||Allgemeine Sortierfunktionen

||1. Sortieren durch Einfügen 
|| T esort (n) = O(n^2)

esort = foldr insert []
esortl = foldl (converse insert)

insert a [] =[a]
insert a (b:l) = a:b:l, if a<=b
               = b:insert a l, otherwise


||2. Sortieren durch Verschmelzen
|| T msort (n) = O(n log n)

msort l = l, if n<=1
         = merge (msort l1) (msort l2), otherwise
           where n=#l
                 l1 = take(n div 2) l
                 l2 = drop(n div 2) l
 
||3. Quicksort nach Tony Hoare
|| T qsort (n) = O(n^2) aber im Durchschnittsfall:
|| T qsort (n) = O(n log n), oft schneller als msort!

qsort [a] = [a]
qsort (a:l) = qsort[b|b<-l;b<=a]++[a]++qsort[b|b<-l;b>a]
qsort [] = []


l0 = [1..100]
l1 = [50,25,75,12,37,62,97]
l2 = [1000,999..1]
l3 = take 1000 (zufall 13)

zufall z = [zahl| zahl<- z, (a*zahl+c) mod p ..]
           where a = 897
                 c = 2111
                 p = 123456
                 
                 
zz n = take n (zufall 13)
%nolist
l10=[13,13772,9995,78794,63497,45704,11207,54854,70661,52100]
l100=[13,13772,9995,78794,63497,45704,11207,54854,70661,52100,69443,70658,49409,1280,39167,73406,45245,93308,119675,67322,19961,6008,82679,91574,45749,51572,89651,49202,62513,27248,122735,96110,40493,28268,50027,61802,6761,17384,40103,48806,77669,42020,39971,53858,41441,14432,108191,13022,77981,74972,91931,119066,14873,9944,33047,15830,4181,48788,61523,3410,97937,74384,58319,92366,15437,22028,8267,10250,60617,54920,6407,70214,21509,36548,69827,44738,8897,81536,53951,1406,28733,96764,9851,73082,1529,15608,51959,66422,76853,50804,18035,6770,25457,121136,19823,5678,33581,1004,38507,98666]
l1000=[13,13772,9995,78794,63497,45704,11207,54854,70661,52100,69443,70658,49409,1280,39167,73406,45245,93308,119675,67322,19961,6008,82679,91574,45749,51572,89651,49202,62513,27248,122735,96110,40493,28268,50027,61802,6761,17384,40103,48806,77669,42020,39971,53858,41441,14432,108191,13022,77981,74972,91931,119066,14873,9944,33047,15830,4181,48788,61523,3410,97937,74384,58319,92366,15437,22028,8267,10250,60617,54920,6407,70214,21509,36548,69827,44738,8897,81536,53951,1406,28733,96764,9851,73082,1529,15608,51959,66422,76853,50804,18035,6770,25457,121136,19823,5678,33581,1004,38507,98666,111017,78824,90407,110054,79205,61796,1379,4514,100577,96800,42143,26846,9053,98012,18203,34010,15449,32792,34007,12758,88085,2516,36755,8594,56657,83024,30671,106766,92813,46028,54923,9098,14921,53000,12551,25862,114053,86084,59459,3842,115073,13376,25151,93566,104189,3452,12155,41018,5369,3320,17207,4790,101237,71540,99827,41330,38321,55280,82415,101678,96749,119852,102635,90986,12137,24872,90215,61286,37733,21668,55715,102242,108833,95072,97055,23966,18269,93212,33563,108314,123353,33176,8087,95702,44885,17300,88211,115538,60113,96656,36431,88334,102413,15308,29771,40202,14153,104840,93575,112262,84485,106628,92483,120386,87809,1856,62015,74366,42173,53756,73403,42554,25145,88184,91319,63926,60149,5492,113651,95858,61361,105008,120815,102254,119597,120812,99563,51434,89321,104,95399,20006,46373,117476,70115,56162,9377,18272,95903,101726,16349,99356,112667,77402,49433,22808,90647,78422,100181,111956,56915,67538,90257,98960,4367,92174,90125,104012,91595,64586,34889,63176,4679,1670,18629,45764,65027,60098,83201,65984,54335,98942,111677,53564,24635,1082,108473,19064,65591,72182,58421,60404,110771,105074,56561,120368,71663,86702,119981,94892,59051,8234,104105,51560,78887,23462,60005,123236,51683,65762,102113,116576,3551,100958,68189,56924,75611,47834,69977,55832,83735,51158,88661,25364,37715,5522,17105,36752,5903,111950,51533,54668,27275,23498,92297,77000,59207,24710,68357,84164,65603,82946,84161,62912,14783,52670,86909,58748,106811,9722,80825,33464,19511,96182,105077,59252,65075,103154,62705,76016,40751,12782,109613,53996,41771,63530,75305,20264,30887,53606,62309,91172,55523,53474,67361,54944,27935,121694,26525,91484,88475,105434,9113,28376,23447,46550,29333,17684,62291,75026,16913,111440,87887,71822,105869,28940,35531,21770,23753,74120,68423,19910,83717,35012,50051,83330,58241,22400,95039,67454,14909,42236,110267,23354,86585,15032,29111,65462,79925,90356,64307,31538,20273,38960,11183,33326,19181,47084,14507,52010,112169,1064,92327,103910,101,92708,75299,14882,18017,114080,110303,55646,40349,22556,111515,31706,47513,28952,46295,47510,26261,101588,16019,50258,22097,70160,96527,44174,120269,106316,59531,68426,22601,28424,66503,26054,39365,4100,99587,72962,17345,5120,26879,38654,107069,117692,16955,25658,54521,18872,16823,30710,18293,114740,85043,113330,54833,51824,68783,95918,115181,110252,9899,116138,104489,25640,38375,103718,74789,51236,35171,69218,115745,122336,108575,110558,37469,31772,106715,47066,121817,13400,46679,21590,109205,58388,30803,101714,5585,73616,110159,49934,101837,115916,28811,43274,53705,27656,118343,107078,2309,97988,120131,105986,10433,101312,15359,75518,87869,55676,67259,86906,56057,38648,101687,104822,77429,73652,18995,3698,109361,74864,118511,10862,115757,9644,10859,113066,64937,102824,13607,108902,33509,59876,7523,83618,69665,22880,31775,109406,115229,29852,112859,2714,90905,62936,36311,104150,91925,113684,2003,70418,81041,103760,112463,17870,105677,103628,117515,105098,78089,48392,76679,18182,15173,32132,59267,78530,73601,96704,79487,67838,112445,1724,67067,38138,14585,121976,32567,79094,85685,71924,73907,818,118577,70064,10415,85166,100205,10028,108395,72554,21737,117608,65063,92390,36965,73508,13283,65186,79265,115616,6623,17054,114461,81692,70427,89114,61337,83480,69335,97238,64661,102164,38867,51218,19025,30608,50255,19406,1997,65036,68171,40778,37001,105800,90503,72710,38213,81860,97667,79106,96449,97664,76415,28286,66173,100412,72251,120314,23225,94328,46967,33014,109685,118580,72755,78578,116657,76208,89519,54254,26285,123116,67499,55274,77033,88808,33767,44390,67109,75812,104675,69026,66977,80864,68447,41438,11741,40028,104987,101978,118937,22616,41879,36950,60053,42836,31187,75794,88529,30416,1487,101390,85325,119372,42443,49034,35273,37256,87623,81926,33413,97220,48515,63554,96833,71744,35903,108542,80957,28412,55739,314,36857,100088,28535,42614,78965,93428,103859,77810,45041,33776,52463,24686,46829,32684,60587,28010,65513,2216,14567,105830,117413,13604,106211,88802,28385,31520,4127,350,69149,53852,36059,1562,45209,61016,42455,59798,61013,39764,115091,29522,63761,35600,83663,110030,57677,10316,119819,73034,81929,36104,41927,80006,39557,52868,17603,113090,86465,30848,18623,40382,52157,120572,7739,30458,39161,68024,32375,30326,44213,31796,4787,98546,3377,68336,65327,82286,109421,5228,299,23402,6185,117992,39143,51878,117221,88292,64739,48674,82721,5792,12383,122078,605,50972,45275,120218,60569,11864,26903,60182,35093,122708,71891,44306,115217,19088,87119,206,63437,115340,5963,42314,56777,67208,41159,8390,120581,15812,111491,10178,119489,23936,114815,28862,89021,101372,69179,80762,100409,69560,52151,115190,118325,90932,87155,32498,17201,122864,88367,8558,24365,5804,23147,24362,3113,78440,116327,27110,122405,47012,73379,21026,97121,83168,36383,45278,122909,5276,43355,2906,16217,104408,76439,49814,117653,105428,3731,15506,83921,94544,117263,2510,31373,119180,117131,7562,118601,91592,61895,90182,31685,28676,45635,72770,92033,87104,110207,92990,81341,2492,15227,80570,51641,28088,12023,46070,92597,99188,85427,87410,14321,8624,83567,23918,98669,113708,23531,121898,86057,35240,7655,78566,105893,50468,87011,26786,78689,92768,5663,20126,30557,4508,95195,83930,102617,74840,96983,82838,110741,78164,115667,52370,64721,32528,44111,63758,32909,15500,78539,81674,54281,50504,119303,104006,86213,51716,95363,111170,92609,109952,111167,89918,41789,79676,113915,85754,10361,36728,107831,60470,46517,123188,8627,86258,92081,6704,89711,103022,67757,39788,13163,81002,68777,90536,102311,47270]
l10000=[13,13772,9995,78794,63497,45704,11207,54854,70661,52100,69443,70658,49409,1280,39167,73406,45245,93308,119675,67322,19961,6008,82679,91574,45749,51572,89651,49202,62513,27248,122735,96110,40493,28268,50027,61802,6761,17384,40103,48806,77669,42020,39971,53858,41441,14432,108191,13022,77981,74972,91931,119066,14873,9944,33047,15830,4181,48788,61523,3410,97937,74384,58319,92366,15437,22028,8267,10250,60617,54920,6407,70214,21509,36548,69827,44738,8897,81536,53951,1406,28733,96764,9851,73082,1529,15608,51959,66422,76853,50804,18035,6770,25457,121136,19823,5678,33581,1004,38507,98666,111017,78824,90407,110054,79205,61796,1379,4514,100577,96800,42143,26846,9053,98012,18203,34010,15449,32792,34007,12758,88085,2516,36755,8594,56657,83024,30671,106766,92813,46028,54923,9098,14921,53000,12551,25862,114053,86084,59459,3842,115073,13376,25151,93566,104189,3452,12155,41018,5369,3320,17207,4790,101237,71540,99827,41330,38321,55280,82415,101678,96749,119852,102635,90986,12137,24872,90215,61286,37733,21668,55715,102242,108833,95072,97055,23966,18269,93212,33563,108314,123353,33176,8087,95702,44885,17300,88211,115538,60113,96656,36431,88334,102413,15308,29771,40202,14153,104840,93575,112262,84485,106628,92483,120386,87809,1856,62015,74366,42173,53756,73403,42554,25145,88184,91319,63926,60149,5492,113651,95858,61361,105008,120815,102254,119597,120812,99563,51434,89321,104,95399,20006,46373,117476,70115,56162,9377,18272,95903,101726,16349,99356,112667,77402,49433,22808,90647,78422,100181,111956,56915,67538,90257,98960,4367,92174,90125,104012,91595,64586,34889,63176,4679,1670,18629,45764,65027,60098,83201,65984,54335,98942,111677,53564,24635,1082,108473,19064,65591,72182,58421,60404,110771,105074,56561,120368,71663,86702,119981,94892,59051,8234,104105,51560,78887,23462,60005,123236,51683,65762,102113,116576,3551,100958,68189,56924,75611,47834,69977,55832,83735,51158,88661,25364,37715,5522,17105,36752,5903,111950,51533,54668,27275,23498,92297,77000,59207,24710,68357,84164,65603,82946,84161,62912,14783,52670,86909,58748,106811,9722,80825,33464,19511,96182,105077,59252,65075,103154,62705,76016,40751,12782,109613,53996,41771,63530,75305,20264,30887,53606,62309,91172,55523,53474,67361,54944,27935,121694,26525,91484,88475,105434,9113,28376,23447,46550,29333,17684,62291,75026,16913,111440,87887,71822,105869,28940,35531,21770,23753,74120,68423,19910,83717,35012,50051,83330,58241,22400,95039,67454,14909,42236,110267,23354,86585,15032,29111,65462,79925,90356,64307,31538,20273,38960,11183,33326,19181,47084,14507,52010,112169,1064,92327,103910,101,92708,75299,14882,18017,114080,110303,55646,40349,22556,111515,31706,47513,28952,46295,47510,26261,101588,16019,50258,22097,70160,96527,44174,120269,106316,59531,68426,22601,28424,66503,26054,39365,4100,99587,72962,17345,5120,26879,38654,107069,117692,16955,25658,54521,18872,16823,30710,18293,114740,85043,113330,54833,51824,68783,95918,115181,110252,9899,116138,104489,25640,38375,103718,74789,51236,35171,69218,115745,122336,108575,110558,37469,31772,106715,47066,121817,13400,46679,21590,109205,58388,30803,101714,5585,73616,110159,49934,101837,115916,28811,43274,53705,27656,118343,107078,2309,97988,120131,105986,10433,101312,15359,75518,87869,55676,67259,86906,56057,38648,101687,104822,77429,73652,18995,3698,109361,74864,118511,10862,115757,9644,10859,113066,64937,102824,13607,108902,33509,59876,7523,83618,69665,22880,31775,109406,115229,29852,112859,2714,90905,62936,36311,104150,91925,113684,2003,70418,81041,103760,112463,17870,105677,103628,117515,105098,78089,48392,76679,18182,15173,32132,59267,78530,73601,96704,79487,67838,112445,1724,67067,38138,14585,121976,32567,79094,85685,71924,73907,818,118577,70064,10415,85166,100205,10028,108395,72554,21737,117608,65063,92390,36965,73508,13283,65186,79265,115616,6623,17054,114461,81692,70427,89114,61337,83480,69335,97238,64661,102164,38867,51218,19025,30608,50255,19406,1997,65036,68171,40778,37001,105800,90503,72710,38213,81860,97667,79106,96449,97664,76415,28286,66173,100412,72251,120314,23225,94328,46967,33014,109685,118580,72755,78578,116657,76208,89519,54254,26285,123116,67499,55274,77033,88808,33767,44390,67109,75812,104675,69026,66977,80864,68447,41438,11741,40028,104987,101978,118937,22616,41879,36950,60053,42836,31187,75794,88529,30416,1487,101390,85325,119372,42443,49034,35273,37256,87623,81926,33413,97220,48515,63554,96833,71744,35903,108542,80957,28412,55739,314,36857,100088,28535,42614,78965,93428,103859,77810,45041,33776,52463,24686,46829,32684,60587,28010,65513,2216,14567,105830,117413,13604,106211,88802,28385,31520,4127,350,69149,53852,36059,1562,45209,61016,42455,59798,61013,39764,115091,29522,63761,35600,83663,110030,57677,10316,119819,73034,81929,36104,41927,80006,39557,52868,17603,113090,86465,30848,18623,40382,52157,120572,7739,30458,39161,68024,32375,30326,44213,31796,4787,98546,3377,68336,65327,82286,109421,5228,299,23402,6185,117992,39143,51878,117221,88292,64739,48674,82721,5792,12383,122078,605,50972,45275,120218,60569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