vaak de binnenste opdracht wordt\nuitgevoerd.",[4440,4441,4443],"h3",{"id":4442},"enkele-lus","Enkele lus",[264,4445,4446,4485],{},[267,4447,4448],{"v-slot:python":269},[271,4449,4451],{"className":273,"code":4450,"language":275,"meta":269,"style":269},"for i in range(n):\n    totaal += a[i]\n",[14,4452,4453,4470],{"__ignoreMap":269},[279,4454,4455,4458,4460,4462,4464,4466,4468],{"class":281,"line":282},[279,4456,4457],{"class":306},"for",[279,4459,2134],{"class":310},[279,4461,314],{"class":306},[279,4463,317],{"class":289},[279,4465,294],{"class":293},[279,4467,2764],{"class":289},[279,4469,300],{"class":293},[279,4471,4472,4475,4477,4479,4481,4483],{"class":281,"line":303},[279,4473,4474],{"class":310},"    totaal ",[279,4476,2214],{"class":293},[279,4478,347],{"class":310},[279,4480,350],{"class":293},[279,4482,2173],{"class":310},[279,4484,355],{"class":293},[267,4486,4487],{"v-slot:java":269},[271,4488,4490],{"className":485,"code":4489,"language":487,"meta":269,"style":269},"for (int i = 0; i \u003C n; i++) {\n    totaal += a[i];\n}\n",[14,4491,4492,4522,4536],{"__ignoreMap":269},[279,4493,4494,4496,4498,4500,4502,4504,4506,4508,4510,4512,4514,4516,4518,4520],{"class":281,"line":282},[279,4495,4457],{"class":306},[279,4497,523],{"class":293},[279,4499,505],{"class":285},[279,4501,2134],{"class":310},[279,4503,344],{"class":293},[279,4505,393],{"class":322},[279,4507,534],{"class":293},[279,4509,2134],{"class":310},[279,4511,539],{"class":293},[279,4513,925],{"class":310},[279,4515,534],{"class":293},[279,4517,3602],{"class":310},[279,4519,554],{"class":293},[279,4521,516],{"class":293},[279,4523,4524,4526,4528,4530,4532,4534],{"class":281,"line":303},[279,4525,4474],{"class":310},[279,4527,2214],{"class":293},[279,4529,347],{"class":310},[279,4531,350],{"class":293},[279,4533,2173],{"class":310},[279,4535,575],{"class":293},[279,4537,4538],{"class":281,"line":338},[279,4539,701],{"class":293},[10,4541,4542,4543,4545,4546,31],{},"De body draait ",[14,4544,2764],{}," keer: ",[22,4547,4548],{},[14,4549,719],{},[4440,4551,4553],{"id":4552},"geneste-lussen","Geneste lussen",[264,4555,4556,4636],{},[267,4557,4558],{"v-slot:python":269},[271,4559,4561],{"className":273,"code":4560,"language":275,"meta":269,"style":269},"for i in range(n):\n    for j in range(i + 1, n):\n        if a[i] == a[j]:\n            gevonden = True\n",[14,4562,4563,4579,4603,4626],{"__ignoreMap":269},[279,4564,4565,4567,4569,4571,4573,4575,4577],{"class":281,"line":282},[279,4566,4457],{"class":306},[279,4568,2134],{"class":310},[279,4570,314],{"class":306},[279,4572,317],{"class":289},[279,4574,294],{"class":293},[279,4576,2764],{"class":289},[279,4578,300],{"class":293},[279,4580,4581,4583,4585,4587,4589,4591,4593,4595,4597,4599,4601],{"class":281,"line":303},[279,4582,307],{"class":306},[279,4584,387],{"class":310},[279,4586,314],{"class":306},[279,4588,317],{"class":289},[279,4590,294],{"class":293},[279,4592,2549],{"class":289},[279,4594,429],{"class":293},[279,4596,432],{"class":322},[279,4598,325],{"class":293},[279,4600,925],{"class":289},[279,4602,300],{"class":293},[279,4604,4605,4607,4609,4611,4613,4615,4618,4620,4622,4624],{"class":281,"line":338},[279,4606,2165],{"class":306},[279,4608,347],{"class":310},[279,4610,350],{"class":293},[279,4612,2173],{"class":310},[279,4614,406],{"class":293},[279,4616,4617],{"class":293}," ==",[279,4619,347],{"class":310},[279,4621,350],{"class":293},[279,4623,403],{"class":310},[279,4625,992],{"class":293},[279,4627,4628,4631,4633],{"class":281,"line":358},[279,4629,4630],{"class":310},"            gevonden ",[279,4632,344],{"class":293},[279,4634,4635],{"class":293}," True\n",[267,4637,4638],{"v-slot:java":269},[271,4639,4641],{"className":485,"code":4640,"language":487,"meta":269,"style":269},"for (int i = 0; i \u003C n; i++) {\n    for (int j = i + 1; j \u003C n; j++) {\n        if (a[i] == a[j]) {\n            gevonden = true;\n        }\n    }\n}\n",[14,4642,4643,4673,4707,4733,4742,4746,4750],{"__ignoreMap":269},[279,4644,4645,4647,4649,4651,4653,4655,4657,4659,4661,4663,4665,4667,4669,4671],{"class":281,"line":282},[279,4646,4457],{"class":306},[279,4648,523],{"class":293},[279,4650,505],{"class":285},[279,4652,2134],{"class":310},[279,4654,344],{"class":293},[279,4656,393],{"class":322},[279,4658,534],{"class":293},[279,4660,2134],{"class":310},[279,4662,539],{"class":293},[279,4664,925],{"class":310},[279,4666,534],{"class":293},[279,4668,3602],{"class":310},[279,4670,554],{"class":293},[279,4672,516],{"class":293},[279,4674,4675,4677,4679,4681,4683,4685,4687,4689,4691,4693,4695,4697,4699,4701,4703,4705],{"class":281,"line":303},[279,4676,307],{"class":306},[279,4678,523],{"class":293},[279,4680,505],{"class":285},[279,4682,387],{"class":310},[279,4684,344],{"class":293},[279,4686,2134],{"class":310},[279,4688,429],{"class":293},[279,4690,432],{"class":322},[279,4692,534],{"class":293},[279,4694,387],{"class":310},[279,4696,539],{"class":293},[279,4698,925],{"class":310},[279,4700,534],{"class":293},[279,4702,1178],{"class":310},[279,4704,554],{"class":293},[279,4706,516],{"class":293},[279,4708,4709,4711,4713,4715,4717,4719,4721,4723,4725,4727,4729,4731],{"class":281,"line":338},[279,4710,2165],{"class":306},[279,4712,523],{"class":293},[279,4714,27],{"class":310},[279,4716,350],{"class":293},[279,4718,2173],{"class":310},[279,4720,406],{"class":293},[279,4722,4617],{"class":293},[279,4724,347],{"class":310},[279,4726,350],{"class":293},[279,4728,403],{"class":310},[279,4730,1207],{"class":293},[279,4732,516],{"class":293},[279,4734,4735,4737,4739],{"class":281,"line":358},[279,4736,4630],{"class":310},[279,4738,344],{"class":293},[279,4740,4741],{"class":293}," true;\n",[279,4743,4744],{"class":281,"line":374},[279,4745,665],{"class":293},[279,4747,4748],{"class":281,"line":381},[279,4749,695],{"class":293},[279,4751,4752],{"class":281,"line":418},[279,4753,701],{"class":293},[10,4755,4756,4757,4760,4761,4763,4764,4226,4767,4770],{},"Voor ",[14,4758,4759],{},"i = 0"," draait de binnenste lus ",[14,4762,1438],{}," keer, voor ",[14,4765,4766],{},"i = 1",[14,4768,4769],{},"n-2"," keer, enzovoort tot 0. Samen:",[10,4772,4773],{},[14,4774,4775],{},"(n-1) + (n-2) + … + 1 + 0 = n(n-1)\u002F2",[10,4777,4778,4779,4782,4783,4785,4786,4788,4789,4793],{},"Bij ",[14,4780,4781],{},"n = 16"," zijn dat 120 vergelijkingen, bij ",[14,4784,4258],{}," precies 499.500. Constante (½) weg,\ndominante term (",[14,4787,4204],{},") houden: ",[22,4790,4791],{},[14,4792,1317],{},". Dat de binnenste lus \"maar half zo lang\" is, verandert de\nklasse niet.",[4440,4795,4797],{"id":4796},"gehalveerde-of-verdubbelde-teller","Gehalveerde of verdubbelde teller",[264,4799,4800,4841],{},[267,4801,4802],{"v-slot:python":269},[271,4803,4805],{"className":273,"code":4804,"language":275,"meta":269,"style":269},"i = n\nwhile i > 0:\n    i \u002F\u002F= 2        # i wordt telkens gehalveerd\n",[14,4806,4807,4816,4829],{"__ignoreMap":269},[279,4808,4809,4811,4813],{"class":281,"line":282},[279,4810,2549],{"class":310},[279,4812,344],{"class":293},[279,4814,4815],{"class":310}," n\n",[279,4817,4818,4820,4822,4825,4827],{"class":281,"line":303},[279,4819,707],{"class":306},[279,4821,2134],{"class":310},[279,4823,4824],{"class":293},">",[279,4826,393],{"class":322},[279,4828,415],{"class":293},[279,4830,4831,4833,4836,4838],{"class":281,"line":338},[279,4832,2117],{"class":310},[279,4834,4835],{"class":293},"\u002F\u002F=",[279,4837,2384],{"class":322},[279,4839,4840],{"class":377},"        # i wordt telkens gehalveerd\n",[267,4842,4843],{"v-slot:java":269},[271,4844,4846],{"className":485,"code":4845,"language":487,"meta":269,"style":269},"int i = n;\nwhile (i > 0) {\n    i \u002F= 2;        \u002F\u002F i wordt telkens gehalveerd (integerdeling)\n}\n",[14,4847,4848,4860,4876,4890],{"__ignoreMap":269},[279,4849,4850,4852,4854,4856,4858],{"class":281,"line":282},[279,4851,505],{"class":285},[279,4853,2134],{"class":310},[279,4855,344],{"class":293},[279,4857,925],{"class":310},[279,4859,592],{"class":293},[279,4861,4862,4864,4866,4868,4870,4872,4874],{"class":281,"line":303},[279,4863,707],{"class":306},[279,4865,523],{"class":293},[279,4867,2549],{"class":310},[279,4869,4824],{"class":293},[279,4871,393],{"class":322},[279,4873,513],{"class":293},[279,4875,516],{"class":293},[279,4877,4878,4880,4883,4885,4887],{"class":281,"line":338},[279,4879,2117],{"class":310},[279,4881,4882],{"class":293},"\u002F=",[279,4884,2384],{"class":322},[279,4886,534],{"class":293},[279,4888,4889],{"class":377},"        \u002F\u002F i wordt telkens gehalveerd (integerdeling)\n",[279,4891,4892],{"class":281,"line":358},[279,4893,701],{"class":293},[10,4895,4778,4896,4898,4899,4901,4902,4165,4904,31],{},[14,4897,4781],{}," neemt ",[14,4900,2173],{}," de waarden 16, 8, 4, 2, 1 aan: 5 iteraties. Elke stap halveert het werk,\ndus het aantal stappen is ongeveer ",[14,4903,4278],{},[22,4905,4906],{},[14,4907,3791],{},[10,4909,4910],{},"Hetzelfde geldt voor een teller die verdubbelt:",[264,4912,4913,4952],{},[267,4914,4915],{"v-slot:python":269},[271,4916,4918],{"className":273,"code":4917,"language":275,"meta":269,"style":269},"i = 1\nwhile i \u003C n:\n    i *= 2         # 1, 2, 4, 8, ... tot n\n",[14,4919,4920,4928,4940],{"__ignoreMap":269},[279,4921,4922,4924,4926],{"class":281,"line":282},[279,4923,2549],{"class":310},[279,4925,344],{"class":293},[279,4927,371],{"class":322},[279,4929,4930,4932,4934,4936,4938],{"class":281,"line":303},[279,4931,707],{"class":306},[279,4933,2134],{"class":310},[279,4935,539],{"class":293},[279,4937,925],{"class":310},[279,4939,415],{"class":293},[279,4941,4942,4944,4947,4949],{"class":281,"line":338},[279,4943,2117],{"class":310},[279,4945,4946],{"class":293},"*=",[279,4948,2384],{"class":322},[279,4950,4951],{"class":377},"         # 1, 2, 4, 8, ... tot n\n",[267,4953,4954],{"v-slot:java":269},[271,4955,4957],{"className":485,"code":4956,"language":487,"meta":269,"style":269},"int i = 1;\nwhile (i \u003C n) {\n    i *= 2;        \u002F\u002F 1, 2, 4, 8, ... tot n\n}\n",[14,4958,4959,4971,4987,5000],{"__ignoreMap":269},[279,4960,4961,4963,4965,4967,4969],{"class":281,"line":282},[279,4962,505],{"class":285},[279,4964,2134],{"class":310},[279,4966,344],{"class":293},[279,4968,432],{"class":322},[279,4970,592],{"class":293},[279,4972,4973,4975,4977,4979,4981,4983,4985],{"class":281,"line":303},[279,4974,707],{"class":306},[279,4976,523],{"class":293},[279,4978,2549],{"class":310},[279,4980,539],{"class":293},[279,4982,925],{"class":310},[279,4984,513],{"class":293},[279,4986,516],{"class":293},[279,4988,4989,4991,4993,4995,4997],{"class":281,"line":338},[279,4990,2117],{"class":310},[279,4992,4946],{"class":293},[279,4994,2384],{"class":322},[279,4996,534],{"class":293},[279,4998,4999],{"class":377},"        \u002F\u002F 1, 2, 4, 8, ... tot n\n",[279,5001,5002],{"class":281,"line":358},[279,5003,701],{"class":293},[41,5005,5006,5019],{},[44,5007,5008],{},[47,5009,5010,5013,5015,5017],{},[50,5011,5012],{},"Lus",[50,5014,4781],{},[50,5016,4258],{},[50,5018,4316],{},[60,5020,5021,5040],{},[47,5022,5023,5032,5034,5036],{},[65,5024,5025,5028,5029,5031],{},[14,5026,5027],{},"i \u002F\u002F= 2"," vanaf ",[14,5030,2764],{}," tot 0",[65,5033,247],{},[65,5035,4363],{},[65,5037,5038],{},[14,5039,3791],{},[47,5041,5042,5050,5052,5054],{},[65,5043,5044,5047,5048],{},[14,5045,5046],{},"i *= 2"," vanaf 1 tot ",[14,5049,2764],{},[65,5051,210],{},[65,5053,4363],{},[65,5055,5056],{},[14,5057,3791],{},[10,5059,5060,5061,5064,5065,5068,5069,5071,5072,31],{},"Let op het verschil met ",[14,5062,5063],{},"i -= 2"," of ",[14,5066,5067],{},"i += 2",": dat zijn ",[14,5070,4235],{}," stappen, dus gewoon ",[22,5073,5074],{},[14,5075,719],{},[4440,5077,5079],{"id":5078},"sequentiële-stukken","Sequentiële stukken",[10,5081,5082],{},"Twee stukken code ná elkaar tel je op, en dan houd je de grootste:",[264,5084,5085,5170],{},[267,5086,5087],{"v-slot:python":269},[271,5088,5090],{"className":273,"code":5089,"language":275,"meta":269,"style":269},"for i in range(n):          # O(n)\n    totaal += a[i]\nfor i in range(n):          # O(n²)\n    for j in range(n):\n        paren += 1\n",[14,5091,5092,5112,5126,5145,5161],{"__ignoreMap":269},[279,5093,5094,5096,5098,5100,5102,5104,5106,5109],{"class":281,"line":282},[279,5095,4457],{"class":306},[279,5097,2134],{"class":310},[279,5099,314],{"class":306},[279,5101,317],{"class":289},[279,5103,294],{"class":293},[279,5105,2764],{"class":289},[279,5107,5108],{"class":293},"):",[279,5110,5111],{"class":377},"          # O(n)\n",[279,5113,5114,5116,5118,5120,5122,5124],{"class":281,"line":303},[279,5115,4474],{"class":310},[279,5117,2214],{"class":293},[279,5119,347],{"class":310},[279,5121,350],{"class":293},[279,5123,2173],{"class":310},[279,5125,355],{"class":293},[279,5127,5128,5130,5132,5134,5136,5138,5140,5142],{"class":281,"line":338},[279,5129,4457],{"class":306},[279,5131,2134],{"class":310},[279,5133,314],{"class":306},[279,5135,317],{"class":289},[279,5137,294],{"class":293},[279,5139,2764],{"class":289},[279,5141,5108],{"class":293},[279,5143,5144],{"class":377},"          # O(n²)\n",[279,5146,5147,5149,5151,5153,5155,5157,5159],{"class":281,"line":358},[279,5148,307],{"class":306},[279,5150,387],{"class":310},[279,5152,314],{"class":306},[279,5154,317],{"class":289},[279,5156,294],{"class":293},[279,5158,2764],{"class":289},[279,5160,300],{"class":293},[279,5162,5163,5166,5168],{"class":281,"line":374},[279,5164,5165],{"class":310},"        paren ",[279,5167,2214],{"class":293},[279,5169,371],{"class":322},[267,5171,5172],{"v-slot:java":269},[271,5173,5175],{"className":485,"code":5174,"language":487,"meta":269,"style":269},"for (int i = 0; i \u003C n; i++) {          \u002F\u002F O(n)\n    totaal += a[i];\n}\nfor (int i = 0; i \u003C n; i++) {          \u002F\u002F O(n²)\n    for (int j = 0; j \u003C n; j++) {\n        paren++;\n    }\n}\n",[14,5176,5177,5210,5224,5228,5261,5291,5298,5302],{"__ignoreMap":269},[279,5178,5179,5181,5183,5185,5187,5189,5191,5193,5195,5197,5199,5201,5203,5205,5207],{"class":281,"line":282},[279,5180,4457],{"class":306},[279,5182,523],{"class":293},[279,5184,505],{"class":285},[279,5186,2134],{"class":310},[279,5188,344],{"class":293},[279,5190,393],{"class":322},[279,5192,534],{"class":293},[279,5194,2134],{"class":310},[279,5196,539],{"class":293},[279,5198,925],{"class":310},[279,5200,534],{"class":293},[279,5202,3602],{"class":310},[279,5204,554],{"class":293},[279,5206,3476],{"class":293},[279,5208,5209],{"class":377},"          \u002F\u002F O(n)\n",[279,5211,5212,5214,5216,5218,5220,5222],{"class":281,"line":303},[279,5213,4474],{"class":310},[279,5215,2214],{"class":293},[279,5217,347],{"class":310},[279,5219,350],{"class":293},[279,5221,2173],{"class":310},[279,5223,575],{"class":293},[279,5225,5226],{"class":281,"line":338},[279,5227,701],{"class":293},[279,5229,5230,5232,5234,5236,5238,5240,5242,5244,5246,5248,5250,5252,5254,5256,5258],{"class":281,"line":358},[279,5231,4457],{"class":306},[279,5233,523],{"class":293},[279,5235,505],{"class":285},[279,5237,2134],{"class":310},[279,5239,344],{"class":293},[279,5241,393],{"class":322},[279,5243,534],{"class":293},[279,5245,2134],{"class":310},[279,5247,539],{"class":293},[279,5249,925],{"class":310},[279,5251,534],{"class":293},[279,5253,3602],{"class":310},[279,5255,554],{"class":293},[279,5257,3476],{"class":293},[279,5259,5260],{"class":377},"          \u002F\u002F O(n²)\n",[279,5262,5263,5265,5267,5269,5271,5273,5275,5277,5279,5281,5283,5285,5287,5289],{"class":281,"line":374},[279,5264,307],{"class":306},[279,5266,523],{"class":293},[279,5268,505],{"class":285},[279,5270,387],{"class":310},[279,5272,344],{"class":293},[279,5274,393],{"class":322},[279,5276,534],{"class":293},[279,5278,387],{"class":310},[279,5280,539],{"class":293},[279,5282,925],{"class":310},[279,5284,534],{"class":293},[279,5286,1178],{"class":310},[279,5288,554],{"class":293},[279,5290,516],{"class":293},[279,5292,5293,5296],{"class":281,"line":381},[279,5294,5295],{"class":310},"        paren",[279,5297,3536],{"class":293},[279,5299,5300],{"class":281,"line":418},[279,5301,695],{"class":293},[279,5303,5304],{"class":281,"line":448},[279,5305,701],{"class":293},[10,5307,5308,5311,5312,5315,5316,31],{},[14,5309,5310],{},"O(n) + O(n²) = O(n²)",". Nesten ",[22,5313,5314],{},"vermenigvuldigt",", achter elkaar zetten ",[22,5317,5318],{},"telt op",[4440,5320,5322],{"id":5321},"een-lus-met-een-logaritmische-binnenlus","Een lus met een logaritmische binnenlus",[264,5324,5325,5377],{},[267,5326,5327],{"v-slot:python":269},[271,5328,5330],{"className":273,"code":5329,"language":275,"meta":269,"style":269},"for i in range(n):\n    j = 1\n    while j \u003C n:\n        j *= 2\n",[14,5331,5332,5348,5357,5369],{"__ignoreMap":269},[279,5333,5334,5336,5338,5340,5342,5344,5346],{"class":281,"line":282},[279,5335,4457],{"class":306},[279,5337,2134],{"class":310},[279,5339,314],{"class":306},[279,5341,317],{"class":289},[279,5343,294],{"class":293},[279,5345,2764],{"class":289},[279,5347,300],{"class":293},[279,5349,5350,5353,5355],{"class":281,"line":303},[279,5351,5352],{"class":310},"    j ",[279,5354,344],{"class":293},[279,5356,371],{"class":322},[279,5358,5359,5361,5363,5365,5367],{"class":281,"line":338},[279,5360,2131],{"class":306},[279,5362,387],{"class":310},[279,5364,539],{"class":293},[279,5366,925],{"class":310},[279,5368,415],{"class":293},[279,5370,5371,5373,5375],{"class":281,"line":358},[279,5372,361],{"class":310},[279,5374,4946],{"class":293},[279,5376,2055],{"class":322},[267,5378,5379],{"v-slot:java":269},[271,5380,5382],{"className":485,"code":5381,"language":487,"meta":269,"style":269},"for (int i = 0; i \u003C n; i++) {\n    int j = 1;\n    while (j \u003C n) {\n        j *= 2;\n    }\n}\n",[14,5383,5384,5414,5426,5442,5452,5456],{"__ignoreMap":269},[279,5385,5386,5388,5390,5392,5394,5396,5398,5400,5402,5404,5406,5408,5410,5412],{"class":281,"line":282},[279,5387,4457],{"class":306},[279,5389,523],{"class":293},[279,5391,505],{"class":285},[279,5393,2134],{"class":310},[279,5395,344],{"class":293},[279,5397,393],{"class":322},[279,5399,534],{"class":293},[279,5401,2134],{"class":310},[279,5403,539],{"class":293},[279,5405,925],{"class":310},[279,5407,534],{"class":293},[279,5409,3602],{"class":310},[279,5411,554],{"class":293},[279,5413,516],{"class":293},[279,5415,5416,5418,5420,5422,5424],{"class":281,"line":303},[279,5417,1086],{"class":285},[279,5419,387],{"class":310},[279,5421,344],{"class":293},[279,5423,432],{"class":322},[279,5425,592],{"class":293},[279,5427,5428,5430,5432,5434,5436,5438,5440],{"class":281,"line":338},[279,5429,2131],{"class":306},[279,5431,523],{"class":293},[279,5433,426],{"class":310},[279,5435,539],{"class":293},[279,5437,925],{"class":310},[279,5439,513],{"class":293},[279,5441,516],{"class":293},[279,5443,5444,5446,5448,5450],{"class":281,"line":358},[279,5445,361],{"class":310},[279,5447,4946],{"class":293},[279,5449,2384],{"class":322},[279,5451,592],{"class":293},[279,5453,5454],{"class":281,"line":374},[279,5455,695],{"class":293},[279,5457,5458],{"class":281,"line":381},[279,5459,701],{"class":293},[10,5461,5462,5463,5465,5466,4545,5468,31],{},"De buitenste lus draait ",[14,5464,2764],{}," keer, de binnenste elke keer ",[14,5467,2753],{},[22,5469,5470],{},[14,5471,2760],{},[33,5473,5475],{"id":5474},"recursie-en-recurrente-betrekkingen","Recursie en recurrente betrekkingen",[10,5477,5478,5479,5482,5483,5486,5487,5489,5490,5493],{},"Bij een recursieve functie schrijf je de looptijd op als een ",[22,5480,5481],{},"recurrente betrekking","\n(",[1825,5484,5485],{},"recurrence relation","): een formule die ",[14,5488,4149],{}," uitdrukt in ",[14,5491,5492],{},"T"," van een kleinere invoer.",[10,5495,5496],{},"Een paar standaardgevallen:",[41,5498,5499,5512],{},[44,5500,5501],{},[47,5502,5503,5506,5509],{},[50,5504,5505],{},"Code-patroon",[50,5507,5508],{},"Recurrente betrekking",[50,5510,5511],{},"Oplossing",[60,5513,5514,5531,5547,5563,5577],{},[47,5515,5516,5522,5527],{},[65,5517,5518,5519,5521],{},"één recursieve aanroep op ",[14,5520,1438],{},", constant werk",[65,5523,5524],{},[14,5525,5526],{},"T(n) = T(n-1) + 1",[65,5528,5529],{},[14,5530,719],{},[47,5532,5533,5539,5543],{},[65,5534,5535,5536,5538],{},"één aanroep op ",[14,5537,1438],{},", lineair werk (bv. een lus)",[65,5540,5541],{},[14,5542,3754],{},[65,5544,5545],{},[14,5546,1317],{},[47,5548,5549,5554,5559],{},[65,5550,5551,5552,513],{},"één aanroep op de helft, constant werk (",[27,5553,4360],{"href":4359},[65,5555,5556],{},[14,5557,5558],{},"T(n) = T(n\u002F2) + 1",[65,5560,5561],{},[14,5562,3791],{},[47,5564,5565,5568,5573],{},[65,5566,5567],{},"twee aanroepen op de helft, lineair werk (merge sort)",[65,5569,5570],{},[14,5571,5572],{},"T(n) = 2T(n\u002F2) + n",[65,5574,5575],{},[14,5576,2760],{},[47,5578,5579,5585,5590],{},[65,5580,5581,5582,5584],{},"twee aanroepen op ",[14,5583,1438],{}," (naïeve Fibonacci)",[65,5586,5587],{},[14,5588,5589],{},"T(n) = 2T(n-1) + 1",[65,5591,5592],{},[14,5593,4307],{},[10,5595,5596],{},"Een voorbeeld: de som van een lijst, recursief.",[264,5598,5599,5731],{},[267,5600,5601],{"v-slot:python":269},[271,5602,5604],{"className":273,"code":5603,"language":275,"meta":269,"style":269},"def som(a, n):\n    # basisgeval: een lege lijst heeft som 0\n    if n == 0:\n        return 0\n    # één recursieve aanroep op n-1, plus constant werk\n    return som(a, n - 1) + a[n - 1]\n\nprint(som([4, 1, 7, 3], 4))  # 15\n",[14,5605,5606,5623,5628,5641,5647,5652,5687,5691],{"__ignoreMap":269},[279,5607,5608,5610,5613,5615,5617,5619,5621],{"class":281,"line":282},[279,5609,286],{"class":285},[279,5611,5612],{"class":289}," som",[279,5614,294],{"class":293},[279,5616,27],{"class":297},[279,5618,325],{"class":293},[279,5620,925],{"class":297},[279,5622,300],{"class":293},[279,5624,5625],{"class":281,"line":303},[279,5626,5627],{"class":377},"    # basisgeval: een lege lijst heeft som 0\n",[279,5629,5630,5632,5634,5637,5639],{"class":281,"line":338},[279,5631,2011],{"class":306},[279,5633,1089],{"class":310},[279,5635,5636],{"class":293},"==",[279,5638,393],{"class":322},[279,5640,415],{"class":293},[279,5642,5643,5645],{"class":281,"line":358},[279,5644,2031],{"class":306},[279,5646,2126],{"class":322},[279,5648,5649],{"class":281,"line":374},[279,5650,5651],{"class":377},"    # één recursieve aanroep op n-1, plus constant werk\n",[279,5653,5654,5656,5658,5660,5662,5664,5666,5668,5670,5672,5675,5677,5679,5681,5683,5685],{"class":281,"line":381},[279,5655,2295],{"class":306},[279,5657,5612],{"class":289},[279,5659,294],{"class":293},[279,5661,27],{"class":289},[279,5663,325],{"class":293},[279,5665,1089],{"class":289},[279,5667,368],{"class":293},[279,5669,432],{"class":322},[279,5671,513],{"class":293},[279,5673,5674],{"class":293}," +",[279,5676,347],{"class":310},[279,5678,350],{"class":293},[279,5680,1516],{"class":310},[279,5682,368],{"class":293},[279,5684,432],{"class":322},[279,5686,355],{"class":293},[279,5688,5689],{"class":281,"line":418},[279,5690,3210],{"emptyLinePlaceholder":3209},[279,5692,5693,5696,5698,5701,5704,5706,5708,5710,5712,5715,5717,5720,5722,5725,5728],{"class":281,"line":448},[279,5694,5695],{"class":289},"print",[279,5697,294],{"class":293},[279,5699,5700],{"class":289},"som",[279,5702,5703],{"class":293},"([",[279,5705,210],{"class":322},[279,5707,325],{"class":293},[279,5709,432],{"class":322},[279,5711,325],{"class":293},[279,5713,5714],{"class":322}," 7",[279,5716,325],{"class":293},[279,5718,5719],{"class":322}," 3",[279,5721,1023],{"class":293},[279,5723,5724],{"class":322}," 4",[279,5726,5727],{"class":293},"))",[279,5729,5730],{"class":377},"  # 15\n",[267,5732,5733],{"v-slot:java":269},[271,5734,5736],{"className":485,"code":5735,"language":487,"meta":269,"style":269},"static int som(int[] a, int n) {\n    \u002F\u002F basisgeval: een lege lijst heeft som 0\n    if (n == 0) {\n        return 0;\n    }\n    \u002F\u002F één recursieve aanroep op n-1, plus constant werk\n    return som(a, n - 1) + a[n - 1];\n}\n",[14,5737,5738,5764,5769,5785,5793,5797,5802,5836],{"__ignoreMap":269},[279,5739,5740,5742,5744,5746,5748,5750,5752,5754,5756,5758,5760,5762],{"class":281,"line":282},[279,5741,494],{"class":285},[279,5743,2312],{"class":285},[279,5745,5612],{"class":289},[279,5747,294],{"class":293},[279,5749,505],{"class":285},[279,5751,508],{"class":293},[279,5753,347],{"class":310},[279,5755,325],{"class":293},[279,5757,2312],{"class":285},[279,5759,925],{"class":310},[279,5761,513],{"class":293},[279,5763,516],{"class":293},[279,5765,5766],{"class":281,"line":303},[279,5767,5768],{"class":377},"    \u002F\u002F basisgeval: een lege lijst heeft som 0\n",[279,5770,5771,5773,5775,5777,5779,5781,5783],{"class":281,"line":338},[279,5772,2011],{"class":306},[279,5774,523],{"class":293},[279,5776,1516],{"class":310},[279,5778,5636],{"class":293},[279,5780,393],{"class":322},[279,5782,513],{"class":293},[279,5784,516],{"class":293},[279,5786,5787,5789,5791],{"class":281,"line":358},[279,5788,2031],{"class":306},[279,5790,393],{"class":322},[279,5792,592],{"class":293},[279,5794,5795],{"class":281,"line":374},[279,5796,695],{"class":293},[279,5798,5799],{"class":281,"line":381},[279,5800,5801],{"class":377},"    \u002F\u002F één recursieve aanroep op n-1, plus constant werk\n",[279,5803,5804,5806,5808,5810,5812,5814,5816,5818,5820,5822,5824,5826,5828,5830,5832,5834],{"class":281,"line":418},[279,5805,2295],{"class":306},[279,5807,5612],{"class":289},[279,5809,294],{"class":293},[279,5811,27],{"class":310},[279,5813,325],{"class":293},[279,5815,1089],{"class":310},[279,5817,368],{"class":293},[279,5819,432],{"class":322},[279,5821,513],{"class":293},[279,5823,5674],{"class":293},[279,5825,347],{"class":310},[279,5827,350],{"class":293},[279,5829,1516],{"class":310},[279,5831,368],{"class":293},[279,5833,432],{"class":322},[279,5835,575],{"class":293},[279,5837,5838],{"class":281,"line":448},[279,5839,701],{"class":293},[10,5841,5842,5843,5845,5846,5849,5850,31],{},"Dit is ",[14,5844,5526],{},". Uitschrijven (\"ontrollen\") laat zien wat er gebeurt:\n",[14,5847,5848],{},"T(n) = T(n-2) + 2 = T(n-3) + 3 = … = T(0) + n",", dus ",[22,5851,5852],{},[14,5853,719],{},[33,5855,5857],{"id":5856},"de-mastermethode","De mastermethode",[10,5859,5860,5861,523,5864,5867],{},"Voor recursies die het probleem in gelijke stukken delen, is er een kant-en-klaar recept: de\n",[22,5862,5863],{},"mastermethode",[1825,5865,5866],{},"master theorem","). Hij werkt voor betrekkingen van de vorm",[10,5869,5870],{},[14,5871,5872],{},"T(n) = a · T(n\u002Fb) + n^d",[10,5874,5875,5876,5879,5880,5883,5884,5887,5888,1835,5890,2812],{},"met ",[14,5877,5878],{},"a ≥ 1"," deelproblemen, elk van grootte ",[14,5881,5882],{},"n\u002Fb",", en ",[14,5885,5886],{},"n^d"," werk buiten de recursie (splitsen en\nsamenvoegen). Je vergelijkt ",[14,5889,27],{},[14,5891,5892],{},"b^d",[41,5894,5895,5910],{},[44,5896,5897],{},[47,5898,5899,5902,5905,5907],{},[50,5900,5901],{},"Geval",[50,5903,5904],{},"Voorwaarde",[50,5906,5511],{},[50,5908,5909],{},"Wat domineert",[60,5911,5912,5929,5946],{},[47,5913,5914,5916,5921,5926],{},[65,5915,191],{},[65,5917,5918],{},[14,5919,5920],{},"a \u003C b^d",[65,5922,5923],{},[14,5924,5925],{},"Θ(n^d)",[65,5927,5928],{},"het werk bovenaan de boom",[47,5930,5931,5933,5938,5943],{},[65,5932,196],{},[65,5934,5935],{},[14,5936,5937],{},"a = b^d",[65,5939,5940],{},[14,5941,5942],{},"Θ(n^d log n)",[65,5944,5945],{},"elk niveau evenveel werk",[47,5947,5948,5950,5955,5960],{},[65,5949,220],{},[65,5951,5952],{},[14,5953,5954],{},"a > b^d",[65,5956,5957],{},[14,5958,5959],{},"Θ(n^(log_b a))",[65,5961,5962],{},"de bladeren onderaan",[10,5964,5965],{},"Uitgewerkt:",[41,5967,5968,5990],{},[44,5969,5970],{},[47,5971,5972,5975,5977,5980,5983,5985,5988],{},[50,5973,5974],{},"Betrekking",[50,5976,27],{},[50,5978,5979],{},"b",[50,5981,5982],{},"d",[50,5984,5892],{},[50,5986,5987],{},"Vergelijking",[50,5989,5511],{},[60,5991,5992,6014,6036,6058,6080],{},[47,5993,5994,5999,6001,6003,6005,6007,6009],{},[65,5995,5996,5998],{},[14,5997,5572],{}," (merge sort)",[65,6000,196],{},[65,6002,196],{},[65,6004,191],{},[65,6006,196],{},[65,6008,5937],{},[65,6010,6011],{},[14,6012,6013],{},"Θ(n log n)",[47,6015,6016,6021,6023,6025,6027,6029,6031],{},[65,6017,6018,6020],{},[14,6019,5558],{}," (binair zoeken)",[65,6022,191],{},[65,6024,196],{},[65,6026,1400],{},[65,6028,191],{},[65,6030,5937],{},[65,6032,6033],{},[14,6034,6035],{},"Θ(log n)",[47,6037,6038,6043,6045,6047,6049,6051,6053],{},[65,6039,6040],{},[14,6041,6042],{},"T(n) = 2T(n\u002F2) + n²",[65,6044,196],{},[65,6046,196],{},[65,6048,196],{},[65,6050,210],{},[65,6052,5920],{},[65,6054,6055],{},[14,6056,6057],{},"Θ(n²)",[47,6059,6060,6065,6067,6069,6071,6073,6075],{},[65,6061,6062],{},[14,6063,6064],{},"T(n) = 8T(n\u002F2) + n²",[65,6066,1967],{},[65,6068,196],{},[65,6070,196],{},[65,6072,210],{},[65,6074,5954],{},[65,6076,6077],{},[14,6078,6079],{},"Θ(n^(log₂ 8)) = Θ(n³)",[47,6081,6082,6087,6089,6091,6093,6095,6097],{},[65,6083,6084],{},[14,6085,6086],{},"T(n) = 4T(n\u002F2) + n",[65,6088,210],{},[65,6090,196],{},[65,6092,191],{},[65,6094,196],{},[65,6096,5954],{},[65,6098,6099],{},[14,6100,6101],{},"Θ(n^(log₂ 4)) = Θ(n²)",[10,6103,6104,6105,5849,6108,91,6111,31],{},"Let op het tweede voorbeeld: constant werk is ",[14,6106,6107],{},"n⁰",[14,6109,6110],{},"d = 0",[14,6112,6113],{},"b^d = 1",[10,6115,6116,6117,6119],{},"De intuïtie: teken de recursieboom. In geval 1 doet de wortel het meeste werk, in geval 3 zitten de\nkosten in de enorme hoeveelheid bladeren, en in geval 2 kost elk van de ",[14,6118,2753],{}," niveaus evenveel.",[10,6121,6122,6123,6125,6126,6128,6129,6131],{},"De mastermethode werkt ",[22,6124,4017],{}," voor ",[14,6127,3754],{},": daar wordt ",[14,6130,2764],{}," niet gedeeld maar met één\nverminderd. Die los je op door te ontrollen, zoals hierboven.",[33,6133,6135],{"id":6134},"complexiteit-in-één-tabel","Complexiteit in één tabel",[41,6137,6138,6147],{},[44,6139,6140],{},[47,6141,6142,6145],{},[50,6143,6144],{},"Situatie",[50,6146,3795],{},[60,6148,6149,6160,6169,6178,6193,6204,6212],{},[47,6150,6151,6156],{},[65,6152,6153,6154],{},"vaste hoeveelheid werk, onafhankelijk van ",[14,6155,2764],{},[65,6157,6158],{},[14,6159,3787],{},[47,6161,6162,6165],{},[65,6163,6164],{},"teller halveert of verdubbelt",[65,6166,6167],{},[14,6168,3791],{},[47,6170,6171,6174],{},[65,6172,6173],{},"één lus over alle elementen",[65,6175,6176],{},[14,6177,719],{},[47,6179,6180,6189],{},[65,6181,6182,6183,6185,6186,6188],{},"lus van ",[14,6184,2764],{}," met daarbinnen een ",[14,6187,2753],{},"-lus",[65,6190,6191],{},[14,6192,2760],{},[47,6194,6195,6200],{},[65,6196,6197,6198],{},"twee geneste lussen over ",[14,6199,2764],{},[65,6201,6202],{},[14,6203,1317],{},[47,6205,6206,6209],{},[65,6207,6208],{},"twee lussen ná elkaar",[65,6210,6211],{},"de grootste van de twee",[47,6213,6214,6217],{},[65,6215,6216],{},"alle deelverzamelingen proberen",[65,6218,6219],{},[14,6220,4307],{},[33,6222,3961],{"id":3960},[3963,6224,6225,6239,6245,6253,6275],{},[3770,6226,6227,6233,6234,6236,6237,31],{},[22,6228,6229,6230,6232],{},"Elke geneste lus is ",[14,6231,1317],{}," noemen."," Kijk naar wat de binnenste lus doet. Halveert de teller,\ndan is het ",[14,6235,2760],{},". Loopt de binnenste lus een vast aantal keer (bijvoorbeeld 3), dan is het\ngewoon ",[14,6238,719],{},[3770,6240,6241,6244],{},[22,6242,6243],{},"Optellen en vermenigvuldigen door elkaar halen."," Lussen ná elkaar: optellen, de grootste\nhouden. Lussen ín elkaar: vermenigvuldigen.",[3770,6246,6247,4226,6250,6252],{},[22,6248,6249],{},"Een te ruime grens geven.",[14,6251,1317],{}," voor een enkele lus is technisch niet fout, maar levert op het\ntentamen geen punten op. Geef de strakke grens.",[3770,6254,6255,6260,6261,6263,6264,6267,6268,1835,6270,6272,6273,31],{},[22,6256,6257,6259],{},[14,6258,5982],{}," verkeerd aflezen bij de mastermethode."," Constant werk betekent ",[14,6262,6110],{},", niet ",[14,6265,6266],{},"d = 1",". En\nvergelijk ",[14,6269,27],{},[14,6271,5892],{},", niet met ",[14,6274,5979],{},[3770,6276,6277,6283,6284,6286],{},[22,6278,6279,6280,31],{},"De mastermethode toepassen op ",[14,6281,6282],{},"T(n-1)"," Alleen bij delen door ",[14,6285,5979],{}," werkt het recept; bij\naftrekken ontrol je de recursie.",[33,6288,4033],{"id":4032},[3767,6290,6291,6300,6311,6316,6327],{},[3770,6292,6293,6294,1835,6297,6299],{},"Big-O beschrijft hoe de looptijd ",[22,6295,6296],{},"groeit",[14,6298,2764],{},"; constanten en lagere termen vallen weg.",[3770,6301,6302,6303,6306,6307,6263,6309,31],{},"Op het tentamen geef je de ",[22,6304,6305],{},"strakke"," grens: een enkele lus is ",[14,6308,719],{},[14,6310,1317],{},[3770,6312,6313,6314,31],{},"Geneste lussen vermenigvuldig je, opeenvolgende lussen tel je op; een halverende teller geeft ",[14,6315,2753],{},[3770,6317,6318,6319,6322,6323,1835,6325,31],{},"Recursie schrijf je als recurrente betrekking; bij ",[14,6320,6321],{},"T(n) = aT(n\u002Fb) + n^d"," vergelijk je ",[14,6324,27],{},[14,6326,5892],{},[3770,6328,6329,6330,4296,6332,4296,6334,4296,6336,4296,6338,4296,6340,31],{},"Volgorde om te onthouden: ",[14,6331,3787],{},[14,6333,3791],{},[14,6335,719],{},[14,6337,2760],{},[14,6339,1317],{},[14,6341,4307],{},[4086,6343,6344],{},"html pre.shiki code .s7zQu, html code.shiki .s7zQu{--shiki-light:#39ADB5;--shiki-light-font-style:italic;--shiki-default:#89DDFF;--shiki-default-font-style:italic;--shiki-dark:#89DDFF;--shiki-dark-font-style:italic}html pre.shiki code .sTEyZ, html code.shiki .sTEyZ{--shiki-light:#90A4AE;--shiki-default:#EEFFFF;--shiki-dark:#BABED8}html pre.shiki code .s2Zo4, html code.shiki .s2Zo4{--shiki-light:#6182B8;--shiki-default:#82AAFF;--shiki-dark:#82AAFF}html pre.shiki code .sMK4o, html code.shiki .sMK4o{--shiki-light:#39ADB5;--shiki-default:#89DDFF;--shiki-dark:#89DDFF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: 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.sHdIc{--shiki-light:#90A4AE;--shiki-light-font-style:italic;--shiki-default:#EEFFFF;--shiki-default-font-style:italic;--shiki-dark:#BABED8;--shiki-dark-font-style:italic}",{"title":269,"searchDepth":303,"depth":303,"links":6346},[6347,6348,6349,6350,6357,6358,6359,6360,6361],{"id":4139,"depth":303,"text":4140},{"id":4214,"depth":303,"text":4215},{"id":4287,"depth":303,"text":4288},{"id":4434,"depth":303,"text":4435,"children":6351},[6352,6353,6354,6355,6356],{"id":4442,"depth":338,"text":4443},{"id":4552,"depth":338,"text":4553},{"id":4796,"depth":338,"text":4797},{"id":5078,"depth":338,"text":5079},{"id":5321,"depth":338,"text":5322},{"id":5474,"depth":303,"text":5475},{"id":5856,"depth":303,"text":5857},{"id":6134,"depth":303,"text":6135},{"id":3960,"depth":303,"text":3961},{"id":4032,"depth":303,"text":4033},"Big-O en Θ zonder wiskundejargon: rekenregels, lussen tellen, recurrente betrekkingen en de mastermethode, met uitgewerkte voorbeelden en tentamenvalkuilen.","i-lucide-gauge",{},"\u002Fpracticely-dsa\u002Fcomplexiteit",{"title":4113,"description":6362},"practicely-dsa\u002Fcomplexiteit","FRnTzgDnOlupyMzKYCNsrD-F9LNSzcJzhvVlXgf7zgI",{"id":6370,"title":6371,"body":6372,"description":8443,"extension":4102,"icon":8444,"meta":8445,"navigation":3209,"order":338,"path":8446,"seo":8447,"stem":8448,"topic":8449,"__hash__":8450},"practicelyDsa\u002Fpracticely-dsa\u002Fzoeken.md","Binair zoeken uitgelegd: van lineair zoeken naar O(log n)",{"type":7,"value":6373,"toc":8431},[6374,6381,6402,6406,6414,6627,6638,6642,6645,6657,6702,6719,6723,6730,6793,6895,6909,6913,6920,7023,7044,7048,7469,7496,7500,7503,7555,7558,7623,7632,7636,7652,7736,7742,8189,8201,8203,8224,8314,8330,8332,8392,8394,8428],[10,6375,6376,6377,6380],{},"Zoeken in een lijst klinkt triviaal: loop alles af tot je het vindt. Dat werkt, maar bij een miljoen\nelementen kost het in het slechtste geval een miljoen vergelijkingen. Is de lijst ",[22,6378,6379],{},"gesorteerd",",\ndan kan het met twintig. Dat is het verschil tussen lineair en binair zoeken.",[10,6382,6383,523,6386,6389,6390,6392,6393,6395,6396,5064,6398,6401],{},[22,6384,6385],{},"Binair zoeken",[1825,6387,6388],{},"binary search",") is een van de meest gevraagde algoritmes op tentamens en in\nsollicitatiegesprekken, juist omdat het er simpel uitziet en toch vol zit met kleine valkuilen: ",[14,6391,539],{},"\nof ",[14,6394,2345],{},", ",[14,6397,2074],{},[14,6399,6400],{},"mid+1","? Op deze pagina zie je precies welke variant we gebruiken en waarom die\nklopt.",[33,6403,6405],{"id":6404},"lineair-zoeken","Lineair zoeken",[10,6407,6408,523,6410,6413],{},[22,6409,6405],{},[1825,6411,6412],{},"linear search",") bekijkt de elementen één voor één, van voor naar achter, tot het\ngezochte element gevonden is of de lijst op is.",[264,6415,6416,6501],{},[267,6417,6418],{"v-slot:python":269},[271,6419,6421],{"className":273,"code":6420,"language":275,"meta":269,"style":269},"def lineair_zoeken(a, x):\n    for i in range(len(a)):\n        if a[i] == x:\n            return i  # gevonden op index i\n    return -1  # niet gevonden\n",[14,6422,6423,6440,6461,6479,6490],{"__ignoreMap":269},[279,6424,6425,6427,6430,6432,6434,6436,6438],{"class":281,"line":282},[279,6426,286],{"class":285},[279,6428,6429],{"class":289}," lineair_zoeken",[279,6431,294],{"class":293},[279,6433,27],{"class":297},[279,6435,325],{"class":293},[279,6437,412],{"class":297},[279,6439,300],{"class":293},[279,6441,6442,6444,6446,6448,6450,6452,6455,6457,6459],{"class":281,"line":303},[279,6443,307],{"class":306},[279,6445,2134],{"class":310},[279,6447,314],{"class":306},[279,6449,317],{"class":289},[279,6451,294],{"class":293},[279,6453,6454],{"class":289},"len",[279,6456,294],{"class":293},[279,6458,27],{"class":289},[279,6460,335],{"class":293},[279,6462,6463,6465,6467,6469,6471,6473,6475,6477],{"class":281,"line":338},[279,6464,2165],{"class":306},[279,6466,347],{"class":310},[279,6468,350],{"class":293},[279,6470,2173],{"class":310},[279,6472,406],{"class":293},[279,6474,4617],{"class":293},[279,6476,412],{"class":310},[279,6478,415],{"class":293},[279,6480,6481,6484,6487],{"class":281,"line":358},[279,6482,6483],{"class":306},"            return",[279,6485,6486],{"class":310}," i  ",[279,6488,6489],{"class":377},"# gevonden op index i\n",[279,6491,6492,6494,6496,6498],{"class":281,"line":374},[279,6493,2295],{"class":306},[279,6495,3267],{"class":293},[279,6497,191],{"class":322},[279,6499,6500],{"class":377},"  # niet gevonden\n",[267,6502,6503],{"v-slot:java":269},[271,6504,6506],{"className":485,"code":6505,"language":487,"meta":269,"style":269},"static int lineairZoeken(int[] a, int x) {\n    for (int i = 0; i \u003C a.length; i++) {\n        if (a[i] == x) {\n            return i; \u002F\u002F gevonden op index i\n        }\n    }\n    return -1; \u002F\u002F niet gevonden\n}\n",[14,6507,6508,6535,6569,6591,6602,6606,6610,6623],{"__ignoreMap":269},[279,6509,6510,6512,6514,6517,6519,6521,6523,6525,6527,6529,6531,6533],{"class":281,"line":282},[279,6511,494],{"class":285},[279,6513,2312],{"class":285},[279,6515,6516],{"class":289}," lineairZoeken",[279,6518,294],{"class":293},[279,6520,505],{"class":285},[279,6522,508],{"class":293},[279,6524,347],{"class":310},[279,6526,325],{"class":293},[279,6528,2312],{"class":285},[279,6530,412],{"class":310},[279,6532,513],{"class":293},[279,6534,516],{"class":293},[279,6536,6537,6539,6541,6543,6545,6547,6549,6551,6553,6555,6557,6559,6561,6563,6565,6567],{"class":281,"line":303},[279,6538,307],{"class":306},[279,6540,523],{"class":293},[279,6542,505],{"class":285},[279,6544,2134],{"class":310},[279,6546,344],{"class":293},[279,6548,393],{"class":322},[279,6550,534],{"class":293},[279,6552,2134],{"class":310},[279,6554,539],{"class":293},[279,6556,347],{"class":310},[279,6558,31],{"class":293},[279,6560,546],{"class":310},[279,6562,534],{"class":293},[279,6564,3602],{"class":310},[279,6566,554],{"class":293},[279,6568,516],{"class":293},[279,6570,6571,6573,6575,6577,6579,6581,6583,6585,6587,6589],{"class":281,"line":338},[279,6572,2165],{"class":306},[279,6574,523],{"class":293},[279,6576,27],{"class":310},[279,6578,350],{"class":293},[279,6580,2173],{"class":310},[279,6582,406],{"class":293},[279,6584,4617],{"class":293},[279,6586,412],{"class":310},[279,6588,513],{"class":293},[279,6590,516],{"class":293},[279,6592,6593,6595,6597,6599],{"class":281,"line":358},[279,6594,6483],{"class":306},[279,6596,3602],{"class":310},[279,6598,534],{"class":293},[279,6600,6601],{"class":377}," \u002F\u002F gevonden op index i\n",[279,6603,6604],{"class":281,"line":374},[279,6605,665],{"class":293},[279,6607,6608],{"class":281,"line":381},[279,6609,695],{"class":293},[279,6611,6612,6614,6616,6618,6620],{"class":281,"line":418},[279,6613,2295],{"class":306},[279,6615,3267],{"class":293},[279,6617,191],{"class":322},[279,6619,534],{"class":293},[279,6621,6622],{"class":377}," \u002F\u002F niet gevonden\n",[279,6624,6625],{"class":281,"line":448},[279,6626,701],{"class":293},[10,6628,6629,6630,6634,6635,6637],{},"Het voordeel: de lijst hoeft niet gesorteerd te zijn, en het werkt ook op een\n",[27,6631,6633],{"href":6632},"\u002Fpracticely\u002Fdsa\u002Fstapels-en-wachtrijen","gelinkte lijst",". Het nadeel: ",[14,6636,719],{},". Staat het element\nachteraan of helemaal niet in de lijst, dan bekijk je alles.",[33,6639,6641],{"id":6640},"binair-zoeken-het-idee","Binair zoeken: het idee",[10,6643,6644],{},"Denk aan een woordenboek. Je zoekt \"kwartel\" en slaat het boek ergens in het midden open bij \"mango\".\nOmdat de woorden alfabetisch staan, weet je meteen: het moet in de eerste helft zitten. De tweede\nhelft hoef je nooit meer te bekijken.",[10,6646,6647,6648,6651,6652,91,6654,6656],{},"Binair zoeken doet hetzelfde met een ",[22,6649,6650],{},"gesorteerde"," array. Je houdt twee grenzen bij, ",[14,6653,3085],{},[14,6655,3056],{},",\nwaartussen het element moet zitten als het er is. Elke stap:",[3963,6658,6659,6666,6677,6691],{},[3770,6660,6661,6662,6665],{},"Bereken ",[14,6663,6664],{},"mid = ⌊(lo + hi) \u002F 2⌋"," (naar beneden afronden).",[3770,6667,6668,6669,6672,6673,6676],{},"Is ",[14,6670,6671],{},"a[mid]"," gelijk aan ",[14,6674,6675],{},"x","? Gevonden.",[3770,6678,6668,6679,6682,6683,6685,6686,4165,6688,31],{},[14,6680,6681],{},"a[mid] \u003C x","? Dan zit ",[14,6684,6675],{}," rechts van ",[14,6687,2074],{},[14,6689,6690],{},"lo = mid + 1",[3770,6692,6693,6694,6696,6697,4165,6699,31],{},"Anders zit ",[14,6695,6675],{}," links van ",[14,6698,2074],{},[14,6700,6701],{},"hi = mid - 1",[10,6703,6704,6705,91,6708,6711,6712,6715,6716,6718],{},"Je begint met ",[14,6706,6707],{},"lo = 0",[14,6709,6710],{},"hi = n - 1",", en je stopt als ",[14,6713,6714],{},"lo > hi",": dan is het zoekgebied leeg en\nstaat ",[14,6717,6675],{}," niet in de array.",[33,6720,6722],{"id":6721},"uitgewerkt-voorbeeld-gevonden","Uitgewerkt voorbeeld: gevonden",[10,6724,6725,6726,6729],{},"We zoeken ",[14,6727,6728],{},"x = 30"," in deze array van tien elementen:",[41,6731,6732,6759],{},[44,6733,6734],{},[47,6735,6736,6739,6741,6743,6745,6747,6749,6751,6753,6755,6757],{},[50,6737,6738],{},"index",[50,6740,1400],{},[50,6742,191],{},[50,6744,196],{},[50,6746,220],{},[50,6748,210],{},[50,6750,247],{},[50,6752,225],{},[50,6754,1951],{},[50,6756,1967],{},[50,6758,2905],{},[60,6760,6761],{},[47,6762,6763,6765,6767,6769,6772,6775,6778,6781,6784,6787,6790],{},[65,6764,27],{},[65,6766,220],{},[65,6768,1967],{},[65,6770,6771],{},"12",[65,6773,6774],{},"17",[65,6776,6777],{},"21",[65,6779,6780],{},"25",[65,6782,6783],{},"30",[65,6785,6786],{},"34",[65,6788,6789],{},"41",[65,6791,6792],{},"50",[41,6794,6795,6815],{},[44,6796,6797],{},[47,6798,6799,6801,6803,6805,6807,6811,6813],{},[50,6800,1847],{},[50,6802,3085],{},[50,6804,3056],{},[50,6806,2074],{},[50,6808,27,6809],{},[279,6810,2074],{},[50,6812,5987],{},[50,6814,2832],{},[60,6816,6817,6837,6857,6877],{},[47,6818,6819,6821,6823,6825,6827,6829,6832],{},[65,6820,191],{},[65,6822,1400],{},[65,6824,2905],{},[65,6826,210],{},[65,6828,6777],{},[65,6830,6831],{},"21 \u003C 30",[65,6833,6834],{},[14,6835,6836],{},"lo = 5",[47,6838,6839,6841,6843,6845,6847,6849,6852],{},[65,6840,196],{},[65,6842,247],{},[65,6844,2905],{},[65,6846,1951],{},[65,6848,6786],{},[65,6850,6851],{},"34 > 30",[65,6853,6854],{},[14,6855,6856],{},"hi = 6",[47,6858,6859,6861,6863,6865,6867,6869,6872],{},[65,6860,220],{},[65,6862,247],{},[65,6864,225],{},[65,6866,247],{},[65,6868,6780],{},[65,6870,6871],{},"25 \u003C 30",[65,6873,6874],{},[14,6875,6876],{},"lo = 6",[47,6878,6879,6881,6883,6885,6887,6889,6892],{},[65,6880,210],{},[65,6882,225],{},[65,6884,225],{},[65,6886,225],{},[65,6888,6783],{},[65,6890,6891],{},"gelijk",[65,6893,6894],{},"gevonden op index 6",[10,6896,6897,6898,6901,6902,6905,6906,31],{},"De waarden die achtereenvolgens worden vergeleken zijn ",[14,6899,6900],{},"21, 34, 25, 30",". Let op stap 3: ",[14,6903,6904],{},"(5 + 6) \u002F 2 = 5,5",", afgerond naar beneden geeft ",[14,6907,6908],{},"mid = 5",[33,6910,6912],{"id":6911},"uitgewerkt-voorbeeld-niet-gevonden","Uitgewerkt voorbeeld: niet gevonden",[10,6914,6915,6916,6919],{},"Nu zoeken we ",[14,6917,6918],{},"x = 10"," in dezelfde array:",[41,6921,6922,6942],{},[44,6923,6924],{},[47,6925,6926,6928,6930,6932,6934,6938,6940],{},[50,6927,1847],{},[50,6929,3085],{},[50,6931,3056],{},[50,6933,2074],{},[50,6935,27,6936],{},[279,6937,2074],{},[50,6939,5987],{},[50,6941,2832],{},[60,6943,6944,6964,6984,7004],{},[47,6945,6946,6948,6950,6952,6954,6956,6959],{},[65,6947,191],{},[65,6949,1400],{},[65,6951,2905],{},[65,6953,210],{},[65,6955,6777],{},[65,6957,6958],{},"21 > 10",[65,6960,6961],{},[14,6962,6963],{},"hi = 3",[47,6965,6966,6968,6970,6972,6974,6976,6979],{},[65,6967,196],{},[65,6969,1400],{},[65,6971,220],{},[65,6973,191],{},[65,6975,1967],{},[65,6977,6978],{},"8 \u003C 10",[65,6980,6981],{},[14,6982,6983],{},"lo = 2",[47,6985,6986,6988,6990,6992,6994,6996,6999],{},[65,6987,220],{},[65,6989,196],{},[65,6991,220],{},[65,6993,196],{},[65,6995,6771],{},[65,6997,6998],{},"12 > 10",[65,7000,7001],{},[14,7002,7003],{},"hi = 1",[47,7005,7006,7008,7010,7012,7014,7016,7020],{},[65,7007,181],{},[65,7009,196],{},[65,7011,191],{},[65,7013,181],{},[65,7015,181],{},[65,7017,7018],{},[14,7019,6714],{},[65,7021,7022],{},"stop: niet gevonden",[10,7024,7025,7026,91,7028,7030,7031,7033,7034,7037,7038,7040,7041,7043],{},"Vergeleken waarden: ",[14,7027,1967],{},[14,7029,6771],{}," liggen naast elkaar en ",[14,7032,4363],{}," zit ertussen. Na drie vergelijkingen\n(",[14,7035,7036],{},"21, 8, 12",") is het zoekgebied leeg. De eindwaarde van ",[14,7039,3085],{}," (hier 2) is precies de plek waar je ",[14,7042,4363],{},"\nzou moeten invoegen om de array gesorteerd te houden; dat is handig om te onthouden.",[33,7045,7047],{"id":7046},"de-code","De code",[264,7049,7050,7232],{},[267,7051,7052],{"v-slot:python":269},[271,7053,7055],{"className":273,"code":7054,"language":275,"meta":269,"style":269},"def binair_zoeken(a, x):\n    lo, hi = 0, len(a) - 1\n    while lo \u003C= hi:  # zolang het zoekgebied niet leeg is\n        mid = (lo + hi) \u002F\u002F 2  # naar beneden afronden\n        if a[mid] == x:\n            return mid\n        elif a[mid] \u003C x:\n            lo = mid + 1  # x zit rechts van mid\n        else:\n            hi = mid - 1  # x zit links van mid\n    return -1  # niet gevonden\n",[14,7056,7057,7074,7101,7116,7140,7158,7165,7184,7200,7206,7222],{"__ignoreMap":269},[279,7058,7059,7061,7064,7066,7068,7070,7072],{"class":281,"line":282},[279,7060,286],{"class":285},[279,7062,7063],{"class":289}," binair_zoeken",[279,7065,294],{"class":293},[279,7067,27],{"class":297},[279,7069,325],{"class":293},[279,7071,412],{"class":297},[279,7073,300],{"class":293},[279,7075,7076,7079,7081,7083,7085,7087,7089,7091,7093,7095,7097,7099],{"class":281,"line":303},[279,7077,7078],{"class":310},"    lo",[279,7080,325],{"class":293},[279,7082,3243],{"class":310},[279,7084,344],{"class":293},[279,7086,393],{"class":322},[279,7088,325],{"class":293},[279,7090,328],{"class":289},[279,7092,294],{"class":293},[279,7094,27],{"class":289},[279,7096,513],{"class":293},[279,7098,3267],{"class":293},[279,7100,371],{"class":322},[279,7102,7103,7105,7107,7109,7111,7113],{"class":281,"line":338},[279,7104,2131],{"class":306},[279,7106,3276],{"class":310},[279,7108,2345],{"class":293},[279,7110,3040],{"class":310},[279,7112,2812],{"class":293},[279,7114,7115],{"class":377},"  # zolang het zoekgebied niet leeg is\n",[279,7117,7118,7121,7123,7125,7127,7129,7131,7133,7135,7137],{"class":281,"line":358},[279,7119,7120],{"class":310},"        mid ",[279,7122,344],{"class":293},[279,7124,523],{"class":293},[279,7126,3653],{"class":310},[279,7128,429],{"class":293},[279,7130,3040],{"class":310},[279,7132,513],{"class":293},[279,7134,2052],{"class":293},[279,7136,2384],{"class":322},[279,7138,7139],{"class":377},"  # naar beneden afronden\n",[279,7141,7142,7144,7146,7148,7150,7152,7154,7156],{"class":281,"line":374},[279,7143,2165],{"class":306},[279,7145,347],{"class":310},[279,7147,350],{"class":293},[279,7149,2074],{"class":310},[279,7151,406],{"class":293},[279,7153,4617],{"class":293},[279,7155,412],{"class":310},[279,7157,415],{"class":293},[279,7159,7160,7162],{"class":281,"line":381},[279,7161,6483],{"class":306},[279,7163,7164],{"class":310}," mid\n",[279,7166,7167,7170,7172,7174,7176,7178,7180,7182],{"class":281,"line":418},[279,7168,7169],{"class":306},"        elif",[279,7171,347],{"class":310},[279,7173,350],{"class":293},[279,7175,2074],{"class":310},[279,7177,406],{"class":293},[279,7179,982],{"class":293},[279,7181,412],{"class":310},[279,7183,415],{"class":293},[279,7185,7186,7189,7191,7193,7195,7197],{"class":281,"line":448},[279,7187,7188],{"class":310},"            lo ",[279,7190,344],{"class":293},[279,7192,2370],{"class":310},[279,7194,429],{"class":293},[279,7196,432],{"class":322},[279,7198,7199],{"class":377},"  # x zit rechts van mid\n",[279,7201,7202,7204],{"class":281,"line":459},[279,7203,2221],{"class":306},[279,7205,415],{"class":293},[279,7207,7208,7211,7213,7215,7217,7219],{"class":281,"line":668},[279,7209,7210],{"class":310},"            hi ",[279,7212,344],{"class":293},[279,7214,2370],{"class":310},[279,7216,368],{"class":293},[279,7218,432],{"class":322},[279,7220,7221],{"class":377},"  # x zit links van mid\n",[279,7223,7224,7226,7228,7230],{"class":281,"line":692},[279,7225,2295],{"class":306},[279,7227,3267],{"class":293},[279,7229,191],{"class":322},[279,7231,6500],{"class":377},[267,7233,7234],{"v-slot:java":269},[271,7235,7237],{"className":485,"code":7236,"language":487,"meta":269,"style":269},"static int binairZoeken(int[] a, int x) {\n    int lo = 0, hi = a.length - 1;\n    while (lo \u003C= hi) { \u002F\u002F zolang het zoekgebied niet leeg is\n        int mid = lo + (hi - lo) \u002F 2; \u002F\u002F gelijk aan ⌊(lo+hi)\u002F2⌋, maar zonder overflow\n        if (a[mid] == x) {\n            return mid;\n        } else if (a[mid] \u003C x) {\n            lo = mid + 1; \u002F\u002F x zit rechts van mid\n        } else {\n            hi = mid - 1; \u002F\u002F x zit links van mid\n        }\n    }\n    return -1; \u002F\u002F niet gevonden\n}\n",[14,7238,7239,7266,7294,7313,7346,7368,7376,7403,7420,7428,7445,7449,7453,7465],{"__ignoreMap":269},[279,7240,7241,7243,7245,7248,7250,7252,7254,7256,7258,7260,7262,7264],{"class":281,"line":282},[279,7242,494],{"class":285},[279,7244,2312],{"class":285},[279,7246,7247],{"class":289}," binairZoeken",[279,7249,294],{"class":293},[279,7251,505],{"class":285},[279,7253,508],{"class":293},[279,7255,347],{"class":310},[279,7257,325],{"class":293},[279,7259,2312],{"class":285},[279,7261,412],{"class":310},[279,7263,513],{"class":293},[279,7265,516],{"class":293},[279,7267,7268,7270,7272,7274,7276,7278,7280,7282,7284,7286,7288,7290,7292],{"class":281,"line":303},[279,7269,1086],{"class":285},[279,7271,3276],{"class":310},[279,7273,344],{"class":293},[279,7275,393],{"class":322},[279,7277,325],{"class":293},[279,7279,3243],{"class":310},[279,7281,344],{"class":293},[279,7283,347],{"class":310},[279,7285,31],{"class":293},[279,7287,2342],{"class":310},[279,7289,368],{"class":293},[279,7291,432],{"class":322},[279,7293,592],{"class":293},[279,7295,7296,7298,7300,7302,7304,7306,7308,7310],{"class":281,"line":338},[279,7297,2131],{"class":306},[279,7299,523],{"class":293},[279,7301,3653],{"class":310},[279,7303,2345],{"class":293},[279,7305,3040],{"class":310},[279,7307,513],{"class":293},[279,7309,3476],{"class":293},[279,7311,7312],{"class":377}," \u002F\u002F zolang het zoekgebied niet leeg is\n",[279,7314,7315,7317,7319,7321,7323,7325,7327,7330,7332,7334,7336,7339,7341,7343],{"class":281,"line":358},[279,7316,561],{"class":285},[279,7318,2370],{"class":310},[279,7320,344],{"class":293},[279,7322,3276],{"class":310},[279,7324,429],{"class":293},[279,7326,523],{"class":293},[279,7328,7329],{"class":310},"hi ",[279,7331,368],{"class":293},[279,7333,3035],{"class":310},[279,7335,513],{"class":293},[279,7337,7338],{"class":293}," \u002F",[279,7340,2384],{"class":322},[279,7342,534],{"class":293},[279,7344,7345],{"class":377}," \u002F\u002F gelijk aan ⌊(lo+hi)\u002F2⌋, maar zonder overflow\n",[279,7347,7348,7350,7352,7354,7356,7358,7360,7362,7364,7366],{"class":281,"line":374},[279,7349,2165],{"class":306},[279,7351,523],{"class":293},[279,7353,27],{"class":310},[279,7355,350],{"class":293},[279,7357,2074],{"class":310},[279,7359,406],{"class":293},[279,7361,4617],{"class":293},[279,7363,412],{"class":310},[279,7365,513],{"class":293},[279,7367,516],{"class":293},[279,7369,7370,7372,7374],{"class":281,"line":381},[279,7371,6483],{"class":306},[279,7373,2431],{"class":310},[279,7375,592],{"class":293},[279,7377,7378,7380,7382,7385,7387,7389,7391,7393,7395,7397,7399,7401],{"class":281,"line":418},[279,7379,2627],{"class":293},[279,7381,2630],{"class":306},[279,7383,7384],{"class":306}," if",[279,7386,523],{"class":293},[279,7388,27],{"class":310},[279,7390,350],{"class":293},[279,7392,2074],{"class":310},[279,7394,406],{"class":293},[279,7396,982],{"class":293},[279,7398,412],{"class":310},[279,7400,513],{"class":293},[279,7402,516],{"class":293},[279,7404,7405,7407,7409,7411,7413,7415,7417],{"class":281,"line":448},[279,7406,7188],{"class":310},[279,7408,344],{"class":293},[279,7410,2370],{"class":310},[279,7412,429],{"class":293},[279,7414,432],{"class":322},[279,7416,534],{"class":293},[279,7418,7419],{"class":377}," \u002F\u002F x zit rechts van mid\n",[279,7421,7422,7424,7426],{"class":281,"line":459},[279,7423,2627],{"class":293},[279,7425,2630],{"class":306},[279,7427,516],{"class":293},[279,7429,7430,7432,7434,7436,7438,7440,7442],{"class":281,"line":668},[279,7431,7210],{"class":310},[279,7433,344],{"class":293},[279,7435,2370],{"class":310},[279,7437,368],{"class":293},[279,7439,432],{"class":322},[279,7441,534],{"class":293},[279,7443,7444],{"class":377}," \u002F\u002F x zit links van mid\n",[279,7446,7447],{"class":281,"line":692},[279,7448,665],{"class":293},[279,7450,7451],{"class":281,"line":698},[279,7452,695],{"class":293},[279,7454,7455,7457,7459,7461,7463],{"class":281,"line":1257},[279,7456,2295],{"class":306},[279,7458,3267],{"class":293},[279,7460,191],{"class":322},[279,7462,534],{"class":293},[279,7464,6622],{"class":377},[279,7466,7467],{"class":281,"line":1282},[279,7468,701],{"class":293},[10,7470,7471,7472,7475,7476,7479,7480,7482,7483,7485,7486,7488,7489,7492,7493,7495],{},"In Java schrijven we ",[14,7473,7474],{},"lo + (hi - lo) \u002F 2"," in plaats van ",[14,7477,7478],{},"(lo + hi) \u002F 2",". Voor niet-negatieve ",[14,7481,3085],{},"\nen ",[14,7484,3056],{}," levert dat dezelfde ",[14,7487,2074],{}," op, maar het voorkomt dat ",[14,7490,7491],{},"lo + hi"," groter wordt dan de maximale\n",[14,7494,505],{}," bij hele grote arrays. In Python bestaat dat probleem niet.",[33,7497,7499],{"id":7498},"off-by-one-valkuilen","Off-by-one-valkuilen",[10,7501,7502],{},"Binair zoeken is berucht om fouten van één positie. De drie keuzes in onze variant horen bij elkaar:",[41,7504,7505,7515],{},[44,7506,7507],{},[47,7508,7509,7512],{},[50,7510,7511],{},"Keuze",[50,7513,7514],{},"Waarom",[60,7516,7517,7528,7542],{},[47,7518,7519,7523],{},[65,7520,7521],{},[14,7522,6710],{},[65,7524,7525,7527],{},[14,7526,3056],{}," is de laatste index die nog kandidaat is (inclusief)",[47,7529,7530,7535],{},[65,7531,7532],{},[14,7533,7534],{},"while lo \u003C= hi",[65,7536,7537,7538,7541],{},"als ",[14,7539,7540],{},"lo == hi"," is er nog precies één kandidaat die je moet bekijken",[47,7543,7544,7550],{},[65,7545,7546,6395,7548],{},[14,7547,6690],{},[14,7549,6701],{},[65,7551,7552,7554],{},[14,7553,6671],{}," is al bekeken, die hoeft niet meer in het zoekgebied",[10,7556,7557],{},"Wat gaat er mis als je een van de drie verandert?",[3767,7559,7560,7579,7607],{},[3770,7561,7562,7567,7568,7571,7572,7575,7576,7578],{},[22,7563,7564],{},[14,7565,7566],{},"while lo \u003C hi",": in het eerste voorbeeld stop je na stap 3 met ",[14,7569,7570],{},"lo = hi = 6",", zonder ",[14,7573,7574],{},"a[6]","\nte bekijken. Je meldt \"niet gevonden\" terwijl ",[14,7577,6783],{}," er wel staat.",[3770,7580,7581,7589,7590,7593,7594,7596,7597,7600,7601,7603,7604,31],{},[22,7582,7583,7475,7586],{},[14,7584,7585],{},"lo = mid",[14,7587,7588],{},"mid + 1",": met ",[14,7591,7592],{},"lo = 5, hi = 6"," krijg je ",[14,7595,6908],{},", en als\n",[14,7598,7599],{},"a[5] \u003C x"," blijft ",[14,7602,3085],{}," op 5 staan. Het zoekgebied krimpt niet: een ",[22,7605,7606],{},"oneindige lus",[3770,7608,7609,1835,7614,7616,7617,7619,7620,7622],{},[22,7610,7611],{},[14,7612,7613],{},"hi = n",[14,7615,2345],{},": dan kan ",[14,7618,2074],{}," gelijk worden aan ",[14,7621,2764],{}," en lees je buiten de array.",[10,7624,7625,7626,7628,7629,7631],{},"Er bestaan ook correcte varianten met ",[14,7627,7613],{}," (exclusief) en ",[14,7630,7566],{},". Die werken prima, maar\nmeng de twee stijlen nooit. Op Practicely gebruiken we altijd de variant hierboven.",[33,7633,7635],{"id":7634},"variant-het-eerste-voorkomen","Variant: het eerste voorkomen",[10,7637,7638,7639,7641,7642,7645,7646,7648,7649,7651],{},"Staat ",[14,7640,6675],{}," meerdere keren in de array, dan geeft gewoon binair zoeken een willekeurige van de\nvoorkomens terug. In ",[14,7643,7644],{},"[1, 3, 3, 3, 3, 7, 9]"," vindt het ",[14,7647,220],{}," al bij de eerste stap, op index 3. Wil je\nhet ",[22,7650,141],{}," voorkomen, dan ga je na een treffer verder zoeken in de linkerhelft en onthoud je de\nbeste index tot nu toe:",[41,7653,7654,7675],{},[44,7655,7656],{},[47,7657,7658,7660,7662,7664,7666,7670,7672],{},[50,7659,1847],{},[50,7661,3085],{},[50,7663,3056],{},[50,7665,2074],{},[50,7667,27,7668],{},[279,7669,2074],{},[50,7671,2832],{},[50,7673,7674],{},"Beste tot nu toe",[60,7676,7677,7697,7716],{},[47,7678,7679,7681,7683,7685,7687,7689,7695],{},[65,7680,191],{},[65,7682,1400],{},[65,7684,225],{},[65,7686,220],{},[65,7688,220],{},[65,7690,7691,7692],{},"gelijk, zoek links: ",[14,7693,7694],{},"hi = 2",[65,7696,220],{},[47,7698,7699,7701,7703,7705,7707,7709,7714],{},[65,7700,196],{},[65,7702,1400],{},[65,7704,196],{},[65,7706,191],{},[65,7708,220],{},[65,7710,7691,7711],{},[14,7712,7713],{},"hi = 0",[65,7715,191],{},[47,7717,7718,7720,7722,7724,7726,7728,7734],{},[65,7719,220],{},[65,7721,1400],{},[65,7723,1400],{},[65,7725,1400],{},[65,7727,191],{},[65,7729,7730,7731],{},"1 \u003C 3: ",[14,7732,7733],{},"lo = 1",[65,7735,191],{},[10,7737,7738,7739,7741],{},"Daarna is ",[14,7740,6714],{}," en is het antwoord index 1.",[264,7743,7744,7936],{},[267,7745,7746],{"v-slot:python":269},[271,7747,7749],{"className":273,"code":7748,"language":275,"meta":269,"style":269},"def eerste_voorkomen(a, x):\n    lo, hi = 0, len(a) - 1\n    antwoord = -1\n    while lo \u003C= hi:\n        mid = (lo + hi) \u002F\u002F 2\n        if a[mid] == x:\n            antwoord = mid  # onthouden en links verder zoeken\n            hi = mid - 1\n        elif a[mid] \u003C x:\n            lo = mid + 1\n        else:\n            hi = mid - 1\n    return antwoord\n",[14,7750,7751,7768,7794,7806,7818,7838,7856,7869,7881,7899,7911,7917,7929],{"__ignoreMap":269},[279,7752,7753,7755,7758,7760,7762,7764,7766],{"class":281,"line":282},[279,7754,286],{"class":285},[279,7756,7757],{"class":289}," eerste_voorkomen",[279,7759,294],{"class":293},[279,7761,27],{"class":297},[279,7763,325],{"class":293},[279,7765,412],{"class":297},[279,7767,300],{"class":293},[279,7769,7770,7772,7774,7776,7778,7780,7782,7784,7786,7788,7790,7792],{"class":281,"line":303},[279,7771,7078],{"class":310},[279,7773,325],{"class":293},[279,7775,3243],{"class":310},[279,7777,344],{"class":293},[279,7779,393],{"class":322},[279,7781,325],{"class":293},[279,7783,328],{"class":289},[279,7785,294],{"class":293},[279,7787,27],{"class":289},[279,7789,513],{"class":293},[279,7791,3267],{"class":293},[279,7793,371],{"class":322},[279,7795,7796,7799,7801,7803],{"class":281,"line":338},[279,7797,7798],{"class":310},"    antwoord ",[279,7800,344],{"class":293},[279,7802,3267],{"class":293},[279,7804,7805],{"class":322},"1\n",[279,7807,7808,7810,7812,7814,7816],{"class":281,"line":358},[279,7809,2131],{"class":306},[279,7811,3276],{"class":310},[279,7813,2345],{"class":293},[279,7815,3040],{"class":310},[279,7817,415],{"class":293},[279,7819,7820,7822,7824,7826,7828,7830,7832,7834,7836],{"class":281,"line":374},[279,7821,7120],{"class":310},[279,7823,344],{"class":293},[279,7825,523],{"class":293},[279,7827,3653],{"class":310},[279,7829,429],{"class":293},[279,7831,3040],{"class":310},[279,7833,513],{"class":293},[279,7835,2052],{"class":293},[279,7837,2055],{"class":322},[279,7839,7840,7842,7844,7846,7848,7850,7852,7854],{"class":281,"line":381},[279,7841,2165],{"class":306},[279,7843,347],{"class":310},[279,7845,350],{"class":293},[279,7847,2074],{"class":310},[279,7849,406],{"class":293},[279,7851,4617],{"class":293},[279,7853,412],{"class":310},[279,7855,415],{"class":293},[279,7857,7858,7861,7863,7866],{"class":281,"line":418},[279,7859,7860],{"class":310},"            antwoord ",[279,7862,344],{"class":293},[279,7864,7865],{"class":310}," mid  ",[279,7867,7868],{"class":377},"# onthouden en links verder zoeken\n",[279,7870,7871,7873,7875,7877,7879],{"class":281,"line":448},[279,7872,7210],{"class":310},[279,7874,344],{"class":293},[279,7876,2370],{"class":310},[279,7878,368],{"class":293},[279,7880,371],{"class":322},[279,7882,7883,7885,7887,7889,7891,7893,7895,7897],{"class":281,"line":459},[279,7884,7169],{"class":306},[279,7886,347],{"class":310},[279,7888,350],{"class":293},[279,7890,2074],{"class":310},[279,7892,406],{"class":293},[279,7894,982],{"class":293},[279,7896,412],{"class":310},[279,7898,415],{"class":293},[279,7900,7901,7903,7905,7907,7909],{"class":281,"line":668},[279,7902,7188],{"class":310},[279,7904,344],{"class":293},[279,7906,2370],{"class":310},[279,7908,429],{"class":293},[279,7910,371],{"class":322},[279,7912,7913,7915],{"class":281,"line":692},[279,7914,2221],{"class":306},[279,7916,415],{"class":293},[279,7918,7919,7921,7923,7925,7927],{"class":281,"line":698},[279,7920,7210],{"class":310},[279,7922,344],{"class":293},[279,7924,2370],{"class":310},[279,7926,368],{"class":293},[279,7928,371],{"class":322},[279,7930,7931,7933],{"class":281,"line":1257},[279,7932,2295],{"class":306},[279,7934,7935],{"class":310}," antwoord\n",[267,7937,7938],{"v-slot:java":269},[271,7939,7941],{"className":485,"code":7940,"language":487,"meta":269,"style":269},"static int eersteVoorkomen(int[] a, int x) {\n    int lo = 0, hi = a.length - 1;\n    int antwoord = -1;\n    while (lo \u003C= hi) {\n        int mid = lo + (hi - lo) \u002F 2;\n        if (a[mid] == x) {\n            antwoord = mid; \u002F\u002F onthouden en links verder zoeken\n            hi = mid - 1;\n        } else if (a[mid] \u003C x) {\n            lo = mid + 1;\n        } else {\n            hi = mid - 1;\n        }\n    }\n    return antwoord;\n}\n",[14,7942,7943,7970,7998,8013,8029,8057,8079,8092,8106,8132,8146,8154,8168,8172,8176,8185],{"__ignoreMap":269},[279,7944,7945,7947,7949,7952,7954,7956,7958,7960,7962,7964,7966,7968],{"class":281,"line":282},[279,7946,494],{"class":285},[279,7948,2312],{"class":285},[279,7950,7951],{"class":289}," eersteVoorkomen",[279,7953,294],{"class":293},[279,7955,505],{"class":285},[279,7957,508],{"class":293},[279,7959,347],{"class":310},[279,7961,325],{"class":293},[279,7963,2312],{"class":285},[279,7965,412],{"class":310},[279,7967,513],{"class":293},[279,7969,516],{"class":293},[279,7971,7972,7974,7976,7978,7980,7982,7984,7986,7988,7990,7992,7994,7996],{"class":281,"line":303},[279,7973,1086],{"class":285},[279,7975,3276],{"class":310},[279,7977,344],{"class":293},[279,7979,393],{"class":322},[279,7981,325],{"class":293},[279,7983,3243],{"class":310},[279,7985,344],{"class":293},[279,7987,347],{"class":310},[279,7989,31],{"class":293},[279,7991,2342],{"class":310},[279,7993,368],{"class":293},[279,7995,432],{"class":322},[279,7997,592],{"class":293},[279,7999,8000,8002,8005,8007,8009,8011],{"class":281,"line":338},[279,8001,1086],{"class":285},[279,8003,8004],{"class":310}," antwoord ",[279,8006,344],{"class":293},[279,8008,3267],{"class":293},[279,8010,191],{"class":322},[279,8012,592],{"class":293},[279,8014,8015,8017,8019,8021,8023,8025,8027],{"class":281,"line":358},[279,8016,2131],{"class":306},[279,8018,523],{"class":293},[279,8020,3653],{"class":310},[279,8022,2345],{"class":293},[279,8024,3040],{"class":310},[279,8026,513],{"class":293},[279,8028,516],{"class":293},[279,8030,8031,8033,8035,8037,8039,8041,8043,8045,8047,8049,8051,8053,8055],{"class":281,"line":374},[279,8032,561],{"class":285},[279,8034,2370],{"class":310},[279,8036,344],{"class":293},[279,8038,3276],{"class":310},[279,8040,429],{"class":293},[279,8042,523],{"class":293},[279,8044,7329],{"class":310},[279,8046,368],{"class":293},[279,8048,3035],{"class":310},[279,8050,513],{"class":293},[279,8052,7338],{"class":293},[279,8054,2384],{"class":322},[279,8056,592],{"class":293},[279,8058,8059,8061,8063,8065,8067,8069,8071,8073,8075,8077],{"class":281,"line":381},[279,8060,2165],{"class":306},[279,8062,523],{"class":293},[279,8064,27],{"class":310},[279,8066,350],{"class":293},[279,8068,2074],{"class":310},[279,8070,406],{"class":293},[279,8072,4617],{"class":293},[279,8074,412],{"class":310},[279,8076,513],{"class":293},[279,8078,516],{"class":293},[279,8080,8081,8083,8085,8087,8089],{"class":281,"line":418},[279,8082,7860],{"class":310},[279,8084,344],{"class":293},[279,8086,2431],{"class":310},[279,8088,534],{"class":293},[279,8090,8091],{"class":377}," \u002F\u002F onthouden en links verder zoeken\n",[279,8093,8094,8096,8098,8100,8102,8104],{"class":281,"line":448},[279,8095,7210],{"class":310},[279,8097,344],{"class":293},[279,8099,2370],{"class":310},[279,8101,368],{"class":293},[279,8103,432],{"class":322},[279,8105,592],{"class":293},[279,8107,8108,8110,8112,8114,8116,8118,8120,8122,8124,8126,8128,8130],{"class":281,"line":459},[279,8109,2627],{"class":293},[279,8111,2630],{"class":306},[279,8113,7384],{"class":306},[279,8115,523],{"class":293},[279,8117,27],{"class":310},[279,8119,350],{"class":293},[279,8121,2074],{"class":310},[279,8123,406],{"class":293},[279,8125,982],{"class":293},[279,8127,412],{"class":310},[279,8129,513],{"class":293},[279,8131,516],{"class":293},[279,8133,8134,8136,8138,8140,8142,8144],{"class":281,"line":668},[279,8135,7188],{"class":310},[279,8137,344],{"class":293},[279,8139,2370],{"class":310},[279,8141,429],{"class":293},[279,8143,432],{"class":322},[279,8145,592],{"class":293},[279,8147,8148,8150,8152],{"class":281,"line":692},[279,8149,2627],{"class":293},[279,8151,2630],{"class":306},[279,8153,516],{"class":293},[279,8155,8156,8158,8160,8162,8164,8166],{"class":281,"line":698},[279,8157,7210],{"class":310},[279,8159,344],{"class":293},[279,8161,2370],{"class":310},[279,8163,368],{"class":293},[279,8165,432],{"class":322},[279,8167,592],{"class":293},[279,8169,8170],{"class":281,"line":1257},[279,8171,665],{"class":293},[279,8173,8174],{"class":281,"line":1282},[279,8175,695],{"class":293},[279,8177,8178,8180,8183],{"class":281,"line":1300},[279,8179,2295],{"class":306},[279,8181,8182],{"class":310}," antwoord",[279,8184,592],{"class":293},[279,8186,8187],{"class":281,"line":1305},[279,8188,701],{"class":293},[10,8190,8191,8192,8194,8195,8197,8198,8200],{},"Het ",[22,8193,134],{}," voorkomen werkt spiegelbeeldig: na een treffer ",[14,8196,6690],{},". Met eerste en laatste\nvoorkomen samen tel je in ",[14,8199,3791],{}," hoe vaak een waarde voorkomt.",[33,8202,3795],{"id":30},[10,8204,8205,8206,8208,8209,8212,8213,8215,8216,8218,8219,8221,8222,31],{},"Elke stap halveert het zoekgebied. Na ",[14,8207,105],{}," stappen zijn er hooguit ",[14,8210,8211],{},"n \u002F 2ᵏ"," kandidaten over, dus na\nongeveer ",[14,8214,4278],{}," stappen is er nog één. Als recurrente betrekking: ",[14,8217,5558],{},", en volgens\nde mastermethode (zie ",[27,8220,30],{"href":29},") is dat ",[14,8223,3791],{},[41,8225,8226,8236],{},[44,8227,8228],{},[47,8229,8230,8232,8234],{},[50,8231],{},[50,8233,6405],{},[50,8235,6385],{},[60,8237,8238,8251,8266,8278,8290,8303],{},[47,8239,8240,8242,8245],{},[65,8241,5904],{},[65,8243,8244],{},"geen",[65,8246,8247,8248,8250],{},"array ",[22,8249,6379],{},", directe toegang via index",[47,8252,8253,8256,8261],{},[65,8254,8255],{},"Best case",[65,8257,8258,8260],{},[14,8259,3787],{}," (eerste element)",[65,8262,8263,8265],{},[14,8264,3787],{}," (middelste element)",[47,8267,8268,8270,8274],{},[65,8269,3809],{},[65,8271,8272],{},[14,8273,719],{},[65,8275,8276],{},[14,8277,3791],{},[47,8279,8280,8282,8286],{},[65,8281,3812],{},[65,8283,8284],{},[14,8285,719],{},[65,8287,8288],{},[14,8289,3791],{},[47,8291,8292,8294,8298],{},[65,8293,3815],{},[65,8295,8296],{},[14,8297,3787],{},[65,8299,8300,8302],{},[14,8301,3787],{}," (iteratief)",[47,8304,8305,8308,8311],{},[65,8306,8307],{},"Vergelijkingen bij n = 1.000.000",[65,8309,8310],{},"tot 1.000.000",[65,8312,8313],{},"hooguit 20",[10,8315,8316,8317,8319,8320,8324,8325,8329],{},"Moet je maar één keer zoeken in ongesorteerde data, dan is lineair zoeken sneller dan eerst sorteren\n(",[14,8318,2760],{},") en dan binair zoeken. Zoek je vaak in dezelfde data, dan verdient het sorteren zich\nsnel terug. Nog sneller opzoeken kan met een ",[27,8321,8323],{"href":8322},"\u002Fpracticely\u002Fdsa\u002Fhashtabellen","hashtabel",", en voor data\ndie steeds verandert is een ",[27,8326,8328],{"href":8327},"\u002Fpracticely\u002Fdsa\u002Fbinaire-zoekbomen","binaire zoekboom"," handig.",[33,8331,3961],{"id":3960},[3963,8333,8334,8340,8359,8367,8383],{},[3770,8335,8336,8339],{},[22,8337,8338],{},"Binair zoeken op een ongesorteerde array."," Het algoritme geeft dan gewoon een fout antwoord,\nzonder foutmelding. Controleer altijd eerst de voorwaarde.",[3770,8341,8342,4226,8347,8350,8351,6263,8353,8355,8356,8358],{},[22,8343,8344,8346],{},[14,8345,2074],{}," naar boven afronden.",[14,8348,8349],{},"(5 + 6) \u002F 2"," wordt ",[14,8352,247],{},[14,8354,225],{},". Bij een traceervraag verschuift\néén verkeerde ",[14,8357,2074],{}," alle volgende stappen.",[3770,8360,8361,8366],{},[22,8362,8363,8365],{},[14,8364,7566],{}," gebruiken"," bij de inclusieve variant, waardoor je het laatste kandidaat-element\nnooit bekijkt.",[3770,8368,8369,7475,8377,91,8379,8382],{},[22,8370,8371,5064,8373,8376],{},[14,8372,7585],{},[14,8374,8375],{},"hi = mid"," schrijven",[14,8378,7588],{},[14,8380,8381],{},"mid - 1",". Dat kan een oneindige\nlus opleveren.",[3770,8384,8385,8388,8389,8391],{},[22,8386,8387],{},"Bij de traceervraag de laatste vergelijking vergeten."," Ook de vergelijking waarin ",[14,8390,6675],{}," gevonden\nwordt, hoort in de lijst van vergeleken waarden.",[33,8393,4033],{"id":4032},[3767,8395,8396,8404,8415,8425],{},[3770,8397,8398,8399,8401,8402,31],{},"Lineair zoeken werkt altijd en kost ",[14,8400,719],{},"; binair zoeken eist een gesorteerde array en kost ",[14,8403,3791],{},[3770,8405,8406,8407,6395,8409,6395,8411,6395,8413,31],{},"Onze variant: ",[14,8408,6707],{},[14,8410,6710],{},[14,8412,6664],{},[14,8414,7534],{},[3770,8416,4778,8417,8350,8419,8421,8422,8424],{},[14,8418,6681],{},[14,8420,6690],{},", anders ",[14,8423,6701],{},"; zo krimpt het zoekgebied altijd.",[3770,8426,8427],{},"Voor het eerste voorkomen zoek je na een treffer links verder en onthoud je de index.",[4086,8429,8430],{},"html pre.shiki code .spNyl, html code.shiki .spNyl{--shiki-light:#9C3EDA;--shiki-default:#C792EA;--shiki-dark:#C792EA}html pre.shiki code .s2Zo4, html code.shiki .s2Zo4{--shiki-light:#6182B8;--shiki-default:#82AAFF;--shiki-dark:#82AAFF}html pre.shiki code .sMK4o, html code.shiki .sMK4o{--shiki-light:#39ADB5;--shiki-default:#89DDFF;--shiki-dark:#89DDFF}html pre.shiki code .sHdIc, html code.shiki .sHdIc{--shiki-light:#90A4AE;--shiki-light-font-style:italic;--shiki-default:#EEFFFF;--shiki-default-font-style:italic;--shiki-dark:#BABED8;--shiki-dark-font-style:italic}html pre.shiki code .s7zQu, html code.shiki .s7zQu{--shiki-light:#39ADB5;--shiki-light-font-style:italic;--shiki-default:#89DDFF;--shiki-default-font-style:italic;--shiki-dark:#89DDFF;--shiki-dark-font-style:italic}html pre.shiki code .sTEyZ, html code.shiki .sTEyZ{--shiki-light:#90A4AE;--shiki-default:#EEFFFF;--shiki-dark:#BABED8}html pre.shiki code .sHwdD, html code.shiki .sHwdD{--shiki-light:#90A4AE;--shiki-light-font-style:italic;--shiki-default:#546E7A;--shiki-default-font-style:italic;--shiki-dark:#676E95;--shiki-dark-font-style:italic}html pre.shiki code .sbssI, html code.shiki .sbssI{--shiki-light:#F76D47;--shiki-default:#F78C6C;--shiki-dark:#F78C6C}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":269,"searchDepth":303,"depth":303,"links":8432},[8433,8434,8435,8436,8437,8438,8439,8440,8441,8442],{"id":6404,"depth":303,"text":6405},{"id":6640,"depth":303,"text":6641},{"id":6721,"depth":303,"text":6722},{"id":6911,"depth":303,"text":6912},{"id":7046,"depth":303,"text":7047},{"id":7498,"depth":303,"text":7499},{"id":7634,"depth":303,"text":7635},{"id":30,"depth":303,"text":3795},{"id":3960,"depth":303,"text":3961},{"id":4032,"depth":303,"text":4033},"Lineair en binair zoeken stap voor stap: een trace met lo, hi en mid, de off-by-one-valkuilen, het eerste voorkomen vinden en code in Python en Java.","i-lucide-search",{},"\u002Fpracticely-dsa\u002Fzoeken",{"title":6371,"description":8443},"practicely-dsa\u002Fzoeken","zoeken","MRqxQRbAp5DYPc2i8AX4gmsTB8-LXQ7_s9tWgGllG9Q",1793084907398]