[{"data":1,"prerenderedAt":9257},["ShallowReactive",2],{"dsa-zoeken":3,"dsa-nav-zoeken":2248},{"id":4,"title":5,"body":6,"description":2238,"extension":2239,"icon":2240,"meta":2241,"navigation":2242,"order":135,"path":2243,"seo":2244,"stem":2245,"topic":2246,"__hash__":2247},"practicelyDsa\u002Fpracticely-dsa\u002Fzoeken.md","Binair zoeken uitgelegd: van lineair zoeken naar O(log n)",{"type":7,"value":8,"toc":2226},"minimark",[9,18,46,51,59,335,347,351,354,369,417,434,438,445,523,628,642,646,653,757,779,783,1235,1262,1266,1269,1321,1324,1392,1401,1405,1422,1506,1512,1962,1976,1980,2005,2100,2117,2121,2183,2187,2222],[10,11,12,13,17],"p",{},"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 ",[14,15,16],"strong",{},"gesorteerd",",\ndan kan het met twintig. Dat is het verschil tussen lineair en binair zoeken.",[10,19,20,23,24,28,29,33,34,37,38,41,42,45],{},[14,21,22],{},"Binair zoeken"," (",[25,26,27],"em",{},"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: ",[30,31,32],"code",{},"\u003C","\nof ",[30,35,36],{},"\u003C=",", ",[30,39,40],{},"mid"," of ",[30,43,44],{},"mid+1","? Op deze pagina zie je precies welke variant we gebruiken en waarom die\nklopt.",[47,48,50],"h2",{"id":49},"lineair-zoeken","Lineair zoeken",[10,52,53,23,55,58],{},[14,54,50],{},[25,56,57],{},"linear search",") bekijkt de elementen één voor één, van voor naar achter, tot het\ngezochte element gevonden is of de lijst op is.",[60,61,62,188],"code-tabs",{},[63,64,66],"template",{"v-slot:python":65},"",[67,68,72],"pre",{"className":69,"code":70,"language":71,"meta":65,"style":65},"language-python shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","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","python",[30,73,74,104,133,159,172],{"__ignoreMap":65},[75,76,79,83,87,91,95,98,101],"span",{"class":77,"line":78},"line",1,[75,80,82],{"class":81},"spNyl","def",[75,84,86],{"class":85},"s2Zo4"," lineair_zoeken",[75,88,90],{"class":89},"sMK4o","(",[75,92,94],{"class":93},"sHdIc","a",[75,96,97],{"class":89},",",[75,99,100],{"class":93}," x",[75,102,103],{"class":89},"):\n",[75,105,107,111,115,118,121,123,126,128,130],{"class":77,"line":106},2,[75,108,110],{"class":109},"s7zQu","    for",[75,112,114],{"class":113},"sTEyZ"," i ",[75,116,117],{"class":109},"in",[75,119,120],{"class":85}," range",[75,122,90],{"class":89},[75,124,125],{"class":85},"len",[75,127,90],{"class":89},[75,129,94],{"class":85},[75,131,132],{"class":89},")):\n",[75,134,136,139,142,145,148,151,154,156],{"class":77,"line":135},3,[75,137,138],{"class":109},"        if",[75,140,141],{"class":113}," a",[75,143,144],{"class":89},"[",[75,146,147],{"class":113},"i",[75,149,150],{"class":89},"]",[75,152,153],{"class":89}," ==",[75,155,100],{"class":113},[75,157,158],{"class":89},":\n",[75,160,162,165,168],{"class":77,"line":161},4,[75,163,164],{"class":109},"            return",[75,166,167],{"class":113}," i  ",[75,169,171],{"class":170},"sHwdD","# gevonden op index i\n",[75,173,175,178,181,185],{"class":77,"line":174},5,[75,176,177],{"class":109},"    return",[75,179,180],{"class":89}," -",[75,182,184],{"class":183},"sbssI","1",[75,186,187],{"class":170},"  # niet gevonden\n",[63,189,190],{"v-slot:java":65},[67,191,195],{"className":192,"code":193,"language":194,"meta":65,"style":65},"language-java shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","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","java",[30,196,197,230,271,293,304,309,315,329],{"__ignoreMap":65},[75,198,199,202,205,208,210,213,216,218,220,222,224,227],{"class":77,"line":78},[75,200,201],{"class":81},"static",[75,203,204],{"class":81}," int",[75,206,207],{"class":85}," lineairZoeken",[75,209,90],{"class":89},[75,211,212],{"class":81},"int",[75,214,215],{"class":89},"[]",[75,217,141],{"class":113},[75,219,97],{"class":89},[75,221,204],{"class":81},[75,223,100],{"class":113},[75,225,226],{"class":89},")",[75,228,229],{"class":89}," {\n",[75,231,232,234,236,238,240,243,246,249,251,253,255,258,261,263,266,269],{"class":77,"line":106},[75,233,110],{"class":109},[75,235,23],{"class":89},[75,237,212],{"class":81},[75,239,114],{"class":113},[75,241,242],{"class":89},"=",[75,244,245],{"class":183}," 0",[75,247,248],{"class":89},";",[75,250,114],{"class":113},[75,252,32],{"class":89},[75,254,141],{"class":113},[75,256,257],{"class":89},".",[75,259,260],{"class":113},"length",[75,262,248],{"class":89},[75,264,265],{"class":113}," i",[75,267,268],{"class":89},"++)",[75,270,229],{"class":89},[75,272,273,275,277,279,281,283,285,287,289,291],{"class":77,"line":135},[75,274,138],{"class":109},[75,276,23],{"class":89},[75,278,94],{"class":113},[75,280,144],{"class":89},[75,282,147],{"class":113},[75,284,150],{"class":89},[75,286,153],{"class":89},[75,288,100],{"class":113},[75,290,226],{"class":89},[75,292,229],{"class":89},[75,294,295,297,299,301],{"class":77,"line":161},[75,296,164],{"class":109},[75,298,265],{"class":113},[75,300,248],{"class":89},[75,302,303],{"class":170}," \u002F\u002F gevonden op index i\n",[75,305,306],{"class":77,"line":174},[75,307,308],{"class":89},"        }\n",[75,310,312],{"class":77,"line":311},6,[75,313,314],{"class":89},"    }\n",[75,316,318,320,322,324,326],{"class":77,"line":317},7,[75,319,177],{"class":109},[75,321,180],{"class":89},[75,323,184],{"class":183},[75,325,248],{"class":89},[75,327,328],{"class":170}," \u002F\u002F niet gevonden\n",[75,330,332],{"class":77,"line":331},8,[75,333,334],{"class":89},"}\n",[10,336,337,338,342,343,346],{},"Het voordeel: de lijst hoeft niet gesorteerd te zijn, en het werkt ook op een\n",[94,339,341],{"href":340},"\u002Fpracticely\u002Fdsa\u002Fstapels-en-wachtrijen","gelinkte lijst",". Het nadeel: ",[30,344,345],{},"O(n)",". Staat het element\nachteraan of helemaal niet in de lijst, dan bekijk je alles.",[47,348,350],{"id":349},"binair-zoeken-het-idee","Binair zoeken: het idee",[10,352,353],{},"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.",[10,355,356,357,360,361,364,365,368],{},"Binair zoeken doet hetzelfde met een ",[14,358,359],{},"gesorteerde"," array. Je houdt twee grenzen bij, ",[30,362,363],{},"lo"," en ",[30,366,367],{},"hi",",\nwaartussen het element moet zitten als het er is. Elke stap:",[370,371,372,380,391,406],"ol",{},[373,374,375,376,379],"li",{},"Bereken ",[30,377,378],{},"mid = ⌊(lo + hi) \u002F 2⌋"," (naar beneden afronden).",[373,381,382,383,386,387,390],{},"Is ",[30,384,385],{},"a[mid]"," gelijk aan ",[30,388,389],{},"x","? Gevonden.",[373,392,382,393,396,397,399,400,402,403,257],{},[30,394,395],{},"a[mid] \u003C x","? Dan zit ",[30,398,389],{}," rechts van ",[30,401,40],{},": ",[30,404,405],{},"lo = mid + 1",[373,407,408,409,411,412,402,414,257],{},"Anders zit ",[30,410,389],{}," links van ",[30,413,40],{},[30,415,416],{},"hi = mid - 1",[10,418,419,420,364,423,426,427,430,431,433],{},"Je begint met ",[30,421,422],{},"lo = 0",[30,424,425],{},"hi = n - 1",", en je stopt als ",[30,428,429],{},"lo > hi",": dan is het zoekgebied leeg en\nstaat ",[30,432,389],{}," niet in de array.",[47,435,437],{"id":436},"uitgewerkt-voorbeeld-gevonden","Uitgewerkt voorbeeld: gevonden",[10,439,440,441,444],{},"We zoeken ",[30,442,443],{},"x = 30"," in deze array van tien elementen:",[446,447,448,487],"table",{},[449,450,451],"thead",{},[452,453,454,458,461,463,466,469,472,475,478,481,484],"tr",{},[455,456,457],"th",{},"index",[455,459,460],{},"0",[455,462,184],{},[455,464,465],{},"2",[455,467,468],{},"3",[455,470,471],{},"4",[455,473,474],{},"5",[455,476,477],{},"6",[455,479,480],{},"7",[455,482,483],{},"8",[455,485,486],{},"9",[488,489,490],"tbody",{},[452,491,492,495,497,499,502,505,508,511,514,517,520],{},[493,494,94],"td",{},[493,496,468],{},[493,498,483],{},[493,500,501],{},"12",[493,503,504],{},"17",[493,506,507],{},"21",[493,509,510],{},"25",[493,512,513],{},"30",[493,515,516],{},"34",[493,518,519],{},"41",[493,521,522],{},"50",[446,524,525,548],{},[449,526,527],{},[452,528,529,532,534,536,538,542,545],{},[455,530,531],{},"Stap",[455,533,363],{},[455,535,367],{},[455,537,40],{},[455,539,94,540],{},[75,541,40],{},[455,543,544],{},"Vergelijking",[455,546,547],{},"Actie",[488,549,550,570,590,610],{},[452,551,552,554,556,558,560,562,565],{},[493,553,184],{},[493,555,460],{},[493,557,486],{},[493,559,471],{},[493,561,507],{},[493,563,564],{},"21 \u003C 30",[493,566,567],{},[30,568,569],{},"lo = 5",[452,571,572,574,576,578,580,582,585],{},[493,573,465],{},[493,575,474],{},[493,577,486],{},[493,579,480],{},[493,581,516],{},[493,583,584],{},"34 > 30",[493,586,587],{},[30,588,589],{},"hi = 6",[452,591,592,594,596,598,600,602,605],{},[493,593,468],{},[493,595,474],{},[493,597,477],{},[493,599,474],{},[493,601,510],{},[493,603,604],{},"25 \u003C 30",[493,606,607],{},[30,608,609],{},"lo = 6",[452,611,612,614,616,618,620,622,625],{},[493,613,471],{},[493,615,477],{},[493,617,477],{},[493,619,477],{},[493,621,513],{},[493,623,624],{},"gelijk",[493,626,627],{},"gevonden op index 6",[10,629,630,631,634,635,638,639,257],{},"De waarden die achtereenvolgens worden vergeleken zijn ",[30,632,633],{},"21, 34, 25, 30",". Let op stap 3: ",[30,636,637],{},"(5 + 6) \u002F 2 = 5,5",", afgerond naar beneden geeft ",[30,640,641],{},"mid = 5",[47,643,645],{"id":644},"uitgewerkt-voorbeeld-niet-gevonden","Uitgewerkt voorbeeld: niet gevonden",[10,647,648,649,652],{},"Nu zoeken we ",[30,650,651],{},"x = 10"," in dezelfde array:",[446,654,655,675],{},[449,656,657],{},[452,658,659,661,663,665,667,671,673],{},[455,660,531],{},[455,662,363],{},[455,664,367],{},[455,666,40],{},[455,668,94,669],{},[75,670,40],{},[455,672,544],{},[455,674,547],{},[488,676,677,697,717,737],{},[452,678,679,681,683,685,687,689,692],{},[493,680,184],{},[493,682,460],{},[493,684,486],{},[493,686,471],{},[493,688,507],{},[493,690,691],{},"21 > 10",[493,693,694],{},[30,695,696],{},"hi = 3",[452,698,699,701,703,705,707,709,712],{},[493,700,465],{},[493,702,460],{},[493,704,468],{},[493,706,184],{},[493,708,483],{},[493,710,711],{},"8 \u003C 10",[493,713,714],{},[30,715,716],{},"lo = 2",[452,718,719,721,723,725,727,729,732],{},[493,720,468],{},[493,722,465],{},[493,724,468],{},[493,726,465],{},[493,728,501],{},[493,730,731],{},"12 > 10",[493,733,734],{},[30,735,736],{},"hi = 1",[452,738,739,742,744,746,748,750,754],{},[493,740,741],{},"–",[493,743,465],{},[493,745,184],{},[493,747,741],{},[493,749,741],{},[493,751,752],{},[30,753,429],{},[493,755,756],{},"stop: niet gevonden",[10,758,759,760,364,762,764,765,768,769,772,773,775,776,778],{},"Vergeleken waarden: ",[30,761,483],{},[30,763,501],{}," liggen naast elkaar en ",[30,766,767],{},"10"," zit ertussen. Na drie vergelijkingen\n(",[30,770,771],{},"21, 8, 12",") is het zoekgebied leeg. De eindwaarde van ",[30,774,363],{}," (hier 2) is precies de plek waar je ",[30,777,767],{},"\nzou moeten invoegen om de array gesorteerd te houden; dat is handig om te onthouden.",[47,780,782],{"id":781},"de-code","De code",[60,784,785,986],{},[63,786,787],{"v-slot:python":65},[67,788,790],{"className":69,"code":789,"language":71,"meta":65,"style":65},"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",[30,791,792,809,839,858,886,904,911,931,949,957,975],{"__ignoreMap":65},[75,793,794,796,799,801,803,805,807],{"class":77,"line":78},[75,795,82],{"class":81},[75,797,798],{"class":85}," binair_zoeken",[75,800,90],{"class":89},[75,802,94],{"class":93},[75,804,97],{"class":89},[75,806,100],{"class":93},[75,808,103],{"class":89},[75,810,811,814,816,819,821,823,825,828,830,832,834,836],{"class":77,"line":106},[75,812,813],{"class":113},"    lo",[75,815,97],{"class":89},[75,817,818],{"class":113}," hi ",[75,820,242],{"class":89},[75,822,245],{"class":183},[75,824,97],{"class":89},[75,826,827],{"class":85}," len",[75,829,90],{"class":89},[75,831,94],{"class":85},[75,833,226],{"class":89},[75,835,180],{"class":89},[75,837,838],{"class":183}," 1\n",[75,840,841,844,847,849,852,855],{"class":77,"line":135},[75,842,843],{"class":109},"    while",[75,845,846],{"class":113}," lo ",[75,848,36],{"class":89},[75,850,851],{"class":113}," hi",[75,853,854],{"class":89},":",[75,856,857],{"class":170},"  # zolang het zoekgebied niet leeg is\n",[75,859,860,863,865,867,870,873,875,877,880,883],{"class":77,"line":161},[75,861,862],{"class":113},"        mid ",[75,864,242],{"class":89},[75,866,23],{"class":89},[75,868,869],{"class":113},"lo ",[75,871,872],{"class":89},"+",[75,874,851],{"class":113},[75,876,226],{"class":89},[75,878,879],{"class":89}," \u002F\u002F",[75,881,882],{"class":183}," 2",[75,884,885],{"class":170},"  # naar beneden afronden\n",[75,887,888,890,892,894,896,898,900,902],{"class":77,"line":174},[75,889,138],{"class":109},[75,891,141],{"class":113},[75,893,144],{"class":89},[75,895,40],{"class":113},[75,897,150],{"class":89},[75,899,153],{"class":89},[75,901,100],{"class":113},[75,903,158],{"class":89},[75,905,906,908],{"class":77,"line":311},[75,907,164],{"class":109},[75,909,910],{"class":113}," mid\n",[75,912,913,916,918,920,922,924,927,929],{"class":77,"line":317},[75,914,915],{"class":109},"        elif",[75,917,141],{"class":113},[75,919,144],{"class":89},[75,921,40],{"class":113},[75,923,150],{"class":89},[75,925,926],{"class":89}," \u003C",[75,928,100],{"class":113},[75,930,158],{"class":89},[75,932,933,936,938,941,943,946],{"class":77,"line":331},[75,934,935],{"class":113},"            lo ",[75,937,242],{"class":89},[75,939,940],{"class":113}," mid ",[75,942,872],{"class":89},[75,944,945],{"class":183}," 1",[75,947,948],{"class":170},"  # x zit rechts van mid\n",[75,950,952,955],{"class":77,"line":951},9,[75,953,954],{"class":109},"        else",[75,956,158],{"class":89},[75,958,960,963,965,967,970,972],{"class":77,"line":959},10,[75,961,962],{"class":113},"            hi ",[75,964,242],{"class":89},[75,966,940],{"class":113},[75,968,969],{"class":89},"-",[75,971,945],{"class":183},[75,973,974],{"class":170},"  # x zit links van mid\n",[75,976,978,980,982,984],{"class":77,"line":977},11,[75,979,177],{"class":109},[75,981,180],{"class":89},[75,983,184],{"class":183},[75,985,187],{"class":170},[63,987,988],{"v-slot:java":65},[67,989,991],{"className":192,"code":990,"language":194,"meta":65,"style":65},"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",[30,992,993,1020,1051,1071,1106,1128,1137,1166,1183,1191,1208,1212,1217,1230],{"__ignoreMap":65},[75,994,995,997,999,1002,1004,1006,1008,1010,1012,1014,1016,1018],{"class":77,"line":78},[75,996,201],{"class":81},[75,998,204],{"class":81},[75,1000,1001],{"class":85}," binairZoeken",[75,1003,90],{"class":89},[75,1005,212],{"class":81},[75,1007,215],{"class":89},[75,1009,141],{"class":113},[75,1011,97],{"class":89},[75,1013,204],{"class":81},[75,1015,100],{"class":113},[75,1017,226],{"class":89},[75,1019,229],{"class":89},[75,1021,1022,1025,1027,1029,1031,1033,1035,1037,1039,1041,1044,1046,1048],{"class":77,"line":106},[75,1023,1024],{"class":81},"    int",[75,1026,846],{"class":113},[75,1028,242],{"class":89},[75,1030,245],{"class":183},[75,1032,97],{"class":89},[75,1034,818],{"class":113},[75,1036,242],{"class":89},[75,1038,141],{"class":113},[75,1040,257],{"class":89},[75,1042,1043],{"class":113},"length ",[75,1045,969],{"class":89},[75,1047,945],{"class":183},[75,1049,1050],{"class":89},";\n",[75,1052,1053,1055,1057,1059,1061,1063,1065,1068],{"class":77,"line":135},[75,1054,843],{"class":109},[75,1056,23],{"class":89},[75,1058,869],{"class":113},[75,1060,36],{"class":89},[75,1062,851],{"class":113},[75,1064,226],{"class":89},[75,1066,1067],{"class":89}," {",[75,1069,1070],{"class":170}," \u002F\u002F zolang het zoekgebied niet leeg is\n",[75,1072,1073,1076,1078,1080,1082,1084,1086,1089,1091,1094,1096,1099,1101,1103],{"class":77,"line":161},[75,1074,1075],{"class":81},"        int",[75,1077,940],{"class":113},[75,1079,242],{"class":89},[75,1081,846],{"class":113},[75,1083,872],{"class":89},[75,1085,23],{"class":89},[75,1087,1088],{"class":113},"hi ",[75,1090,969],{"class":89},[75,1092,1093],{"class":113}," lo",[75,1095,226],{"class":89},[75,1097,1098],{"class":89}," \u002F",[75,1100,882],{"class":183},[75,1102,248],{"class":89},[75,1104,1105],{"class":170}," \u002F\u002F gelijk aan ⌊(lo+hi)\u002F2⌋, maar zonder overflow\n",[75,1107,1108,1110,1112,1114,1116,1118,1120,1122,1124,1126],{"class":77,"line":174},[75,1109,138],{"class":109},[75,1111,23],{"class":89},[75,1113,94],{"class":113},[75,1115,144],{"class":89},[75,1117,40],{"class":113},[75,1119,150],{"class":89},[75,1121,153],{"class":89},[75,1123,100],{"class":113},[75,1125,226],{"class":89},[75,1127,229],{"class":89},[75,1129,1130,1132,1135],{"class":77,"line":311},[75,1131,164],{"class":109},[75,1133,1134],{"class":113}," mid",[75,1136,1050],{"class":89},[75,1138,1139,1142,1145,1148,1150,1152,1154,1156,1158,1160,1162,1164],{"class":77,"line":317},[75,1140,1141],{"class":89},"        }",[75,1143,1144],{"class":109}," else",[75,1146,1147],{"class":109}," if",[75,1149,23],{"class":89},[75,1151,94],{"class":113},[75,1153,144],{"class":89},[75,1155,40],{"class":113},[75,1157,150],{"class":89},[75,1159,926],{"class":89},[75,1161,100],{"class":113},[75,1163,226],{"class":89},[75,1165,229],{"class":89},[75,1167,1168,1170,1172,1174,1176,1178,1180],{"class":77,"line":331},[75,1169,935],{"class":113},[75,1171,242],{"class":89},[75,1173,940],{"class":113},[75,1175,872],{"class":89},[75,1177,945],{"class":183},[75,1179,248],{"class":89},[75,1181,1182],{"class":170}," \u002F\u002F x zit rechts van mid\n",[75,1184,1185,1187,1189],{"class":77,"line":951},[75,1186,1141],{"class":89},[75,1188,1144],{"class":109},[75,1190,229],{"class":89},[75,1192,1193,1195,1197,1199,1201,1203,1205],{"class":77,"line":959},[75,1194,962],{"class":113},[75,1196,242],{"class":89},[75,1198,940],{"class":113},[75,1200,969],{"class":89},[75,1202,945],{"class":183},[75,1204,248],{"class":89},[75,1206,1207],{"class":170}," \u002F\u002F x zit links van mid\n",[75,1209,1210],{"class":77,"line":977},[75,1211,308],{"class":89},[75,1213,1215],{"class":77,"line":1214},12,[75,1216,314],{"class":89},[75,1218,1220,1222,1224,1226,1228],{"class":77,"line":1219},13,[75,1221,177],{"class":109},[75,1223,180],{"class":89},[75,1225,184],{"class":183},[75,1227,248],{"class":89},[75,1229,328],{"class":170},[75,1231,1233],{"class":77,"line":1232},14,[75,1234,334],{"class":89},[10,1236,1237,1238,1241,1242,1245,1246,1248,1249,1251,1252,1254,1255,1258,1259,1261],{},"In Java schrijven we ",[30,1239,1240],{},"lo + (hi - lo) \u002F 2"," in plaats van ",[30,1243,1244],{},"(lo + hi) \u002F 2",". Voor niet-negatieve ",[30,1247,363],{},"\nen ",[30,1250,367],{}," levert dat dezelfde ",[30,1253,40],{}," op, maar het voorkomt dat ",[30,1256,1257],{},"lo + hi"," groter wordt dan de maximale\n",[30,1260,212],{}," bij hele grote arrays. In Python bestaat dat probleem niet.",[47,1263,1265],{"id":1264},"off-by-one-valkuilen","Off-by-one-valkuilen",[10,1267,1268],{},"Binair zoeken is berucht om fouten van één positie. De drie keuzes in onze variant horen bij elkaar:",[446,1270,1271,1281],{},[449,1272,1273],{},[452,1274,1275,1278],{},[455,1276,1277],{},"Keuze",[455,1279,1280],{},"Waarom",[488,1282,1283,1294,1308],{},[452,1284,1285,1289],{},[493,1286,1287],{},[30,1288,425],{},[493,1290,1291,1293],{},[30,1292,367],{}," is de laatste index die nog kandidaat is (inclusief)",[452,1295,1296,1301],{},[493,1297,1298],{},[30,1299,1300],{},"while lo \u003C= hi",[493,1302,1303,1304,1307],{},"als ",[30,1305,1306],{},"lo == hi"," is er nog precies één kandidaat die je moet bekijken",[452,1309,1310,1316],{},[493,1311,1312,37,1314],{},[30,1313,405],{},[30,1315,416],{},[493,1317,1318,1320],{},[30,1319,385],{}," is al bekeken, die hoeft niet meer in het zoekgebied",[10,1322,1323],{},"Wat gaat er mis als je een van de drie verandert?",[1325,1326,1327,1346,1374],"ul",{},[373,1328,1329,1334,1335,1338,1339,1342,1343,1345],{},[14,1330,1331],{},[30,1332,1333],{},"while lo \u003C hi",": in het eerste voorbeeld stop je na stap 3 met ",[30,1336,1337],{},"lo = hi = 6",", zonder ",[30,1340,1341],{},"a[6]","\nte bekijken. Je meldt \"niet gevonden\" terwijl ",[30,1344,513],{}," er wel staat.",[373,1347,1348,1356,1357,1360,1361,1363,1364,1367,1368,1370,1371,257],{},[14,1349,1350,1241,1353],{},[30,1351,1352],{},"lo = mid",[30,1354,1355],{},"mid + 1",": met ",[30,1358,1359],{},"lo = 5, hi = 6"," krijg je ",[30,1362,641],{},", en als\n",[30,1365,1366],{},"a[5] \u003C x"," blijft ",[30,1369,363],{}," op 5 staan. Het zoekgebied krimpt niet: een ",[14,1372,1373],{},"oneindige lus",[373,1375,1376,1381,1382,1384,1385,1387,1388,1391],{},[14,1377,1378],{},[30,1379,1380],{},"hi = n"," met ",[30,1383,36],{},": dan kan ",[30,1386,40],{}," gelijk worden aan ",[30,1389,1390],{},"n"," en lees je buiten de array.",[10,1393,1394,1395,1397,1398,1400],{},"Er bestaan ook correcte varianten met ",[30,1396,1380],{}," (exclusief) en ",[30,1399,1333],{},". Die werken prima, maar\nmeng de twee stijlen nooit. Op Practicely gebruiken we altijd de variant hierboven.",[47,1402,1404],{"id":1403},"variant-het-eerste-voorkomen","Variant: het eerste voorkomen",[10,1406,1407,1408,1410,1411,1414,1415,1417,1418,1421],{},"Staat ",[30,1409,389],{}," meerdere keren in de array, dan geeft gewoon binair zoeken een willekeurige van de\nvoorkomens terug. In ",[30,1412,1413],{},"[1, 3, 3, 3, 3, 7, 9]"," vindt het ",[30,1416,468],{}," al bij de eerste stap, op index 3. Wil je\nhet ",[14,1419,1420],{},"eerste"," voorkomen, dan ga je na een treffer verder zoeken in de linkerhelft en onthoud je de\nbeste index tot nu toe:",[446,1423,1424,1445],{},[449,1425,1426],{},[452,1427,1428,1430,1432,1434,1436,1440,1442],{},[455,1429,531],{},[455,1431,363],{},[455,1433,367],{},[455,1435,40],{},[455,1437,94,1438],{},[75,1439,40],{},[455,1441,547],{},[455,1443,1444],{},"Beste tot nu toe",[488,1446,1447,1467,1486],{},[452,1448,1449,1451,1453,1455,1457,1459,1465],{},[493,1450,184],{},[493,1452,460],{},[493,1454,477],{},[493,1456,468],{},[493,1458,468],{},[493,1460,1461,1462],{},"gelijk, zoek links: ",[30,1463,1464],{},"hi = 2",[493,1466,468],{},[452,1468,1469,1471,1473,1475,1477,1479,1484],{},[493,1470,465],{},[493,1472,460],{},[493,1474,465],{},[493,1476,184],{},[493,1478,468],{},[493,1480,1461,1481],{},[30,1482,1483],{},"hi = 0",[493,1485,184],{},[452,1487,1488,1490,1492,1494,1496,1498,1504],{},[493,1489,468],{},[493,1491,460],{},[493,1493,460],{},[493,1495,460],{},[493,1497,184],{},[493,1499,1500,1501],{},"1 \u003C 3: ",[30,1502,1503],{},"lo = 1",[493,1505,184],{},[10,1507,1508,1509,1511],{},"Daarna is ",[30,1510,429],{}," en is het antwoord index 1.",[60,1513,1514,1707],{},[63,1515,1516],{"v-slot:python":65},[67,1517,1519],{"className":69,"code":1518,"language":71,"meta":65,"style":65},"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",[30,1520,1521,1538,1564,1576,1588,1609,1627,1640,1652,1670,1682,1688,1700],{"__ignoreMap":65},[75,1522,1523,1525,1528,1530,1532,1534,1536],{"class":77,"line":78},[75,1524,82],{"class":81},[75,1526,1527],{"class":85}," eerste_voorkomen",[75,1529,90],{"class":89},[75,1531,94],{"class":93},[75,1533,97],{"class":89},[75,1535,100],{"class":93},[75,1537,103],{"class":89},[75,1539,1540,1542,1544,1546,1548,1550,1552,1554,1556,1558,1560,1562],{"class":77,"line":106},[75,1541,813],{"class":113},[75,1543,97],{"class":89},[75,1545,818],{"class":113},[75,1547,242],{"class":89},[75,1549,245],{"class":183},[75,1551,97],{"class":89},[75,1553,827],{"class":85},[75,1555,90],{"class":89},[75,1557,94],{"class":85},[75,1559,226],{"class":89},[75,1561,180],{"class":89},[75,1563,838],{"class":183},[75,1565,1566,1569,1571,1573],{"class":77,"line":135},[75,1567,1568],{"class":113},"    antwoord ",[75,1570,242],{"class":89},[75,1572,180],{"class":89},[75,1574,1575],{"class":183},"1\n",[75,1577,1578,1580,1582,1584,1586],{"class":77,"line":161},[75,1579,843],{"class":109},[75,1581,846],{"class":113},[75,1583,36],{"class":89},[75,1585,851],{"class":113},[75,1587,158],{"class":89},[75,1589,1590,1592,1594,1596,1598,1600,1602,1604,1606],{"class":77,"line":174},[75,1591,862],{"class":113},[75,1593,242],{"class":89},[75,1595,23],{"class":89},[75,1597,869],{"class":113},[75,1599,872],{"class":89},[75,1601,851],{"class":113},[75,1603,226],{"class":89},[75,1605,879],{"class":89},[75,1607,1608],{"class":183}," 2\n",[75,1610,1611,1613,1615,1617,1619,1621,1623,1625],{"class":77,"line":311},[75,1612,138],{"class":109},[75,1614,141],{"class":113},[75,1616,144],{"class":89},[75,1618,40],{"class":113},[75,1620,150],{"class":89},[75,1622,153],{"class":89},[75,1624,100],{"class":113},[75,1626,158],{"class":89},[75,1628,1629,1632,1634,1637],{"class":77,"line":317},[75,1630,1631],{"class":113},"            antwoord ",[75,1633,242],{"class":89},[75,1635,1636],{"class":113}," mid  ",[75,1638,1639],{"class":170},"# onthouden en links verder zoeken\n",[75,1641,1642,1644,1646,1648,1650],{"class":77,"line":331},[75,1643,962],{"class":113},[75,1645,242],{"class":89},[75,1647,940],{"class":113},[75,1649,969],{"class":89},[75,1651,838],{"class":183},[75,1653,1654,1656,1658,1660,1662,1664,1666,1668],{"class":77,"line":951},[75,1655,915],{"class":109},[75,1657,141],{"class":113},[75,1659,144],{"class":89},[75,1661,40],{"class":113},[75,1663,150],{"class":89},[75,1665,926],{"class":89},[75,1667,100],{"class":113},[75,1669,158],{"class":89},[75,1671,1672,1674,1676,1678,1680],{"class":77,"line":959},[75,1673,935],{"class":113},[75,1675,242],{"class":89},[75,1677,940],{"class":113},[75,1679,872],{"class":89},[75,1681,838],{"class":183},[75,1683,1684,1686],{"class":77,"line":977},[75,1685,954],{"class":109},[75,1687,158],{"class":89},[75,1689,1690,1692,1694,1696,1698],{"class":77,"line":1214},[75,1691,962],{"class":113},[75,1693,242],{"class":89},[75,1695,940],{"class":113},[75,1697,969],{"class":89},[75,1699,838],{"class":183},[75,1701,1702,1704],{"class":77,"line":1219},[75,1703,177],{"class":109},[75,1705,1706],{"class":113}," antwoord\n",[63,1708,1709],{"v-slot:java":65},[67,1710,1712],{"className":192,"code":1711,"language":194,"meta":65,"style":65},"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",[30,1713,1714,1741,1769,1784,1800,1828,1850,1863,1877,1903,1917,1925,1939,1943,1947,1957],{"__ignoreMap":65},[75,1715,1716,1718,1720,1723,1725,1727,1729,1731,1733,1735,1737,1739],{"class":77,"line":78},[75,1717,201],{"class":81},[75,1719,204],{"class":81},[75,1721,1722],{"class":85}," eersteVoorkomen",[75,1724,90],{"class":89},[75,1726,212],{"class":81},[75,1728,215],{"class":89},[75,1730,141],{"class":113},[75,1732,97],{"class":89},[75,1734,204],{"class":81},[75,1736,100],{"class":113},[75,1738,226],{"class":89},[75,1740,229],{"class":89},[75,1742,1743,1745,1747,1749,1751,1753,1755,1757,1759,1761,1763,1765,1767],{"class":77,"line":106},[75,1744,1024],{"class":81},[75,1746,846],{"class":113},[75,1748,242],{"class":89},[75,1750,245],{"class":183},[75,1752,97],{"class":89},[75,1754,818],{"class":113},[75,1756,242],{"class":89},[75,1758,141],{"class":113},[75,1760,257],{"class":89},[75,1762,1043],{"class":113},[75,1764,969],{"class":89},[75,1766,945],{"class":183},[75,1768,1050],{"class":89},[75,1770,1771,1773,1776,1778,1780,1782],{"class":77,"line":135},[75,1772,1024],{"class":81},[75,1774,1775],{"class":113}," antwoord ",[75,1777,242],{"class":89},[75,1779,180],{"class":89},[75,1781,184],{"class":183},[75,1783,1050],{"class":89},[75,1785,1786,1788,1790,1792,1794,1796,1798],{"class":77,"line":161},[75,1787,843],{"class":109},[75,1789,23],{"class":89},[75,1791,869],{"class":113},[75,1793,36],{"class":89},[75,1795,851],{"class":113},[75,1797,226],{"class":89},[75,1799,229],{"class":89},[75,1801,1802,1804,1806,1808,1810,1812,1814,1816,1818,1820,1822,1824,1826],{"class":77,"line":174},[75,1803,1075],{"class":81},[75,1805,940],{"class":113},[75,1807,242],{"class":89},[75,1809,846],{"class":113},[75,1811,872],{"class":89},[75,1813,23],{"class":89},[75,1815,1088],{"class":113},[75,1817,969],{"class":89},[75,1819,1093],{"class":113},[75,1821,226],{"class":89},[75,1823,1098],{"class":89},[75,1825,882],{"class":183},[75,1827,1050],{"class":89},[75,1829,1830,1832,1834,1836,1838,1840,1842,1844,1846,1848],{"class":77,"line":311},[75,1831,138],{"class":109},[75,1833,23],{"class":89},[75,1835,94],{"class":113},[75,1837,144],{"class":89},[75,1839,40],{"class":113},[75,1841,150],{"class":89},[75,1843,153],{"class":89},[75,1845,100],{"class":113},[75,1847,226],{"class":89},[75,1849,229],{"class":89},[75,1851,1852,1854,1856,1858,1860],{"class":77,"line":317},[75,1853,1631],{"class":113},[75,1855,242],{"class":89},[75,1857,1134],{"class":113},[75,1859,248],{"class":89},[75,1861,1862],{"class":170}," \u002F\u002F onthouden en links verder zoeken\n",[75,1864,1865,1867,1869,1871,1873,1875],{"class":77,"line":331},[75,1866,962],{"class":113},[75,1868,242],{"class":89},[75,1870,940],{"class":113},[75,1872,969],{"class":89},[75,1874,945],{"class":183},[75,1876,1050],{"class":89},[75,1878,1879,1881,1883,1885,1887,1889,1891,1893,1895,1897,1899,1901],{"class":77,"line":951},[75,1880,1141],{"class":89},[75,1882,1144],{"class":109},[75,1884,1147],{"class":109},[75,1886,23],{"class":89},[75,1888,94],{"class":113},[75,1890,144],{"class":89},[75,1892,40],{"class":113},[75,1894,150],{"class":89},[75,1896,926],{"class":89},[75,1898,100],{"class":113},[75,1900,226],{"class":89},[75,1902,229],{"class":89},[75,1904,1905,1907,1909,1911,1913,1915],{"class":77,"line":959},[75,1906,935],{"class":113},[75,1908,242],{"class":89},[75,1910,940],{"class":113},[75,1912,872],{"class":89},[75,1914,945],{"class":183},[75,1916,1050],{"class":89},[75,1918,1919,1921,1923],{"class":77,"line":977},[75,1920,1141],{"class":89},[75,1922,1144],{"class":109},[75,1924,229],{"class":89},[75,1926,1927,1929,1931,1933,1935,1937],{"class":77,"line":1214},[75,1928,962],{"class":113},[75,1930,242],{"class":89},[75,1932,940],{"class":113},[75,1934,969],{"class":89},[75,1936,945],{"class":183},[75,1938,1050],{"class":89},[75,1940,1941],{"class":77,"line":1219},[75,1942,308],{"class":89},[75,1944,1945],{"class":77,"line":1232},[75,1946,314],{"class":89},[75,1948,1950,1952,1955],{"class":77,"line":1949},15,[75,1951,177],{"class":109},[75,1953,1954],{"class":113}," antwoord",[75,1956,1050],{"class":89},[75,1958,1960],{"class":77,"line":1959},16,[75,1961,334],{"class":89},[10,1963,1964,1965,1968,1969,1971,1972,1975],{},"Het ",[14,1966,1967],{},"laatste"," voorkomen werkt spiegelbeeldig: na een treffer ",[30,1970,405],{},". Met eerste en laatste\nvoorkomen samen tel je in ",[30,1973,1974],{},"O(log n)"," hoe vaak een waarde voorkomt.",[47,1977,1979],{"id":1978},"complexiteit","Complexiteit",[10,1981,1982,1983,1986,1987,1990,1991,1994,1995,1998,1999,2002,2003,257],{},"Elke stap halveert het zoekgebied. Na ",[30,1984,1985],{},"k"," stappen zijn er hooguit ",[30,1988,1989],{},"n \u002F 2ᵏ"," kandidaten over, dus na\nongeveer ",[30,1992,1993],{},"log₂ n"," stappen is er nog één. Als recurrente betrekking: ",[30,1996,1997],{},"T(n) = T(n\u002F2) + 1",", en volgens\nde mastermethode (zie ",[94,2000,1978],{"href":2001},"\u002Fpracticely\u002Fdsa\u002Fcomplexiteit",") is dat ",[30,2004,1974],{},[446,2006,2007,2017],{},[449,2008,2009],{},[452,2010,2011,2013,2015],{},[455,2012],{},[455,2014,50],{},[455,2016,22],{},[488,2018,2019,2033,2049,2062,2075,2089],{},[452,2020,2021,2024,2027],{},[493,2022,2023],{},"Voorwaarde",[493,2025,2026],{},"geen",[493,2028,2029,2030,2032],{},"array ",[14,2031,16],{},", directe toegang via index",[452,2034,2035,2038,2044],{},[493,2036,2037],{},"Best case",[493,2039,2040,2043],{},[30,2041,2042],{},"O(1)"," (eerste element)",[493,2045,2046,2048],{},[30,2047,2042],{}," (middelste element)",[452,2050,2051,2054,2058],{},[493,2052,2053],{},"Gemiddeld",[493,2055,2056],{},[30,2057,345],{},[493,2059,2060],{},[30,2061,1974],{},[452,2063,2064,2067,2071],{},[493,2065,2066],{},"Slechtst",[493,2068,2069],{},[30,2070,345],{},[493,2072,2073],{},[30,2074,1974],{},[452,2076,2077,2080,2084],{},[493,2078,2079],{},"Extra geheugen",[493,2081,2082],{},[30,2083,2042],{},[493,2085,2086,2088],{},[30,2087,2042],{}," (iteratief)",[452,2090,2091,2094,2097],{},[493,2092,2093],{},"Vergelijkingen bij n = 1.000.000",[493,2095,2096],{},"tot 1.000.000",[493,2098,2099],{},"hooguit 20",[10,2101,2102,2103,2106,2107,2111,2112,2116],{},"Moet je maar één keer zoeken in ongesorteerde data, dan is lineair zoeken sneller dan eerst sorteren\n(",[30,2104,2105],{},"O(n log n)",") en dan binair zoeken. Zoek je vaak in dezelfde data, dan verdient het sorteren zich\nsnel terug. Nog sneller opzoeken kan met een ",[94,2108,2110],{"href":2109},"\u002Fpracticely\u002Fdsa\u002Fhashtabellen","hashtabel",", en voor data\ndie steeds verandert is een ",[94,2113,2115],{"href":2114},"\u002Fpracticely\u002Fdsa\u002Fbinaire-zoekbomen","binaire zoekboom"," handig.",[47,2118,2120],{"id":2119},"veelgemaakte-fouten-op-het-tentamen","Veelgemaakte fouten op het tentamen",[370,2122,2123,2129,2150,2158,2174],{},[373,2124,2125,2128],{},[14,2126,2127],{},"Binair zoeken op een ongesorteerde array."," Het algoritme geeft dan gewoon een fout antwoord,\nzonder foutmelding. Controleer altijd eerst de voorwaarde.",[373,2130,2131,2136,2137,2140,2141,2143,2144,2146,2147,2149],{},[14,2132,2133,2135],{},[30,2134,40],{}," naar boven afronden."," ",[30,2138,2139],{},"(5 + 6) \u002F 2"," wordt ",[30,2142,474],{},", niet ",[30,2145,477],{},". Bij een traceervraag verschuift\néén verkeerde ",[30,2148,40],{}," alle volgende stappen.",[373,2151,2152,2157],{},[14,2153,2154,2156],{},[30,2155,1333],{}," gebruiken"," bij de inclusieve variant, waardoor je het laatste kandidaat-element\nnooit bekijkt.",[373,2159,2160,1241,2168,364,2170,2173],{},[14,2161,2162,41,2164,2167],{},[30,2163,1352],{},[30,2165,2166],{},"hi = mid"," schrijven",[30,2169,1355],{},[30,2171,2172],{},"mid - 1",". Dat kan een oneindige\nlus opleveren.",[373,2175,2176,2179,2180,2182],{},[14,2177,2178],{},"Bij de traceervraag de laatste vergelijking vergeten."," Ook de vergelijking waarin ",[30,2181,389],{}," gevonden\nwordt, hoort in de lijst van vergeleken waarden.",[47,2184,2186],{"id":2185},"samenvatting","Samenvatting",[1325,2188,2189,2197,2208,2219],{},[373,2190,2191,2192,2194,2195,257],{},"Lineair zoeken werkt altijd en kost ",[30,2193,345],{},"; binair zoeken eist een gesorteerde array en kost ",[30,2196,1974],{},[373,2198,2199,2200,37,2202,37,2204,37,2206,257],{},"Onze variant: ",[30,2201,422],{},[30,2203,425],{},[30,2205,378],{},[30,2207,1300],{},[373,2209,2210,2211,2140,2213,2215,2216,2218],{},"Bij ",[30,2212,395],{},[30,2214,405],{},", anders ",[30,2217,416],{},"; zo krimpt het zoekgebied altijd.",[373,2220,2221],{},"Voor het eerste voorkomen zoek je na een treffer links verder en onthoud je de index.",[2223,2224,2225],"style",{},"html pre.shiki code .spNyl, html code.shiki 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var(--shiki-dark-text-decoration);}",{"title":65,"searchDepth":106,"depth":106,"links":2227},[2228,2229,2230,2231,2232,2233,2234,2235,2236,2237],{"id":49,"depth":106,"text":50},{"id":349,"depth":106,"text":350},{"id":436,"depth":106,"text":437},{"id":644,"depth":106,"text":645},{"id":781,"depth":106,"text":782},{"id":1264,"depth":106,"text":1265},{"id":1403,"depth":106,"text":1404},{"id":1978,"depth":106,"text":1979},{"id":2119,"depth":106,"text":2120},{"id":2185,"depth":106,"text":2186},"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.","md","i-lucide-search",{},true,"\u002Fpracticely-dsa\u002Fzoeken",{"title":5,"description":2238},"practicely-dsa\u002Fzoeken","zoeken","MRqxQRbAp5DYPc2i8AX4gmsTB8-LXQ7_s9tWgGllG9Q",{"prev":2249,"next":6204},{"id":2250,"title":2251,"body":2252,"description":6196,"extension":2239,"icon":6197,"meta":6198,"navigation":2242,"order":106,"path":6199,"seo":6200,"stem":6201,"topic":6202,"__hash__":6203},"practicelyDsa\u002Fpracticely-dsa\u002Fsorteren.md","Sorteeralgoritmes uitgelegd: van insertion sort tot quicksort",{"type":7,"value":2253,"toc":6184},[2254,2261,2270,2274,2277,2370,2376,2379,2384,2477,2483,2857,2874,2877,2882,3002,3023,3456,3466,3469,3474,3552,3580,3587,3962,3966,3984,4120,4127,4873,4889,4893,4909,4917,4926,4935,5116,5131,5848,5868,5872,5875,5898,5900,6045,6059,6061,6128,6130,6181],[10,2255,2256,2257,2260],{},"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 ",[30,2258,2259],{},"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.",[10,2262,2263,2264,2267,2268,257],{},"Op deze pagina behandelen we vijf algoritmes. Bij elk staat een uitgewerkt voorbeeld met de toestand\n",[14,2265,2266],{},"na elke ronde",", precies zoals de oefeningen eronder het vragen. Ken je Big-O nog niet goed, lees\ndan eerst ",[94,2269,1978],{"href":2001},[47,2271,2273],{"id":2272},"wat-betekent-na-ronde-k","Wat betekent \"na ronde k\"?",[10,2275,2276],{},"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):",[446,2278,2279,2292],{},[449,2280,2281],{},[452,2282,2283,2286,2289],{},[455,2284,2285],{},"Algoritme",[455,2287,2288],{},"Eén ronde",[455,2290,2291],{},"Toestand na ronde k",[488,2293,2294,2311,2336,2353],{},[452,2295,2296,2299,2305],{},[493,2297,2298],{},"Insertion sort",[493,2300,2301,2304],{},[30,2302,2303],{},"a[k]"," wordt ingevoegd in het gesorteerde deel links ervan",[493,2306,2307,2310],{},[30,2308,2309],{},"a[0..k]"," gesorteerd, de rest onveranderd",[452,2312,2313,2316,2330],{},[493,2314,2315],{},"Selection sort",[493,2317,2318,2319,364,2322,2325,2326,2329],{},"zoek het minimum in ",[30,2320,2321],{},"a[k-1..n-1]",[14,2323,2324],{},"wissel"," het met ",[30,2327,2328],{},"a[k-1]",", ook als dat hetzelfde element is",[493,2331,2332,2333,2335],{},"de ",[30,2334,1985],{}," kleinste staan gesorteerd vooraan",[452,2337,2338,2341,2348],{},[493,2339,2340],{},"Bubble sort",[493,2342,2343,2344,2347],{},"één volledige doorloop van links naar rechts, wissel buren als ",[30,2345,2346],{},"a[j] > a[j+1]",", geen vroegtijdige stop",[493,2349,2332,2350,2352],{},[30,2351,1985],{}," grootste staan gesorteerd achteraan",[452,2354,2355,2358,2364],{},[493,2356,2357],{},"Quicksort",[493,2359,2360,2361,2363],{},"Lomuto-partitie met het ",[14,2362,1967],{}," element als pivot",[493,2365,2366,2367,2369],{},"de vraag gaat over de array na de ",[14,2368,1420],{}," partitie",[10,2371,2372,2373,257],{},"In alle voorbeelden hieronder sorteren we dezelfde array: ",[30,2374,2375],{},"[5, 2, 4, 6, 1, 3]",[47,2377,2298],{"id":2378},"insertion-sort",[10,2380,2381,2383],{},[14,2382,2298],{}," (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.",[446,2385,2386,2399],{},[449,2387,2388],{},[452,2389,2390,2393,2396],{},[455,2391,2392],{},"Ronde",[455,2394,2395],{},"Ingevoegd element",[455,2397,2398],{},"Array na de ronde",[488,2400,2401,2413,2426,2439,2451,2464],{},[452,2402,2403,2406,2408],{},[493,2404,2405],{},"start",[493,2407,741],{},[493,2409,2410],{},[30,2411,2412],{},"5, 2, 4, 6, 1, 3",[452,2414,2415,2417,2421],{},[493,2416,184],{},[493,2418,2419],{},[30,2420,465],{},[493,2422,2423],{},[30,2424,2425],{},"2, 5, 4, 6, 1, 3",[452,2427,2428,2430,2434],{},[493,2429,465],{},[493,2431,2432],{},[30,2433,471],{},[493,2435,2436],{},[30,2437,2438],{},"2, 4, 5, 6, 1, 3",[452,2440,2441,2443,2447],{},[493,2442,468],{},[493,2444,2445],{},[30,2446,477],{},[493,2448,2449],{},[30,2450,2438],{},[452,2452,2453,2455,2459],{},[493,2454,471],{},[493,2456,2457],{},[30,2458,184],{},[493,2460,2461],{},[30,2462,2463],{},"1, 2, 4, 5, 6, 3",[452,2465,2466,2468,2472],{},[493,2467,474],{},[493,2469,2470],{},[30,2471,468],{},[493,2473,2474],{},[30,2475,2476],{},"1, 2, 3, 4, 5, 6",[10,2478,2479,2480,2482],{},"Let op ronde 3: ",[30,2481,477],{}," is groter dan alles links ervan, dus er verandert niets. Dat telt wél als ronde.",[60,2484,2485,2656],{},[63,2486,2487],{"v-slot:python":65},[67,2488,2490],{"className":69,"code":2489,"language":71,"meta":65,"style":65},"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",[30,2491,2492,2505,2530,2546,2559,2564,2596,2623,2633],{"__ignoreMap":65},[75,2493,2494,2496,2499,2501,2503],{"class":77,"line":78},[75,2495,82],{"class":81},[75,2497,2498],{"class":85}," insertion_sort",[75,2500,90],{"class":89},[75,2502,94],{"class":93},[75,2504,103],{"class":89},[75,2506,2507,2509,2512,2514,2516,2518,2520,2522,2524,2526,2528],{"class":77,"line":106},[75,2508,110],{"class":109},[75,2510,2511],{"class":113}," k ",[75,2513,117],{"class":109},[75,2515,120],{"class":85},[75,2517,90],{"class":89},[75,2519,184],{"class":183},[75,2521,97],{"class":89},[75,2523,827],{"class":85},[75,2525,90],{"class":89},[75,2527,94],{"class":85},[75,2529,132],{"class":89},[75,2531,2532,2535,2537,2539,2541,2543],{"class":77,"line":135},[75,2533,2534],{"class":113},"        x ",[75,2536,242],{"class":89},[75,2538,141],{"class":113},[75,2540,144],{"class":89},[75,2542,1985],{"class":113},[75,2544,2545],{"class":89},"]\n",[75,2547,2548,2551,2553,2555,2557],{"class":77,"line":161},[75,2549,2550],{"class":113},"        j ",[75,2552,242],{"class":89},[75,2554,2511],{"class":113},[75,2556,969],{"class":89},[75,2558,838],{"class":183},[75,2560,2561],{"class":77,"line":174},[75,2562,2563],{"class":170},"        # schuif grotere elementen één plek naar rechts\n",[75,2565,2566,2569,2572,2575,2577,2580,2582,2584,2587,2589,2592,2594],{"class":77,"line":311},[75,2567,2568],{"class":109},"        while",[75,2570,2571],{"class":113}," j ",[75,2573,2574],{"class":89},">=",[75,2576,245],{"class":183},[75,2578,2579],{"class":89}," and",[75,2581,141],{"class":113},[75,2583,144],{"class":89},[75,2585,2586],{"class":113},"j",[75,2588,150],{"class":89},[75,2590,2591],{"class":89}," >",[75,2593,100],{"class":113},[75,2595,158],{"class":89},[75,2597,2598,2601,2603,2606,2608,2610,2612,2615,2617,2619,2621],{"class":77,"line":317},[75,2599,2600],{"class":113},"            a",[75,2602,144],{"class":89},[75,2604,2605],{"class":113},"j ",[75,2607,872],{"class":89},[75,2609,945],{"class":183},[75,2611,150],{"class":89},[75,2613,2614],{"class":89}," =",[75,2616,141],{"class":113},[75,2618,144],{"class":89},[75,2620,2586],{"class":113},[75,2622,2545],{"class":89},[75,2624,2625,2628,2631],{"class":77,"line":331},[75,2626,2627],{"class":113},"            j ",[75,2629,2630],{"class":89},"-=",[75,2632,838],{"class":183},[75,2634,2635,2638,2640,2642,2644,2646,2648,2650,2653],{"class":77,"line":951},[75,2636,2637],{"class":113},"        a",[75,2639,144],{"class":89},[75,2641,2605],{"class":113},[75,2643,872],{"class":89},[75,2645,945],{"class":183},[75,2647,150],{"class":89},[75,2649,2614],{"class":89},[75,2651,2652],{"class":113}," x  ",[75,2654,2655],{"class":170},"# na ronde k is a[0..k] gesorteerd\n",[63,2657,2658],{"v-slot:java":65},[67,2659,2661],{"className":192,"code":2660,"language":194,"meta":65,"style":65},"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",[30,2662,2663,2685,2720,2738,2754,2759,2790,2814,2822,2826,2849,2853],{"__ignoreMap":65},[75,2664,2665,2667,2670,2673,2675,2677,2679,2681,2683],{"class":77,"line":78},[75,2666,201],{"class":81},[75,2668,2669],{"class":81}," void",[75,2671,2672],{"class":85}," insertionSort",[75,2674,90],{"class":89},[75,2676,212],{"class":81},[75,2678,215],{"class":89},[75,2680,141],{"class":113},[75,2682,226],{"class":89},[75,2684,229],{"class":89},[75,2686,2687,2689,2691,2693,2695,2697,2699,2701,2703,2705,2707,2709,2711,2713,2716,2718],{"class":77,"line":106},[75,2688,110],{"class":109},[75,2690,23],{"class":89},[75,2692,212],{"class":81},[75,2694,2511],{"class":113},[75,2696,242],{"class":89},[75,2698,945],{"class":183},[75,2700,248],{"class":89},[75,2702,2511],{"class":113},[75,2704,32],{"class":89},[75,2706,141],{"class":113},[75,2708,257],{"class":89},[75,2710,260],{"class":113},[75,2712,248],{"class":89},[75,2714,2715],{"class":113}," k",[75,2717,268],{"class":89},[75,2719,229],{"class":89},[75,2721,2722,2724,2727,2729,2731,2733,2735],{"class":77,"line":135},[75,2723,1075],{"class":81},[75,2725,2726],{"class":113}," x ",[75,2728,242],{"class":89},[75,2730,141],{"class":113},[75,2732,144],{"class":89},[75,2734,1985],{"class":113},[75,2736,2737],{"class":89},"];\n",[75,2739,2740,2742,2744,2746,2748,2750,2752],{"class":77,"line":161},[75,2741,1075],{"class":81},[75,2743,2571],{"class":113},[75,2745,242],{"class":89},[75,2747,2511],{"class":113},[75,2749,969],{"class":89},[75,2751,945],{"class":183},[75,2753,1050],{"class":89},[75,2755,2756],{"class":77,"line":174},[75,2757,2758],{"class":170},"        \u002F\u002F schuif grotere elementen één plek naar rechts\n",[75,2760,2761,2763,2765,2767,2769,2771,2774,2776,2778,2780,2782,2784,2786,2788],{"class":77,"line":311},[75,2762,2568],{"class":109},[75,2764,23],{"class":89},[75,2766,2605],{"class":113},[75,2768,2574],{"class":89},[75,2770,245],{"class":183},[75,2772,2773],{"class":89}," &&",[75,2775,141],{"class":113},[75,2777,144],{"class":89},[75,2779,2586],{"class":113},[75,2781,150],{"class":89},[75,2783,2591],{"class":89},[75,2785,100],{"class":113},[75,2787,226],{"class":89},[75,2789,229],{"class":89},[75,2791,2792,2794,2796,2798,2800,2802,2804,2806,2808,2810,2812],{"class":77,"line":317},[75,2793,2600],{"class":113},[75,2795,144],{"class":89},[75,2797,2605],{"class":113},[75,2799,872],{"class":89},[75,2801,945],{"class":183},[75,2803,150],{"class":89},[75,2805,2614],{"class":89},[75,2807,141],{"class":113},[75,2809,144],{"class":89},[75,2811,2586],{"class":113},[75,2813,2737],{"class":89},[75,2815,2816,2819],{"class":77,"line":331},[75,2817,2818],{"class":113},"            j",[75,2820,2821],{"class":89},"--;\n",[75,2823,2824],{"class":77,"line":951},[75,2825,308],{"class":89},[75,2827,2828,2830,2832,2834,2836,2838,2840,2842,2844,2846],{"class":77,"line":959},[75,2829,2637],{"class":113},[75,2831,144],{"class":89},[75,2833,2605],{"class":113},[75,2835,872],{"class":89},[75,2837,945],{"class":183},[75,2839,150],{"class":89},[75,2841,2614],{"class":89},[75,2843,100],{"class":113},[75,2845,248],{"class":89},[75,2847,2848],{"class":170}," \u002F\u002F na ronde k is a[0..k] gesorteerd\n",[75,2850,2851],{"class":77,"line":977},[75,2852,314],{"class":89},[75,2854,2855],{"class":77,"line":1214},[75,2856,334],{"class":89},[10,2858,2859,2860,2863,2864,2867,2868,2871,2872,257],{},"Omdat de ",[30,2861,2862],{},"while"," stopt zodra ",[30,2865,2866],{},"a[j] > x"," niet meer geldt, schuiven gelijke elementen nooit langs\nelkaar. Daardoor is insertion sort ",[14,2869,2870],{},"stabiel",". Op een al gesorteerde array doet de binnenlus niets:\ndan is het ",[30,2873,345],{},[47,2875,2315],{"id":2876},"selection-sort",[10,2878,2879,2881],{},[14,2880,2315],{}," (selecterend sorteren) zoekt in elke ronde het kleinste element van het\nongesorteerde deel en wisselt het naar voren.",[446,2883,2884,2898],{},[449,2885,2886],{},[452,2887,2888,2890,2893,2896],{},[455,2889,2392],{},[455,2891,2892],{},"Zoekgebied",[455,2894,2895],{},"Minimum (index)",[455,2897,2398],{},[488,2899,2900,2912,2931,2949,2968,2985],{},[452,2901,2902,2904,2906,2908],{},[493,2903,2405],{},[493,2905,741],{},[493,2907,741],{},[493,2909,2910],{},[30,2911,2412],{},[452,2913,2914,2916,2921,2926],{},[493,2915,184],{},[493,2917,2918],{},[30,2919,2920],{},"a[0..5]",[493,2922,2923,2925],{},[30,2924,184],{}," (4)",[493,2927,2928],{},[30,2929,2930],{},"1, 2, 4, 6, 5, 3",[452,2932,2933,2935,2940,2945],{},[493,2934,465],{},[493,2936,2937],{},[30,2938,2939],{},"a[1..5]",[493,2941,2942,2944],{},[30,2943,465],{}," (1)",[493,2946,2947],{},[30,2948,2930],{},[452,2950,2951,2953,2958,2963],{},[493,2952,468],{},[493,2954,2955],{},[30,2956,2957],{},"a[2..5]",[493,2959,2960,2962],{},[30,2961,468],{}," (5)",[493,2964,2965],{},[30,2966,2967],{},"1, 2, 3, 6, 5, 4",[452,2969,2970,2972,2977,2981],{},[493,2971,471],{},[493,2973,2974],{},[30,2975,2976],{},"a[3..5]",[493,2978,2979,2962],{},[30,2980,471],{},[493,2982,2983],{},[30,2984,2476],{},[452,2986,2987,2989,2994,2998],{},[493,2988,474],{},[493,2990,2991],{},[30,2992,2993],{},"a[4..5]",[493,2995,2996,2925],{},[30,2997,474],{},[493,2999,3000],{},[30,3001,2476],{},[10,3003,3004,3005,3008,3009,3012,3013,3015,3016,3019,3020,257],{},"In ronde 2 staat het minimum al op zijn plek; de \"wissel\" van ",[30,3006,3007],{},"a[1]"," met zichzelf verandert niets.\nIn ronde 1 zie je ook waarom selection sort ",[14,3010,3011],{},"niet stabiel"," is: de ",[30,3014,474],{}," springt in één keer van\nvoren naar index 4, over andere elementen heen. Bij gelijke waarden kan zo'n sprong hun volgorde\nomdraaien: ",[30,3017,3018],{},"[3a, 3b, 1]"," wordt na ronde 1 ",[30,3021,3022],{},"[1, 3b, 3a]",[60,3024,3025,3207],{},[63,3026,3027],{"v-slot:python":65},[67,3028,3030],{"className":69,"code":3029,"language":71,"meta":65,"style":65},"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",[30,3031,3032,3045,3061,3082,3087,3100,3121,3146,3156,3161],{"__ignoreMap":65},[75,3033,3034,3036,3039,3041,3043],{"class":77,"line":78},[75,3035,82],{"class":81},[75,3037,3038],{"class":85}," selection_sort",[75,3040,90],{"class":89},[75,3042,94],{"class":93},[75,3044,103],{"class":89},[75,3046,3047,3050,3052,3054,3056,3058],{"class":77,"line":106},[75,3048,3049],{"class":113},"    n ",[75,3051,242],{"class":89},[75,3053,827],{"class":85},[75,3055,90],{"class":89},[75,3057,94],{"class":85},[75,3059,3060],{"class":89},")\n",[75,3062,3063,3065,3067,3069,3071,3073,3075,3077,3080],{"class":77,"line":135},[75,3064,110],{"class":109},[75,3066,2511],{"class":113},[75,3068,117],{"class":109},[75,3070,120],{"class":85},[75,3072,90],{"class":89},[75,3074,184],{"class":183},[75,3076,97],{"class":89},[75,3078,3079],{"class":85}," n",[75,3081,103],{"class":89},[75,3083,3084],{"class":77,"line":161},[75,3085,3086],{"class":170},"        # zoek het minimum in a[k-1..n-1]\n",[75,3088,3089,3092,3094,3096,3098],{"class":77,"line":174},[75,3090,3091],{"class":113},"        m ",[75,3093,242],{"class":89},[75,3095,2511],{"class":113},[75,3097,969],{"class":89},[75,3099,838],{"class":183},[75,3101,3102,3105,3107,3109,3111,3113,3115,3117,3119],{"class":77,"line":311},[75,3103,3104],{"class":109},"        for",[75,3106,2571],{"class":113},[75,3108,117],{"class":109},[75,3110,120],{"class":85},[75,3112,90],{"class":89},[75,3114,1985],{"class":85},[75,3116,97],{"class":89},[75,3118,3079],{"class":85},[75,3120,103],{"class":89},[75,3122,3123,3126,3128,3130,3132,3134,3136,3138,3140,3143],{"class":77,"line":317},[75,3124,3125],{"class":109},"            if",[75,3127,141],{"class":113},[75,3129,144],{"class":89},[75,3131,2586],{"class":113},[75,3133,150],{"class":89},[75,3135,926],{"class":89},[75,3137,141],{"class":113},[75,3139,144],{"class":89},[75,3141,3142],{"class":113},"m",[75,3144,3145],{"class":89},"]:\n",[75,3147,3148,3151,3153],{"class":77,"line":331},[75,3149,3150],{"class":113},"                m ",[75,3152,242],{"class":89},[75,3154,3155],{"class":113}," j\n",[75,3157,3158],{"class":77,"line":951},[75,3159,3160],{"class":170},"        # wissel altijd, ook als m == k-1\n",[75,3162,3163,3165,3167,3170,3172,3174,3177,3179,3181,3183,3185,3187,3189,3191,3193,3195,3197,3199,3201,3203,3205],{"class":77,"line":959},[75,3164,2637],{"class":113},[75,3166,144],{"class":89},[75,3168,3169],{"class":113},"k ",[75,3171,969],{"class":89},[75,3173,945],{"class":183},[75,3175,3176],{"class":89},"],",[75,3178,141],{"class":113},[75,3180,144],{"class":89},[75,3182,3142],{"class":113},[75,3184,150],{"class":89},[75,3186,2614],{"class":89},[75,3188,141],{"class":113},[75,3190,144],{"class":89},[75,3192,3142],{"class":113},[75,3194,3176],{"class":89},[75,3196,141],{"class":113},[75,3198,144],{"class":89},[75,3200,3169],{"class":113},[75,3202,969],{"class":89},[75,3204,945],{"class":183},[75,3206,2545],{"class":89},[63,3208,3209],{"v-slot:java":65},[67,3210,3212],{"className":192,"code":3211,"language":194,"meta":65,"style":65},"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",[30,3213,3214,3235,3252,3282,3287,3304,3335,3362,3372,3377,3381,3386,3407,3431,3448,3452],{"__ignoreMap":65},[75,3215,3216,3218,3220,3223,3225,3227,3229,3231,3233],{"class":77,"line":78},[75,3217,201],{"class":81},[75,3219,2669],{"class":81},[75,3221,3222],{"class":85}," selectionSort",[75,3224,90],{"class":89},[75,3226,212],{"class":81},[75,3228,215],{"class":89},[75,3230,141],{"class":113},[75,3232,226],{"class":89},[75,3234,229],{"class":89},[75,3236,3237,3239,3242,3244,3246,3248,3250],{"class":77,"line":106},[75,3238,1024],{"class":81},[75,3240,3241],{"class":113}," n ",[75,3243,242],{"class":89},[75,3245,141],{"class":113},[75,3247,257],{"class":89},[75,3249,260],{"class":113},[75,3251,1050],{"class":89},[75,3253,3254,3256,3258,3260,3262,3264,3266,3268,3270,3272,3274,3276,3278,3280],{"class":77,"line":135},[75,3255,110],{"class":109},[75,3257,23],{"class":89},[75,3259,212],{"class":81},[75,3261,2511],{"class":113},[75,3263,242],{"class":89},[75,3265,945],{"class":183},[75,3267,248],{"class":89},[75,3269,2511],{"class":113},[75,3271,32],{"class":89},[75,3273,3079],{"class":113},[75,3275,248],{"class":89},[75,3277,2715],{"class":113},[75,3279,268],{"class":89},[75,3281,229],{"class":89},[75,3283,3284],{"class":77,"line":161},[75,3285,3286],{"class":170},"        \u002F\u002F zoek het minimum in a[k-1..n-1]\n",[75,3288,3289,3291,3294,3296,3298,3300,3302],{"class":77,"line":174},[75,3290,1075],{"class":81},[75,3292,3293],{"class":113}," m ",[75,3295,242],{"class":89},[75,3297,2511],{"class":113},[75,3299,969],{"class":89},[75,3301,945],{"class":183},[75,3303,1050],{"class":89},[75,3305,3306,3308,3310,3312,3314,3316,3318,3320,3322,3324,3326,3328,3331,3333],{"class":77,"line":311},[75,3307,3104],{"class":109},[75,3309,23],{"class":89},[75,3311,212],{"class":81},[75,3313,2571],{"class":113},[75,3315,242],{"class":89},[75,3317,2715],{"class":113},[75,3319,248],{"class":89},[75,3321,2571],{"class":113},[75,3323,32],{"class":89},[75,3325,3079],{"class":113},[75,3327,248],{"class":89},[75,3329,3330],{"class":113}," j",[75,3332,268],{"class":89},[75,3334,229],{"class":89},[75,3336,3337,3339,3341,3343,3345,3347,3349,3351,3353,3355,3357,3360],{"class":77,"line":317},[75,3338,3125],{"class":109},[75,3340,23],{"class":89},[75,3342,94],{"class":113},[75,3344,144],{"class":89},[75,3346,2586],{"class":113},[75,3348,150],{"class":89},[75,3350,926],{"class":89},[75,3352,141],{"class":113},[75,3354,144],{"class":89},[75,3356,3142],{"class":113},[75,3358,3359],{"class":89},"])",[75,3361,229],{"class":89},[75,3363,3364,3366,3368,3370],{"class":77,"line":331},[75,3365,3150],{"class":113},[75,3367,242],{"class":89},[75,3369,3330],{"class":113},[75,3371,1050],{"class":89},[75,3373,3374],{"class":77,"line":951},[75,3375,3376],{"class":89},"            }\n",[75,3378,3379],{"class":77,"line":959},[75,3380,308],{"class":89},[75,3382,3383],{"class":77,"line":977},[75,3384,3385],{"class":170},"        \u002F\u002F wissel altijd, ook als m == k-1\n",[75,3387,3388,3390,3393,3395,3397,3399,3401,3403,3405],{"class":77,"line":1214},[75,3389,1075],{"class":81},[75,3391,3392],{"class":113}," tmp ",[75,3394,242],{"class":89},[75,3396,141],{"class":113},[75,3398,144],{"class":89},[75,3400,3169],{"class":113},[75,3402,969],{"class":89},[75,3404,945],{"class":183},[75,3406,2737],{"class":89},[75,3408,3409,3411,3413,3415,3417,3419,3421,3423,3425,3427,3429],{"class":77,"line":1219},[75,3410,2637],{"class":113},[75,3412,144],{"class":89},[75,3414,3169],{"class":113},[75,3416,969],{"class":89},[75,3418,945],{"class":183},[75,3420,150],{"class":89},[75,3422,2614],{"class":89},[75,3424,141],{"class":113},[75,3426,144],{"class":89},[75,3428,3142],{"class":113},[75,3430,2737],{"class":89},[75,3432,3433,3435,3437,3439,3441,3443,3446],{"class":77,"line":1232},[75,3434,2637],{"class":113},[75,3436,144],{"class":89},[75,3438,3142],{"class":113},[75,3440,150],{"class":89},[75,3442,2614],{"class":89},[75,3444,3445],{"class":113}," tmp",[75,3447,1050],{"class":89},[75,3449,3450],{"class":77,"line":1949},[75,3451,314],{"class":89},[75,3453,3454],{"class":77,"line":1959},[75,3455,334],{"class":89},[10,3457,3458,3459,3462,3463,257],{},"Selection sort doet altijd evenveel vergelijkingen, ongeacht de invoer: ",[30,3460,3461],{},"n(n-1)\u002F2",". Ook een al\ngesorteerde array kost dus ",[30,3464,3465],{},"O(n²)",[47,3467,2340],{"id":3468},"bubble-sort",[10,3470,3471,3473],{},[14,3472,2340],{}," 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.",[446,3475,3476,3487],{},[449,3477,3478],{},[452,3479,3480,3482,3485],{},[455,3481,2392],{},[455,3483,3484],{},"Aantal wissels",[455,3486,2398],{},[488,3488,3489,3499,3510,3521,3532,3542],{},[452,3490,3491,3493,3495],{},[493,3492,2405],{},[493,3494,741],{},[493,3496,3497],{},[30,3498,2412],{},[452,3500,3501,3503,3505],{},[493,3502,184],{},[493,3504,471],{},[493,3506,3507],{},[30,3508,3509],{},"2, 4, 5, 1, 3, 6",[452,3511,3512,3514,3516],{},[493,3513,465],{},[493,3515,465],{},[493,3517,3518],{},[30,3519,3520],{},"2, 4, 1, 3, 5, 6",[452,3522,3523,3525,3527],{},[493,3524,468],{},[493,3526,465],{},[493,3528,3529],{},[30,3530,3531],{},"2, 1, 3, 4, 5, 6",[452,3533,3534,3536,3538],{},[493,3535,471],{},[493,3537,184],{},[493,3539,3540],{},[30,3541,2476],{},[452,3543,3544,3546,3548],{},[493,3545,474],{},[493,3547,460],{},[493,3549,3550],{},[30,3551,2476],{},[10,3553,3554,3555,3558,3559,3558,3562,3565,3566,3558,3569,3572,3573,3575,3576,3579],{},"Ronde 1 in detail: ",[30,3556,3557],{},"5>2"," wissel, ",[30,3560,3561],{},"5>4",[30,3563,3564],{},"5\u003C6"," niets, ",[30,3567,3568],{},"6>1",[30,3570,3571],{},"6>3"," wissel. Na ronde 1\nstaat ",[30,3574,477],{}," achteraan, na ronde 2 staan ",[30,3577,3578],{},"5, 6"," achteraan, enzovoort.",[10,3581,3582,3583,3586],{},"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 ",[30,3584,3585],{},"n-1"," rondes door.",[60,3588,3589,3742],{},[63,3590,3591],{"v-slot:python":65},[67,3592,3594],{"className":69,"code":3593,"language":71,"meta":65,"style":65},"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",[30,3595,3596,3609,3623,3644,3649,3671,3697],{"__ignoreMap":65},[75,3597,3598,3600,3603,3605,3607],{"class":77,"line":78},[75,3599,82],{"class":81},[75,3601,3602],{"class":85}," bubble_sort",[75,3604,90],{"class":89},[75,3606,94],{"class":93},[75,3608,103],{"class":89},[75,3610,3611,3613,3615,3617,3619,3621],{"class":77,"line":106},[75,3612,3049],{"class":113},[75,3614,242],{"class":89},[75,3616,827],{"class":85},[75,3618,90],{"class":89},[75,3620,94],{"class":85},[75,3622,3060],{"class":89},[75,3624,3625,3627,3630,3632,3634,3636,3638,3640,3642],{"class":77,"line":135},[75,3626,110],{"class":109},[75,3628,3629],{"class":113}," r ",[75,3631,117],{"class":109},[75,3633,120],{"class":85},[75,3635,90],{"class":89},[75,3637,184],{"class":183},[75,3639,97],{"class":89},[75,3641,3079],{"class":85},[75,3643,103],{"class":89},[75,3645,3646],{"class":77,"line":161},[75,3647,3648],{"class":170},"        # na ronde r staan de r grootste achteraan, die slaan we over\n",[75,3650,3651,3653,3655,3657,3659,3661,3664,3666,3669],{"class":77,"line":174},[75,3652,3104],{"class":109},[75,3654,2571],{"class":113},[75,3656,117],{"class":109},[75,3658,120],{"class":85},[75,3660,90],{"class":89},[75,3662,3663],{"class":85},"n ",[75,3665,969],{"class":89},[75,3667,3668],{"class":85}," r",[75,3670,103],{"class":89},[75,3672,3673,3675,3677,3679,3681,3683,3685,3687,3689,3691,3693,3695],{"class":77,"line":311},[75,3674,3125],{"class":109},[75,3676,141],{"class":113},[75,3678,144],{"class":89},[75,3680,2586],{"class":113},[75,3682,150],{"class":89},[75,3684,2591],{"class":89},[75,3686,141],{"class":113},[75,3688,144],{"class":89},[75,3690,2605],{"class":113},[75,3692,872],{"class":89},[75,3694,945],{"class":183},[75,3696,3145],{"class":89},[75,3698,3699,3702,3704,3706,3708,3710,3712,3714,3716,3718,3720,3722,3724,3726,3728,3730,3732,3734,3736,3738,3740],{"class":77,"line":317},[75,3700,3701],{"class":113},"                a",[75,3703,144],{"class":89},[75,3705,2586],{"class":113},[75,3707,3176],{"class":89},[75,3709,141],{"class":113},[75,3711,144],{"class":89},[75,3713,2605],{"class":113},[75,3715,872],{"class":89},[75,3717,945],{"class":183},[75,3719,150],{"class":89},[75,3721,2614],{"class":89},[75,3723,141],{"class":113},[75,3725,144],{"class":89},[75,3727,2605],{"class":113},[75,3729,872],{"class":89},[75,3731,945],{"class":183},[75,3733,3176],{"class":89},[75,3735,141],{"class":113},[75,3737,144],{"class":89},[75,3739,2586],{"class":113},[75,3741,2545],{"class":89},[63,3743,3744],{"v-slot:java":65},[67,3745,3747],{"className":192,"code":3746,"language":194,"meta":65,"style":65},"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",[30,3748,3749,3770,3786,3816,3821,3855,3885,3902,3926,3946,3950,3954,3958],{"__ignoreMap":65},[75,3750,3751,3753,3755,3758,3760,3762,3764,3766,3768],{"class":77,"line":78},[75,3752,201],{"class":81},[75,3754,2669],{"class":81},[75,3756,3757],{"class":85}," bubbleSort",[75,3759,90],{"class":89},[75,3761,212],{"class":81},[75,3763,215],{"class":89},[75,3765,141],{"class":113},[75,3767,226],{"class":89},[75,3769,229],{"class":89},[75,3771,3772,3774,3776,3778,3780,3782,3784],{"class":77,"line":106},[75,3773,1024],{"class":81},[75,3775,3241],{"class":113},[75,3777,242],{"class":89},[75,3779,141],{"class":113},[75,3781,257],{"class":89},[75,3783,260],{"class":113},[75,3785,1050],{"class":89},[75,3787,3788,3790,3792,3794,3796,3798,3800,3802,3804,3806,3808,3810,3812,3814],{"class":77,"line":135},[75,3789,110],{"class":109},[75,3791,23],{"class":89},[75,3793,212],{"class":81},[75,3795,3629],{"class":113},[75,3797,242],{"class":89},[75,3799,945],{"class":183},[75,3801,248],{"class":89},[75,3803,3629],{"class":113},[75,3805,32],{"class":89},[75,3807,3079],{"class":113},[75,3809,248],{"class":89},[75,3811,3668],{"class":113},[75,3813,268],{"class":89},[75,3815,229],{"class":89},[75,3817,3818],{"class":77,"line":161},[75,3819,3820],{"class":170},"        \u002F\u002F na ronde r staan de r grootste achteraan, die slaan we over\n",[75,3822,3823,3825,3827,3829,3831,3833,3835,3837,3839,3841,3843,3845,3847,3849,3851,3853],{"class":77,"line":174},[75,3824,3104],{"class":109},[75,3826,23],{"class":89},[75,3828,212],{"class":81},[75,3830,2571],{"class":113},[75,3832,242],{"class":89},[75,3834,245],{"class":183},[75,3836,248],{"class":89},[75,3838,2571],{"class":113},[75,3840,32],{"class":89},[75,3842,3241],{"class":113},[75,3844,969],{"class":89},[75,3846,3668],{"class":113},[75,3848,248],{"class":89},[75,3850,3330],{"class":113},[75,3852,268],{"class":89},[75,3854,229],{"class":89},[75,3856,3857,3859,3861,3863,3865,3867,3869,3871,3873,3875,3877,3879,3881,3883],{"class":77,"line":311},[75,3858,3125],{"class":109},[75,3860,23],{"class":89},[75,3862,94],{"class":113},[75,3864,144],{"class":89},[75,3866,2586],{"class":113},[75,3868,150],{"class":89},[75,3870,2591],{"class":89},[75,3872,141],{"class":113},[75,3874,144],{"class":89},[75,3876,2605],{"class":113},[75,3878,872],{"class":89},[75,3880,945],{"class":183},[75,3882,3359],{"class":89},[75,3884,229],{"class":89},[75,3886,3887,3890,3892,3894,3896,3898,3900],{"class":77,"line":317},[75,3888,3889],{"class":81},"                int",[75,3891,3392],{"class":113},[75,3893,242],{"class":89},[75,3895,141],{"class":113},[75,3897,144],{"class":89},[75,3899,2586],{"class":113},[75,3901,2737],{"class":89},[75,3903,3904,3906,3908,3910,3912,3914,3916,3918,3920,3922,3924],{"class":77,"line":331},[75,3905,3701],{"class":113},[75,3907,144],{"class":89},[75,3909,2586],{"class":113},[75,3911,150],{"class":89},[75,3913,2614],{"class":89},[75,3915,141],{"class":113},[75,3917,144],{"class":89},[75,3919,2605],{"class":113},[75,3921,872],{"class":89},[75,3923,945],{"class":183},[75,3925,2737],{"class":89},[75,3927,3928,3930,3932,3934,3936,3938,3940,3942,3944],{"class":77,"line":951},[75,3929,3701],{"class":113},[75,3931,144],{"class":89},[75,3933,2605],{"class":113},[75,3935,872],{"class":89},[75,3937,945],{"class":183},[75,3939,150],{"class":89},[75,3941,2614],{"class":89},[75,3943,3445],{"class":113},[75,3945,1050],{"class":89},[75,3947,3948],{"class":77,"line":959},[75,3949,3376],{"class":89},[75,3951,3952],{"class":77,"line":977},[75,3953,308],{"class":89},[75,3955,3956],{"class":77,"line":1214},[75,3957,314],{"class":89},[75,3959,3960],{"class":77,"line":1219},[75,3961,334],{"class":89},[47,3963,3965],{"id":3964},"merge-sort","Merge sort",[10,3967,3968,3970,3971,3974,3975,364,3978,1381,3981,257],{},[14,3969,3965],{}," (samenvoegend sorteren) is verdeel-en-heers (",[25,3972,3973],{},"divide and conquer","): splits de array\nin twee helften, sorteer elke helft recursief en voeg de twee gesorteerde helften samen. We splitsen\nin ",[30,3976,3977],{},"a[0..mid-1]",[30,3979,3980],{},"a[mid..n-1]",[30,3982,3983],{},"mid = ⌊n\u002F2⌋",[446,3985,3986,3998],{},[449,3987,3988],{},[452,3989,3990,3992,3995],{},[455,3991,531],{},[455,3993,3994],{},"Wat gebeurt er",[455,3996,3997],{},"Resultaat",[488,3999,4000,4018,4034,4047,4064,4079,4091,4106],{},[452,4001,4002,4004,4010],{},[493,4003,184],{},[493,4005,4006,4007,4009],{},"splits ",[30,4008,2412],{}," (mid = 3)",[493,4011,4012,364,4015],{},[30,4013,4014],{},"5, 2, 4",[30,4016,4017],{},"6, 1, 3",[452,4019,4020,4022,4027],{},[493,4021,465],{},[493,4023,4006,4024,4026],{},[30,4025,4014],{}," (mid = 1)",[493,4028,4029,364,4031],{},[30,4030,474],{},[30,4032,4033],{},"2, 4",[452,4035,4036,4038,4043],{},[493,4037,468],{},[493,4039,4006,4040,4042],{},[30,4041,4033],{},", voeg samen",[493,4044,4045],{},[30,4046,4033],{},[452,4048,4049,4051,4059],{},[493,4050,471],{},[493,4052,4053,4054,364,4056,4058],{},"voeg ",[30,4055,474],{},[30,4057,4033],{}," samen",[493,4060,4061],{},[30,4062,4063],{},"2, 4, 5",[452,4065,4066,4068,4072],{},[493,4067,474],{},[493,4069,4006,4070,4026],{},[30,4071,4017],{},[493,4073,4074,364,4076],{},[30,4075,477],{},[30,4077,4078],{},"1, 3",[452,4080,4081,4083,4087],{},[493,4082,477],{},[493,4084,4006,4085,4042],{},[30,4086,4078],{},[493,4088,4089],{},[30,4090,4078],{},[452,4092,4093,4095,4101],{},[493,4094,480],{},[493,4096,4053,4097,364,4099,4058],{},[30,4098,477],{},[30,4100,4078],{},[493,4102,4103],{},[30,4104,4105],{},"1, 3, 6",[452,4107,4108,4110,4116],{},[493,4109,483],{},[493,4111,4053,4112,364,4114,4058],{},[30,4113,4063],{},[30,4115,4105],{},[493,4117,4118],{},[30,4119,2476],{},[10,4121,4122,4123,4126],{},"Bij het samenvoegen vergelijk je steeds de voorste elementen van beide helften en pak je de\nkleinste. Bij gelijke waarden pak je ",[14,4124,4125],{},"eerst links",": daardoor is merge sort stabiel.",[60,4128,4129,4432],{},[63,4130,4131],{"v-slot:python":65},[67,4132,4134],{"className":69,"code":4133,"language":71,"meta":65,"style":65},"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",[30,4135,4136,4149,4169,4177,4196,4217,4237,4242,4252,4266,4298,4322,4342,4352,4358,4376,4384,4405,4424],{"__ignoreMap":65},[75,4137,4138,4140,4143,4145,4147],{"class":77,"line":78},[75,4139,82],{"class":81},[75,4141,4142],{"class":85}," merge_sort",[75,4144,90],{"class":89},[75,4146,94],{"class":93},[75,4148,103],{"class":89},[75,4150,4151,4154,4156,4158,4160,4162,4165,4167],{"class":77,"line":106},[75,4152,4153],{"class":109},"    if",[75,4155,827],{"class":85},[75,4157,90],{"class":89},[75,4159,94],{"class":85},[75,4161,226],{"class":89},[75,4163,4164],{"class":89}," \u003C=",[75,4166,945],{"class":183},[75,4168,158],{"class":89},[75,4170,4171,4174],{"class":77,"line":135},[75,4172,4173],{"class":109},"        return",[75,4175,4176],{"class":113}," a\n",[75,4178,4179,4182,4184,4186,4188,4190,4192,4194],{"class":77,"line":161},[75,4180,4181],{"class":113},"    mid ",[75,4183,242],{"class":89},[75,4185,827],{"class":85},[75,4187,90],{"class":89},[75,4189,94],{"class":85},[75,4191,226],{"class":89},[75,4193,879],{"class":89},[75,4195,1608],{"class":183},[75,4197,4198,4201,4203,4205,4207,4209,4212,4214],{"class":77,"line":174},[75,4199,4200],{"class":113},"    links ",[75,4202,242],{"class":89},[75,4204,4142],{"class":85},[75,4206,90],{"class":89},[75,4208,94],{"class":85},[75,4210,4211],{"class":89},"[:",[75,4213,40],{"class":85},[75,4215,4216],{"class":89},"])\n",[75,4218,4219,4222,4224,4226,4228,4230,4232,4234],{"class":77,"line":311},[75,4220,4221],{"class":113},"    rechts ",[75,4223,242],{"class":89},[75,4225,4142],{"class":85},[75,4227,90],{"class":89},[75,4229,94],{"class":85},[75,4231,144],{"class":89},[75,4233,40],{"class":85},[75,4235,4236],{"class":89},":])\n",[75,4238,4239],{"class":77,"line":317},[75,4240,4241],{"class":170},"    # samenvoegen: bij gelijke waarden eerst links (stabiel)\n",[75,4243,4244,4247,4249],{"class":77,"line":331},[75,4245,4246],{"class":113},"    res ",[75,4248,242],{"class":89},[75,4250,4251],{"class":89}," []\n",[75,4253,4254,4257,4259,4261,4263],{"class":77,"line":951},[75,4255,4256],{"class":113},"    i ",[75,4258,242],{"class":89},[75,4260,2571],{"class":113},[75,4262,242],{"class":89},[75,4264,4265],{"class":183}," 0\n",[75,4267,4268,4270,4272,4274,4276,4278,4281,4283,4285,4287,4289,4291,4293,4296],{"class":77,"line":959},[75,4269,843],{"class":109},[75,4271,114],{"class":113},[75,4273,32],{"class":89},[75,4275,827],{"class":85},[75,4277,90],{"class":89},[75,4279,4280],{"class":85},"links",[75,4282,226],{"class":89},[75,4284,2579],{"class":89},[75,4286,2571],{"class":113},[75,4288,32],{"class":89},[75,4290,827],{"class":85},[75,4292,90],{"class":89},[75,4294,4295],{"class":85},"rechts",[75,4297,103],{"class":89},[75,4299,4300,4302,4305,4307,4309,4311,4313,4316,4318,4320],{"class":77,"line":977},[75,4301,138],{"class":109},[75,4303,4304],{"class":113}," links",[75,4306,144],{"class":89},[75,4308,147],{"class":113},[75,4310,150],{"class":89},[75,4312,4164],{"class":89},[75,4314,4315],{"class":113}," rechts",[75,4317,144],{"class":89},[75,4319,2586],{"class":113},[75,4321,3145],{"class":89},[75,4323,4324,4327,4329,4332,4334,4336,4338,4340],{"class":77,"line":1214},[75,4325,4326],{"class":113},"            res",[75,4328,257],{"class":89},[75,4330,4331],{"class":85},"append",[75,4333,90],{"class":89},[75,4335,4280],{"class":85},[75,4337,144],{"class":89},[75,4339,147],{"class":85},[75,4341,4216],{"class":89},[75,4343,4344,4347,4350],{"class":77,"line":1219},[75,4345,4346],{"class":113},"            i ",[75,4348,4349],{"class":89},"+=",[75,4351,838],{"class":183},[75,4353,4354,4356],{"class":77,"line":1232},[75,4355,954],{"class":109},[75,4357,158],{"class":89},[75,4359,4360,4362,4364,4366,4368,4370,4372,4374],{"class":77,"line":1949},[75,4361,4326],{"class":113},[75,4363,257],{"class":89},[75,4365,4331],{"class":85},[75,4367,90],{"class":89},[75,4369,4295],{"class":85},[75,4371,144],{"class":89},[75,4373,2586],{"class":85},[75,4375,4216],{"class":89},[75,4377,4378,4380,4382],{"class":77,"line":1959},[75,4379,2627],{"class":113},[75,4381,4349],{"class":89},[75,4383,838],{"class":183},[75,4385,4387,4390,4392,4395,4397,4399,4401,4403],{"class":77,"line":4386},17,[75,4388,4389],{"class":113},"    res",[75,4391,257],{"class":89},[75,4393,4394],{"class":85},"extend",[75,4396,90],{"class":89},[75,4398,4280],{"class":85},[75,4400,144],{"class":89},[75,4402,147],{"class":85},[75,4404,4236],{"class":89},[75,4406,4408,4410,4412,4414,4416,4418,4420,4422],{"class":77,"line":4407},18,[75,4409,4389],{"class":113},[75,4411,257],{"class":89},[75,4413,4394],{"class":85},[75,4415,90],{"class":89},[75,4417,4295],{"class":85},[75,4419,144],{"class":89},[75,4421,2586],{"class":85},[75,4423,4236],{"class":89},[75,4425,4427,4429],{"class":77,"line":4426},19,[75,4428,177],{"class":109},[75,4430,4431],{"class":113}," res\n",[63,4433,4434],{"v-slot:java":65},[67,4435,4437],{"className":192,"code":4436,"language":194,"meta":65,"style":65},"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",[30,4438,4439,4462,4482,4490,4494,4515,4562,4609,4614,4640,4668,4702,4728,4750,4758,4778,4782,4786,4823,4859,4868],{"__ignoreMap":65},[75,4440,4441,4443,4445,4447,4450,4452,4454,4456,4458,4460],{"class":77,"line":78},[75,4442,201],{"class":81},[75,4444,204],{"class":81},[75,4446,215],{"class":89},[75,4448,4449],{"class":85}," mergeSort",[75,4451,90],{"class":89},[75,4453,212],{"class":81},[75,4455,215],{"class":89},[75,4457,141],{"class":113},[75,4459,226],{"class":89},[75,4461,229],{"class":89},[75,4463,4464,4466,4468,4470,4472,4474,4476,4478,4480],{"class":77,"line":106},[75,4465,4153],{"class":109},[75,4467,23],{"class":89},[75,4469,94],{"class":113},[75,4471,257],{"class":89},[75,4473,1043],{"class":113},[75,4475,36],{"class":89},[75,4477,945],{"class":183},[75,4479,226],{"class":89},[75,4481,229],{"class":89},[75,4483,4484,4486,4488],{"class":77,"line":135},[75,4485,4173],{"class":109},[75,4487,141],{"class":113},[75,4489,1050],{"class":89},[75,4491,4492],{"class":77,"line":161},[75,4493,314],{"class":89},[75,4495,4496,4498,4500,4502,4504,4506,4508,4511,4513],{"class":77,"line":174},[75,4497,1024],{"class":81},[75,4499,940],{"class":113},[75,4501,242],{"class":89},[75,4503,141],{"class":113},[75,4505,257],{"class":89},[75,4507,1043],{"class":113},[75,4509,4510],{"class":89},"\u002F",[75,4512,882],{"class":183},[75,4514,1050],{"class":89},[75,4516,4517,4519,4521,4524,4526,4528,4530,4532,4534,4537,4539,4542,4544,4547,4549,4551,4553,4555,4557,4559],{"class":77,"line":311},[75,4518,1024],{"class":81},[75,4520,215],{"class":89},[75,4522,4523],{"class":113}," links ",[75,4525,242],{"class":89},[75,4527,4449],{"class":85},[75,4529,90],{"class":89},[75,4531,194],{"class":113},[75,4533,257],{"class":89},[75,4535,4536],{"class":113},"util",[75,4538,257],{"class":89},[75,4540,4541],{"class":113},"Arrays",[75,4543,257],{"class":89},[75,4545,4546],{"class":85},"copyOfRange",[75,4548,90],{"class":89},[75,4550,94],{"class":113},[75,4552,97],{"class":89},[75,4554,245],{"class":183},[75,4556,97],{"class":89},[75,4558,1134],{"class":113},[75,4560,4561],{"class":89},"));\n",[75,4563,4564,4566,4568,4571,4573,4575,4577,4579,4581,4583,4585,4587,4589,4591,4593,4595,4597,4599,4601,4603,4605,4607],{"class":77,"line":317},[75,4565,1024],{"class":81},[75,4567,215],{"class":89},[75,4569,4570],{"class":113}," rechts ",[75,4572,242],{"class":89},[75,4574,4449],{"class":85},[75,4576,90],{"class":89},[75,4578,194],{"class":113},[75,4580,257],{"class":89},[75,4582,4536],{"class":113},[75,4584,257],{"class":89},[75,4586,4541],{"class":113},[75,4588,257],{"class":89},[75,4590,4546],{"class":85},[75,4592,90],{"class":89},[75,4594,94],{"class":113},[75,4596,97],{"class":89},[75,4598,1134],{"class":113},[75,4600,97],{"class":89},[75,4602,141],{"class":113},[75,4604,257],{"class":89},[75,4606,260],{"class":113},[75,4608,4561],{"class":89},[75,4610,4611],{"class":77,"line":331},[75,4612,4613],{"class":170},"    \u002F\u002F samenvoegen: bij gelijke waarden eerst links (stabiel)\n",[75,4615,4616,4618,4620,4623,4625,4628,4630,4632,4634,4636,4638],{"class":77,"line":951},[75,4617,1024],{"class":81},[75,4619,215],{"class":89},[75,4621,4622],{"class":113}," res ",[75,4624,242],{"class":89},[75,4626,4627],{"class":109}," new",[75,4629,204],{"class":81},[75,4631,144],{"class":89},[75,4633,94],{"class":113},[75,4635,257],{"class":89},[75,4637,260],{"class":113},[75,4639,2737],{"class":89},[75,4641,4642,4644,4646,4648,4650,4652,4654,4656,4658,4660,4662,4664,4666],{"class":77,"line":959},[75,4643,1024],{"class":81},[75,4645,114],{"class":113},[75,4647,242],{"class":89},[75,4649,245],{"class":183},[75,4651,97],{"class":89},[75,4653,2571],{"class":113},[75,4655,242],{"class":89},[75,4657,245],{"class":183},[75,4659,97],{"class":89},[75,4661,2511],{"class":113},[75,4663,242],{"class":89},[75,4665,245],{"class":183},[75,4667,1050],{"class":89},[75,4669,4670,4672,4674,4677,4679,4681,4683,4685,4688,4690,4692,4694,4696,4698,4700],{"class":77,"line":977},[75,4671,843],{"class":109},[75,4673,23],{"class":89},[75,4675,4676],{"class":113},"i ",[75,4678,32],{"class":89},[75,4680,4304],{"class":113},[75,4682,257],{"class":89},[75,4684,1043],{"class":113},[75,4686,4687],{"class":89},"&&",[75,4689,2571],{"class":113},[75,4691,32],{"class":89},[75,4693,4315],{"class":113},[75,4695,257],{"class":89},[75,4697,260],{"class":113},[75,4699,226],{"class":89},[75,4701,229],{"class":89},[75,4703,4704,4706,4708,4710,4712,4714,4716,4718,4720,4722,4724,4726],{"class":77,"line":1214},[75,4705,138],{"class":109},[75,4707,23],{"class":89},[75,4709,4280],{"class":113},[75,4711,144],{"class":89},[75,4713,147],{"class":113},[75,4715,150],{"class":89},[75,4717,4164],{"class":89},[75,4719,4315],{"class":113},[75,4721,144],{"class":89},[75,4723,2586],{"class":113},[75,4725,3359],{"class":89},[75,4727,229],{"class":89},[75,4729,4730,4732,4734,4736,4739,4741,4743,4745,4747],{"class":77,"line":1219},[75,4731,4326],{"class":113},[75,4733,144],{"class":89},[75,4735,1985],{"class":113},[75,4737,4738],{"class":89},"++]",[75,4740,2614],{"class":89},[75,4742,4304],{"class":113},[75,4744,144],{"class":89},[75,4746,147],{"class":113},[75,4748,4749],{"class":89},"++];\n",[75,4751,4752,4754,4756],{"class":77,"line":1232},[75,4753,1141],{"class":89},[75,4755,1144],{"class":109},[75,4757,229],{"class":89},[75,4759,4760,4762,4764,4766,4768,4770,4772,4774,4776],{"class":77,"line":1949},[75,4761,4326],{"class":113},[75,4763,144],{"class":89},[75,4765,1985],{"class":113},[75,4767,4738],{"class":89},[75,4769,2614],{"class":89},[75,4771,4315],{"class":113},[75,4773,144],{"class":89},[75,4775,2586],{"class":113},[75,4777,4749],{"class":89},[75,4779,4780],{"class":77,"line":1959},[75,4781,308],{"class":89},[75,4783,4784],{"class":77,"line":4386},[75,4785,314],{"class":89},[75,4787,4788,4790,4792,4794,4796,4798,4800,4802,4804,4807,4809,4811,4813,4815,4817,4819,4821],{"class":77,"line":4407},[75,4789,843],{"class":109},[75,4791,23],{"class":89},[75,4793,4676],{"class":113},[75,4795,32],{"class":89},[75,4797,4304],{"class":113},[75,4799,257],{"class":89},[75,4801,260],{"class":113},[75,4803,226],{"class":89},[75,4805,4806],{"class":113}," res",[75,4808,144],{"class":89},[75,4810,1985],{"class":113},[75,4812,4738],{"class":89},[75,4814,2614],{"class":89},[75,4816,4304],{"class":113},[75,4818,144],{"class":89},[75,4820,147],{"class":113},[75,4822,4749],{"class":89},[75,4824,4825,4827,4829,4831,4833,4835,4837,4839,4841,4843,4845,4847,4849,4851,4853,4855,4857],{"class":77,"line":4426},[75,4826,843],{"class":109},[75,4828,23],{"class":89},[75,4830,2605],{"class":113},[75,4832,32],{"class":89},[75,4834,4315],{"class":113},[75,4836,257],{"class":89},[75,4838,260],{"class":113},[75,4840,226],{"class":89},[75,4842,4806],{"class":113},[75,4844,144],{"class":89},[75,4846,1985],{"class":113},[75,4848,4738],{"class":89},[75,4850,2614],{"class":89},[75,4852,4315],{"class":113},[75,4854,144],{"class":89},[75,4856,2586],{"class":113},[75,4858,4749],{"class":89},[75,4860,4862,4864,4866],{"class":77,"line":4861},20,[75,4863,177],{"class":109},[75,4865,4806],{"class":113},[75,4867,1050],{"class":89},[75,4869,4871],{"class":77,"line":4870},21,[75,4872,334],{"class":89},[10,4874,4875,4876,4879,4880,4882,4883,4885,4886,4888],{},"Er zijn ",[30,4877,4878],{},"log n"," niveaus van splitsen, en op elk niveau kost samenvoegen samen ",[30,4881,345],{},". Totaal:\n",[30,4884,2105],{},", altijd. Het nadeel: je hebt een extra array van grootte ",[30,4887,1390],{}," nodig.",[47,4890,4892],{"id":4891},"quicksort-met-lomuto-partitie","Quicksort met Lomuto-partitie",[10,4894,4895,4897,4898,4901,4902,4905,4906,4908],{},[14,4896,2357],{}," kiest een spil (",[25,4899,4900],{},"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",[14,4903,4904],{},"Lomuto-partitie"," met het ",[14,4907,1967],{}," element als pivot:",[67,4910,4915],{"className":4911,"code":4913,"language":4914},[4912],"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",[30,4916,4913],{"__ignoreMap":65},[10,4918,4919,4921,4922,4925],{},[30,4920,147],{}," wijst naar de eerste plek waar het volgende \"kleine\" element moet komen. Elementen die\n",[14,4923,4924],{},"strikt kleiner"," zijn dan de pivot gaan naar links; gelijke elementen blijven rechts.",[10,4927,4928,4929,4932,4933,854],{},"Uitgewerkt op ",[30,4930,4931],{},"[7, 2, 9, 4, 1, 8, 5]",", pivot = ",[30,4934,474],{},[446,4936,4937,4960],{},[449,4938,4939],{},[452,4940,4941,4943,4947,4952,4954,4957],{},[455,4942,2586],{},[455,4944,94,4945],{},[75,4946,2586],{},[455,4948,94,4949,4951],{},[75,4950,2586],{}," \u003C 5?",[455,4953,547],{},[455,4955,4956],{},"i daarna",[455,4958,4959],{},"Array",[488,4961,4962,4979,4996,5020,5036,5057,5078,5094],{},[452,4963,4964,4966,4968,4970,4972,4974],{},[493,4965,2405],{},[493,4967,741],{},[493,4969,741],{},[493,4971,741],{},[493,4973,460],{},[493,4975,4976],{},[30,4977,4978],{},"7, 2, 9, 4, 1, 8, 5",[452,4980,4981,4983,4985,4988,4990,4992],{},[493,4982,460],{},[493,4984,480],{},[493,4986,4987],{},"nee",[493,4989,741],{},[493,4991,460],{},[493,4993,4994],{},[30,4995,4978],{},[452,4997,4998,5000,5002,5005,5013,5015],{},[493,4999,184],{},[493,5001,465],{},[493,5003,5004],{},"ja",[493,5006,5007,5008,5010,5011],{},"wissel a",[75,5009,460],{},", a",[75,5012,184],{},[493,5014,184],{},[493,5016,5017],{},[30,5018,5019],{},"2, 7, 9, 4, 1, 8, 5",[452,5021,5022,5024,5026,5028,5030,5032],{},[493,5023,465],{},[493,5025,486],{},[493,5027,4987],{},[493,5029,741],{},[493,5031,184],{},[493,5033,5034],{},[30,5035,5019],{},[452,5037,5038,5040,5042,5044,5050,5052],{},[493,5039,468],{},[493,5041,471],{},[493,5043,5004],{},[493,5045,5007,5046,5010,5048],{},[75,5047,184],{},[75,5049,468],{},[493,5051,465],{},[493,5053,5054],{},[30,5055,5056],{},"2, 4, 9, 7, 1, 8, 5",[452,5058,5059,5061,5063,5065,5071,5073],{},[493,5060,471],{},[493,5062,184],{},[493,5064,5004],{},[493,5066,5007,5067,5010,5069],{},[75,5068,465],{},[75,5070,471],{},[493,5072,468],{},[493,5074,5075],{},[30,5076,5077],{},"2, 4, 1, 7, 9, 8, 5",[452,5079,5080,5082,5084,5086,5088,5090],{},[493,5081,474],{},[493,5083,483],{},[493,5085,4987],{},[493,5087,741],{},[493,5089,468],{},[493,5091,5092],{},[30,5093,5077],{},[452,5095,5096,5099,5101,5103,5109,5111],{},[493,5097,5098],{},"eind",[493,5100,741],{},[493,5102,741],{},[493,5104,5007,5105,5010,5107],{},[75,5106,468],{},[75,5108,477],{},[493,5110,468],{},[493,5112,5113],{},[30,5114,5115],{},"2, 4, 1, 5, 9, 8, 7",[10,5117,5118,5119,5121,5122,5124,5125,364,5128,257],{},"Na de eerste partitie is de array ",[30,5120,5115],{}," en staat de pivot ",[30,5123,474],{}," 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 ",[30,5126,5127],{},"a[0..2]",[30,5129,5130],{},"a[4..6]",[60,5132,5133,5464],{},[63,5134,5135],{"v-slot:python":65},[67,5136,5138],{"className":69,"code":5137,"language":71,"meta":65,"style":65},"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",[30,5139,5140,5161,5179,5188,5208,5230,5266,5274,5314,5321,5326,5352,5364,5383,5395,5418,5442],{"__ignoreMap":65},[75,5141,5142,5144,5147,5149,5151,5153,5155,5157,5159],{"class":77,"line":78},[75,5143,82],{"class":81},[75,5145,5146],{"class":85}," partition",[75,5148,90],{"class":89},[75,5150,94],{"class":93},[75,5152,97],{"class":89},[75,5154,1093],{"class":93},[75,5156,97],{"class":89},[75,5158,851],{"class":93},[75,5160,103],{"class":89},[75,5162,5163,5166,5168,5170,5172,5174,5176],{"class":77,"line":106},[75,5164,5165],{"class":113},"    pivot ",[75,5167,242],{"class":89},[75,5169,141],{"class":113},[75,5171,144],{"class":89},[75,5173,367],{"class":113},[75,5175,150],{"class":89},[75,5177,5178],{"class":170},"  # laatste element is de pivot\n",[75,5180,5181,5183,5185],{"class":77,"line":135},[75,5182,4256],{"class":113},[75,5184,242],{"class":89},[75,5186,5187],{"class":113}," lo\n",[75,5189,5190,5192,5194,5196,5198,5200,5202,5204,5206],{"class":77,"line":161},[75,5191,110],{"class":109},[75,5193,2571],{"class":113},[75,5195,117],{"class":109},[75,5197,120],{"class":85},[75,5199,90],{"class":89},[75,5201,363],{"class":85},[75,5203,97],{"class":89},[75,5205,851],{"class":85},[75,5207,103],{"class":89},[75,5209,5210,5212,5214,5216,5218,5220,5222,5225,5227],{"class":77,"line":174},[75,5211,138],{"class":109},[75,5213,141],{"class":113},[75,5215,144],{"class":89},[75,5217,2586],{"class":113},[75,5219,150],{"class":89},[75,5221,926],{"class":89},[75,5223,5224],{"class":113}," pivot",[75,5226,854],{"class":89},[75,5228,5229],{"class":170},"  # strikt kleiner gaat naar links\n",[75,5231,5232,5234,5236,5238,5240,5242,5244,5246,5248,5250,5252,5254,5256,5258,5260,5262,5264],{"class":77,"line":311},[75,5233,2600],{"class":113},[75,5235,144],{"class":89},[75,5237,147],{"class":113},[75,5239,3176],{"class":89},[75,5241,141],{"class":113},[75,5243,144],{"class":89},[75,5245,2586],{"class":113},[75,5247,150],{"class":89},[75,5249,2614],{"class":89},[75,5251,141],{"class":113},[75,5253,144],{"class":89},[75,5255,2586],{"class":113},[75,5257,3176],{"class":89},[75,5259,141],{"class":113},[75,5261,144],{"class":89},[75,5263,147],{"class":113},[75,5265,2545],{"class":89},[75,5267,5268,5270,5272],{"class":77,"line":317},[75,5269,4346],{"class":113},[75,5271,4349],{"class":89},[75,5273,838],{"class":183},[75,5275,5276,5279,5281,5283,5285,5287,5289,5291,5293,5295,5297,5299,5301,5303,5305,5307,5309,5311],{"class":77,"line":331},[75,5277,5278],{"class":113},"    a",[75,5280,144],{"class":89},[75,5282,147],{"class":113},[75,5284,3176],{"class":89},[75,5286,141],{"class":113},[75,5288,144],{"class":89},[75,5290,367],{"class":113},[75,5292,150],{"class":89},[75,5294,2614],{"class":89},[75,5296,141],{"class":113},[75,5298,144],{"class":89},[75,5300,367],{"class":113},[75,5302,3176],{"class":89},[75,5304,141],{"class":113},[75,5306,144],{"class":89},[75,5308,147],{"class":113},[75,5310,150],{"class":89},[75,5312,5313],{"class":170},"  # pivot op zijn definitieve plek\n",[75,5315,5316,5318],{"class":77,"line":951},[75,5317,177],{"class":109},[75,5319,5320],{"class":113}," i\n",[75,5322,5323],{"class":77,"line":959},[75,5324,5325],{"emptyLinePlaceholder":2242},"\n",[75,5327,5328,5330,5333,5335,5337,5339,5341,5343,5345,5347,5349],{"class":77,"line":977},[75,5329,82],{"class":81},[75,5331,5332],{"class":85}," quicksort",[75,5334,90],{"class":89},[75,5336,94],{"class":93},[75,5338,97],{"class":89},[75,5340,1093],{"class":93},[75,5342,242],{"class":89},[75,5344,460],{"class":183},[75,5346,97],{"class":89},[75,5348,851],{"class":93},[75,5350,5351],{"class":89},"=None):\n",[75,5353,5354,5356,5358,5361],{"class":77,"line":1214},[75,5355,4153],{"class":109},[75,5357,818],{"class":113},[75,5359,5360],{"class":89},"is",[75,5362,5363],{"class":89}," None:\n",[75,5365,5366,5369,5371,5373,5375,5377,5379,5381],{"class":77,"line":1219},[75,5367,5368],{"class":113},"        hi ",[75,5370,242],{"class":89},[75,5372,827],{"class":85},[75,5374,90],{"class":89},[75,5376,94],{"class":85},[75,5378,226],{"class":89},[75,5380,180],{"class":89},[75,5382,838],{"class":183},[75,5384,5385,5387,5389,5391,5393],{"class":77,"line":1232},[75,5386,4153],{"class":109},[75,5388,846],{"class":113},[75,5390,32],{"class":89},[75,5392,851],{"class":113},[75,5394,158],{"class":89},[75,5396,5397,5400,5402,5404,5406,5408,5410,5412,5414,5416],{"class":77,"line":1949},[75,5398,5399],{"class":113},"        p ",[75,5401,242],{"class":89},[75,5403,5146],{"class":85},[75,5405,90],{"class":89},[75,5407,94],{"class":85},[75,5409,97],{"class":89},[75,5411,1093],{"class":85},[75,5413,97],{"class":89},[75,5415,851],{"class":85},[75,5417,3060],{"class":89},[75,5419,5420,5423,5425,5427,5429,5431,5433,5436,5438,5440],{"class":77,"line":1959},[75,5421,5422],{"class":85},"        quicksort",[75,5424,90],{"class":89},[75,5426,94],{"class":85},[75,5428,97],{"class":89},[75,5430,1093],{"class":85},[75,5432,97],{"class":89},[75,5434,5435],{"class":85}," p ",[75,5437,969],{"class":89},[75,5439,945],{"class":183},[75,5441,3060],{"class":89},[75,5443,5444,5446,5448,5450,5452,5454,5456,5458,5460,5462],{"class":77,"line":4386},[75,5445,5422],{"class":85},[75,5447,90],{"class":89},[75,5449,94],{"class":85},[75,5451,97],{"class":89},[75,5453,5435],{"class":85},[75,5455,872],{"class":89},[75,5457,945],{"class":183},[75,5459,97],{"class":89},[75,5461,851],{"class":85},[75,5463,3060],{"class":89},[63,5465,5466],{"v-slot:java":65},[67,5467,5469],{"className":192,"code":5468,"language":194,"meta":65,"style":65},"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",[30,5470,5471,5503,5524,5536,5566,5591,5640,5648,5652,5656,5707,5715,5719,5723,5755,5771,5796,5818,5840,5844],{"__ignoreMap":65},[75,5472,5473,5475,5477,5479,5481,5483,5485,5487,5489,5491,5493,5495,5497,5499,5501],{"class":77,"line":78},[75,5474,201],{"class":81},[75,5476,204],{"class":81},[75,5478,5146],{"class":85},[75,5480,90],{"class":89},[75,5482,212],{"class":81},[75,5484,215],{"class":89},[75,5486,141],{"class":113},[75,5488,97],{"class":89},[75,5490,204],{"class":81},[75,5492,1093],{"class":113},[75,5494,97],{"class":89},[75,5496,204],{"class":81},[75,5498,851],{"class":113},[75,5500,226],{"class":89},[75,5502,229],{"class":89},[75,5504,5505,5507,5510,5512,5514,5516,5518,5521],{"class":77,"line":106},[75,5506,1024],{"class":81},[75,5508,5509],{"class":113}," pivot ",[75,5511,242],{"class":89},[75,5513,141],{"class":113},[75,5515,144],{"class":89},[75,5517,367],{"class":113},[75,5519,5520],{"class":89},"];",[75,5522,5523],{"class":170}," \u002F\u002F laatste element is de pivot\n",[75,5525,5526,5528,5530,5532,5534],{"class":77,"line":135},[75,5527,1024],{"class":81},[75,5529,114],{"class":113},[75,5531,242],{"class":89},[75,5533,1093],{"class":113},[75,5535,1050],{"class":89},[75,5537,5538,5540,5542,5544,5546,5548,5550,5552,5554,5556,5558,5560,5562,5564],{"class":77,"line":161},[75,5539,110],{"class":109},[75,5541,23],{"class":89},[75,5543,212],{"class":81},[75,5545,2571],{"class":113},[75,5547,242],{"class":89},[75,5549,1093],{"class":113},[75,5551,248],{"class":89},[75,5553,2571],{"class":113},[75,5555,32],{"class":89},[75,5557,851],{"class":113},[75,5559,248],{"class":89},[75,5561,3330],{"class":113},[75,5563,268],{"class":89},[75,5565,229],{"class":89},[75,5567,5568,5570,5572,5574,5576,5578,5580,5582,5584,5586,5588],{"class":77,"line":174},[75,5569,138],{"class":109},[75,5571,23],{"class":89},[75,5573,94],{"class":113},[75,5575,144],{"class":89},[75,5577,2586],{"class":113},[75,5579,150],{"class":89},[75,5581,926],{"class":89},[75,5583,5224],{"class":113},[75,5585,226],{"class":89},[75,5587,1067],{"class":89},[75,5589,5590],{"class":170}," \u002F\u002F strikt kleiner gaat naar links\n",[75,5592,5593,5596,5598,5600,5602,5604,5606,5608,5610,5612,5614,5616,5618,5620,5622,5624,5626,5628,5630,5632,5634,5636,5638],{"class":77,"line":311},[75,5594,5595],{"class":81},"            int",[75,5597,3392],{"class":113},[75,5599,242],{"class":89},[75,5601,141],{"class":113},[75,5603,144],{"class":89},[75,5605,147],{"class":113},[75,5607,5520],{"class":89},[75,5609,141],{"class":113},[75,5611,144],{"class":89},[75,5613,147],{"class":113},[75,5615,150],{"class":89},[75,5617,2614],{"class":89},[75,5619,141],{"class":113},[75,5621,144],{"class":89},[75,5623,2586],{"class":113},[75,5625,5520],{"class":89},[75,5627,141],{"class":113},[75,5629,144],{"class":89},[75,5631,2586],{"class":113},[75,5633,150],{"class":89},[75,5635,2614],{"class":89},[75,5637,3445],{"class":113},[75,5639,1050],{"class":89},[75,5641,5642,5645],{"class":77,"line":317},[75,5643,5644],{"class":113},"            i",[75,5646,5647],{"class":89},"++;\n",[75,5649,5650],{"class":77,"line":331},[75,5651,308],{"class":89},[75,5653,5654],{"class":77,"line":951},[75,5655,314],{"class":89},[75,5657,5658,5660,5662,5664,5666,5668,5670,5672,5674,5676,5678,5680,5682,5684,5686,5688,5690,5692,5694,5696,5698,5700,5702,5704],{"class":77,"line":959},[75,5659,1024],{"class":81},[75,5661,3392],{"class":113},[75,5663,242],{"class":89},[75,5665,141],{"class":113},[75,5667,144],{"class":89},[75,5669,147],{"class":113},[75,5671,5520],{"class":89},[75,5673,141],{"class":113},[75,5675,144],{"class":89},[75,5677,147],{"class":113},[75,5679,150],{"class":89},[75,5681,2614],{"class":89},[75,5683,141],{"class":113},[75,5685,144],{"class":89},[75,5687,367],{"class":113},[75,5689,5520],{"class":89},[75,5691,141],{"class":113},[75,5693,144],{"class":89},[75,5695,367],{"class":113},[75,5697,150],{"class":89},[75,5699,2614],{"class":89},[75,5701,3445],{"class":113},[75,5703,248],{"class":89},[75,5705,5706],{"class":170}," \u002F\u002F pivot op zijn definitieve plek\n",[75,5708,5709,5711,5713],{"class":77,"line":977},[75,5710,177],{"class":109},[75,5712,265],{"class":113},[75,5714,1050],{"class":89},[75,5716,5717],{"class":77,"line":1214},[75,5718,334],{"class":89},[75,5720,5721],{"class":77,"line":1219},[75,5722,5325],{"emptyLinePlaceholder":2242},[75,5724,5725,5727,5729,5731,5733,5735,5737,5739,5741,5743,5745,5747,5749,5751,5753],{"class":77,"line":1232},[75,5726,201],{"class":81},[75,5728,2669],{"class":81},[75,5730,5332],{"class":85},[75,5732,90],{"class":89},[75,5734,212],{"class":81},[75,5736,215],{"class":89},[75,5738,141],{"class":113},[75,5740,97],{"class":89},[75,5742,204],{"class":81},[75,5744,1093],{"class":113},[75,5746,97],{"class":89},[75,5748,204],{"class":81},[75,5750,851],{"class":113},[75,5752,226],{"class":89},[75,5754,229],{"class":89},[75,5756,5757,5759,5761,5763,5765,5767,5769],{"class":77,"line":1949},[75,5758,4153],{"class":109},[75,5760,23],{"class":89},[75,5762,869],{"class":113},[75,5764,32],{"class":89},[75,5766,851],{"class":113},[75,5768,226],{"class":89},[75,5770,229],{"class":89},[75,5772,5773,5775,5777,5779,5781,5783,5785,5787,5789,5791,5793],{"class":77,"line":1959},[75,5774,1075],{"class":81},[75,5776,5435],{"class":113},[75,5778,242],{"class":89},[75,5780,5146],{"class":85},[75,5782,90],{"class":89},[75,5784,94],{"class":113},[75,5786,97],{"class":89},[75,5788,1093],{"class":113},[75,5790,97],{"class":89},[75,5792,851],{"class":113},[75,5794,5795],{"class":89},");\n",[75,5797,5798,5800,5802,5804,5806,5808,5810,5812,5814,5816],{"class":77,"line":4386},[75,5799,5422],{"class":85},[75,5801,90],{"class":89},[75,5803,94],{"class":113},[75,5805,97],{"class":89},[75,5807,1093],{"class":113},[75,5809,97],{"class":89},[75,5811,5435],{"class":113},[75,5813,969],{"class":89},[75,5815,945],{"class":183},[75,5817,5795],{"class":89},[75,5819,5820,5822,5824,5826,5828,5830,5832,5834,5836,5838],{"class":77,"line":4407},[75,5821,5422],{"class":85},[75,5823,90],{"class":89},[75,5825,94],{"class":113},[75,5827,97],{"class":89},[75,5829,5435],{"class":113},[75,5831,872],{"class":89},[75,5833,945],{"class":183},[75,5835,97],{"class":89},[75,5837,851],{"class":113},[75,5839,5795],{"class":89},[75,5841,5842],{"class":77,"line":4426},[75,5843,314],{"class":89},[75,5845,5846],{"class":77,"line":4861},[75,5847,334],{"class":89},[10,5849,5850,5851,5853,5854,5857,5858,5860,5861,5864,5865,5867],{},"Valt de pivot steeds ongeveer in het midden, dan halveer je het probleem en kom je op\n",[30,5852,2105],{},". Maar is de array ",[14,5855,5856],{},"al gesorteerd",", dan is het laatste element steeds het grootste. De\npartitie levert dan een linkerdeel van ",[30,5859,3585],{}," elementen en een leeg rechterdeel op. Dat geeft\n",[30,5862,5863],{},"T(n) = T(n-1) + n",", en dus ",[30,5866,3465],{},". In de praktijk kies je daarom vaak een willekeurige pivot.",[47,5869,5871],{"id":5870},"stabiel-en-in-place","Stabiel en in-place",[10,5873,5874],{},"Twee eigenschappen die op het tentamen vaak gevraagd worden:",[1325,5876,5877,5886],{},[373,5878,5879,23,5882,5885],{},[14,5880,5881],{},"Stabiel",[25,5883,5884],{},"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.",[373,5887,5888,5891,5892,5894,5895,5897],{},[14,5889,5890],{},"In-place",": het algoritme gebruikt maar ",[30,5893,2042],{}," (of hooguit ",[30,5896,1974],{},") extra geheugen naast de\narray zelf.",[47,5899,1979],{"id":1978},[446,5901,5902,5921],{},[449,5903,5904],{},[452,5905,5906,5908,5911,5913,5915,5917,5919],{},[455,5907,2285],{},[455,5909,5910],{},"Best",[455,5912,2053],{},[455,5914,2066],{},[455,5916,2079],{},[455,5918,5881],{},[455,5920,5890],{},[488,5922,5923,5947,5971,5995,6019],{},[452,5924,5925,5927,5931,5935,5939,5943,5945],{},[493,5926,2298],{},[493,5928,5929],{},[30,5930,345],{},[493,5932,5933],{},[30,5934,3465],{},[493,5936,5937],{},[30,5938,3465],{},[493,5940,5941],{},[30,5942,2042],{},[493,5944,5004],{},[493,5946,5004],{},[452,5948,5949,5951,5955,5959,5963,5967,5969],{},[493,5950,2315],{},[493,5952,5953],{},[30,5954,3465],{},[493,5956,5957],{},[30,5958,3465],{},[493,5960,5961],{},[30,5962,3465],{},[493,5964,5965],{},[30,5966,2042],{},[493,5968,4987],{},[493,5970,5004],{},[452,5972,5973,5975,5979,5983,5987,5991,5993],{},[493,5974,2340],{},[493,5976,5977],{},[30,5978,3465],{},[493,5980,5981],{},[30,5982,3465],{},[493,5984,5985],{},[30,5986,3465],{},[493,5988,5989],{},[30,5990,2042],{},[493,5992,5004],{},[493,5994,5004],{},[452,5996,5997,5999,6003,6007,6011,6015,6017],{},[493,5998,3965],{},[493,6000,6001],{},[30,6002,2105],{},[493,6004,6005],{},[30,6006,2105],{},[493,6008,6009],{},[30,6010,2105],{},[493,6012,6013],{},[30,6014,345],{},[493,6016,5004],{},[493,6018,4987],{},[452,6020,6021,6024,6028,6032,6036,6041,6043],{},[493,6022,6023],{},"Quicksort (Lomuto)",[493,6025,6026],{},[30,6027,2105],{},[493,6029,6030],{},[30,6031,2105],{},[493,6033,6034],{},[30,6035,3465],{},[493,6037,6038,6040],{},[30,6039,1974],{}," gemiddeld",[493,6042,4987],{},[493,6044,5004],{},[10,6046,6047,6048,6050,6051,6053,6054,6056,6057,257],{},"Bubble sort met vroegtijdige stop heeft een best case van ",[30,6049,345],{},"; zonder stop, zoals wij hem\ndefiniëren, is ook de best case ",[30,6052,3465],{},". Het geheugen van quicksort is de recursiestapel: gemiddeld\n",[30,6055,1974],{},", in het slechtste geval ",[30,6058,345],{},[47,6060,2120],{"id":2119},[370,6062,6063,6085,6091,6100,6117],{},[373,6064,6065,6068,6069,6072,6073,6076,6077,6079,6080,6082,6083,257],{},[14,6066,6067],{},"Insertion en selection sort verwisselen."," Insertion sort pakt het ",[25,6070,6071],{},"volgende"," element en schuift\nhet op zijn plek; het gesorteerde deel bevat dan nog niet per se de kleinste. Selection sort\n",[25,6074,6075],{},"zoekt"," het kleinste in de rest. Na ronde 1 van ",[30,6078,2412],{}," geeft insertion\n",[30,6081,2425],{},", selection ",[30,6084,2930],{},[373,6086,6087,6090],{},[14,6088,6089],{},"Een ronde overslaan omdat er niets verandert."," Bij insertion sort telt ronde 3 hierboven\ngewoon mee, ook al blijft de array gelijk.",[373,6092,6093,6096,6097,6099],{},[14,6094,6095],{},"Bubble sort vroegtijdig stoppen."," Volgens de afspraak loop je alle ",[30,6098,3585],{}," rondes door. Bij een\nvraag als \"hoeveel vergelijkingen?\" maakt dat uit.",[373,6101,6102,6105,6106,6109,6110,6112,6113,6116],{},[14,6103,6104],{},"De laatste wissel van Lomuto vergeten."," Na de lus staat de pivot nog achteraan; pas de\n",[30,6107,6108],{},"swap(a[i], a[hi])"," zet hem op index ",[30,6111,147],{},". Ook: gelijke waarden aan de pivot gaan ",[25,6114,6115],{},"niet"," naar\nlinks, alleen strikt kleinere.",[373,6118,6119,6125,6126,257],{},[14,6120,6121,6122,6124],{},"Denken dat quicksort altijd ",[30,6123,2105],{}," is."," Met het laatste element als pivot is een\ngesorteerde invoer het slechtste geval: ",[30,6127,3465],{},[47,6129,2186],{"id":2185},[1325,6131,6132,6141,6153,6164,6173],{},[373,6133,6134,6135,6137,6138,6140],{},"Insertion sort: na ronde ",[30,6136,1985],{}," is ",[30,6139,2309],{}," gesorteerd; snel op bijna gesorteerde data, stabiel.",[373,6142,6143,6144,6146,6147,6149,6150,6152],{},"Selection sort: na ronde ",[30,6145,1985],{}," staan de ",[30,6148,1985],{}," kleinsten vooraan; altijd ",[30,6151,3465],{},", niet stabiel.",[373,6154,6155,6156,6146,6158,6160,6161,6163],{},"Bubble sort: na ronde ",[30,6157,1985],{},[30,6159,1985],{}," grootsten achteraan; ",[30,6162,3465],{},", stabiel.",[373,6165,6166,6167,6169,6170,6172],{},"Merge sort: altijd ",[30,6168,2105],{}," en stabiel, maar kost ",[30,6171,345],{}," extra geheugen.",[373,6174,6175,6176,6178,6179,257],{},"Quicksort (Lomuto, laatste element als pivot): gemiddeld ",[30,6177,2105],{}," en in-place, slechtst ",[30,6180,3465],{},[2223,6182,6183],{},"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":65,"searchDepth":106,"depth":106,"links":6185},[6186,6187,6188,6189,6190,6191,6192,6193,6194,6195],{"id":2272,"depth":106,"text":2273},{"id":2378,"depth":106,"text":2298},{"id":2876,"depth":106,"text":2315},{"id":3468,"depth":106,"text":2340},{"id":3964,"depth":106,"text":3965},{"id":4891,"depth":106,"text":4892},{"id":5870,"depth":106,"text":5871},{"id":1978,"depth":106,"text":1979},{"id":2119,"depth":106,"text":2120},{"id":2185,"depth":106,"text":2186},"Insertion, selection, bubble, merge sort en quicksort stap voor stap: tabellen per ronde, Python- en Java-code, stabiliteit en complexiteit voor je tentamen.","i-lucide-arrow-down-wide-narrow",{},"\u002Fpracticely-dsa\u002Fsorteren",{"title":2251,"description":6196},"practicely-dsa\u002Fsorteren","sorteren","UIA63XLS5o3aeifdip2qZtjYjc5fIIaub0fKqIQnEWs",{"id":6205,"title":6206,"body":6207,"description":9249,"extension":2239,"icon":9250,"meta":9251,"navigation":2242,"order":161,"path":9252,"seo":9253,"stem":9254,"topic":9255,"__hash__":9256},"practicelyDsa\u002Fpracticely-dsa\u002Fstapels-en-wachtrijen.md","Stapels en wachtrijen uitgelegd: LIFO, FIFO en gelinkte lijsten",{"type":7,"value":6208,"toc":9237},[6209,6230,6233,6237,6246,6249,6282,6289,6429,6433,6442,6472,6479,6617,6625,6629,6647,7171,7196,7200,7222,7228,7237,7262,7282,7358,7362,7377,7402,8139,8161,8165,8180,8189,8313,8338,8888,8892,8975,8982,8984,9107,9117,9119,9189,9191,9234],[10,6210,6211,6212,23,6215,6218,6219,23,6222,6225,6226,6229],{},"Een ",[14,6213,6214],{},"stapel",[25,6216,6217],{},"stack",") en een ",[14,6220,6221],{},"wachtrij",[25,6223,6224],{},"queue",") zijn de twee eenvoudigste datastructuren die\ner bestaan, en tegelijk twee van de meest gebruikte. Elke keer dat je op Ctrl+Z drukt, gebruikt je\neditor een stapel. Elke keer dat je iets naar de printer stuurt, komt het in een wachtrij. En elke\nfunctieaanroep in je programma belandt op de aanroepstapel (",[25,6227,6228],{},"call stack",").",[10,6231,6232],{},"Op het tentamen krijg je meestal een reeks operaties en moet je de toestand erna opschrijven, of moet\nje uitleggen welke structuur bij een probleem past. In sollicitatiegesprekken is \"controleer of de\nhaakjes kloppen\" een klassieker. Allebei komen hieronder aan bod.",[47,6234,6236],{"id":6235},"stapel-last-in-first-out","Stapel: last in, first out",[10,6238,6239,6240,23,6243,6229],{},"Een stapel werkt als een stapel borden: je legt een nieuw bord bovenop en je pakt ook altijd het\nbovenste weer weg. Wat het laatst erop kwam, gaat er het eerst af: ",[14,6241,6242],{},"LIFO",[25,6244,6245],{},"last in, first out",[10,6247,6248],{},"De operaties:",[1325,6250,6251,6260,6266,6276],{},[373,6252,6253,6256,6257,6259],{},[30,6254,6255],{},"push(x)",": leg ",[30,6258,389],{}," bovenop de stapel.",[373,6261,6262,6265],{},[30,6263,6264],{},"pop()",": haal het bovenste element weg en geef het terug.",[373,6267,6268,6271,6272,6275],{},[30,6269,6270],{},"peek()"," (of ",[30,6273,6274],{},"top()","): bekijk het bovenste element zonder het weg te halen.",[373,6277,6278,6281],{},[30,6279,6280],{},"isEmpty()",": is de stapel leeg?",[10,6283,6284,6285,6288],{},"We noteren de toestand van een stapel altijd van ",[14,6286,6287],{},"onder naar boven",": het meest rechtse element is\nde bovenkant.",[446,6290,6291,6306],{},[449,6292,6293],{},[452,6294,6295,6297,6300,6303],{},[455,6296,531],{},[455,6298,6299],{},"Operatie",[455,6301,6302],{},"Teruggegeven",[455,6304,6305],{},"Stapel (onder → boven)",[488,6307,6308,6323,6339,6355,6369,6385,6399,6413],{},[452,6309,6310,6312,6317,6319],{},[493,6311,184],{},[493,6313,6314],{},[30,6315,6316],{},"push(4)",[493,6318,741],{},[493,6320,6321],{},[30,6322,471],{},[452,6324,6325,6327,6332,6334],{},[493,6326,465],{},[493,6328,6329],{},[30,6330,6331],{},"push(7)",[493,6333,741],{},[493,6335,6336],{},[30,6337,6338],{},"4, 7",[452,6340,6341,6343,6348,6350],{},[493,6342,468],{},[493,6344,6345],{},[30,6346,6347],{},"push(1)",[493,6349,741],{},[493,6351,6352],{},[30,6353,6354],{},"4, 7, 1",[452,6356,6357,6359,6363,6365],{},[493,6358,471],{},[493,6360,6361],{},[30,6362,6264],{},[493,6364,184],{},[493,6366,6367],{},[30,6368,6338],{},[452,6370,6371,6373,6378,6380],{},[493,6372,474],{},[493,6374,6375],{},[30,6376,6377],{},"push(9)",[493,6379,741],{},[493,6381,6382],{},[30,6383,6384],{},"4, 7, 9",[452,6386,6387,6389,6393,6395],{},[493,6388,477],{},[493,6390,6391],{},[30,6392,6264],{},[493,6394,486],{},[493,6396,6397],{},[30,6398,6338],{},[452,6400,6401,6403,6407,6409],{},[493,6402,480],{},[493,6404,6405],{},[30,6406,6264],{},[493,6408,480],{},[493,6410,6411],{},[30,6412,471],{},[452,6414,6415,6417,6422,6424],{},[493,6416,483],{},[493,6418,6419],{},[30,6420,6421],{},"push(5)",[493,6423,741],{},[493,6425,6426],{},[30,6427,6428],{},"4, 5",[47,6430,6432],{"id":6431},"wachtrij-first-in-first-out","Wachtrij: first in, first out",[10,6434,6435,6436,23,6439,6229],{},"Een wachtrij werkt als de rij bij de kassa: wie het eerst aansluit, wordt het eerst geholpen:\n",[14,6437,6438],{},"FIFO",[25,6440,6441],{},"first in, first out",[1325,6443,6444,6456,6466],{},[373,6445,6446,6449,6450,2136,6452,6455],{},[30,6447,6448],{},"enqueue(x)",": zet ",[30,6451,389],{},[14,6453,6454],{},"achteraan"," in de rij.",[373,6457,6458,6461,6462,6465],{},[30,6459,6460],{},"dequeue()",": haal het ",[14,6463,6464],{},"voorste"," element weg en geef het terug.",[373,6467,6468,6471],{},[30,6469,6470],{},"front()",": bekijk het voorste element.",[10,6473,6474,6475,6478],{},"De toestand noteren we van ",[14,6476,6477],{},"voor naar achter",": het meest linkse element is als eerste aan de beurt.\nDezelfde reeks als hierboven, maar nu met een wachtrij:",[446,6480,6481,6494],{},[449,6482,6483],{},[452,6484,6485,6487,6489,6491],{},[455,6486,531],{},[455,6488,6299],{},[455,6490,6302],{},[455,6492,6493],{},"Wachtrij (voor → achter)",[488,6495,6496,6511,6526,6541,6556,6572,6587,6601],{},[452,6497,6498,6500,6505,6507],{},[493,6499,184],{},[493,6501,6502],{},[30,6503,6504],{},"enqueue(4)",[493,6506,741],{},[493,6508,6509],{},[30,6510,471],{},[452,6512,6513,6515,6520,6522],{},[493,6514,465],{},[493,6516,6517],{},[30,6518,6519],{},"enqueue(7)",[493,6521,741],{},[493,6523,6524],{},[30,6525,6338],{},[452,6527,6528,6530,6535,6537],{},[493,6529,468],{},[493,6531,6532],{},[30,6533,6534],{},"enqueue(1)",[493,6536,741],{},[493,6538,6539],{},[30,6540,6354],{},[452,6542,6543,6545,6549,6551],{},[493,6544,471],{},[493,6546,6547],{},[30,6548,6460],{},[493,6550,471],{},[493,6552,6553],{},[30,6554,6555],{},"7, 1",[452,6557,6558,6560,6565,6567],{},[493,6559,474],{},[493,6561,6562],{},[30,6563,6564],{},"enqueue(9)",[493,6566,741],{},[493,6568,6569],{},[30,6570,6571],{},"7, 1, 9",[452,6573,6574,6576,6580,6582],{},[493,6575,477],{},[493,6577,6578],{},[30,6579,6460],{},[493,6581,480],{},[493,6583,6584],{},[30,6585,6586],{},"1, 9",[452,6588,6589,6591,6595,6597],{},[493,6590,480],{},[493,6592,6593],{},[30,6594,6460],{},[493,6596,184],{},[493,6598,6599],{},[30,6600,486],{},[452,6602,6603,6605,6610,6612],{},[493,6604,483],{},[493,6606,6607],{},[30,6608,6609],{},"enqueue(5)",[493,6611,741],{},[493,6613,6614],{},[30,6615,6616],{},"9, 5",[10,6618,6619,6620,6622,6623,257],{},"Zelfde invoer, totaal ander resultaat: de stapel eindigt met ",[30,6621,6428],{},", de wachtrij met ",[30,6624,6616],{},[47,6626,6628],{"id":6627},"een-stapel-met-een-array-of-lijst","Een stapel met een array of lijst",[10,6630,6631,6632,6635,6636,6639,6640,6643,6644,6646],{},"Een stapel is eenvoudig te bouwen op een dynamische array (Python ",[30,6633,6634],{},"list",", Java ",[30,6637,6638],{},"ArrayList","). De\nbovenkant is het ",[14,6641,6642],{},"einde"," van de lijst: toevoegen en weghalen aan het einde kost ",[30,6645,2042],{}," (bij een\ndynamische array gemiddeld, omdat de array af en toe moet groeien).",[60,6648,6649,6883],{},[63,6650,6651],{"v-slot:python":65},[67,6652,6654],{"className":69,"code":6653,"language":71,"meta":65,"style":65},"class Stapel:\n    def __init__(self):\n        self.data = []\n\n    def push(self, x):\n        self.data.append(x)  # bovenkant = einde van de lijst\n\n    def pop(self):\n        if not self.data:\n            raise IndexError(\"pop op lege stapel\")\n        return self.data.pop()\n\n    def peek(self):\n        return self.data[-1]\n\n    def is_empty(self):\n        return len(self.data) == 0\n",[30,6655,6656,6667,6683,6698,6702,6719,6740,6744,6757,6773,6794,6812,6816,6829,6846,6850,6863],{"__ignoreMap":65},[75,6657,6658,6661,6665],{"class":77,"line":78},[75,6659,6660],{"class":81},"class",[75,6662,6664],{"class":6663},"sBMFI"," Stapel",[75,6666,158],{"class":89},[75,6668,6669,6672,6675,6677,6681],{"class":77,"line":106},[75,6670,6671],{"class":81},"    def",[75,6673,6674],{"class":85}," __init__",[75,6676,90],{"class":89},[75,6678,6680],{"class":6679},"s5tWE","self",[75,6682,103],{"class":89},[75,6684,6685,6688,6690,6694,6696],{"class":77,"line":135},[75,6686,6687],{"class":113},"        self",[75,6689,257],{"class":89},[75,6691,6693],{"class":6692},"swJcz","data",[75,6695,2614],{"class":89},[75,6697,4251],{"class":89},[75,6699,6700],{"class":77,"line":161},[75,6701,5325],{"emptyLinePlaceholder":2242},[75,6703,6704,6706,6709,6711,6713,6715,6717],{"class":77,"line":174},[75,6705,6671],{"class":81},[75,6707,6708],{"class":85}," push",[75,6710,90],{"class":89},[75,6712,6680],{"class":6679},[75,6714,97],{"class":89},[75,6716,100],{"class":93},[75,6718,103],{"class":89},[75,6720,6721,6723,6725,6727,6729,6731,6733,6735,6737],{"class":77,"line":311},[75,6722,6687],{"class":113},[75,6724,257],{"class":89},[75,6726,6693],{"class":6692},[75,6728,257],{"class":89},[75,6730,4331],{"class":85},[75,6732,90],{"class":89},[75,6734,389],{"class":85},[75,6736,226],{"class":89},[75,6738,6739],{"class":170},"  # bovenkant = einde van de lijst\n",[75,6741,6742],{"class":77,"line":317},[75,6743,5325],{"emptyLinePlaceholder":2242},[75,6745,6746,6748,6751,6753,6755],{"class":77,"line":331},[75,6747,6671],{"class":81},[75,6749,6750],{"class":85}," pop",[75,6752,90],{"class":89},[75,6754,6680],{"class":6679},[75,6756,103],{"class":89},[75,6758,6759,6761,6764,6767,6769,6771],{"class":77,"line":951},[75,6760,138],{"class":109},[75,6762,6763],{"class":89}," not",[75,6765,6766],{"class":113}," self",[75,6768,257],{"class":89},[75,6770,6693],{"class":6692},[75,6772,158],{"class":89},[75,6774,6775,6778,6781,6783,6786,6790,6792],{"class":77,"line":959},[75,6776,6777],{"class":109},"            raise",[75,6779,6780],{"class":6663}," IndexError",[75,6782,90],{"class":89},[75,6784,6785],{"class":89},"\"",[75,6787,6789],{"class":6788},"sfazB","pop op lege stapel",[75,6791,6785],{"class":89},[75,6793,3060],{"class":89},[75,6795,6796,6798,6800,6802,6804,6806,6809],{"class":77,"line":977},[75,6797,4173],{"class":109},[75,6799,6766],{"class":113},[75,6801,257],{"class":89},[75,6803,6693],{"class":6692},[75,6805,257],{"class":89},[75,6807,6808],{"class":85},"pop",[75,6810,6811],{"class":89},"()\n",[75,6813,6814],{"class":77,"line":1214},[75,6815,5325],{"emptyLinePlaceholder":2242},[75,6817,6818,6820,6823,6825,6827],{"class":77,"line":1219},[75,6819,6671],{"class":81},[75,6821,6822],{"class":85}," peek",[75,6824,90],{"class":89},[75,6826,6680],{"class":6679},[75,6828,103],{"class":89},[75,6830,6831,6833,6835,6837,6839,6842,6844],{"class":77,"line":1232},[75,6832,4173],{"class":109},[75,6834,6766],{"class":113},[75,6836,257],{"class":89},[75,6838,6693],{"class":6692},[75,6840,6841],{"class":89},"[-",[75,6843,184],{"class":183},[75,6845,2545],{"class":89},[75,6847,6848],{"class":77,"line":1949},[75,6849,5325],{"emptyLinePlaceholder":2242},[75,6851,6852,6854,6857,6859,6861],{"class":77,"line":1959},[75,6853,6671],{"class":81},[75,6855,6856],{"class":85}," is_empty",[75,6858,90],{"class":89},[75,6860,6680],{"class":6679},[75,6862,103],{"class":89},[75,6864,6865,6867,6869,6871,6873,6875,6877,6879,6881],{"class":77,"line":4386},[75,6866,4173],{"class":109},[75,6868,827],{"class":85},[75,6870,90],{"class":89},[75,6872,6680],{"class":113},[75,6874,257],{"class":89},[75,6876,6693],{"class":6692},[75,6878,226],{"class":89},[75,6880,153],{"class":89},[75,6882,4265],{"class":183},[63,6884,6885],{"v-slot:java":65},[67,6886,6888],{"className":192,"code":6887,"language":194,"meta":65,"style":65},"import java.util.ArrayList;\n\nclass Stapel {\n    private final ArrayList\u003CInteger> data = new ArrayList\u003C>();\n\n    void push(int x) {\n        data.add(x); \u002F\u002F bovenkant = einde van de lijst\n    }\n\n    int pop() {\n        if (data.isEmpty()) {\n            throw new IllegalStateException(\"pop op lege stapel\");\n        }\n        return data.remove(data.size() - 1);\n    }\n\n    int peek() {\n        return data.get(data.size() - 1);\n    }\n\n    boolean isEmpty() {\n        return data.isEmpty();\n    }\n}\n",[30,6889,6890,6908,6912,6920,6951,6955,6972,6992,6996,7000,7011,7029,7049,7053,7082,7086,7090,7100,7127,7131,7135,7147,7161,7166],{"__ignoreMap":65},[75,6891,6892,6895,6898,6900,6902,6904,6906],{"class":77,"line":78},[75,6893,6894],{"class":183},"import",[75,6896,6897],{"class":81}," java",[75,6899,257],{"class":89},[75,6901,4536],{"class":81},[75,6903,257],{"class":89},[75,6905,6638],{"class":81},[75,6907,1050],{"class":89},[75,6909,6910],{"class":77,"line":106},[75,6911,5325],{"emptyLinePlaceholder":2242},[75,6913,6914,6916,6918],{"class":77,"line":135},[75,6915,6660],{"class":81},[75,6917,6664],{"class":6663},[75,6919,229],{"class":89},[75,6921,6922,6925,6928,6931,6933,6936,6939,6942,6944,6946,6948],{"class":77,"line":161},[75,6923,6924],{"class":81},"    private",[75,6926,6927],{"class":81}," final",[75,6929,6930],{"class":81}," ArrayList",[75,6932,32],{"class":89},[75,6934,6935],{"class":81},"Integer",[75,6937,6938],{"class":89},">",[75,6940,6941],{"class":113}," data ",[75,6943,242],{"class":89},[75,6945,4627],{"class":109},[75,6947,6930],{"class":81},[75,6949,6950],{"class":89},"\u003C>();\n",[75,6952,6953],{"class":77,"line":174},[75,6954,5325],{"emptyLinePlaceholder":2242},[75,6956,6957,6960,6962,6964,6966,6968,6970],{"class":77,"line":311},[75,6958,6959],{"class":81},"    void",[75,6961,6708],{"class":85},[75,6963,90],{"class":89},[75,6965,212],{"class":81},[75,6967,100],{"class":93},[75,6969,226],{"class":89},[75,6971,229],{"class":89},[75,6973,6974,6977,6979,6982,6984,6986,6989],{"class":77,"line":317},[75,6975,6976],{"class":113},"        data",[75,6978,257],{"class":89},[75,6980,6981],{"class":85},"add",[75,6983,90],{"class":89},[75,6985,389],{"class":113},[75,6987,6988],{"class":89},");",[75,6990,6991],{"class":170}," \u002F\u002F bovenkant = einde van de lijst\n",[75,6993,6994],{"class":77,"line":331},[75,6995,314],{"class":89},[75,6997,6998],{"class":77,"line":951},[75,6999,5325],{"emptyLinePlaceholder":2242},[75,7001,7002,7004,7006,7009],{"class":77,"line":959},[75,7003,1024],{"class":81},[75,7005,6750],{"class":85},[75,7007,7008],{"class":89},"()",[75,7010,229],{"class":89},[75,7012,7013,7015,7017,7019,7021,7024,7027],{"class":77,"line":977},[75,7014,138],{"class":109},[75,7016,23],{"class":89},[75,7018,6693],{"class":113},[75,7020,257],{"class":89},[75,7022,7023],{"class":85},"isEmpty",[75,7025,7026],{"class":89},"())",[75,7028,229],{"class":89},[75,7030,7031,7034,7036,7039,7041,7043,7045,7047],{"class":77,"line":1214},[75,7032,7033],{"class":109},"            throw",[75,7035,4627],{"class":109},[75,7037,7038],{"class":85}," IllegalStateException",[75,7040,90],{"class":89},[75,7042,6785],{"class":89},[75,7044,6789],{"class":6788},[75,7046,6785],{"class":89},[75,7048,5795],{"class":89},[75,7050,7051],{"class":77,"line":1219},[75,7052,308],{"class":89},[75,7054,7055,7057,7060,7062,7065,7067,7069,7071,7074,7076,7078,7080],{"class":77,"line":1232},[75,7056,4173],{"class":109},[75,7058,7059],{"class":113}," data",[75,7061,257],{"class":89},[75,7063,7064],{"class":85},"remove",[75,7066,90],{"class":89},[75,7068,6693],{"class":113},[75,7070,257],{"class":89},[75,7072,7073],{"class":85},"size",[75,7075,7008],{"class":89},[75,7077,180],{"class":89},[75,7079,945],{"class":183},[75,7081,5795],{"class":89},[75,7083,7084],{"class":77,"line":1949},[75,7085,314],{"class":89},[75,7087,7088],{"class":77,"line":1959},[75,7089,5325],{"emptyLinePlaceholder":2242},[75,7091,7092,7094,7096,7098],{"class":77,"line":4386},[75,7093,1024],{"class":81},[75,7095,6822],{"class":85},[75,7097,7008],{"class":89},[75,7099,229],{"class":89},[75,7101,7102,7104,7106,7108,7111,7113,7115,7117,7119,7121,7123,7125],{"class":77,"line":4407},[75,7103,4173],{"class":109},[75,7105,7059],{"class":113},[75,7107,257],{"class":89},[75,7109,7110],{"class":85},"get",[75,7112,90],{"class":89},[75,7114,6693],{"class":113},[75,7116,257],{"class":89},[75,7118,7073],{"class":85},[75,7120,7008],{"class":89},[75,7122,180],{"class":89},[75,7124,945],{"class":183},[75,7126,5795],{"class":89},[75,7128,7129],{"class":77,"line":4426},[75,7130,314],{"class":89},[75,7132,7133],{"class":77,"line":4861},[75,7134,5325],{"emptyLinePlaceholder":2242},[75,7136,7137,7140,7143,7145],{"class":77,"line":4870},[75,7138,7139],{"class":81},"    boolean",[75,7141,7142],{"class":85}," isEmpty",[75,7144,7008],{"class":89},[75,7146,229],{"class":89},[75,7148,7150,7152,7154,7156,7158],{"class":77,"line":7149},22,[75,7151,4173],{"class":109},[75,7153,7059],{"class":113},[75,7155,257],{"class":89},[75,7157,7023],{"class":85},[75,7159,7160],{"class":89},"();\n",[75,7162,7164],{"class":77,"line":7163},23,[75,7165,314],{"class":89},[75,7167,7169],{"class":77,"line":7168},24,[75,7170,334],{"class":89},[10,7172,7173,7174,7177,7178,7180,7181,7184,7185,7187,7188,7191,7192,7195],{},"Voor een wachtrij werkt een gewone lijst slecht: ",[30,7175,7176],{},"dequeue"," haalt het ",[14,7179,1420],{}," element weg, en dan\nmoeten alle andere elementen een plek opschuiven. In Python is ",[30,7182,7183],{},"list.pop(0)"," daarom ",[30,7186,345],{},". Gebruik\nvoor een wachtrij ",[30,7189,7190],{},"collections.deque"," (Python) of ",[30,7193,7194],{},"ArrayDeque"," (Java), of bouw er een met een\ngelinkte lijst.",[47,7197,7199],{"id":7198},"gelinkte-lijsten","Gelinkte lijsten",[10,7201,6211,7202,23,7204,7207,7208,7211,7212,23,7215,7218,7219,257],{},[14,7203,341],{},[25,7205,7206],{},"linked list",") bestaat uit losse knopen (",[25,7209,7210],{},"nodes","). Elke knoop bevat een\nwaarde en een verwijzing naar de volgende knoop. In een ",[14,7213,7214],{},"enkel gelinkte lijst",[25,7216,7217],{},"singly linked\nlist",") wijst elke knoop alleen naar zijn opvolger; de lijst zelf onthoudt alleen de eerste knoop, de\n",[30,7220,7221],{},"head",[67,7223,7226],{"className":7224,"code":7225,"language":4914},[4912],"head → [4 | •] → [7 | •] → [1 | •] → null\n",[30,7227,7225],{"__ignoreMap":65},[10,7229,7230,7231,7236],{},"Het grote voordeel: ",[14,7232,7233,7234],{},"vooraan invoegen of verwijderen kost ",[30,7235,2042],{},", want je verandert alleen een\npaar verwijzingen. Niets hoeft op te schuiven.",[1325,7238,7239,7250],{},[373,7240,7241,7244,7245,7247,7248,257],{},[14,7242,7243],{},"Vooraan invoegen:"," maak een nieuwe knoop, laat hem naar de oude ",[30,7246,7221],{}," wijzen, maak hem de\nnieuwe ",[30,7249,7221],{},[373,7251,7252,7255,7256,7259,7260,257],{},[14,7253,7254],{},"Vooraan verwijderen:"," maak ",[30,7257,7258],{},"head.next"," de nieuwe ",[30,7261,7221],{},[10,7263,7264,7265,7267,7268,7270,7271,7273,7274,7276,7277,7281],{},"Het nadeel: je kunt niet direct naar index ",[30,7266,147],{}," springen. Om het ",[30,7269,147],{},"-de element te vinden, loop je\nvanaf ",[30,7272,7221],{}," de verwijzingen af: ",[30,7275,345],{},". Daarom werkt ",[94,7278,7280],{"href":7279},"\u002Fpracticely\u002Fdsa\u002Fzoeken","binair zoeken"," niet\nop een gelinkte lijst.",[446,7283,7284,7295],{},[449,7285,7286],{},[452,7287,7288,7290,7292],{},[455,7289,6299],{},[455,7291,4959],{},[455,7293,7294],{},"Enkel gelinkte lijst",[488,7296,7297,7312,7325,7344],{},[452,7298,7299,7304,7308],{},[493,7300,7301,7302],{},"element op index ",[30,7303,147],{},[493,7305,7306],{},[30,7307,2042],{},[493,7309,7310],{},[30,7311,345],{},[452,7313,7314,7317,7321],{},[493,7315,7316],{},"vooraan invoegen\u002Fverwijderen",[493,7318,7319],{},[30,7320,345],{},[493,7322,7323],{},[30,7324,2042],{},[452,7326,7327,7330,7334],{},[493,7328,7329],{},"achteraan invoegen",[493,7331,7332,6040],{},[30,7333,2042],{},[493,7335,7336,1381,7338,7341,7342],{},[30,7337,2042],{},[30,7339,7340],{},"tail","-verwijzing, anders ",[30,7343,345],{},[452,7345,7346,7349,7353],{},[493,7347,7348],{},"achteraan verwijderen",[493,7350,7351],{},[30,7352,2042],{},[493,7354,7355,7357],{},[30,7356,345],{}," (je moet de voorlaatste knoop vinden)",[47,7359,7361],{"id":7360},"stapel-en-wachtrij-met-een-gelinkte-lijst","Stapel en wachtrij met een gelinkte lijst",[10,7363,6211,7364,7366,7367,7370,7371,7373,7374,7376],{},[14,7365,6214],{}," is een gelinkte lijst waarbij je alleen vooraan werkt: ",[30,7368,7369],{},"push"," voegt vooraan in, ",[30,7372,6808],{},"\nverwijdert vooraan. De ",[30,7375,7221],{}," is de bovenkant van de stapel.",[10,7378,6211,7379,7381,7382,7384,7385,7387,7388,7391,7392,37,7394,7396,7397,7399,7400,257],{},[14,7380,6221],{}," houdt twee verwijzingen bij: ",[30,7383,7221],{}," (voorkant) en ",[30,7386,7340],{}," (achterkant).\n",[30,7389,7390],{},"enqueue"," hangt een knoop achter ",[30,7393,7340],{},[30,7395,7176],{}," haalt ",[30,7398,7221],{}," weg. Allebei ",[30,7401,2042],{},[60,7403,7404,7766],{},[63,7405,7406],{"v-slot:python":65},[67,7407,7409],{"className":69,"code":7408,"language":71,"meta":65,"style":65},"class Knoop:\n    def __init__(self, waarde, volgende=None):\n        self.waarde = waarde\n        self.volgende = volgende\n\n\nclass Wachtrij:\n    def __init__(self):\n        self.head = None  # voorkant: hier gaat het eruit\n        self.tail = None  # achterkant: hier komt het erbij\n\n    def enqueue(self, x):\n        knoop = Knoop(x)\n        if self.tail is None:  # lege wachtrij\n            self.head = self.tail = knoop\n        else:\n            self.tail.volgende = knoop\n            self.tail = knoop\n\n    def dequeue(self):\n        if self.head is None:\n            raise IndexError(\"dequeue op lege wachtrij\")\n        x = self.head.waarde\n        self.head = self.head.volgende\n        if self.head is None:  # wachtrij is nu leeg\n            self.tail = None\n        return x\n",[30,7410,7411,7420,7442,7456,7469,7473,7477,7486,7498,7514,7529,7533,7550,7565,7584,7606,7612,7628,7640,7644,7657,7671,7688,7705,7726,7744,7758],{"__ignoreMap":65},[75,7412,7413,7415,7418],{"class":77,"line":78},[75,7414,6660],{"class":81},[75,7416,7417],{"class":6663}," Knoop",[75,7419,158],{"class":89},[75,7421,7422,7424,7426,7428,7430,7432,7435,7437,7440],{"class":77,"line":106},[75,7423,6671],{"class":81},[75,7425,6674],{"class":85},[75,7427,90],{"class":89},[75,7429,6680],{"class":6679},[75,7431,97],{"class":89},[75,7433,7434],{"class":93}," waarde",[75,7436,97],{"class":89},[75,7438,7439],{"class":93}," volgende",[75,7441,5351],{"class":89},[75,7443,7444,7446,7448,7451,7453],{"class":77,"line":135},[75,7445,6687],{"class":113},[75,7447,257],{"class":89},[75,7449,7450],{"class":6692},"waarde",[75,7452,2614],{"class":89},[75,7454,7455],{"class":113}," waarde\n",[75,7457,7458,7460,7462,7464,7466],{"class":77,"line":161},[75,7459,6687],{"class":113},[75,7461,257],{"class":89},[75,7463,6071],{"class":6692},[75,7465,2614],{"class":89},[75,7467,7468],{"class":113}," volgende\n",[75,7470,7471],{"class":77,"line":174},[75,7472,5325],{"emptyLinePlaceholder":2242},[75,7474,7475],{"class":77,"line":311},[75,7476,5325],{"emptyLinePlaceholder":2242},[75,7478,7479,7481,7484],{"class":77,"line":317},[75,7480,6660],{"class":81},[75,7482,7483],{"class":6663}," Wachtrij",[75,7485,158],{"class":89},[75,7487,7488,7490,7492,7494,7496],{"class":77,"line":331},[75,7489,6671],{"class":81},[75,7491,6674],{"class":85},[75,7493,90],{"class":89},[75,7495,6680],{"class":6679},[75,7497,103],{"class":89},[75,7499,7500,7502,7504,7506,7508,7511],{"class":77,"line":951},[75,7501,6687],{"class":113},[75,7503,257],{"class":89},[75,7505,7221],{"class":6692},[75,7507,2614],{"class":89},[75,7509,7510],{"class":89}," None",[75,7512,7513],{"class":170},"  # voorkant: hier gaat het eruit\n",[75,7515,7516,7518,7520,7522,7524,7526],{"class":77,"line":959},[75,7517,6687],{"class":113},[75,7519,257],{"class":89},[75,7521,7340],{"class":6692},[75,7523,2614],{"class":89},[75,7525,7510],{"class":89},[75,7527,7528],{"class":170},"  # achterkant: hier komt het erbij\n",[75,7530,7531],{"class":77,"line":977},[75,7532,5325],{"emptyLinePlaceholder":2242},[75,7534,7535,7537,7540,7542,7544,7546,7548],{"class":77,"line":1214},[75,7536,6671],{"class":81},[75,7538,7539],{"class":85}," enqueue",[75,7541,90],{"class":89},[75,7543,6680],{"class":6679},[75,7545,97],{"class":89},[75,7547,100],{"class":93},[75,7549,103],{"class":89},[75,7551,7552,7555,7557,7559,7561,7563],{"class":77,"line":1219},[75,7553,7554],{"class":113},"        knoop ",[75,7556,242],{"class":89},[75,7558,7417],{"class":85},[75,7560,90],{"class":89},[75,7562,389],{"class":85},[75,7564,3060],{"class":89},[75,7566,7567,7569,7571,7573,7575,7578,7581],{"class":77,"line":1232},[75,7568,138],{"class":109},[75,7570,6766],{"class":113},[75,7572,257],{"class":89},[75,7574,7340],{"class":6692},[75,7576,7577],{"class":89}," is",[75,7579,7580],{"class":89}," None:",[75,7582,7583],{"class":170},"  # lege wachtrij\n",[75,7585,7586,7589,7591,7593,7595,7597,7599,7601,7603],{"class":77,"line":1949},[75,7587,7588],{"class":113},"            self",[75,7590,257],{"class":89},[75,7592,7221],{"class":6692},[75,7594,2614],{"class":89},[75,7596,6766],{"class":113},[75,7598,257],{"class":89},[75,7600,7340],{"class":6692},[75,7602,2614],{"class":89},[75,7604,7605],{"class":113}," knoop\n",[75,7607,7608,7610],{"class":77,"line":1959},[75,7609,954],{"class":109},[75,7611,158],{"class":89},[75,7613,7614,7616,7618,7620,7622,7624,7626],{"class":77,"line":4386},[75,7615,7588],{"class":113},[75,7617,257],{"class":89},[75,7619,7340],{"class":6692},[75,7621,257],{"class":89},[75,7623,6071],{"class":6692},[75,7625,2614],{"class":89},[75,7627,7605],{"class":113},[75,7629,7630,7632,7634,7636,7638],{"class":77,"line":4407},[75,7631,7588],{"class":113},[75,7633,257],{"class":89},[75,7635,7340],{"class":6692},[75,7637,2614],{"class":89},[75,7639,7605],{"class":113},[75,7641,7642],{"class":77,"line":4426},[75,7643,5325],{"emptyLinePlaceholder":2242},[75,7645,7646,7648,7651,7653,7655],{"class":77,"line":4861},[75,7647,6671],{"class":81},[75,7649,7650],{"class":85}," dequeue",[75,7652,90],{"class":89},[75,7654,6680],{"class":6679},[75,7656,103],{"class":89},[75,7658,7659,7661,7663,7665,7667,7669],{"class":77,"line":4870},[75,7660,138],{"class":109},[75,7662,6766],{"class":113},[75,7664,257],{"class":89},[75,7666,7221],{"class":6692},[75,7668,7577],{"class":89},[75,7670,5363],{"class":89},[75,7672,7673,7675,7677,7679,7681,7684,7686],{"class":77,"line":7149},[75,7674,6777],{"class":109},[75,7676,6780],{"class":6663},[75,7678,90],{"class":89},[75,7680,6785],{"class":89},[75,7682,7683],{"class":6788},"dequeue op lege wachtrij",[75,7685,6785],{"class":89},[75,7687,3060],{"class":89},[75,7689,7690,7692,7694,7696,7698,7700,7702],{"class":77,"line":7163},[75,7691,2534],{"class":113},[75,7693,242],{"class":89},[75,7695,6766],{"class":113},[75,7697,257],{"class":89},[75,7699,7221],{"class":6692},[75,7701,257],{"class":89},[75,7703,7704],{"class":6692},"waarde\n",[75,7706,7707,7709,7711,7713,7715,7717,7719,7721,7723],{"class":77,"line":7168},[75,7708,6687],{"class":113},[75,7710,257],{"class":89},[75,7712,7221],{"class":6692},[75,7714,2614],{"class":89},[75,7716,6766],{"class":113},[75,7718,257],{"class":89},[75,7720,7221],{"class":6692},[75,7722,257],{"class":89},[75,7724,7725],{"class":6692},"volgende\n",[75,7727,7729,7731,7733,7735,7737,7739,7741],{"class":77,"line":7728},25,[75,7730,138],{"class":109},[75,7732,6766],{"class":113},[75,7734,257],{"class":89},[75,7736,7221],{"class":6692},[75,7738,7577],{"class":89},[75,7740,7580],{"class":89},[75,7742,7743],{"class":170},"  # wachtrij is nu leeg\n",[75,7745,7747,7749,7751,7753,7755],{"class":77,"line":7746},26,[75,7748,7588],{"class":113},[75,7750,257],{"class":89},[75,7752,7340],{"class":6692},[75,7754,2614],{"class":89},[75,7756,7757],{"class":89}," None\n",[75,7759,7761,7763],{"class":77,"line":7760},27,[75,7762,4173],{"class":109},[75,7764,7765],{"class":113}," x\n",[63,7767,7768],{"v-slot:java":65},[67,7769,7771],{"className":192,"code":7770,"language":194,"meta":65,"style":65},"class Wachtrij {\n    private static class Knoop {\n        int waarde;\n        Knoop volgende;\n\n        Knoop(int waarde) {\n            this.waarde = waarde;\n        }\n    }\n\n    private Knoop head; \u002F\u002F voorkant: hier gaat het eruit\n    private Knoop tail; \u002F\u002F achterkant: hier komt het erbij\n\n    void enqueue(int x) {\n        Knoop knoop = new Knoop(x);\n        if (tail == null) { \u002F\u002F lege wachtrij\n            head = tail = knoop;\n        } else {\n            tail.volgende = knoop;\n            tail = knoop;\n        }\n    }\n\n    int dequeue() {\n        if (head == null) {\n            throw new IllegalStateException(\"dequeue op lege wachtrij\");\n        }\n        int x = head.waarde;\n        head = head.volgende;\n        if (head == null) { \u002F\u002F wachtrij is nu leeg\n            tail = null;\n        }\n        return x;\n    }\n}\n",[30,7772,7773,7781,7795,7803,7812,7816,7830,7844,7848,7852,7856,7870,7884,7888,7904,7923,7943,7960,7968,7984,7995,7999,8003,8007,8017,8032,8050,8054,8071,8087,8105,8115,8120,8129,8134],{"__ignoreMap":65},[75,7774,7775,7777,7779],{"class":77,"line":78},[75,7776,6660],{"class":81},[75,7778,7483],{"class":6663},[75,7780,229],{"class":89},[75,7782,7783,7785,7788,7791,7793],{"class":77,"line":106},[75,7784,6924],{"class":81},[75,7786,7787],{"class":81}," static",[75,7789,7790],{"class":81}," class",[75,7792,7417],{"class":6663},[75,7794,229],{"class":89},[75,7796,7797,7799,7801],{"class":77,"line":135},[75,7798,1075],{"class":81},[75,7800,7434],{"class":113},[75,7802,1050],{"class":89},[75,7804,7805,7808,7810],{"class":77,"line":161},[75,7806,7807],{"class":81},"        Knoop",[75,7809,7439],{"class":113},[75,7811,1050],{"class":89},[75,7813,7814],{"class":77,"line":174},[75,7815,5325],{"emptyLinePlaceholder":2242},[75,7817,7818,7820,7822,7824,7826,7828],{"class":77,"line":311},[75,7819,7807],{"class":85},[75,7821,90],{"class":89},[75,7823,212],{"class":81},[75,7825,7434],{"class":93},[75,7827,226],{"class":89},[75,7829,229],{"class":89},[75,7831,7832,7835,7838,7840,7842],{"class":77,"line":317},[75,7833,7834],{"class":89},"            this.",[75,7836,7837],{"class":113},"waarde ",[75,7839,242],{"class":89},[75,7841,7434],{"class":113},[75,7843,1050],{"class":89},[75,7845,7846],{"class":77,"line":331},[75,7847,308],{"class":89},[75,7849,7850],{"class":77,"line":951},[75,7851,314],{"class":89},[75,7853,7854],{"class":77,"line":959},[75,7855,5325],{"emptyLinePlaceholder":2242},[75,7857,7858,7860,7862,7865,7867],{"class":77,"line":977},[75,7859,6924],{"class":81},[75,7861,7417],{"class":81},[75,7863,7864],{"class":113}," head",[75,7866,248],{"class":89},[75,7868,7869],{"class":170}," \u002F\u002F voorkant: hier gaat het eruit\n",[75,7871,7872,7874,7876,7879,7881],{"class":77,"line":1214},[75,7873,6924],{"class":81},[75,7875,7417],{"class":81},[75,7877,7878],{"class":113}," tail",[75,7880,248],{"class":89},[75,7882,7883],{"class":170}," \u002F\u002F achterkant: hier komt het erbij\n",[75,7885,7886],{"class":77,"line":1219},[75,7887,5325],{"emptyLinePlaceholder":2242},[75,7889,7890,7892,7894,7896,7898,7900,7902],{"class":77,"line":1232},[75,7891,6959],{"class":81},[75,7893,7539],{"class":85},[75,7895,90],{"class":89},[75,7897,212],{"class":81},[75,7899,100],{"class":93},[75,7901,226],{"class":89},[75,7903,229],{"class":89},[75,7905,7906,7908,7911,7913,7915,7917,7919,7921],{"class":77,"line":1949},[75,7907,7807],{"class":81},[75,7909,7910],{"class":113}," knoop ",[75,7912,242],{"class":89},[75,7914,4627],{"class":109},[75,7916,7417],{"class":85},[75,7918,90],{"class":89},[75,7920,389],{"class":113},[75,7922,5795],{"class":89},[75,7924,7925,7927,7929,7932,7935,7938,7940],{"class":77,"line":1959},[75,7926,138],{"class":109},[75,7928,23],{"class":89},[75,7930,7931],{"class":113},"tail ",[75,7933,7934],{"class":89},"==",[75,7936,7937],{"class":89}," null)",[75,7939,1067],{"class":89},[75,7941,7942],{"class":170}," \u002F\u002F lege wachtrij\n",[75,7944,7945,7948,7950,7953,7955,7958],{"class":77,"line":4386},[75,7946,7947],{"class":113},"            head ",[75,7949,242],{"class":89},[75,7951,7952],{"class":113}," tail ",[75,7954,242],{"class":89},[75,7956,7957],{"class":113}," knoop",[75,7959,1050],{"class":89},[75,7961,7962,7964,7966],{"class":77,"line":4407},[75,7963,1141],{"class":89},[75,7965,1144],{"class":109},[75,7967,229],{"class":89},[75,7969,7970,7973,7975,7978,7980,7982],{"class":77,"line":4426},[75,7971,7972],{"class":113},"            tail",[75,7974,257],{"class":89},[75,7976,7977],{"class":113},"volgende ",[75,7979,242],{"class":89},[75,7981,7957],{"class":113},[75,7983,1050],{"class":89},[75,7985,7986,7989,7991,7993],{"class":77,"line":4861},[75,7987,7988],{"class":113},"            tail ",[75,7990,242],{"class":89},[75,7992,7957],{"class":113},[75,7994,1050],{"class":89},[75,7996,7997],{"class":77,"line":4870},[75,7998,308],{"class":89},[75,8000,8001],{"class":77,"line":7149},[75,8002,314],{"class":89},[75,8004,8005],{"class":77,"line":7163},[75,8006,5325],{"emptyLinePlaceholder":2242},[75,8008,8009,8011,8013,8015],{"class":77,"line":7168},[75,8010,1024],{"class":81},[75,8012,7650],{"class":85},[75,8014,7008],{"class":89},[75,8016,229],{"class":89},[75,8018,8019,8021,8023,8026,8028,8030],{"class":77,"line":7728},[75,8020,138],{"class":109},[75,8022,23],{"class":89},[75,8024,8025],{"class":113},"head ",[75,8027,7934],{"class":89},[75,8029,7937],{"class":89},[75,8031,229],{"class":89},[75,8033,8034,8036,8038,8040,8042,8044,8046,8048],{"class":77,"line":7746},[75,8035,7033],{"class":109},[75,8037,4627],{"class":109},[75,8039,7038],{"class":85},[75,8041,90],{"class":89},[75,8043,6785],{"class":89},[75,8045,7683],{"class":6788},[75,8047,6785],{"class":89},[75,8049,5795],{"class":89},[75,8051,8052],{"class":77,"line":7760},[75,8053,308],{"class":89},[75,8055,8057,8059,8061,8063,8065,8067,8069],{"class":77,"line":8056},28,[75,8058,1075],{"class":81},[75,8060,2726],{"class":113},[75,8062,242],{"class":89},[75,8064,7864],{"class":113},[75,8066,257],{"class":89},[75,8068,7450],{"class":113},[75,8070,1050],{"class":89},[75,8072,8074,8077,8079,8081,8083,8085],{"class":77,"line":8073},29,[75,8075,8076],{"class":113},"        head ",[75,8078,242],{"class":89},[75,8080,7864],{"class":113},[75,8082,257],{"class":89},[75,8084,6071],{"class":113},[75,8086,1050],{"class":89},[75,8088,8090,8092,8094,8096,8098,8100,8102],{"class":77,"line":8089},30,[75,8091,138],{"class":109},[75,8093,23],{"class":89},[75,8095,8025],{"class":113},[75,8097,7934],{"class":89},[75,8099,7937],{"class":89},[75,8101,1067],{"class":89},[75,8103,8104],{"class":170}," \u002F\u002F wachtrij is nu leeg\n",[75,8106,8108,8110,8112],{"class":77,"line":8107},31,[75,8109,7988],{"class":113},[75,8111,242],{"class":89},[75,8113,8114],{"class":89}," null;\n",[75,8116,8118],{"class":77,"line":8117},32,[75,8119,308],{"class":89},[75,8121,8123,8125,8127],{"class":77,"line":8122},33,[75,8124,4173],{"class":109},[75,8126,100],{"class":113},[75,8128,1050],{"class":89},[75,8130,8132],{"class":77,"line":8131},34,[75,8133,314],{"class":89},[75,8135,8137],{"class":77,"line":8136},35,[75,8138,334],{"class":89},[10,8140,8141,8142,8144,8145,8147,8148,8150,8151,8153,8154,8157,8158,8160],{},"Let op de randgevallen: bij de eerste ",[30,8143,7390],{}," moeten ",[30,8146,7221],{}," én ",[30,8149,7340],{}," naar de nieuwe knoop wijzen,\nen als de laatste knoop eruit gaat moet ",[30,8152,7340],{}," weer ",[30,8155,8156],{},"null"," worden. Vergeet je dat, dan wijst ",[30,8159,7340],{},"\nnaar een knoop die niet meer in de lijst zit.",[47,8162,8164],{"id":8163},"toepassing-haakjes-controleren","Toepassing: haakjes controleren",[10,8166,8167,8168,8171,8172,8175,8176,8179],{},"Klopt ",[30,8169,8170],{},"{[()()]}","? En ",[30,8173,8174],{},"([)]","? Elk sluithaakje moet passen bij het ",[14,8177,8178],{},"laatst geopende"," haakje dat nog\nopen staat. \"Laatst geopend, eerst gesloten\": dat is LIFO, dus een stapel.",[10,8181,8182,8183,8185,8186,8188],{},"Het algoritme: openingshaakje → ",[30,8184,7369],{},". Sluithaakje → ",[30,8187,6808],{}," en controleer of het bijbehorende\nopeningshaakje eruit komt. Aan het eind moet de stapel leeg zijn.",[446,8190,8191,8202],{},[449,8192,8193],{},[452,8194,8195,8198,8200],{},[455,8196,8197],{},"Teken",[455,8199,547],{},[455,8201,6305],{},[488,8203,8204,8217,8230,8243,8259,8271,8285,8299],{},[452,8205,8206,8211,8213],{},[493,8207,8208],{},[30,8209,8210],{},"{",[493,8212,7369],{},[493,8214,8215],{},[30,8216,8210],{},[452,8218,8219,8223,8225],{},[493,8220,8221],{},[30,8222,144],{},[493,8224,7369],{},[493,8226,8227],{},[30,8228,8229],{},"{ [",[452,8231,8232,8236,8238],{},[493,8233,8234],{},[30,8235,90],{},[493,8237,7369],{},[493,8239,8240],{},[30,8241,8242],{},"{ [ (",[452,8244,8245,8249,8255],{},[493,8246,8247],{},[30,8248,226],{},[493,8250,8251,8252,8254],{},"pop ",[30,8253,90],{},", past",[493,8256,8257],{},[30,8258,8229],{},[452,8260,8261,8265,8267],{},[493,8262,8263],{},[30,8264,90],{},[493,8266,7369],{},[493,8268,8269],{},[30,8270,8242],{},[452,8272,8273,8277,8281],{},[493,8274,8275],{},[30,8276,226],{},[493,8278,8251,8279,8254],{},[30,8280,90],{},[493,8282,8283],{},[30,8284,8229],{},[452,8286,8287,8291,8295],{},[493,8288,8289],{},[30,8290,150],{},[493,8292,8251,8293,8254],{},[30,8294,144],{},[493,8296,8297],{},[30,8298,8210],{},[452,8300,8301,8306,8310],{},[493,8302,8303],{},[30,8304,8305],{},"}",[493,8307,8251,8308,8254],{},[30,8309,8210],{},[493,8311,8312],{},"leeg",[10,8314,8315,8316,8318,8319,8321,8322,8324,8325,8327,8328,8330,8331,8334,8335,8337],{},"De stapel is leeg aan het einde: ",[30,8317,8170],{}," klopt. Bij ",[30,8320,8174],{}," gaat het mis bij het derde teken:\n",[30,8323,226],{}," komt binnen, maar ",[30,8326,6808],{}," levert ",[30,8329,144],{}," op. Fout. En bij ",[30,8332,8333],{},"(()"," blijft er aan het eind een ",[30,8336,90],{}," op de\nstapel staan: ook fout.",[60,8339,8340,8548],{},[63,8341,8342],{"v-slot:python":65},[67,8343,8345],{"className":69,"code":8344,"language":71,"meta":65,"style":65},"def haakjes_kloppen(s):\n    paren = {\")\": \"(\", \"]\": \"[\", \"}\": \"{\"}\n    stapel = []\n    for c in s:\n        if c in \"([{\":\n            stapel.append(c)  # openingshaakje: push\n        elif c in paren:\n            # sluithaakje: de bovenkant moet het juiste openingshaakje zijn\n            if not stapel or stapel.pop() != paren[c]:\n                return False\n    return not stapel  # alles moet gesloten zijn\n",[30,8346,8347,8361,8419,8428,8442,8459,8478,8491,8496,8528,8536],{"__ignoreMap":65},[75,8348,8349,8351,8354,8356,8359],{"class":77,"line":78},[75,8350,82],{"class":81},[75,8352,8353],{"class":85}," haakjes_kloppen",[75,8355,90],{"class":89},[75,8357,8358],{"class":93},"s",[75,8360,103],{"class":89},[75,8362,8363,8366,8368,8370,8372,8374,8376,8378,8381,8383,8385,8387,8389,8391,8393,8395,8397,8399,8401,8403,8405,8407,8409,8411,8413,8415,8417],{"class":77,"line":106},[75,8364,8365],{"class":113},"    paren ",[75,8367,242],{"class":89},[75,8369,1067],{"class":89},[75,8371,6785],{"class":89},[75,8373,226],{"class":6788},[75,8375,6785],{"class":89},[75,8377,854],{"class":89},[75,8379,8380],{"class":89}," \"",[75,8382,90],{"class":6788},[75,8384,6785],{"class":89},[75,8386,97],{"class":89},[75,8388,8380],{"class":89},[75,8390,150],{"class":6788},[75,8392,6785],{"class":89},[75,8394,854],{"class":89},[75,8396,8380],{"class":89},[75,8398,144],{"class":6788},[75,8400,6785],{"class":89},[75,8402,97],{"class":89},[75,8404,8380],{"class":89},[75,8406,8305],{"class":6788},[75,8408,6785],{"class":89},[75,8410,854],{"class":89},[75,8412,8380],{"class":89},[75,8414,8210],{"class":6788},[75,8416,6785],{"class":89},[75,8418,334],{"class":89},[75,8420,8421,8424,8426],{"class":77,"line":135},[75,8422,8423],{"class":113},"    stapel ",[75,8425,242],{"class":89},[75,8427,4251],{"class":89},[75,8429,8430,8432,8435,8437,8440],{"class":77,"line":161},[75,8431,110],{"class":109},[75,8433,8434],{"class":113}," c ",[75,8436,117],{"class":109},[75,8438,8439],{"class":113}," s",[75,8441,158],{"class":89},[75,8443,8444,8446,8448,8450,8452,8455,8457],{"class":77,"line":174},[75,8445,138],{"class":109},[75,8447,8434],{"class":113},[75,8449,117],{"class":89},[75,8451,8380],{"class":89},[75,8453,8454],{"class":6788},"([{",[75,8456,6785],{"class":89},[75,8458,158],{"class":89},[75,8460,8461,8464,8466,8468,8470,8473,8475],{"class":77,"line":311},[75,8462,8463],{"class":113},"            stapel",[75,8465,257],{"class":89},[75,8467,4331],{"class":85},[75,8469,90],{"class":89},[75,8471,8472],{"class":85},"c",[75,8474,226],{"class":89},[75,8476,8477],{"class":170},"  # openingshaakje: push\n",[75,8479,8480,8482,8484,8486,8489],{"class":77,"line":317},[75,8481,915],{"class":109},[75,8483,8434],{"class":113},[75,8485,117],{"class":89},[75,8487,8488],{"class":113}," paren",[75,8490,158],{"class":89},[75,8492,8493],{"class":77,"line":331},[75,8494,8495],{"class":170},"            # sluithaakje: de bovenkant moet het juiste openingshaakje zijn\n",[75,8497,8498,8500,8502,8505,8508,8511,8513,8515,8517,8520,8522,8524,8526],{"class":77,"line":951},[75,8499,3125],{"class":109},[75,8501,6763],{"class":89},[75,8503,8504],{"class":113}," stapel ",[75,8506,8507],{"class":89},"or",[75,8509,8510],{"class":113}," stapel",[75,8512,257],{"class":89},[75,8514,6808],{"class":85},[75,8516,7008],{"class":89},[75,8518,8519],{"class":89}," !=",[75,8521,8488],{"class":113},[75,8523,144],{"class":89},[75,8525,8472],{"class":113},[75,8527,3145],{"class":89},[75,8529,8530,8533],{"class":77,"line":959},[75,8531,8532],{"class":109},"                return",[75,8534,8535],{"class":89}," False\n",[75,8537,8538,8540,8542,8545],{"class":77,"line":977},[75,8539,177],{"class":109},[75,8541,6763],{"class":89},[75,8543,8544],{"class":113}," stapel  ",[75,8546,8547],{"class":170},"# alles moet gesloten zijn\n",[63,8549,8550],{"v-slot:java":65},[67,8551,8553],{"className":192,"code":8552,"language":194,"meta":65,"style":65},"static boolean haakjesKloppen(String s) {\n    java.util.ArrayDeque\u003CCharacter> stapel = new java.util.ArrayDeque\u003C>();\n    for (char c : s.toCharArray()) {\n        if (c == '(' || c == '[' || c == '{') {\n            stapel.push(c); \u002F\u002F openingshaakje: push\n        } else if (c == ')' || c == ']' || c == '}') {\n            char verwacht = c == ')' ? '(' : c == ']' ? '[' : '{';\n            \u002F\u002F sluithaakje: de bovenkant moet het juiste openingshaakje zijn\n            if (stapel.isEmpty() || stapel.pop() != verwacht) {\n                return false;\n            }\n        }\n    }\n    return stapel.isEmpty(); \u002F\u002F alles moet gesloten zijn\n}\n",[30,8554,8555,8576,8614,8638,8686,8703,8751,8811,8816,8849,8856,8860,8864,8868,8884],{"__ignoreMap":65},[75,8556,8557,8559,8562,8565,8567,8570,8572,8574],{"class":77,"line":78},[75,8558,201],{"class":81},[75,8560,8561],{"class":81}," boolean",[75,8563,8564],{"class":85}," haakjesKloppen",[75,8566,90],{"class":89},[75,8568,8569],{"class":81},"String",[75,8571,8439],{"class":113},[75,8573,226],{"class":89},[75,8575,229],{"class":89},[75,8577,8578,8581,8583,8585,8587,8589,8591,8594,8596,8598,8600,8602,8604,8606,8608,8610,8612],{"class":77,"line":106},[75,8579,8580],{"class":81},"    java",[75,8582,257],{"class":89},[75,8584,4536],{"class":81},[75,8586,257],{"class":89},[75,8588,7194],{"class":81},[75,8590,32],{"class":89},[75,8592,8593],{"class":81},"Character",[75,8595,6938],{"class":89},[75,8597,8504],{"class":113},[75,8599,242],{"class":89},[75,8601,4627],{"class":109},[75,8603,6897],{"class":81},[75,8605,257],{"class":89},[75,8607,4536],{"class":81},[75,8609,257],{"class":89},[75,8611,7194],{"class":81},[75,8613,6950],{"class":89},[75,8615,8616,8618,8620,8623,8625,8627,8629,8631,8634,8636],{"class":77,"line":135},[75,8617,110],{"class":109},[75,8619,23],{"class":89},[75,8621,8622],{"class":81},"char",[75,8624,8434],{"class":113},[75,8626,854],{"class":109},[75,8628,8439],{"class":113},[75,8630,257],{"class":89},[75,8632,8633],{"class":85},"toCharArray",[75,8635,7026],{"class":89},[75,8637,229],{"class":89},[75,8639,8640,8642,8644,8647,8649,8652,8654,8657,8660,8662,8664,8666,8668,8670,8672,8674,8676,8678,8680,8682,8684],{"class":77,"line":161},[75,8641,138],{"class":109},[75,8643,23],{"class":89},[75,8645,8646],{"class":113},"c ",[75,8648,7934],{"class":89},[75,8650,8651],{"class":89}," '",[75,8653,90],{"class":6788},[75,8655,8656],{"class":89},"'",[75,8658,8659],{"class":89}," ||",[75,8661,8434],{"class":113},[75,8663,7934],{"class":89},[75,8665,8651],{"class":89},[75,8667,144],{"class":6788},[75,8669,8656],{"class":89},[75,8671,8659],{"class":89},[75,8673,8434],{"class":113},[75,8675,7934],{"class":89},[75,8677,8651],{"class":89},[75,8679,8210],{"class":6788},[75,8681,8656],{"class":89},[75,8683,226],{"class":89},[75,8685,229],{"class":89},[75,8687,8688,8690,8692,8694,8696,8698,8700],{"class":77,"line":174},[75,8689,8463],{"class":113},[75,8691,257],{"class":89},[75,8693,7369],{"class":85},[75,8695,90],{"class":89},[75,8697,8472],{"class":113},[75,8699,6988],{"class":89},[75,8701,8702],{"class":170}," \u002F\u002F openingshaakje: push\n",[75,8704,8705,8707,8709,8711,8713,8715,8717,8719,8721,8723,8725,8727,8729,8731,8733,8735,8737,8739,8741,8743,8745,8747,8749],{"class":77,"line":311},[75,8706,1141],{"class":89},[75,8708,1144],{"class":109},[75,8710,1147],{"class":109},[75,8712,23],{"class":89},[75,8714,8646],{"class":113},[75,8716,7934],{"class":89},[75,8718,8651],{"class":89},[75,8720,226],{"class":6788},[75,8722,8656],{"class":89},[75,8724,8659],{"class":89},[75,8726,8434],{"class":113},[75,8728,7934],{"class":89},[75,8730,8651],{"class":89},[75,8732,150],{"class":6788},[75,8734,8656],{"class":89},[75,8736,8659],{"class":89},[75,8738,8434],{"class":113},[75,8740,7934],{"class":89},[75,8742,8651],{"class":89},[75,8744,8305],{"class":6788},[75,8746,8656],{"class":89},[75,8748,226],{"class":89},[75,8750,229],{"class":89},[75,8752,8753,8756,8759,8761,8763,8765,8767,8769,8771,8774,8776,8778,8780,8783,8785,8787,8789,8791,8793,8795,8797,8799,8801,8803,8805,8807,8809],{"class":77,"line":317},[75,8754,8755],{"class":81},"            char",[75,8757,8758],{"class":113}," verwacht ",[75,8760,242],{"class":89},[75,8762,8434],{"class":113},[75,8764,7934],{"class":89},[75,8766,8651],{"class":89},[75,8768,226],{"class":6788},[75,8770,8656],{"class":89},[75,8772,8773],{"class":109}," ?",[75,8775,8651],{"class":89},[75,8777,90],{"class":6788},[75,8779,8656],{"class":89},[75,8781,8782],{"class":109}," :",[75,8784,8434],{"class":113},[75,8786,7934],{"class":89},[75,8788,8651],{"class":89},[75,8790,150],{"class":6788},[75,8792,8656],{"class":89},[75,8794,8773],{"class":109},[75,8796,8651],{"class":89},[75,8798,144],{"class":6788},[75,8800,8656],{"class":89},[75,8802,8782],{"class":109},[75,8804,8651],{"class":89},[75,8806,8210],{"class":6788},[75,8808,8656],{"class":89},[75,8810,1050],{"class":89},[75,8812,8813],{"class":77,"line":331},[75,8814,8815],{"class":170},"            \u002F\u002F sluithaakje: de bovenkant moet het juiste openingshaakje zijn\n",[75,8817,8818,8820,8822,8824,8826,8828,8830,8832,8834,8836,8838,8840,8842,8845,8847],{"class":77,"line":951},[75,8819,3125],{"class":109},[75,8821,23],{"class":89},[75,8823,6214],{"class":113},[75,8825,257],{"class":89},[75,8827,7023],{"class":85},[75,8829,7008],{"class":89},[75,8831,8659],{"class":89},[75,8833,8510],{"class":113},[75,8835,257],{"class":89},[75,8837,6808],{"class":85},[75,8839,7008],{"class":89},[75,8841,8519],{"class":89},[75,8843,8844],{"class":113}," verwacht",[75,8846,226],{"class":89},[75,8848,229],{"class":89},[75,8850,8851,8853],{"class":77,"line":959},[75,8852,8532],{"class":109},[75,8854,8855],{"class":89}," false;\n",[75,8857,8858],{"class":77,"line":977},[75,8859,3376],{"class":89},[75,8861,8862],{"class":77,"line":1214},[75,8863,308],{"class":89},[75,8865,8866],{"class":77,"line":1219},[75,8867,314],{"class":89},[75,8869,8870,8872,8874,8876,8878,8881],{"class":77,"line":1232},[75,8871,177],{"class":109},[75,8873,8510],{"class":113},[75,8875,257],{"class":89},[75,8877,7023],{"class":85},[75,8879,8880],{"class":89},"();",[75,8882,8883],{"class":170}," \u002F\u002F alles moet gesloten zijn\n",[75,8885,8886],{"class":77,"line":1949},[75,8887,334],{"class":89},[47,8889,8891],{"id":8890},"meer-toepassingen","Meer toepassingen",[446,8893,8894,8906],{},[449,8895,8896],{},[452,8897,8898,8901,8904],{},[455,8899,8900],{},"Toepassing",[455,8902,8903],{},"Structuur",[455,8905,1280],{},[488,8907,8908,8918,8930,8941,8951,8965],{},[452,8909,8910,8913,8915],{},[493,8911,8912],{},"Undo in een editor",[493,8914,6214],{},[493,8916,8917],{},"de laatste wijziging maak je als eerste ongedaan",[452,8919,8920,8925,8927],{},[493,8921,8922,8923,226],{},"Functieaanroepen (",[25,8924,6228],{},[493,8926,6214],{},[493,8928,8929],{},"de laatst aangeroepen functie keert als eerste terug",[452,8931,8932,8935,8938],{},[493,8933,8934],{},"DFS in een graaf",[493,8936,8937],{},"stapel (of recursie)",[493,8939,8940],{},"ga zo diep mogelijk, keer terug naar de laatste splitsing",[452,8942,8943,8946,8948],{},[493,8944,8945],{},"Printerwachtrij",[493,8947,6221],{},[493,8949,8950],{},"opdrachten in volgorde van binnenkomst",[452,8952,8953,8960,8962],{},[493,8954,8955,8956],{},"BFS in een ",[94,8957,8959],{"href":8958},"\u002Fpracticely\u002Fdsa\u002Fgrafen","graaf",[493,8961,6221],{},[493,8963,8964],{},"knopen per laag verwerken, dichtstbijzijnde eerst",[452,8966,8967,8970,8972],{},[493,8968,8969],{},"Verzoeken op een webserver",[493,8971,6221],{},[493,8973,8974],{},"eerlijk: wie eerst komt, wordt eerst bediend",[10,8976,8977,8978,257],{},"Wil je in plaats van \"eerst binnen\" juist \"kleinste eerst\" verwerken, dan heb je een\nprioriteitswachtrij nodig. Die bouw je met een ",[94,8979,8981],{"href":8980},"\u002Fpracticely\u002Fdsa\u002Fheaps","heap",[47,8983,1979],{"id":1978},[446,8985,8986,9009],{},[449,8987,8988],{},[452,8989,8990,8992,8995,8998,9006],{},[455,8991,6299],{},[455,8993,8994],{},"Stapel (array)",[455,8996,8997],{},"Stapel (gelinkte lijst)",[455,8999,9000,9001,4510,9004,226],{},"Wachtrij (",[30,9002,9003],{},"deque",[30,9005,7194],{},[455,9007,9008],{},"Wachtrij (gelinkte lijst met tail)",[488,9010,9011,9036,9060,9086],{},[452,9012,9013,9020,9024,9028,9032],{},[493,9014,9015,9017,9018],{},[30,9016,7369],{}," \u002F ",[30,9019,7390],{},[493,9021,9022,6040],{},[30,9023,2042],{},[493,9025,9026],{},[30,9027,2042],{},[493,9029,9030,6040],{},[30,9031,2042],{},[493,9033,9034],{},[30,9035,2042],{},[452,9037,9038,9044,9048,9052,9056],{},[493,9039,9040,9017,9042],{},[30,9041,6808],{},[30,9043,7176],{},[493,9045,9046],{},[30,9047,2042],{},[493,9049,9050],{},[30,9051,2042],{},[493,9053,9054],{},[30,9055,2042],{},[493,9057,9058],{},[30,9059,2042],{},[452,9061,9062,9070,9074,9078,9082],{},[493,9063,9064,9017,9067],{},[30,9065,9066],{},"peek",[30,9068,9069],{},"front",[493,9071,9072],{},[30,9073,2042],{},[493,9075,9076],{},[30,9077,2042],{},[493,9079,9080],{},[30,9081,2042],{},[493,9083,9084],{},[30,9085,2042],{},[452,9087,9088,9091,9095,9099,9103],{},[493,9089,9090],{},"zoeken naar een waarde",[493,9092,9093],{},[30,9094,345],{},[493,9096,9097],{},[30,9098,345],{},[493,9100,9101],{},[30,9102,345],{},[493,9104,9105],{},[30,9106,345],{},[10,9108,9109,9110,9113,9114,9116],{},"\"Gemiddeld\" (",[25,9111,9112],{},"amortized",") bij de array: meestal is er nog plek, maar af en toe moet de array\nverdubbelen en wordt alles gekopieerd. Verdeeld over alle operaties is dat nog steeds ",[30,9115,2042],{}," per\noperatie.",[47,9118,2120],{"id":2119},[370,9120,9121,9137,9149,9167,9176],{},[373,9122,9123,9126,9127,9130,9131,2143,9133,9136],{},[14,9124,9125],{},"De stapel in de verkeerde richting opschrijven."," Wij noteren van onder naar boven: na\n",[30,9128,9129],{},"push(4), push(7)"," is het ",[30,9132,6338],{},[30,9134,9135],{},"7, 4",". Het meest rechtse element gaat er als eerste af.",[373,9138,9139,2136,9142,9144,9145,9148],{},[14,9140,9141],{},"Bij de wachtrij aan de verkeerde kant weghalen.",[30,9143,7176],{}," haalt het element weg dat het\nlangst wacht, dus het meest ",[14,9146,9147],{},"linkse"," in de notatie voor → achter.",[373,9150,9151,9154,9155,41,9158,2136,9161,9163,9164,9166],{},[14,9152,9153],{},"Een gewone lijst als wachtrij gebruiken"," en denken dat ",[30,9156,9157],{},"pop(0)",[30,9159,9160],{},"remove(0)",[30,9162,2042],{}," is. Het\nis ",[30,9165,345],{},", want alles schuift op.",[373,9168,9169,9172,9173,9175],{},[14,9170,9171],{},"Bij haakjes controleren vergeten te kijken of de stapel aan het eind leeg is."," Dan keur je\n",[30,9174,8333],{}," ten onrechte goed.",[373,9177,9178,9183,9184,9186,9187,257],{},[14,9179,9180,9182],{},[30,9181,7340],{}," niet bijwerken"," in een gelinkte wachtrij als de laatste knoop verdwijnt, of ",[30,9185,7221],{},"\nvergeten bij de eerste ",[30,9188,7390],{},[47,9190,2186],{"id":2185},[1325,9192,9193,9203,9214,9223,9231],{},[373,9194,9195,9196,402,9198,364,9200,9202],{},"Stapel = ",[14,9197,6242],{},[30,9199,7369],{},[30,9201,6808],{}," aan dezelfde kant; noteer van onder naar boven.",[373,9204,9205,9206,402,9208,9210,9211,9213],{},"Wachtrij = ",[14,9207,6438],{},[30,9209,7390],{}," achteraan, ",[30,9212,7176],{}," vooraan; noteer van voor naar achter.",[373,9215,9216,9217,9219,9220,9222],{},"Alle kernoperaties zijn ",[30,9218,2042],{},", mits je de juiste implementatie kiest (geen ",[30,9221,9157],{}," op een lijst).",[373,9224,9225,9226,9228,9229,257],{},"Een enkel gelinkte lijst kan vooraan invoegen en verwijderen in ",[30,9227,2042],{},", maar indexeren kost ",[30,9230,345],{},[373,9232,9233],{},"Stapel: haakjes, undo, call stack, DFS. 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