做了codility网站上一题：CountBoundedSlices
在写上一随笔之前，在Codility网站上还做了一个道题（非Demo题）：CountBoundedSlices，得了60分（害臊呀）。今天又重新做了一下这个算法，性能提高了不少，但由于此题不是Demo题，不能重新在Codility网站测试了。
可以从http://codility.com/cert/view/certAWY5VP-D46CA7989XU4XEZT/details看到题目的详细信息。
这里把题目copy出来：
An integer K and a non-empty zero-indexed array A consisting of N integers are given.
A pair of integers (P, Q), such that 0 ≤ P ≤ Q < N, is called aslice of array A.
A bounded_slice is a slice in which the difference between the maximum and minimum values in the slice is less than or equal to K. More precisely it is a slice, such that max(A[P], A[P + 1], ..., A[Q]) − min(A[P], A[P + 1], ..., A[Q]) ≤ K.
The goal is to calculate the number of bounded_slices.
以下新做的算法及第一次做的算法贴在下面：
def solution(K, A): # http://codility.com/cert/view/certAWY5VP-D46CA7989XU4XEZT/details _ret_numer = 0 _count = len(A) for _inx in range(_count): _max_int = None _min_int = None for _inx2 in range(_inx,_count): if _max_int is None: _max_int = A[_inx2] else: if _max_int < A[_inx2]: _max_int = A[_inx2] if _min_int is None: _min_int = A[_inx2] else: if _min_int > A[_inx2]: _min_int = A[_inx2] if _max_int - _min_int <= K: _ret_numer += 1 else: break return _ret_numer def solution2(K, A): def sum_special(number, times): return sum(range(number, number-times, -1)) _ret_numer = 0 _current_inx = 0 # current index _loop_inx = _current_inx # loop index for array. _minvalue_inx = _current_inx # index of min value for a loop break. _maxvalue_inx = _current_inx # index of max value for a loop break. _count = len(A) # array length while _loop_inx < _count: # compare two values, get max if A[_maxvalue_inx] < A[_loop_inx]: _maxvalue_inx = _loop_inx # compare two values, get min if A[_minvalue_inx] > A[_loop_inx]: _minvalue_inx = _loop_inx # break if meeting condition. if A[_maxvalue_inx] - A[_minvalue_inx] > K: _first_inx = None _second_inx = None if _minvalue_inx <= _maxvalue_inx: _first_inx, _second_inx = _minvalue_inx, _maxvalue_inx else: _first_inx, _second_inx = _maxvalue_inx, _minvalue_inx _ret_numer += sum_special(_second_inx-_current_inx, _first_inx-_current_inx+1) _current_inx = _first_inx + 1 # move next to first_inx _loop_inx = _current_inx _minvalue_inx = _current_inx # index of min value for a loop break. _maxvalue_inx = _current_inx # index of max value for a loop break else: _loop_inx += 1 # increment one if _current_inx != _loop_inx: _ret_numer += sum_special(_loop_inx-_current_inx, _loop_inx-_current_inx) return _ret_numer
关于新做的算法，虽然性能提高了很多，但我还是不是很满意，因为_loop_inx在每次满足K条件计算后还要重新回溯到_current_inx位置，按理说应该通过记录更多数据达到不需要回退，试了几次发现复杂度陡升。
列了测试case：
def test(K, A): print K, len(A), A[:10] import time _start = time.time() _value = solution(K, A) _end = time.time() print "solution result: time=%f, value=%d" % (_end-_start, _value) _start = time.time() _value2 = solution2(K, A) _end = time.time() print "solution2 result: time=%f, value=%d" % (_end-_start, _value2) return _value == _value2 def sample_test(): import random N = random.randint(1,100000) A = [random.randint(-1000000000,1000000000) for _ in xrange(N)] K = random.randint(0,1000000000) return test(K, A) def simulate_test(times=100): _error_occur = False print "simulate start..." for _ in range(times): if not sample_test(): _error_occur = True break if _error_occur: print "occur error, please check it" print "simulate complete"
以下是随机做100次，两次算法测试结果对比。可以看到两此算法得到time差距挺大的，如果codility网站测试，应该能够高于60分吧。
>>> simulate_test(times=100) simulate start... 712518820 21893 [233628416, -652563058, 551353390, -217560133, -154138713, 563467537, 808230529, -205481433, 561911746, -750371596] solution result: time=2.067000, value=46806 solution2 result: time=0.028000, value=46806 871940175 46368 [937986329, -952927755, -932362380, -469631039, -306238711, 696474641, -783179175, -931362077, -937403887, -681449512] solution result: time=9.547000, value=118063 solution2 result: time=0.060000, value=118063 477409879 75579 [-995189110, 153461080, 383822333, -755867874, -499883883, -432680163, 96191219, 580653424, 423158838, -182965136] solution result: time=25.332000, value=123214 solution2 result: time=0.104000, value=123214 488625751 1591 [558870329, 608903479, 550502154, 81531055, 707009330, 376372020, -276696701, -161031308, -8064320, 88712047] solution result: time=0.013000, value=2571 solution2 result: time=0.002000, value=2571 436684262 20033 [-83885888, 463772906, 24144710, -480048118, 217531317, -104917140, 67141243, 714708231, -593590958, -980170193] solution result: time=1.731000, value=31133 solution2 result: time=0.030000, value=31133 155090300 81187 [-482815444, 400503737, 33426826, 421085581, -175168617, -849832660, 780212059, 694032115, -636059844, -746589641] solution result: time=29.778000, value=94954 solution2 result: time=0.124000, value=94954 465594288 40508 [521794630, -723650954, -690791173, -765608385, -393134645, 740067734, 516698048, -992683360, -335416969, -827405186] solution result: time=7.330000, value=65321 solution2 result: time=0.055000, value=65321 907687848 11438 [895044686, 806244941, -690502444, 706872903, -15439789, -491691160, -33510875, -850504728, 627498209, 178781503] solution result: time=0.580000, value=30599 solution2 result: time=0.014000, value=30599 917658188 1416 [-82302265, -328719536, 84686291, 226567716, -198056874, -651427652, -518158222, 459874316, -996196104, 762641325] solution result: time=0.011000, value=3821 solution2 result: time=0.002000, value=3821 22150008 15811 [-359774811, -601356389, -349038488, -393355819, 200142427, -247051785, 79855294, 762147974, 349270442, -543063059] solution result: time=1.124000, value=16154 solution2 result: time=0.026000, value=16154 806546890 39666 [225604285, 699280534, 574919735, -222005860, -756343609, 364653794, -642289525, -132214696, -531522216, 668841925] solution result: time=7.352000, value=93516 solution2 result: time=0.053000, value=93516 446767256 61167 [-797312962, 859493626, -481645569, -885060421, 378198746, -630555365, -714358149, -224569996, 366913479, 572567757] solution result: time=17.873000, value=96243 solution2 result: time=0.084000, value=96243 908894749 14304 [126236598, -325056547, -567716458, 756952836, 963930898, -761802348, 579888315, -191851495, -888831957, 223176046] solution result: time=0.894000, value=37720 solution2 result: time=0.017000, value=37720 445662903 43594 [-77115444, -146497457, -201219950, 298322886, 699626045, -721141178, 620626818, -656768352, 779191843, -496056951] solution result: time=9.026000, value=68633 solution2 result: time=0.064000, value=68633 896193106 87799 [225127782, -499401589, 576280745, -193205926, -378379146, 201195499, 240271554, 1990460, 524040734, 276918545] solution result: time=37.246000, value=229708 solution2 result: time=0.106000, value=229708 898616436 3450 [-263848570, 466852557, 87733905, -345331987, 194432951, -122943788, 407961797, 253794919, 869433356, 175595518] solution result: time=0.057000, value=9435 solution2 result: time=0.005000, value=9435 346182055 75038 [451820085, 404626026, -312042611, -316557991, 563084929, 371309936, -245776405, -127691048, -243875924, -494809654] solution result: time=27.318000, value=106255 solution2 result: time=0.116000, value=106255 534249547 79539 [-891387059, 567285015, -664026466, -101133107, 510858959, -446038753, 566859262, -566626952, 365507295, 476351425] solution result: time=29.328000, value=136652 solution2 result: time=0.108000, value=136652 504143400 31603 [972028042, 283415620, 607959186, -642899634, -686734313, 810373520, -695705028, -836014133, 168291764, 756721934] solution result: time=4.457000, value=52865 solution2 result: time=0.044000, value=52865 384581802 77375 [124172689, -989437467, 213271375, 767367034, -635598230, 573627766, -17536139, 529795086, -403202636, 145615315] solution result: time=27.306000, value=114084 solution2 result: time=0.112000, value=114084 818348046 9450 [867092810, -949286543, 710835399, -753470788, -461126327, -232093661, -971742891, 367646003, 269914630, -404115168] solution result: time=0.406000, value=22305 solution2 result: time=0.012000, value=22305 173852970 60865 [-620839314, -542468951, -756181557, 561495967, 377686974, 577437042, -377448675, 886945237, 89270904, -610962060] solution result: time=16.640000, value=72461 solution2 result: time=0.094000, value=72461 499297656 13388 [-658918296, 573321638, -881032247, 133944805, 107632459, 404755776, -349641260, 499223348, 616340316, 209652460] solution result: time=0.816000, value=22225 solution2 result: time=0.019000, value=22225 405777536 4712 [991132018, -555754397, 815968493, 341471300, 349248457, -366471082, -502991469, -904956372, -410473995, 154448524] solution result: time=0.104000, value=7171 solution2 result: time=0.007000, value=7171 645972146 48874 [207036460, 777964439, -869769768, 632827966, 492357468, -897393398, 144409238, 790113060, 527670908, -371291798] solution result: time=10.739000, value=95091 solution2 result: time=0.064000, value=95091 808578966 98628 [634313108, -942656305, -643190985, -416688166, -983545086, 912481211, 163493211, 74856124, 711407211, -266978307] solution result: time=43.970000, value=232592 solution2 result: time=0.121000, value=232592 355325933 76586 [662937721, -145146531, -398164748, 673949927, 308331782, 325586368, 23113293, 986270073, -816944356, -730811600] solution result: time=26.614000, value=110348 solution2 result: time=0.114000, value=110348 761216523 93577 [-837332680, 771328205, -719811887, 791884900, -13712154, 283433368, 918649998, -655057859, -788172865, 455689690] solution result: time=40.215000, value=207636 solution2 result: time=0.116000, value=207636 783573895 55337 [245850466, 177512999, 972610314, -537276190, 510326842, 943461244, 814218276, 775038330, 258371520, 381553002] solution result: time=13.974000, value=127198 solution2 result: time=0.075000, value=127198 832961419 8705 [527690176, -142454319, -833394683, -23090434, 983716699, 949421655, 66180144, -63036290, 527943121, -167037530] solution result: time=0.337000, value=21191 solution2 result: time=0.010000, value=21191 327033249 19748 [-422213445, -39921808, -587681736, 557326963, 708249854, 879393396, -408082146, 122508216, 651860574, 407392392] solution result: time=1.821000, value=27434 solution2 result: time=0.029000, value=27434 585634165 70062 [425757413, 803383603, 161247508, -916557044, 595616918, 768806511, 237103747, 236377526, 12194813, -866313211] solution result: time=23.379000, value=128177 solution2 result: time=0.098000, value=128177 563474140 94150 [-703235352, 35870455, 335996845, -595442340, 421192010, 648244845, 840504662, 302486161, 616434154, 400639679] solution result: time=46.241000, value=168336 solution2 result: time=0.137000, value=168336 82122439 62173 [489853684, 563492429, 789310745, 472733566, -743742866, -399996889, 104565340, -687414875, -504564072, 737758124] solution result: time=19.033000, value=67597 solution2 result: time=0.096000, value=67597 109729378 7307 [633154092, -57032773, 558099426, 4039547, -8965147, 149102167, -886781021, -30871882, 513890435, 652674395] solution result: time=0.246000, value=8152 solution2 result: time=0.011000, value=8152 822838845 71765 [167311255, -474601042, -127570038, 385860789, 580427297, 463957253, 493028118, 254566413, 730987268, 872890654] solution result: time=25.029000, value=172331 solution2 result: time=0.093000, value=172331 337754458 70673 [-462598416, 962379077, 170887493, -732389260, -684586478, -136816765, -170107401, 951118787, -834481478, 79708570] solution result: time=24.828000, value=98952 solution2 result: time=0.113000, value=98952 153483349 82204 [-404359860, 376658497, -435203359, -726096623, 691866378, -685408854, -636659789, -756316181, -277011379, 564607832] solution result: time=33.016000, value=95720 solution2 result: time=0.121000, value=95720 762844266 14208 [83806463, 132385188, 102461415, 968336292, 188351300, -428967587, -61086466, 201214276, -871725323, 86747156] solution result: time=0.939000, value=31248 solution2 result: time=0.018000, value=31248 897408826 72107 [35258331, 315858099, -223428272, 533245539, -610000767, 662929147, 651812106, -909524082, 243889270, -901410127] solution result: time=24.851000, value=190545 solution2 result: time=0.088000, value=190545 743698423 29084 [419956009, -553181412, 678881476, 409448464, 140269216, 740233466, 100032755, 439377696, -57410744, 152443857] solution result: time=4.077000, value=64165 solution2 result: time=0.038000, value=64165 326295028 16648 [-798168361, 457779581, 908568446, -473471277, -221084137, 270011445, 736569831, -669910270, -176674556, 143606485] solution result: time=1.293000, value=23065 solution2 result: time=0.025000, value=23065 436796613 80483 [727731281, -964077429, -917817354, 251377572, 859200396, -893534473, 289487629, -260281044, 837685396, 645482629] solution result: time=30.663000, value=125454 solution2 result: time=0.113000, value=125454 93425419 15686 [562256985, 8031239, 586441668, 414353339, -645037703, -896644019, -764560767, -69489267, 390240171, -50267606] solution result: time=1.144000, value=17191 solution2 result: time=0.024000, value=17191 674636947 21055 [550084099, -802488786, 609915011, -586347975, 526196054, -45129218, -733855544, 588035730, -4877919, 301136186] solution result: time=2.057000, value=42626 solution2 result: time=0.030000, value=42626 834244298 56637 [342849532, 247426826, -408774084, -271290404, -844270714, -540658336, -924957693, 215269084, 68698466, 20471291] solution result: time=15.251000, value=139012 solution2 result: time=0.076000, value=139012 36645599 16550 [921658471, 896437246, 505287263, 940913814, 691022604, -99749202, -314310287, -357254151, 422328865, -529373634] solution result: time=1.286000, value=17159 solution2 result: time=0.026000, value=17159 627767452 7071 [-281962597, -343073587, -159309745, 483694105, 316782190, -720949731, 457460273, 738448118, -526524719, -925886631] solution result: time=0.239000, value=13441 solution2 result: time=0.009000, value=13441 68618630 3501 [-629773285, 911119600, 279067796, -120085978, -788279714, -426147905, 709014529, -880362509, 163920372, 15117878] solution result: time=0.073000, value=3754 solution2 result: time=0.009000, value=3754 438229966 85292 [564210654, -666516923, -821492950, -592644856, 21851293, 320812012, -371769959, 343554559, 239479135, -614081644] solution result: time=34.535000, value=133209 solution2 result: time=0.140000, value=133209 60590254 44959 [802293468, -868006856, 717045106, 431953073, 232681248, -715567245, 161989388, 396482999, -360885655, -452082510] solution result: time=9.660000, value=47734 solution2 result: time=0.076000, value=47734 367136486 49884 [-569156615, 913618240, -986936913, -940493527, 891341874, 693443649, 884924425, -856141178, 69173897, -919026395] solution result: time=11.874000, value=72178 solution2 result: time=0.073000, value=72178 795304404 50530 [860065037, -235481529, -253357520, 92286946, 852038144, -81322281, 679320675, 84736643, -956217945, -987449813] solution result: time=11.689000, value=116212 solution2 result: time=0.063000, value=116212 673542513 67615 [107244507, -451962005, -275019984, 135368790, 419474092, -742250690, 509036286, 111926590, -575869367, 749708273] solution result: time=20.965000, value=136532 solution2 result: time=0.088000, value=136532 490294164 27654 [-541928294, -831893921, 382579626, -502987376, -210162522, 135048583, -116677670, -706590577, -478384698, 389698878] solution result: time=3.483000, value=45851 solution2 result: time=0.040000, value=45851 401372908 53232 [-481058407, 298484033, 408625876, 972746889, -560687223, 974105405, -302224935, 631935384, 822204678, 476219625] solution result: time=12.949000, value=80131 solution2 result: time=0.077000, value=80131 284735741 51881 [-345807207, -129261965, -352380669, 277914830, 291780286, 152315428, -184992070, 483307946, -446674379, 948115430] solution result: time=12.332000, value=69129 solution2 result: time=0.077000, value=69129 432883620 62480 [469503850, -539457993, -842789654, -479584582, 908984876, -696502180, -840353152, 737456491, 757536480, -439888052] solution result: time=17.879000, value=96916 solution2 result: time=0.087000, value=96916 164951982 89712 [779076511, -232870291, -861584260, -52539474, -673546529, -96336485, -96756249, 17707699, 98505217, -205525504] solution result: time=37.262000, value=106016 solution2 result: time=0.137000, value=106016 513937832 84274 [-21513836, 376554427, -979373372, -962866844, -457971106, -385902011, 882198155, -525170096, -294492860, -352508630] solution result: time=34.129000, value=142527 solution2 result: time=0.129000, value=142527 307963635 81777 [932178349, -527949859, -383956924, -753712604, 47089792, 690444342, 739063913, 224219373, 833574786, 971852315] solution result: time=31.118000, value=111762 solution2 result: time=0.130000, value=111762 687779571 89275 [-99308024, 658491819, -158599952, -620935925, 287375981, 838267355, -267627981, -800768276, 625181447, 19883648] solution result: time=37.183000, value=183069 solution2 result: time=0.117000, value=183069 567904914 57606 [-367813911, 30467460, 206847465, 549982402, 676142457, -453426240, -595993045, -226172178, 627387247, -98718053] solution result: time=15.267000, value=103433 solution2 result: time=0.080000, value=103433 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