python堆排序算法_python 排序 堆排序
算法思想 ：
堆排序利用堆數(shù)據(jù)結(jié)構(gòu)設(shè)計(jì)的一種排序算法，堆是一種近似完全二叉樹的結(jié)構(gòu)，同時(shí)滿足堆積的性質(zhì)，即對(duì)于任意的i均有ki>=k(2i+1),ki>=k(2i+2)
步驟：
將數(shù)組轉(zhuǎn)化為最大堆
將當(dāng)前堆的根結(jié)點(diǎn)和最后一個(gè)結(jié)點(diǎn)交換，然后將前n-1個(gè)元素轉(zhuǎn)化為最大堆
重復(fù)上一過程
為什么要是最大堆呢，因?yàn)檫@樣方便再第二步交換的時(shí)候可以將最大的放在最后，得到最后升序的結(jié)果
算法實(shí)現(xiàn)：
堆排序的主要復(fù)雜的地方就是在于生成最大堆的算法，而且這一算法要能被后面調(diào)整最大堆的時(shí)候用上，因?yàn)檎{(diào)整最大堆時(shí)候是從根節(jié)點(diǎn)開始向下的，所以生成最大堆的算法也設(shè)計(jì)為 從堆中只有只有一個(gè)或兩個(gè)子節(jié)點(diǎn)的結(jié)點(diǎn)開始(很好找n-2//2),一層一層的向上 ，而在每個(gè)節(jié)點(diǎn)的調(diào)整過程中，都是從上到下的，如果和子節(jié)點(diǎn)交換了，就再對(duì)這個(gè)子節(jié)點(diǎn)調(diào)整。經(jīng)過對(duì)比，這也是生成最大堆的算法中最快的一種。
def heap_sort5(collection):
length=len(collection)
def adjustment(collection,index,heap_length):
#index要加入堆中的一個(gè)數(shù)，index是collection中的下標(biāo)
#當(dāng)隊(duì)列已經(jīng)變成大頂堆的時(shí)候，通過讓根節(jié)點(diǎn)和最后一個(gè)元素交換，然后在對(duì)前n-1個(gè)元素組成的堆進(jìn)行調(diào)整，重新變?yōu)榇箜敹?/p>
#為了實(shí)現(xiàn)上面的功能，就必須在調(diào)整大頂堆的算法中加入一個(gè)變量，用來標(biāo)識(shí)collection中是堆中的元素的長(zhǎng)度，這個(gè)變量名為heap_lenght
left_index=index*2+1
right_index=index*2+2
temp=collection[index]
# if right_index>=length-1:#竟然有這樣的錯(cuò)誤
while right_index<=heap_length-1:
if collection[left_index]>collection[right_index]:
if temp
collection[index]=collection[left_index]
index=left_index
left_index=index*2+1
right_index=index*2+2
else:
collection[index]=temp
break
elif temp
collection[index]=collection[right_index]
index=right_index
right_index=index*2+2
left_index=index*2+1
else:
collection[index]=temp
break
collection[index]=temp
if left_index<=heap_length-1:#只有左子樹說明就到底了
if collection[index]
collection[index],collection[left_index]=collection[left_index],collection[index]
#生成最大堆
for i in range((length-2)//2,-1,-1):
adjustment(collection,i,length)
#堆排序
for i in range(length-1):
collection[0],collection[length-1-i]=collection[length-1-i],collection[0]#注意每次是和第一個(gè)交換，不是i是0
adjustment(collection,0,length-i-1)#這個(gè)也是從0開始
return collection
效率分析：
對(duì)比
1000pic 隨機(jī)數(shù)據(jù)：
與桶排序(平均O(n+K)):比桶排序慢，時(shí)間是桶排序的4倍
詳細(xì)數(shù)據(jù)：[0.0030105114, 0.00298571587, 0.00298523903, 0.00296974182, 0.00300073624, 0.00302100182, 0.0019993782, 0.00198626518, 0.00301527977, 0.00298166275, 0.0040140152, 0.00301671028, 0.00198078
156, 0.00299835205, 0.00301647186, 0.00298070908, 0.00299263, 0.00300550461, 0.00298094749, 0.0029938221, 0.00299906731, 0.00301623344, 0.00298047066, 0.00200772285, 0.00198721886, 0.00299811363, 0.00301504135, 0.00399470329, 0.0029861927, 0.00301098824, 0.00198554993, 0.00301480293, 0.00198483467, 0.0029964447, 0.00299835205, 0.0020263195, 0.00401711464, 0.00200629234, 0.00299668312, 0.00302457809, 0.00199437141, 0.00300264359, 0.00302124023, 0.00298285484, 0.00301980972, 0.0029835701, 0.00301551819, 0.00299835205, 0.00199890137, 0.00499534607, 0.00301027298, 0.00401067734, 0.00299453735, 0.00300312042, 0.00299811363, 0.0019774437, 0.0029771328, 0.00199961662, 0.003002882, 0.00298476219, 0.0019993782, 0.00299906731, 0.0020108223, 0.00297951698, 0.00202202797, 0.00199866295, 0.00198745728, 0.00399780273, 0.00299715996, 0.00199818611, 0.00397968292, 0.00300979614, 0.00198554993, 0.00199079514, 0.00398445129, 0.00299572945, 0.00398278236, 0.00300073624, 0.00199818611, 0.00399780273, 0.00301170349, 0.00299835205, 0.00296235085, 0.00202345848, 0.00399947166, 0.00299429893, 0.00398445129, 0.00299811363, 0.00398445129, 0.00300931931, 0.00298428535, 0.00301766396, 0.0029976368, 0.00202298164, 0.00401210785, 0.00299596786, 0.00398468971, 0.00199770927, 0.00298476219, 0.00299715996]
運(yùn)行了100次，平均運(yùn)行時(shí)間差(heap_sort5-bucket_sort3)(正數(shù)代表你是個(gè)弟弟)是：0.00290829897
前者(heap_sort5)平均運(yùn)行時(shí)間0.00392773628,后者(bucket_sort3)平均運(yùn)行時(shí)間0.00101943731,前者約是后者的3.8528倍
與快排(平均O(nlogn))：比快排慢，時(shí)間是快排的2.4倍
詳細(xì)數(shù)據(jù)：[0.00201654434, 0.00297951698, 0.00201129913, 0.00196933746, 0.00198483467, 0.00199818611, 0.0019993782, 0.00100493431, 0.00298690796, 0.00099802017, 0.00199866295, 0.00300002098, 0.002963
78136, 0.00300335884, 0.00201702118, 0.00296258926, 0.00198817253, 0.00298595428, 0.00100684166, 0.00099444389, 0.00298118591, 0.00301027298, 0.0019865036, 0.00302529335, 0.00298523903, 0.00199794769, 0.00299739838, 0.00199866295, 0.00198602676, 0.0019865036, 0.00299787521, 0.00299954414, 0.0029976368, 0.00299859047, 0.00299811363, 0.00199818611, 0.0019993782, 0.00299739838, 0.00299835205, 0.00199794769, 0.00199818611, 0.0009996891, 0.00299787521, 0.00299692154, 0.0029976368, 0.00299930573, 0.0019993782, 0.00199961662, 0.0029976368, 0.0020005703, 0.00199818611, 0.00097441673, 0.00325942039, 0.00203251839, 0.00299954414, 0.0020236969, 0.00298595428, 0.00201702118, 0.00198149681, 0.00298118591, 0.00198149681, 0.00199890137, 0.0020236969, 0.00201678276, 0.00201177597, 0.00199770927, 0.00290203094, 0.00201177597, 0.00197386742, 0.00299882889, 0.00299882889, 0.00199460983, 0.00102114677, 0.00298571587, 0.00301146507, 0.0029861927, 0.00199913979, 0.00199842453, 0.00402283669, 0.0030105114, 0.0029976368, 0.00202226639, 0.00296854973, 0.0020160675, 0.00201106071, 0.00198984146, 0.00101685524, 0.00199794769, 0.00302910805, 0.00299811363, 0.0010368824, 0.00299811363, 0.00199842453, 0.00201964378, 0.00298213959, 0.00199866295, 0.0019993782, 0.00199818611, 0.0019865036, 0.00299906731]
運(yùn)行了100次，平均運(yùn)行時(shí)間差(heap_sort5-quick_sort2)(正數(shù)代表你是個(gè)弟弟)是：0.00235058308
前者(heap_sort5)平均運(yùn)行時(shí)間0.00402917624,后者(quick_sort2)平均運(yùn)行時(shí)間0.00167859316,前者約是后者的2.4003倍
與歸并(平均O(nlogn))：與歸并差不多，實(shí)際浮動(dòng)10%
詳細(xì)數(shù)據(jù)：[1.764297e-05, 0.00099945068, 1.740456e-05, -0.00101423264, 0.00097084045, 0.0009701252, -0.00096297264, 1.811981e-05, 0.00096440315, 0.00198078156, -0.00097417831, 0.00101184845, -5.48363
e-06, 0.00099921227, -4.7684e-07, 0.00101065636, 0.0, 0.00098347664, 0.00100016594, -0.00098752975, 0.00098752975, -1.144409e-05, 9.77516e-06, -1.573563e-05, 0.00099873543, -0.00099945068, 0.00101733208, -1.001358e-05, 9.5367e-07, 0.00097441673, 0.00098729134, -0.00097298622, 0.00099992752, 0.0, -0.00097846985, 1.645088e-05, 0.00097513199, 0.00097751617, -0.00098800659, -9.5367e-07, 0.00098729134, 0.0009868145, 0.00099849701, -0.0009624958, 1.764297e-05, -2.14577e-06, 0.00197386742, -0.00200939178, 0.00098705292, -1.072884e-05, 0.00099825859, -0.00097560883, 0.00101137161, 0.00097537041, 0.00096106529, -1.66893e-06, -7.1526e-07, 0.00100588799, -1.716614e-05, 0.00101280212, 0.00096774101, 0.00096273422, 1.40667e-05, -0.00098156929, 0.00098705292, 3.8147e-06, -0.00098156929, 0.0010008812, 9.5367e-07, -2.3842e-07, 3.671646e-05, 3.623962e-05, -4.7684e-07, 0.00097966194, -3.576279e-05, -1.66893e-05, -3.647804e-05, 7.86781e-06, 0.00100302696, 3.433228e-05, 4.05312e-06, 0.00099158287, 3.433228e-05, 4.05312e-06, 0.00098752975, 0.00198554993, 0.00102448463, 0.00101280212, -1.239777e-05, 2.098083e-05, 0.00099825859, -1.358986e-05, 0.00098633766, -0.00098776817, 0.00101685524, -1.311302e-05, -2.598763e-05, 1.144409e-05, 1.192093e-05, 0.00097417831]
運(yùn)行了100次，平均運(yùn)行時(shí)間差(heap_sort5-merge_sort3)(正數(shù)代表你是個(gè)弟弟)是：0.00031897068
前者(heap_sort5)平均運(yùn)行時(shí)間0.00396824121,后者(merge_sort3)平均運(yùn)行時(shí)間0.00364927053,前者約是后者的1.0874倍
與希爾排序()：比希爾慢，時(shí)間是希爾的1.2倍
詳細(xì)數(shù)據(jù)：[1.335144e-05, 0.00201821327, -5.24521e-06, 0.00099253654, -1.311302e-05, 0.0020070076, 0.00099611282, 0.00096917152, 2.43187e-05, -5.24521e-06, -1.43051e-06, 1.28746e-05, 0.00096964836, 0
.00100708008, 0.00100922585, 0.00099921227, -0.00100970268, 5.24521e-06, 0.00099039078, 0.00099992752, -3.57628e-06, 0.0009829998, 0.00099992752, 0.00198245049, -1.478195e-05, 0.00100398064, 0.00098252296, -4.7684e-07, 0.00198626518, 0.00099468231, 0.0009970665, 0.00097560883, 0.00099992752, 0.00099849701, 0.00199985504, 0.00099897385, 0.00203323364, 0.00099825859, -7.1526e-07, -7.1526e-07, 0.00099921227, -2.3842e-07, 0.00099921227, 0.00099921227, -1.43051e-06, 0.00100111961, 2.3842e-07, 0.00100064278, -7.1526e-07, -2.3842e-07, 2.38419e-06, 0.0, 0.00099992752, -0.00100040436, 0.00099897385, 0.00199961662, 0.0010099411, 0.00102591515, 0.00099945068, 1.66893e-06, 0.00101184845, 0.00199985504, 0.00017309189, -2.31266e-05, 0.00097489357, 0.00198602676, 0.00102424622, -2.3842e-07, 0.00098109245, 0.00099468231, 1.788139e-05, -2.3842e-07, 0.00098013878, 1.43051e-06, 0.00096201897, 0.00100421906, -0.00098609924, 1.263618e-05, 0.00099945068, 0.00099945068, 0.00099897385, 0.00096940994, 1.788139e-05, -0.0010035038, 0.0009906292, 0.0019724369, -5.96046e-06, 0.00100493431, 6.19888e-06, -1.239777e-05, 9.77516e-06, 0.00098276138, -0.00100016594, 1.192093e-05, 0.00200486183, 7.86781e-06, 4.7684e-07, -3.09944e-06, 8.34465e-06, 0.00099611282]
運(yùn)行了100次，平均運(yùn)行時(shí)間差(heap_sort5-shell_sort3)(正數(shù)代表你是個(gè)弟弟)是：0.00062998772
前者(heap_sort5)平均運(yùn)行時(shí)間0.00394880772,后者(shell_sort3)平均運(yùn)行時(shí)間0.00331882000,前者約是后者的1.1898倍
與選擇排序(O(n^2)):比選擇快，是選擇時(shí)間的九分之一
詳細(xì)數(shù)據(jù)：[-0.03098297119, -0.03199076653, -0.03198218346, -0.03198122978, -0.03098106384, -0.03198075294, -0.0309817791, -0.03097701073, -0.03196048737, -0.03194522858, -0.03298187256, -0.030964136
12, -0.03097605705, -0.03295016289, -0.02898311615, -0.03000020981, -0.0329887867, -0.02998185158, -0.03198099136, -0.03098106384, -0.03298187256, -0.03098273277, -0.03100085258, -0.03200554848, -0.03200006485, -0.03198170662, -0.03196406364, -0.02997612953, -0.03097915649, -0.03096842766, -0.03198003769, -0.03099584579, -0.03197383881, -0.03098273277, -0.03098297119, -0.0319545269, -0.03097319603, -0.0320045948, -0.02999281883, -0.03101181984, -0.03199768066, -0.03097224236, -0.03094625473, -0.03100132942, -0.03198194504, -0.03099894524, -0.03197240829, -0.03098273277, -0.03099250793, -0.03298354149, -0.03197526932, -0.03198218346, -0.03200125694, -0.03199028969, -0.02902030945, -0.02996492386, -0.03098249435, -0.0299885273, -0.03198456764, -0.03000354767, -0.03098773956, -0.02900099754, -0.03199529648, -0.03196907043, -0.03195810318, -0.03095602989, -0.03194713593, -0.03198242188, -0.03098273277, -0.03198242188, -0.03098154068, -0.02998065948, -0.03198289871, -0.03298139572, -0.0309817791, -0.03099584579, -0.03101348877, -0.03197312355, -0.03200078011, -0.02999806404, -0.03199219704, -0.03098058701, -0.03095769882, -0.02999162674, -0.03095960617, -0.03098225594, -0.0319507122, -0.03199577332, -0.03299593925, -0.03000020981, -0.03098058701, -0.03100943565, -0.0309586525, -0.03098368645, -0.03195118904, -0.03098011017, -0.03100037575, -0.03000617027, -0.03198218346, -0.03198266029]
運(yùn)行了100次，平均運(yùn)行時(shí)間差(heap_sort5-select_sort2)(正數(shù)代表你是個(gè)弟弟)是：-0.03132260799
前者(heap_sort5)平均運(yùn)行時(shí)間0.00397776127,后者(select_sort2)平均運(yùn)行時(shí)間0.03530036926,前者約是后者的0.1127倍
與插入排序(O(n^2)):比插入快，是插入的九分之一
詳細(xì)數(shù)據(jù)：[-0.02899861336, -0.02996730804, -0.03100061417, -0.02997756004, -0.03021883965, -0.02996373177, -0.03097391129, -0.03092384338, -0.03199481964, -0.02900743484, -0.0319890976, -0.028993606
57, -0.02900671959, -0.02995681763, -0.02899456024, -0.0300078392, -0.02999472618, -0.03012704849, -0.03000092506, -0.03001236916, -0.02998304367, -0.0309548378, -0.03105306625, -0.03097820282, -0.02950978279, -0.03198122978, -0.02900028229, -0.02998232841, -0.03000259399, -0.02996039391, -0.02998280525, -0.03099131584, -0.02996897697, -0.03098130226, -0.02997732162, -0.03198027611, -0.0309650898, -0.03096795082, -0.03196811676, -0.03000283241, -0.02998304367, -0.03099298477, -0.03100728989, -0.02998328209, -0.02994346619, -0.03098249435, -0.0319852829, -0.02908825874, -0.03198170662, -0.03098082542, -0.02995967865, -0.03098034859, -0.02999520302, -0.03000998497, -0.02799153328, -0.02997493744, -0.03000164032, -0.02906346321, -0.03098011017, -0.02997016907, -0.03105521202, -0.02998423576, -0.03099560738, -0.02998161316, -0.03099656105, -0.02998256683, -0.02899646759, -0.02998304367, -0.03199863434, -0.02996826172, -0.03199887276, -0.03097033501, -0.02926707268, -0.03097510338, -0.03095555305, -0.03206801414, -0.02901434898, -0.03094601631, -0.02995657921, -0.0289683342, -0.02895879745, -0.02997756004, -0.02998709679, -0.02998375893, -0.03096938133, -0.0302259922, -0.02998423576, -0.03197407722, -0.02994465828, -0.02999520302, -0.02899694443, -0.03098726273, -0.02901959419, -0.03000187874, -0.02998280525, -0.02896547318, -0.02996993065, -0.02997756004, -0.02914905548, -0.03098154068]
運(yùn)行了100次，平均運(yùn)行時(shí)間差(heap_sort5-insertion_sort4)(正數(shù)代表你是個(gè)弟弟)是：-0.03028253078
前者(heap_sort5)平均運(yùn)行時(shí)間0.00394899845,后者(insertion_sort4)平均運(yùn)行時(shí)間0.03423152924,前者約是后者的0.1154倍
與雙向冒泡(O(n^2)):比雙向冒泡快，是其0.06倍
詳細(xì)數(shù)據(jù)：[-0.06394600868, -0.06296277046, -0.06496214867, -0.06496310234, -0.06196260452, -0.06313633919, -0.06294035912, -0.06199359894, -0.06495571136, -0.06296420097, -0.06696176529, -0.06396317
482, -0.06496310234, -0.06396389008, -0.06396532059, -0.06496357918, -0.06495523453, -0.06297588348, -0.06297802925, -0.06296396255, -0.06296420097, -0.06310391426, -0.06396174431, -0.06396341324, -0.0639629364, -0.06496334076, -0.06396412849, -0.06493639946, -0.06296396255, -0.06394505501, -0.06496310234, -0.06296372414, -0.06297707558, -0.06298160553, -0.06497168541, -0.06299304962, -0.06345295906, -0.06507635117, -0.06296348572, -0.06296467781, -0.0630466938, -0.06496119499, -0.06198263168, -0.06491446495, -0.06296181679, -0.06296348572, -0.0639629364, -0.06296348572, -0.06397724152, -0.06397509575, -0.06496334076, -0.06397604942, -0.06198978424, -0.06342983246, -0.06496357918, -0.06196522713, -0.06296300888, -0.06216788292, -0.06396389008, -0.06412982941, -0.06496143341, -0.0642516613, -0.06396579742, -0.06517672539, -0.06194090843, -0.06196451187, -0.06305217743, -0.06396389008, -0.06396245956, -0.06389951706, -0.06196451187, -0.06396150589, -0.06296372414, -0.06428790092, -0.06198167801, -0.06294608116, -0.06409454346, -0.06496357918, -0.0639629364, -0.06296539307, -0.06296277046, -0.06398153305, -0.06296467781, -0.06396436691, -0.06497693062, -0.06397914886, -0.06296396255, -0.06497597694, -0.06421637535, -0.06296396255, -0.06402182579, -0.06401872635, -0.06594610214, -0.06696248055, -0.06395411491, -0.0639629364, -0.06396508217, -0.06296205521, -0.0639629364, -0.06596231461]
運(yùn)行了100次，平均運(yùn)行時(shí)間差(heap_sort5-bidirectional_bubble_sort3)(正數(shù)代表你是個(gè)弟弟)是：-0.06377598286
前者(heap_sort5)平均運(yùn)行時(shí)間0.00407264948,后者(bidirectional_bubble_sort3)平均運(yùn)行時(shí)間0.06784863234,前者約是后者的0.0600倍
其他的版本：
主要是生成堆積的算法
版本1：
依舊是采用尋找結(jié)點(diǎn)中的數(shù)值，不同的是從根節(jié)點(diǎn)向下。要找根結(jié)點(diǎn)，就必須和左右子樹對(duì)比，所以就必須找左右結(jié)點(diǎn)的。。。這樣的話，每一個(gè)結(jié)點(diǎn)都必須要和他所有的子節(jié)點(diǎn)比較；
而且一旦最上面的點(diǎn)發(fā)生了變化，即把根節(jié)點(diǎn)取出來的時(shí)候，也不能只對(duì)index=0的結(jié)點(diǎn)進(jìn)行調(diào)整，因?yàn)?adjustment(0)#只會(huì)對(duì)任何結(jié)點(diǎn)下面的子節(jié)點(diǎn)的做一次最大堆調(diào)整，而遞歸結(jié)束后加入發(fā)生了交換，是不會(huì)對(duì)下面頂點(diǎn)再進(jìn)行調(diào)整的。即不能利用之前已經(jīng)有序的堆積。采用這樣的辦法排序所需時(shí)間是最快的4000多倍
是最快的生成堆積的8倍(不過我很奇怪，他到底比最快的慢在哪里，最快的不也是從上到下嗎)
def adjustment(root):
length=len(collection)
left_index=root*2+1
right_index=root*2+2
#分別尋找左右子樹上的最小值
#左右子樹都存在
if right_index
adjustment(left_index)
adjustment(right_index)
#其實(shí)從底層找，并交換能避免一些額外的交換
if collection[left_index]>collection[right_index]:
if collection[root]>collection[right_index]:
collection[root],collection[right_index]=collection[right_index],collection[root]
#這里要不要return呢
elif collection[root]>collection[left_index]:
collection[root],collection[left_index]=collection[left_index],collection[root]
# collection[left_index],collection[right_index]=collection[right_index],collection[left_index]#左右不必交換
# return min(collection[root],adjustment(right_index),adjustment(left_index))
#只有左子樹存在
elif left_index
adjustment(left_index)
if collection[left_index]
collection[left_index],collection[root]=collection[root],collection[left_index]
# return min(collection[root],adjustment(left_index))
return collection[root]
版本2：
通過不斷想堆中的最末尾插入元素，通過和上面的結(jié)點(diǎn)比較進(jìn)行調(diào)整
是最快生成堆算法的1.4倍
def adjustment(collection,add_index):
'''collection是整個(gè)集合，add_index是向小堆中添加元素的collection中的下標(biāo)'''
#找父節(jié)點(diǎn)
temp=collection[add_index]
while (add_index-1)//2>=0 and temp
collection[add_index]=collection[(add_index-1)//2]
add_index=(add_index-1)//2
collection[add_index]=temp
版本3
并不是覺得上面的版本2效率不高才改進(jìn)的，說實(shí)話我也不知道這個(gè)為什么比那個(gè)效率高，不過因?yàn)榘姹?不能用在后面調(diào)整最大堆的里面，所以想到希爾排序里里面的一種思想
def adjustment(collection,index,heap_length):
left_index=index*2+1
right_index=index*2+2
# if right_index>=length-1:#竟然有這樣的錯(cuò)誤
while right_index<=heap_length-1:
if collection[left_index]>collection[right_index]:
if collection[index]
collection[index],collection[left_index]=collection[left_index],collection[index]
index=left_index
left_index=index*2+1
right_index=index*2+2
else:
break
elif collection[index]
collection[index],collection[right_index]=collection[right_index],collection[index]
index=right_index
right_index=index*2+2
left_index=index*2+1
else:
break
if left_index<=heap_length-1:#只有左子樹說明就到底了
if collection[index]
collection[index],collection[left_index]=collection[left_index],collection[index]
總結(jié)
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