排序算法

世界上有很多种对序列排序的算法（序列可以不是整数序列，只要可比较即可）。下表列出了许多主流排序算法的性能，其中的表头和第一列我后面会讲：

data size std::sort std::stable_sort Timsort PDQ-sort Insertion sort Selection sort Bubble sort Cocktail sort Gnome sort Comb sort Merge sort Heap sort Smooth sort Shell sort Bitonic sort Quick sort (LR, pivot=first) Quick sort (LR, pivot=last) Quick sort (LR, pivot=middle) Quick sort (LR, pivot=median of 3) Quick sort (LR, pivot=median of 9) Quick sort (LR, pivot=random) Quick sort (LL, pivot=first) Quick sort (LL, pivot=last) Quick sort (LL, pivot=middle) Quick sort (LL, pivot=median of 3) Quick sort (LL, pivot=median of 9) Quick sort (LL, pivot=random)
1024(random) \(0.043\text{ms}(12641)\) \(0.070\text{ms}(9985)\) \(0.062\text{ms}(15070)\) \(0.071\text{ms}(13878)\) \(0.193\text{ms}(265364)\) \(0.394\text{ms}(523776)\) \(1.008\text{ms}(519395)\) \(0.835\text{ms}(357318)\) \(0.991\text{ms}(529712)\) \(0.063\text{ms}(23260)\) \(0.182\text{ms}(8932)\) \(0.079\text{ms}(10601)\) \(0.118\text{ms}(22626)\) \(0.057\text{ms}(12808)\) \(0.252\text{ms}(28160)\) \(0.094\text{ms}(13653)\) \(0.061\text{ms}(13238)\) \(0.054\text{ms}(12784)\) \(0.052\text{ms}(12635)\) \(0.174\text{ms}(25923)\) \(0.064\text{ms}(11464)\) \(0.049\text{ms}(10518)\) \(0.069\text{ms}(11674)\) \(0.052\text{ms}(10455)\) \(0.050\text{ms}(11575)\) \(0.136\text{ms}(20132)\) \(0.075\text{ms}(10162)\)
1024(ascending) \(0.009\text{ms}(10899)\) \(0.011\text{ms}(6142)\) \(0.003\text{ms}(1023)\) \(0.002\text{ms}(1023)\) \(0.002\text{ms}(1023)\) \(0.584\text{ms}(523776)\) \(0.003\text{ms}(1023)\) \(0.001\text{ms}(1023)\) \(0.002\text{ms}(1023)\) \(0.001\text{ms}(237)\) \(0.098\text{ms}(5120)\) \(0.053\text{ms}(10654)\) \(0.010\text{ms}(2029)\) \(0.009\text{ms}(5380)\) \(0.122\text{ms}(28160)\) \(0.333\text{ms}(524797)\) \(0.237\text{ms}(262654)\) \(0.010\text{ms}(8714)\) \(0.010\text{ms}(10247)\) \(0.090\text{ms}(22009)\) \(0.030\text{ms}(12324)\) \(0.320\text{ms}(262655)\) \(0.277\text{ms}(262143)\) \(0.015\text{ms}(8149)\) \(0.037\text{ms}(22656)\) \(0.095\text{ms}(19403)\) \(0.046\text{ms}(11230)\)
1024(descending) \(0.007\text{ms}(8330)\) \(0.014\text{ms}(4390)\) \(0.003\text{ms}(1023)\) \(0.001\text{ms}(1023)\) \(0.386\text{ms}(523776)\) \(0.334\text{ms}(523776)\) \(0.720\text{ms}(523776)\) \(0.882\text{ms}(524799)\) \(1.932\text{ms}(1047552)\) \(0.001\text{ms}(656)\) \(0.089\text{ms}(5120)\) \(0.060\text{ms}(11053)\) \(0.072\text{ms}(20113)\) \(0.017\text{ms}(9092)\) \(0.121\text{ms}(28160)\) \(0.219\text{ms}(350205)\) \(0.219\text{ms}(350548)\) \(0.011\text{ms}(8714)\) \(0.011\text{ms}(10247)\) \(0.058\text{ms}(22013)\) \(0.031\text{ms}(10806)\) \(0.419\text{ms}(262143)\) \(0.370\text{ms}(349525)\) \(0.016\text{ms}(8241)\) \(0.030\text{ms}(16103)\) \(0.059\text{ms}(20405)\) \(0.036\text{ms}(10849)\)
1024(pipe organ) \(0.063\text{ms}(24324)\) \(0.014\text{ms}(5777)\) \(0.005\text{ms}(2046)\) \(0.006\text{ms}(2557)\) \(0.186\text{ms}(263166)\) \(0.381\text{ms}(523776)\) \(0.708\text{ms}(523776)\) \(0.535\text{ms}(350888)\) \(0.973\text{ms}(525310)\) \(0.027\text{ms}(20191)\) \(0.088\text{ms}(5631)\) \(0.058\text{ms}(10693)\) \(0.076\text{ms}(22679)\) \(0.016\text{ms}(7903)\) \(0.137\text{ms}(28160)\) \(0.041\text{ms}(27950)\) \(0.040\text{ms}(30858)\) \(0.048\text{ms}(37135)\) \(0.044\text{ms}(24018)\) \(0.091\text{ms}(24959)\) \(0.053\text{ms}(12298)\) \(0.162\text{ms}(96087)\) \(0.072\text{ms}(54145)\) \(0.058\text{ms}(34294)\) \(0.051\text{ms}(28689)\) \(0.076\text{ms}(20041)\) \(0.037\text{ms}(10824)\)
1024(final merge) \(0.007\text{ms}(8332)\) \(0.011\text{ms}(6142)\) \(0.004\text{ms}(1535)\) \(0.009\text{ms}(2046)\) \(0.186\text{ms}(263166)\) \(0.328\text{ms}(523776)\) \(0.538\text{ms}(393471)\) \(0.817\text{ms}(524799)\) \(0.945\text{ms}(525310)\) \(0.030\text{ms}(20191)\) \(0.089\text{ms}(5120)\) \(0.058\text{ms}(11054)\) \(0.077\text{ms}(18426)\) \(0.010\text{ms}(5380)\) \(0.120\text{ms}(28160)\) \(0.121\text{ms}(176465)\) \(0.120\text{ms}(176807)\) \(0.181\text{ms}(263163)\) \(0.013\text{ms}(11565)\) \(0.059\text{ms}(22058)\) \(0.033\text{ms}(12517)\) \(0.171\text{ms}(132348)\) \(0.215\text{ms}(131583)\) \(0.355\text{ms}(262143)\) \(0.040\text{ms}(23395)\) \(0.062\text{ms}(19341)\) \(0.034\text{ms}(9965)\)
1024(final merge reversed) \(0.052\text{ms}(25037)\) \(0.014\text{ms}(4901)\) \(0.004\text{ms}(2046)\) \(0.005\text{ms}(2557)\) \(0.278\text{ms}(393471)\) \(0.382\text{ms}(523776)\) \(0.718\text{ms}(523776)\) \(0.775\text{ms}(466488)\) \(1.482\text{ms}(786431)\) \(0.001\text{ms}(656)\) \(0.089\text{ms}(5631)\) \(0.058\text{ms}(11005)\) \(0.098\text{ms}(23826)\) \(0.020\text{ms}(11020)\) \(0.140\text{ms}(28160)\) \(0.044\text{ms}(30278)\) \(0.041\text{ms}(25748)\) \(0.051\text{ms}(36666)\) \(0.043\text{ms}(23805)\) \(0.094\text{ms}(25720)\) \(0.050\text{ms}(13693)\) \(0.259\text{ms}(180735)\) \(0.116\text{ms}(107097)\) \(0.441\text{ms}(390923)\) \(0.097\text{ms}(91379)\) \(0.077\text{ms}(19691)\) \(0.040\text{ms}(11648)\)
1024(heapified) \(0.032\text{ms}(12635)\) \(0.031\text{ms}(9097)\) \(0.034\text{ms}(11897)\) \(0.043\text{ms}(13123)\) \(0.239\text{ms}(343244)\) \(0.437\text{ms}(523776)\) \(0.804\text{ms}(523348)\) \(0.753\text{ms}(455353)\) \(1.256\text{ms}(685483)\) \(0.055\text{ms}(22237)\) \(0.103\text{ms}(8028)\) \(0.054\text{ms}(11157)\) \(0.083\text{ms}(21162)\) \(0.051\text{ms}(10922)\) \(0.205\text{ms}(28160)\) \(0.050\text{ms}(17229)\) \(0.046\text{ms}(17033)\) \(0.048\text{ms}(11115)\) \(0.047\text{ms}(12368)\) \(0.125\text{ms}(25922)\) \(0.060\text{ms}(12746)\) \(0.043\text{ms}(14792)\) \(0.044\text{ms}(16914)\) \(0.047\text{ms}(11016)\) \(0.039\text{ms}(11012)\) \(0.102\text{ms}(20122)\) \(0.048\text{ms}(11858)\)
1024(binary search tree) \(0.030\text{ms}(16070)\) \(0.015\text{ms}(7450)\) \(0.008\text{ms}(3184)\) \(0.040\text{ms}(14908)\) \(0.127\text{ms}(176287)\) \(0.352\text{ms}(523776)\) \(0.357\text{ms}(262655)\) \(0.475\text{ms}(290954)\) \(0.656\text{ms}(351561)\) \(0.046\text{ms}(22237)\) \(0.095\text{ms}(6133)\) \(0.051\text{ms}(10218)\) \(0.082\text{ms}(22586)\) \(0.034\text{ms}(10206)\) \(0.141\text{ms}(28160)\) \(0.045\text{ms}(23687)\) \(0.039\text{ms}(21237)\) \(0.040\text{ms}(16679)\) \(0.042\text{ms}(17478)\) \(0.123\text{ms}(31191)\) \(0.052\text{ms}(11708)\) \(0.027\text{ms}(9984)\) \(0.157\text{ms}(131840)\) \(0.067\text{ms}(41984)\) \(0.158\text{ms}(133626)\) \(0.088\text{ms}(22223)\) \(0.043\text{ms}(12615)\)
1024(sawtooth) \(0.031\text{ms}(11828)\) \(0.018\text{ms}(9580)\) \(0.029\text{ms}(12032)\) \(0.046\text{ms}(13186)\) \(0.141\text{ms}(196863)\) \(0.345\text{ms}(523776)\) \(0.684\text{ms}(489093)\) \(0.425\text{ms}(311169)\) \(0.791\text{ms}(392703)\) \(0.008\text{ms}(7092)\) \(0.100\text{ms}(8192)\) \(0.062\text{ms}(10510)\) \(0.083\text{ms}(21987)\) \(0.014\text{ms}(7938)\) \(0.130\text{ms}(28160)\) \(0.044\text{ms}(15563)\) \(0.040\text{ms}(15061)\) \(0.049\text{ms}(12510)\) \(0.041\text{ms}(11673)\) \(0.110\text{ms}(25532)\) \(0.055\text{ms}(12432)\) \(0.055\text{ms}(27972)\) \(0.049\text{ms}(26103)\) \(0.038\text{ms}(14647)\) \(0.035\text{ms}(11590)\) \(0.087\text{ms}(19992)\) \(0.041\text{ms}(10295)\)
1024(scrambled head) \(0.025\text{ms}(13041)\) \(0.018\text{ms}(7097)\) \(0.011\text{ms}(4310)\) \(0.030\text{ms}(10619)\) \(0.124\text{ms}(159871)\) \(0.349\text{ms}(523776)\) \(0.686\text{ms}(514541)\) \(0.353\text{ms}(228298)\) \(0.580\text{ms}(318721)\) \(0.051\text{ms}(23260)\) \(0.095\text{ms}(6266)\) \(0.058\text{ms}(10754)\) \(0.089\text{ms}(20274)\) \(0.042\text{ms}(10593)\) \(0.150\text{ms}(28160)\) \(0.037\text{ms}(17270)\) \(0.036\text{ms}(21502)\) \(0.038\text{ms}(19711)\) \(0.037\text{ms}(11633)\) \(0.113\text{ms}(25131)\) \(0.049\text{ms}(12123)\) \(0.033\text{ms}(14901)\) \(0.044\text{ms}(25298)\) \(0.052\text{ms}(34952)\) \(0.032\text{ms}(11603)\) \(0.089\text{ms}(19790)\) \(0.040\text{ms}(10736)\)
1024(scrambled tail) \(0.028\text{ms}(15439)\) \(0.016\text{ms}(6624)\) \(0.009\text{ms}(3422)\) \(0.009\text{ms}(3296)\) \(0.044\text{ms}(62337)\) \(0.352\text{ms}(523776)\) \(0.739\text{ms}(523520)\) \(0.195\text{ms}(117627)\) \(0.236\text{ms}(123651)\) \(0.050\text{ms}(21214)\) \(0.095\text{ms}(5699)\) \(0.057\text{ms}(10648)\) \(0.073\text{ms}(18474)\) \(0.042\text{ms}(9781)\) \(0.140\text{ms}(28160)\) \(0.054\text{ms}(47096)\) \(0.065\text{ms}(61876)\) \(0.071\text{ms}(19619)\) \(0.039\text{ms}(12706)\) \(0.098\text{ms}(23990)\) \(0.050\text{ms}(12385)\) \(0.068\text{ms}(38646)\) \(0.068\text{ms}(48375)\) \(0.041\text{ms}(18688)\) \(0.048\text{ms}(25059)\) \(0.083\text{ms}(19670)\) \(0.045\text{ms}(11742)\)
1024(half-reversed) \(0.037\text{ms}(20739)\) \(0.014\text{ms}(5266)\) \(0.004\text{ms}(1535)\) \(0.004\text{ms}(2045)\) \(0.096\text{ms}(131839)\) \(0.352\text{ms}(523776)\) \(0.530\text{ms}(392960)\) \(0.248\text{ms}(132351)\) \(0.487\text{ms}(262655)\) \(0.001\text{ms}(237)\) \(0.110\text{ms}(5120)\) \(0.053\text{ms}(10612)\) \(0.044\text{ms}(11316)\) \(0.013\text{ms}(7480)\) \(0.121\text{ms}(28160)\) \(0.306\text{ms}(481192)\) \(0.112\text{ms}(154450)\) \(0.010\text{ms}(8714)\) \(0.010\text{ms}(10247)\) \(0.058\text{ms}(22010)\) \(0.031\text{ms}(11240)\) \(0.376\text{ms}(262400)\) \(0.176\text{ms}(153427)\) \(0.018\text{ms}(8191)\) \(0.033\text{ms}(15839)\) \(0.063\text{ms}(19875)\) \(0.035\text{ms}(10754)\)
1024(adversary) \(0.015\text{ms}(9645)\) \(0.017\text{ms}(8053)\) \(0.025\text{ms}(6161)\) \(0.025\text{ms}(9369)\) \(0.214\text{ms}(306090)\) \(0.359\text{ms}(523776)\) \(0.536\text{ms}(392960)\) \(0.791\text{ms}(523776)\) \(1.130\text{ms}(611157)\) \(0.033\text{ms}(23260)\) \(0.095\text{ms}(6914)\) \(0.039\text{ms}(10231)\) \(0.054\text{ms}(14671)\) \(0.014\text{ms}(6117)\) \(0.138\text{ms}(28160)\) \(0.026\text{ms}(12695)\) \(0.025\text{ms}(15640)\) \(0.026\text{ms}(11670)\) \(0.025\text{ms}(11013)\) \(0.082\text{ms}(20927)\) \(0.036\text{ms}(10498)\) \(0.198\text{ms}(151379)\) \(0.281\text{ms}(168246)\) \(0.267\text{ms}(296161)\) \(0.473\text{ms}(526841)\) \(0.218\text{ms}(150468)\) \(0.172\text{ms}(154323)\)
16384(random) \(0.869\text{ms}(273405)\) \(1.142\text{ms}(226030)\) \(1.211\text{ms}(345310)\) \(1.058\text{ms}(312517)\) \(48.338\text{ms}(67175004)\) \(84.215\text{ms}(134209536)\) \(377.773\text{ms}(134178290)\) \(290.775\text{ms}(89652688)\) \(238.980\text{ms}(134333632)\) \(1.543\text{ms}(617194)\) \(2.335\text{ms}(208685)\) \(1.496\text{ms}(235143)\) \(1.939\text{ms}(573752)\) \(1.663\text{ms}(446532)\) \(5.035\text{ms}(860160)\) \(1.095\text{ms}(310841)\) \(1.028\text{ms}(305324)\) \(1.047\text{ms}(293550)\) \(1.263\text{ms}(274760)\) \(2.262\text{ms}(488197)\) \(1.246\text{ms}(282719)\) \(0.986\text{ms}(267205)\) \(0.977\text{ms}(262651)\) \(0.966\text{ms}(277347)\) \(1.005\text{ms}(243492)\) \(1.905\text{ms}(403307)\) \(1.116\text{ms}(260391)\)
16384(ascending) \(0.160\text{ms}(272411)\) \(0.237\text{ms}(131070)\) \(0.012\text{ms}(16383)\) \(0.025\text{ms}(16383)\) \(0.028\text{ms}(16383)\) \(82.542\text{ms}(134209536)\) \(0.021\text{ms}(16383)\) \(0.023\text{ms}(16383)\) \(0.030\text{ms}(16383)\) \(0.004\text{ms}(3781)\) \(1.411\text{ms}(114688)\) \(0.896\text{ms}(236485)\) \(0.126\text{ms}(32743)\) \(0.266\text{ms}(135172)\) \(1.980\text{ms}(860160)\) \(81.785\text{ms}(134225917)\) \(41.257\text{ms}(67117054)\) \(0.172\text{ms}(204814)\) \(0.172\text{ms}(229387)\) \(0.914\text{ms}(417793)\) \(0.481\text{ms}(262587)\) \(81.152\text{ms}(67117055)\) \(71.805\text{ms}(67108863)\) \(0.285\text{ms}(195745)\) \(1.506\text{ms}(1346728)\) \(0.963\text{ms}(385782)\) \(0.559\text{ms}(255083)\)
16384(descending) \(0.134\text{ms}(198666)\) \(0.267\text{ms}(102988)\) \(0.018\text{ms}(16383)\) \(0.016\text{ms}(16383)\) \(92.893\text{ms}(134209536)\) \(86.406\text{ms}(134209536)\) \(186.139\text{ms}(134209536)\) \(219.323\text{ms}(134225919)\) \(500.478\text{ms}(268419072)\) \(0.010\text{ms}(10471)\) \(2.028\text{ms}(114688)\) \(1.041\text{ms}(242159)\) \(1.253\text{ms}(460904)\) \(0.412\text{ms}(245822)\) \(2.066\text{ms}(860160)\) \(57.938\text{ms}(89489405)\) \(61.424\text{ms}(89494868)\) \(0.178\text{ms}(204814)\) \(0.210\text{ms}(229387)\) \(0.935\text{ms}(417797)\) \(0.512\text{ms}(273011)\) \(113.454\text{ms}(67108863)\) \(117.257\text{ms}(89478485)\) \(0.351\text{ms}(197246)\) \(0.614\text{ms}(462959)\) \(1.137\text{ms}(395480)\) \(0.766\text{ms}(264304)\)
16384(pipe organ) \(1.467\text{ms}(638262)\) \(0.277\text{ms}(125220)\) \(0.069\text{ms}(32766)\) \(0.111\text{ms}(40957)\) \(54.273\text{ms}(67125246)\) \(102.061\text{ms}(134209536)\) \(201.656\text{ms}(134209536)\) \(153.588\text{ms}(89500328)\) \(314.204\text{ms}(134234110)\) \(0.831\text{ms}(502513)\) \(1.904\text{ms}(122879)\) \(1.257\text{ms}(237860)\) \(1.938\text{ms}(576331)\) \(0.435\text{ms}(202217)\) \(2.557\text{ms}(860160)\) \(1.028\text{ms}(865169)\) \(1.049\text{ms}(967904)\) \(2.173\text{ms}(2254818)\) \(1.312\text{ms}(700809)\) \(1.537\text{ms}(466873)\) \(0.937\text{ms}(293457)\) \(42.283\text{ms}(22574423)\) \(16.216\text{ms}(11418225)\) \(2.946\text{ms}(2106422)\) \(7.548\text{ms}(6117283)\) \(1.087\text{ms}(386456)\) \(0.641\text{ms}(262698)\)
16384(final merge) \(0.142\text{ms}(198668)\) \(0.238\text{ms}(131070)\) \(0.047\text{ms}(24575)\) \(0.086\text{ms}(32766)\) \(50.884\text{ms}(67125246)\) \(96.169\text{ms}(134209536)\) \(201.151\text{ms}(100667391)\) \(225.122\text{ms}(134225919)\) \(280.666\text{ms}(134234110)\) \(0.770\text{ms}(502513)\) \(1.550\text{ms}(114688)\) \(1.101\text{ms}(243517)\) \(1.197\text{ms}(417125)\) \(0.258\text{ms}(135172)\) \(2.105\text{ms}(860160)\) \(31.164\text{ms}(44766545)\) \(31.688\text{ms}(44772007)\) \(50.273\text{ms}(67125243)\) \(0.264\text{ms}(253525)\) \(0.989\text{ms}(417866)\) \(0.641\text{ms}(262483)\) \(48.212\text{ms}(33574908)\) \(42.214\text{ms}(33562623)\) \(99.946\text{ms}(67108863)\) \(1.756\text{ms}(1362125)\) \(1.114\text{ms}(383684)\) \(0.676\text{ms}(256719)\)
16384(final merge reversed) \(1.304\text{ms}(625996)\) \(0.305\text{ms}(111179)\) \(0.053\text{ms}(32766)\) \(0.115\text{ms}(40957)\) \(114.136\text{ms}(100667391)\) \(101.498\text{ms}(134209536)\) \(226.645\text{ms}(134209536)\) \(230.679\text{ms}(119311928)\) \(442.340\text{ms}(201326591)\) \(0.016\text{ms}(10471)\) \(1.580\text{ms}(122879)\) \(1.210\text{ms}(242696)\) \(1.963\text{ms}(597224)\) \(0.599\text{ms}(298632)\) \(2.606\text{ms}(860160)\) \(1.143\text{ms}(1024757)\) \(0.974\text{ms}(801618)\) \(1.743\text{ms}(1432379)\) \(0.916\text{ms}(664214)\) \(1.631\text{ms}(475112)\) \(0.929\text{ms}(276722)\) \(86.519\text{ms}(46145535)\) \(50.690\text{ms}(26879577)\) \(207.739\text{ms}(100626443)\) \(50.560\text{ms}(22433779)\) \(1.814\text{ms}(383042)\) \(0.985\text{ms}(262551)\)
16384(heapified) \(0.936\text{ms}(281663)\) \(0.617\text{ms}(195499)\) \(0.578\text{ms}(242015)\) \(0.922\text{ms}(285064)\) \(72.566\text{ms}(86564745)\) \(102.179\text{ms}(134209536)\) \(240.136\text{ms}(134202877)\) \(221.239\text{ms}(115833739)\) \(356.537\text{ms}(173113132)\) \(1.716\text{ms}(600811)\) \(1.601\text{ms}(178071)\) \(1.259\text{ms}(244664)\) \(1.838\text{ms}(498317)\) \(1.520\text{ms}(370531)\) \(4.335\text{ms}(860160)\) \(0.990\text{ms}(436577)\) \(1.004\text{ms}(464902)\) \(1.039\text{ms}(258870)\) \(1.018\text{ms}(279555)\) \(2.229\text{ms}(484164)\) \(1.302\text{ms}(290579)\) \(1.152\text{ms}(368091)\) \(4.065\text{ms}(2004307)\) \(1.091\text{ms}(414175)\) \(0.883\text{ms}(256039)\) \(2.049\text{ms}(396232)\) \(1.011\text{ms}(256779)\)
16384(binary search tree) \(0.784\text{ms}(418939)\) \(0.301\text{ms}(152126)\) \(0.090\text{ms}(49260)\) \(0.732\text{ms}(307859)\) \(41.099\text{ms}(44763803)\) \(152.853\text{ms}(134209536)\) \(126.134\text{ms}(67117055)\) \(145.696\text{ms}(74116422)\) \(211.301\text{ms}(89511237)\) \(1.262\text{ms}(568045)\) \(1.568\text{ms}(131057)\) \(1.200\text{ms}(227871)\) \(1.962\text{ms}(572347)\) \(0.950\text{ms}(284229)\) \(2.461\text{ms}(860160)\) \(1.051\text{ms}(685658)\) \(1.037\text{ms}(584474)\) \(0.998\text{ms}(472348)\) \(0.896\text{ms}(444253)\) \(2.329\text{ms}(640082)\) \(1.103\text{ms}(282181)\) \(0.738\text{ms}(253260)\) \(49.008\text{ms}(33566720)\) \(3.288\text{ms}(2587004)\) \(48.909\text{ms}(33595386)\) \(1.604\text{ms}(429593)\) \(0.848\text{ms}(245834)\)
16384(sawtooth) \(0.734\text{ms}(266483)\) \(0.383\text{ms}(210654)\) \(0.474\text{ms}(273952)\) \(0.897\text{ms}(295452)\) \(42.852\text{ms}(50335743)\) \(102.813\text{ms}(134209536)\) \(286.825\text{ms}(125790213)\) \(138.987\text{ms}(79689729)\) \(213.257\text{ms}(100655103)\) \(0.022\text{ms}(19399)\) \(1.732\text{ms}(188416)\) \(1.395\text{ms}(234076)\) \(1.871\text{ms}(566593)\) \(0.592\text{ms}(259891)\) \(2.859\text{ms}(860160)\) \(1.187\text{ms}(380851)\) \(1.506\text{ms}(616866)\) \(1.902\text{ms}(295964)\) \(2.074\text{ms}(262617)\) \(4.570\text{ms}(470378)\) \(2.418\text{ms}(279580)\) \(20.432\text{ms}(4876814)\) \(23.024\text{ms}(4432662)\) \(11.184\text{ms}(4107812)\) \(3.504\text{ms}(384368)\) \(6.597\text{ms}(394983)\) \(3.075\text{ms}(256834)\)
16384(scrambled head) \(2.345\text{ms}(270474)\) \(1.486\text{ms}(150952)\) \(0.453\text{ms}(78781)\) \(1.427\text{ms}(213225)\) \(67.737\text{ms}(40918396)\) \(153.001\text{ms}(134209536)\) \(332.154\text{ms}(131814838)\) \(104.598\text{ms}(58322596)\) \(193.058\text{ms}(81820413)\) \(1.728\text{ms}(600811)\) \(1.899\text{ms}(137364)\) \(1.293\text{ms}(237974)\) \(1.883\text{ms}(537613)\) \(1.839\text{ms}(356490)\) \(5.955\text{ms}(860160)\) \(1.057\text{ms}(470716)\) \(1.072\text{ms}(683873)\) \(3.128\text{ms}(3301625)\) \(0.831\text{ms}(263876)\) \(2.072\text{ms}(465402)\) \(1.124\text{ms}(284782)\) \(1.061\text{ms}(387321)\) \(4.702\text{ms}(3148382)\) \(10.180\text{ms}(7636400)\) \(0.868\text{ms}(263357)\) \(1.683\text{ms}(382817)\) \(0.907\text{ms}(265407)\)
16384(scrambled tail) \(0.760\text{ms}(442079)\) \(0.492\text{ms}(143882)\) \(0.169\text{ms}(64453)\) \(0.177\text{ms}(64529)\) \(14.325\text{ms}(15764864)\) \(101.786\text{ms}(134209536)\) \(216.539\text{ms}(134189762)\) \(61.050\text{ms}(29574367)\) \(96.701\text{ms}(31513345)\) \(1.601\text{ms}(584428)\) \(1.814\text{ms}(128295)\) \(1.200\text{ms}(235995)\) \(1.766\text{ms}(511091)\) \(1.462\text{ms}(336460)\) \(2.995\text{ms}(860160)\) \(1.581\text{ms}(1355051)\) \(0.936\text{ms}(679289)\) \(2.869\text{ms}(3398237)\) \(0.731\text{ms}(261375)\) \(2.095\text{ms}(466367)\) \(1.062\text{ms}(284174)\) \(2.193\text{ms}(1185220)\) \(1.155\text{ms}(603408)\) \(4.676\text{ms}(3421392)\) \(0.679\text{ms}(310601)\) \(1.341\text{ms}(387185)\) \(0.746\text{ms}(268343)\)
16384(half-reversed) \(0.823\text{ms}(488862)\) \(0.418\text{ms}(117029)\) \(0.037\text{ms}(24575)\) \(0.072\text{ms}(32765)\) \(29.020\text{ms}(33566719)\) \(104.806\text{ms}(134209536)\) \(198.847\text{ms}(100659200)\) \(66.715\text{ms}(33574911)\) \(207.096\text{ms}(67117055)\) \(0.004\text{ms}(3781)\) \(1.515\text{ms}(114688)\) \(1.035\text{ms}(236807)\) \(0.693\text{ms}(239172)\) \(0.354\text{ms}(194576)\) \(2.397\text{ms}(860160)\) \(92.228\text{ms}(123042472)\) \(36.833\text{ms}(39171410)\) \(0.341\text{ms}(204814)\) \(0.402\text{ms}(229387)\) \(2.686\text{ms}(417794)\) \(1.095\text{ms}(269198)\) \(151.400\text{ms}(67112960)\) \(49.283\text{ms}(39155027)\) \(0.326\text{ms}(196506)\) \(0.983\text{ms}(703973)\) \(1.470\text{ms}(389123)\) \(1.125\text{ms}(255972)\)
16384(adversary) \(0.342\text{ms}(223881)\) \(0.328\text{ms}(178027)\) \(0.270\text{ms}(139062)\) \(0.461\text{ms}(171697)\) \(80.011\text{ms}(78297770)\) \(134.257\text{ms}(134209536)\) \(218.098\text{ms}(100659200)\) \(230.928\text{ms}(134209536)\) \(500.174\text{ms}(156579157)\) \(0.858\text{ms}(649960)\) \(1.544\text{ms}(159746)\) \(0.762\text{ms}(229276)\) \(1.101\text{ms}(339666)\) \(0.414\text{ms}(191661)\) \(3.058\text{ms}(860160)\) \(0.544\text{ms}(306543)\) \(1.541\text{ms}(1682034)\) \(0.790\text{ms}(264744)\) \(0.506\text{ms}(247225)\) \(1.466\text{ms}(398444)\) \(0.813\text{ms}(240217)\) \(55.384\text{ms}(37833275)\) \(61.936\text{ms}(42150967)\) \(91.850\text{ms}(75546639)\) \(302.622\text{ms}(134258681)\) \(76.394\text{ms}(33900120)\) \(62.637\text{ms}(34712211)\)
131072(random) \(13.131\text{ms}(2639511)\) \(15.335\text{ms}(2203088)\) \(16.691\text{ms}(3338447)\) \(18.325\text{ms}(2841361)\) \(3560.487\text{ms}(4294035285)\) \(5865.733\text{ms}(8589869056)\) \(31307.700\text{ms}(8589456381)\) \(22290.987\text{ms}(5722066232)\) \(15918.790\text{ms}(8587939507)\) \(14.706\text{ms}(5461420)\) \(19.694\text{ms}(2062729)\) \(15.012\text{ms}(2274391)\) \(19.509\text{ms}(5872698)\) \(19.738\text{ms}(5819771)\) \(54.738\text{ms}(10027008)\) \(10.694\text{ms}(3172349)\) \(9.923\text{ms}(3143883)\) \(10.429\text{ms}(2783755)\) \(10.327\text{ms}(2647945)\) \(19.579\text{ms}(4410192)\) \(11.570\text{ms}(2873342)\) \(9.793\text{ms}(2657616)\) \(9.752\text{ms}(2587712)\) \(9.779\text{ms}(2646900)\) \(9.605\text{ms}(2602579)\) \(17.265\text{ms}(3636117)\) \(11.009\text{ms}(2659061)\)
131072(ascending) \(1.667\text{ms}(2768929)\) \(1.866\text{ms}(1245182)\) \(0.090\text{ms}(131071)\) \(0.220\text{ms}(131071)\) \(0.271\text{ms}(131071)\) \(5250.243\text{ms}(8589869056)\) \(0.167\text{ms}(131071)\) \(0.123\text{ms}(131071)\) \(0.232\text{ms}(131071)\) \(0.029\text{ms}(30248)\) \(10.741\text{ms}(1114112)\) \(7.383\text{ms}(2283581)\) \(1.031\text{ms}(262113)\) \(2.203\text{ms}(1343494)\) \(20.558\text{ms}(10027008)\) \(5751.980\text{ms}(8590000125)\) \(3013.977\text{ms}(4295032830)\) \(1.785\text{ms}(2031633)\) \(1.974\text{ms}(2228238)\) \(10.341\text{ms}(3735559)\) \(4.942\text{ms}(2921005)\) \(6275.986\text{ms}(4295032831)\) \(5594.626\text{ms}(4294967295)\) \(3.100\text{ms}(1959076)\) \(33.458\text{ms}(29558583)\) \(8.601\text{ms}(3537076)\) \(6.458\text{ms}(2677870)\)
131072(descending) \(1.415\text{ms}(1982474)\) \(2.331\text{ms}(1020492)\) \(0.138\text{ms}(131071)\) \(0.134\text{ms}(131071)\) \(6904.255\text{ms}(8589869056)\) \(6446.063\text{ms}(8589869056)\) \(13945.832\text{ms}(8589869056)\) \(16041.752\text{ms}(8590000127)\) \(36044.323\text{ms}(17179738112)\) \(0.092\text{ms}(83764)\) \(10.956\text{ms}(1114112)\) \(8.701\text{ms}(2337036)\) \(11.416\text{ms}(4475879)\) \(4.769\text{ms}(2458234)\) \(23.046\text{ms}(10027008)\) \(4397.927\text{ms}(5726710440)\) \(4183.762\text{ms}(5726754130)\) \(2.284\text{ms}(2031633)\) \(1.808\text{ms}(2228238)\) \(9.287\text{ms}(3735563)\) \(5.275\text{ms}(3196336)\) \(7096.338\text{ms}(4294967295)\) \(7222.475\text{ms}(5726623060)\) \(3.147\text{ms}(1970781)\) \(8.242\text{ms}(5015574)\) \(10.795\text{ms}(3581498)\) \(7.387\text{ms}(2592741)\)
131072(pipe organ) \(13.630\text{ms}(6465407)\) \(2.759\text{ms}(1198372)\) \(0.461\text{ms}(262142)\) \(0.739\text{ms}(327677)\) \(3795.289\text{ms}(4295098366)\) \(7272.228\text{ms}(8589869056)\) \(13479.140\text{ms}(8589869056)\) \(10312.043\text{ms}(5726797822)\) \(17400.462\text{ms}(8590065662)\) \(6.716\text{ms}(5068207)\) \(23.068\text{ms}(1179647)\) \(10.450\text{ms}(2300431)\) \(17.356\text{ms}(5915619)\) \(4.070\text{ms}(1998901)\) \(26.399\text{ms}(10027008)\) \(11.970\text{ms}(10201169)\) \(13.516\text{ms}(11425050)\) \(63.845\text{ms}(49580731)\) \(24.980\text{ms}(7876485)\) \(34.683\text{ms}(4191298)\) \(21.561\text{ms}(2737712)\) \(2410.989\text{ms}(1433687383)\) \(806.950\text{ms}(718088805)\) \(59.377\text{ms}(46491921)\) \(490.642\text{ms}(401109415)\) \(8.881\text{ms}(3490389)\) \(7.787\text{ms}(2811900)\)
131072(final merge) \(1.556\text{ms}(1982476)\) \(2.176\text{ms}(1245182)\) \(0.390\text{ms}(196607)\) \(0.631\text{ms}(262142)\) \(3285.796\text{ms}(4295098366)\) \(5767.009\text{ms}(8589869056)\) \(9776.981\text{ms}(6442483711)\) \(14726.550\text{ms}(8590000127)\) \(16754.675\text{ms}(8590065662)\) \(6.280\text{ms}(5068207)\) \(10.565\text{ms}(1114112)\) \(8.381\text{ms}(2339980)\) \(10.169\text{ms}(4111575)\) \(2.459\text{ms}(1343494)\) \(21.730\text{ms}(10027008)\) \(1846.689\text{ms}(2863529980)\) \(1849.141\text{ms}(2863573669)\) \(2829.219\text{ms}(4295098363)\) \(1.964\text{ms}(2424201)\) \(7.972\text{ms}(3735650)\) \(4.833\text{ms}(2712569)\) \(3008.168\text{ms}(2147647484)\) \(2597.166\text{ms}(2147549183)\) \(5669.601\text{ms}(4294967295)\) \(35.192\text{ms}(29689369)\) \(9.326\text{ms}(3518320)\) \(5.770\text{ms}(2613544)\)
131072(final merge reversed) \(12.537\text{ms}(6321560)\) \(2.719\text{ms}(1086027)\) \(0.410\text{ms}(262142)\) \(0.624\text{ms}(327677)\) \(5125.468\text{ms}(6442483711)\) \(6415.716\text{ms}(8589869056)\) \(13627.847\text{ms}(8589869056)\) \(13755.536\text{ms}(7635570232)\) \(25793.912\text{ms}(12884901887)\) \(0.089\text{ms}(83764)\) \(10.794\text{ms}(1179647)\) \(10.094\text{ms}(2337227)\) \(15.541\text{ms}(6077913)\) \(5.210\text{ms}(3009191)\) \(22.988\text{ms}(10027008)\) \(11.624\text{ms}(11780206)\) \(11.845\text{ms}(9567114)\) \(65.939\text{ms}(63922573)\) \(12.208\text{ms}(7592421)\) \(18.821\text{ms}(4128200)\) \(15.651\text{ms}(2792602)\) \(4627.641\text{ms}(2952855551)\) \(2040.151\text{ms}(1718249053)\) \(7725.541\text{ms}(6442156043)\) \(1568.539\text{ms}(1432158195)\) \(10.988\text{ms}(3458824)\) \(6.031\text{ms}(2655978)\)
131072(heapified) \(5.782\text{ms}(2868339)\) \(2.804\text{ms}(1859656)\) \(5.190\text{ms}(2387422)\) \(7.339\text{ms}(2679776)\) \(4426.392\text{ms}(5533146484)\) \(6000.307\text{ms}(8589869056)\) \(13269.253\text{ms}(8589815456)\) \(13100.395\text{ms}(7409392845)\) \(23055.890\text{ms}(11066161928)\) \(17.931\text{ms}(5461420)\) \(16.588\text{ms}(1719820)\) \(9.285\text{ms}(2349101)\) \(18.732\text{ms}(4909604)\) \(17.344\text{ms}(3709348)\) \(81.382\text{ms}(10027008)\) \(15.219\text{ms}(4442304)\) \(13.551\text{ms}(5030179)\) \(11.162\text{ms}(2635821)\) \(9.463\text{ms}(2680195)\) \(20.703\text{ms}(4326984)\) \(10.810\text{ms}(2828109)\) \(9.974\text{ms}(3986988)\) \(118.331\text{ms}(81459081)\) \(14.235\text{ms}(10276743)\) \(6.863\text{ms}(2613954)\) \(13.813\text{ms}(3574259)\) \(8.018\text{ms}(2878110)\)
131072(binary search tree) \(6.711\text{ms}(4369082)\) \(2.298\text{ms}(1413695)\) \(0.563\text{ms}(393321)\) \(6.128\text{ms}(3219899)\) \(2224.023\text{ms}(2863508120)\) \(5732.476\text{ms}(8589869056)\) \(6763.876\text{ms}(4295032831)\) \(8208.105\text{ms}(4742075478)\) \(11611.279\text{ms}(5726885186)\) \(9.105\text{ms}(5330349)\) \(10.935\text{ms}(1245166)\) \(9.254\text{ms}(2211925)\) \(17.904\text{ms}(5899730)\) \(9.703\text{ms}(2999803)\) \(27.170\text{ms}(10027008)\) \(12.991\text{ms}(7679313)\) \(11.411\text{ms}(6399676)\) \(12.783\text{ms}(7229857)\) \(10.171\text{ms}(4615744)\) \(22.904\text{ms}(6021819)\) \(11.043\text{ms}(2990090)\) \(11.369\text{ms}(2555271)\) \(3393.205\text{ms}(2147581952)\) \(63.217\text{ms}(56640686)\) \(2811.634\text{ms}(2147811322)\) \(12.607\text{ms}(4026009)\) \(7.214\text{ms}(2624761)\)
131072(sawtooth) \(7.878\text{ms}(2666996)\) \(4.142\text{ms}(2029278)\) \(6.372\text{ms}(2682912)\) \(10.945\text{ms}(2659914)\) \(2515.499\text{ms}(3221258239)\) \(6132.442\text{ms}(8589869056)\) \(13642.029\text{ms}(8052752389)\) \(7294.218\text{ms}(5100257281)\) \(13624.257\text{ms}(6442385407)\) \(0.031\text{ms}(30248)\) \(12.577\text{ms}(1851392)\) \(10.030\text{ms}(2262907)\) \(19.549\text{ms}(5807913)\) \(5.239\text{ms}(2241226)\) \(33.708\text{ms}(10027008)\) \(12.178\text{ms}(3906054)\) \(29.687\text{ms}(20347796)\) \(11.220\text{ms}(2948400)\) \(11.569\text{ms}(2559308)\) \(24.319\text{ms}(4171198)\) \(14.139\text{ms}(2722952)\) \(400.241\text{ms}(276795256)\) \(388.475\text{ms}(271542722)\) \(266.828\text{ms}(141864628)\) \(14.324\text{ms}(6046979)\) \(30.183\text{ms}(3588243)\) \(20.159\text{ms}(2689539)\)
131072(scrambled head) \(15.868\text{ms}(3204338)\) \(8.049\text{ms}(1428683)\) \(4.491\text{ms}(705749)\) \(7.679\text{ms}(1055890)\) \(2203.177\text{ms}(2617369180)\) \(6704.447\text{ms}(8589869056)\) \(12879.586\text{ms}(8436493750)\) \(6203.627\text{ms}(3730843824)\) \(10539.158\text{ms}(5234607296)\) \(21.465\text{ms}(5461420)\) \(21.314\text{ms}(1320451)\) \(18.348\text{ms}(2297016)\) \(39.355\text{ms}(5580401)\) \(45.848\text{ms}(4402738)\) \(65.078\text{ms}(10027008)\) \(22.658\text{ms}(5371217)\) \(21.053\text{ms}(6563461)\) \(192.464\text{ms}(202527178)\) \(6.317\text{ms}(2526225)\) \(15.128\text{ms}(4165243)\) \(8.169\text{ms}(2755051)\) \(5.958\text{ms}(3440467)\) \(212.173\text{ms}(179224512)\) \(536.947\text{ms}(482820061)\) \(8.426\text{ms}(2603340)\) \(25.486\text{ms}(3478135)\) \(19.316\text{ms}(2598609)\)
131072(scrambled tail) \(13.568\text{ms}(2687471)\) \(8.971\text{ms}(1372817)\) \(4.204\text{ms}(591069)\) \(4.329\text{ms}(574841)\) \(1018.387\text{ms}(1006854755)\) \(5956.928\text{ms}(8589869056)\) \(16201.864\text{ms}(8589595282)\) \(3524.616\text{ms}(1890426047)\) \(3846.089\text{ms}(2013578439)\) \(19.069\text{ms}(5592491)\) \(12.053\text{ms}(1247894)\) \(10.433\text{ms}(2280883)\) \(15.624\text{ms}(5354295)\) \(20.138\text{ms}(4229698)\) \(44.632\text{ms}(10027008)\) \(25.070\text{ms}(14267263)\) \(16.372\text{ms}(7620162)\) \(280.632\text{ms}(210454957)\) \(11.733\text{ms}(2582435)\) \(29.484\text{ms}(4165740)\) \(21.845\text{ms}(2724798)\) \(53.654\text{ms}(13621799)\) \(25.764\text{ms}(6547928)\) \(489.867\text{ms}(210777782)\) \(6.758\text{ms}(3413581)\) \(11.010\text{ms}(3532550)\) \(6.554\text{ms}(2588605)\)
131072(half-reversed) \(6.334\text{ms}(4808569)\) \(2.070\text{ms}(1132837)\) \(0.309\text{ms}(196607)\) \(0.500\text{ms}(262141)\) \(1605.139\text{ms}(2147581951)\) \(6077.700\text{ms}(8589869056)\) \(9411.972\text{ms}(6442418176)\) \(3733.551\text{ms}(2147647487)\) \(8518.458\text{ms}(4295032831)\) \(0.165\text{ms}(30248)\) \(10.693\text{ms}(1114112)\) \(7.639\text{ms}(2292212)\) \(5.750\text{ms}(2352819)\) \(3.444\text{ms}(1933606)\) \(25.718\text{ms}(10027008)\) \(5082.894\text{ms}(7874183165)\) \(1580.156\text{ms}(2505594196)\) \(1.931\text{ms}(2031633)\) \(1.710\text{ms}(2228238)\) \(7.864\text{ms}(3735560)\) \(4.265\text{ms}(2674964)\) \(5946.211\text{ms}(4295000064)\) \(2747.047\text{ms}(2505463124)\) \(2.627\text{ms}(1964957)\) \(14.918\text{ms}(12958055)\) \(8.240\text{ms}(3545780)\) \(5.604\text{ms}(2817338)\)
131072(adversary) \(2.988\text{ms}(2195283)\) \(2.685\text{ms}(1719146)\) \(2.823\text{ms}(1358033)\) \(3.824\text{ms}(1579170)\) \(3952.256\text{ms}(5010827946)\) \(5826.698\text{ms}(8589869056)\) \(10065.897\text{ms}(6442418176)\) \(14324.222\text{ms}(8589869056)\) \(20133.672\text{ms}(10021524821)\) \(339.841\text{ms}(357124913)\) \(10.929\text{ms}(1572866)\) \(5.734\text{ms}(2227444)\) \(8.139\text{ms}(3386134)\) \(3.219\text{ms}(1704209)\) \(21.156\text{ms}(10027008)\) \(4.707\text{ms}(3074298)\) \(61.877\text{ms}(95859104)\) \(4.789\text{ms}(2529755)\) \(5.577\text{ms}(2391197)\) \(13.247\text{ms}(3587200)\) \(6.775\text{ms}(2394073)\) \(3698.420\text{ms}(2420298931)\) \(2696.626\text{ms}(2692729308)\) \(4808.696\text{ms}(4832460452)\) \(8491.709\text{ms}(8590262265)\) \(2517.525\text{ms}(2150477603)\) \(2072.902\text{ms}(2155288663)\)