Find the Mersenne Twister seed fastest-code
Given a sequence of N 32-bit unsigned integers, find a 32-bit seed for the Mersenne Twister PRNG (specifically, MT19337) such that the first N 32-bit unsigned integers produced are the input sequence.
Rules
- Solutions will be tested and timed on a free Cloud9 workspace (512 MB RAM, 1 8-core CPU). Full CPU specifications can be found in this Gist.
- There will be 50 sequences used to time solutions, each containing at least 20 and at most 50 integers. All sequences will be generated using CPython 3.4's MT19337 implementation (the source code can be found here).
- Brute force (by way of iterating through all possible seeds) is not allowed, as it would take an obscene amount of time to run all 50 timing cases with such a solution.
- Hard-coding seeds is not allowed, as it undermines the point of this challenge.
- I reserve the right to change the timing sequences to different sequences of similar complexity if needed, such as in the event that two seeds are found for the same sequence.
- Please include instructions on how to run your solution, including installation instructions for any software that is not included with a standard Ubuntu installation.
Test Cases
Note that the seeds given may not be the only seeds which produce the given sequence (if other seeds are found, please let me know). These smaller test cases are provided for verification purposes only, and will not be used for scoring.
[859552199, 418371998] -> 765976290
[3575669016, 3345750943, 1425199743, 3641622143, 468413882, 1201820413, 440223465, 4032367274, 1303769163] -> 3089232394
[3301913871, 2465802243, 3612732284, 2327984155, 3125193467, 1186355054, 3586515345, 1676699096] -> 3317482306
[1187719129, 4252341260, 3652285377, 2546267472, 259146681, 3132024105] -> 618872552
[567043356, 3386297553, 3291980436] -> 2064328469
[2371812852] -> 3402334589
[2169144927, 1612138200, 2367065602, 3106703576, 3360699020, 2044583150] -> 1508970517
[4264152408, 93510901, 2140553491, 2298459244, 3988997159] -> 3805008435
[815695699, 3390998580, 1837233431, 35472600] -> 1298560578
[2785297506, 692193253, 1505379580, 2810620241, 2299478120, 233996693] -> 1856467397
Timing Cases
These are the 50 sequences, along with the respective seeds that produced them, that will be used for scoring solutions. Once again, if any other seeds are found that produce the given sequence, please let me know.
[3626764237, 1654615998, 3255389356, 3823568514, 1806341205, 173879092, 1112038970, 4146640122, 2195908194, 2087043557, 1739178872, 3943786419, 3366389305, 3564191072, 1302718217, 4156669319, 2046968324, 1537810351, 2505606783, 3829653368, 3900315155, 938204377, 2167613558, 598176026, 1210484339, 600203567, 3246154361, 407295012, 2655874620, 3433407905, 1075916535, 4240245955, 3907330410, 2287343378, 4221031477, 3028691745, 3479856542, 2585149702, 3874773259, 631194409, 1332073689, 424185324, 3134603515, 316721330] -> 0
[3393124633, 2450474977, 1966463085, 3673681320, 1729202683, 1167867720, 325264180, 3917283871, 100160351, 791524511, 2930202830, 3113143968, 1502082504, 1809749915, 418618347, 1516663034, 578608165, 3127414055, 3472262548, 308161377, 135281507, 4131277967, 3953099834, 1042116387, 1985078128, 1789355090, 2975834429, 2756451880, 1853842973] -> 80552670
[3501423986, 1904817736, 3722254077, 4209805889, 624241735, 3072497443, 3348948634, 948724253, 2775088165, 653145320, 699931897, 2271688288, 965327734, 3611254581, 4021716510, 3489649715, 590896686, 2492882151, 2449284001, 1709766651, 2373030892, 1906330141, 3281376004, 542155191, 654946082, 3866707349, 675539429, 3153689518, 2192976919, 2369760520, 1789539597] -> 123863960
[161627675, 758641073, 3882484966, 1142624247, 4128058828, 2063104815, 1532506610, 4133456839, 2543581728, 18178196, 2276191025, 6278001, 3128406689, 2146406812, 39141315, 1050571803, 2511216100, 2411368419, 3269811767, 815334548, 3812711899] -> 178693462
[1006603821, 2040840228, 2217261808, 3301867033, 3944952417, 1692780898, 40334807, 2573488161, 1195239502, 1063781197, 758636410, 1944506134, 1022411961, 3709537934, 175021745, 3183030828, 1196557078, 11946672, 1551403327, 4143434962, 3283348277, 1825370082, 2293735756, 429108850, 745523037] -> 227497455
[2252079699, 1086590868, 525211993, 209343944, 1861419840, 2057307759, 2083384643, 2590024292, 4135416707, 3508386594, 1358765199, 3089076939, 3719484781, 516962076, 4107295833, 723033883, 1857756581, 434940583, 919038598, 2441529245, 1687894943, 13982251, 1940221612, 220848786, 1518435648] -> 260282679
[1821793358, 3054510267, 1906284293, 3380915352, 2593544407, 3915598365, 216223976, 4179796969, 2252681786, 35956624, 2373486206, 877849443, 3555235079, 3667331109, 2387597923, 2892840935, 1697182374, 4016309999, 3498537950, 2841634562, 3522184350, 1705717875, 4162597164, 2056807023, 2211204973, 3267303967, 3919558114] -> 325889376
[1201670212, 746140380, 1320204973, 751872422, 3310421711, 1963946901, 625374447, 2435010607, 3055683554, 3426449636, 4008426547, 337682689, 4056318014, 2315028303, 3896431367, 3153777187, 595649858, 3945299365, 113301178, 437820390, 2219035549, 284287245, 3156511236, 3954981533, 599197497, 3946167954, 3728124202, 733618224, 2033404503, 2973733622, 2705618778, 3966553008, 4036118888] -> 389267947
[1910148876, 4015517082, 1214608849, 988091919, 2525094197, 81939600, 3978887728, 2847303411, 66064807, 3605598571, 819502713, 233898591, 1970756897, 2621444751, 213250142, 3439913424, 1332746382, 4063692407, 869169264, 660008864, 2526902458, 3155477426, 1686496804, 3877857092, 4248058769, 2220603751, 465407251, 3418337662, 362811108] -> 424148743
[2663034465, 347641133, 1266329350, 494434286, 24416336, 1697535896, 233051569, 1134030615, 821790629, 1645020605, 2310228737, 63596966, 3832219398, 465243130, 4070794284, 1062758865, 2070536142, 2272514237, 440192702, 3490367376, 3000125608, 1175130963, 339129292, 1200804986, 3560746354, 1043913893, 489469329, 3588157041, 415367051, 1506938118, 519839008, 3921307375, 1017013313] -> 481818733
[2125426152, 580419999, 1942656966, 733532664, 1002041383, 4276401064, 3164003602, 1600445806, 87486541, 585241213, 1822489492, 3670405099, 2371866217, 293071217, 1698095716, 2860716495, 4096732631, 860271933, 1698519068, 1453446230, 2296564613, 1034887983, 3124580892, 3613882243, 3142206150, 1201496338, 262241539, 2658580629, 75299337, 1543495990, 1079614000, 1988996951, 1393947112, 3686457188] -> 503218192
[849928291, 3109119200, 641398141, 953565598, 1651963094, 2973763708, 2409024299, 2638872282, 3438675501, 2024561790, 2574711112, 2224233243, 2145875524, 2483785498, 832036542, 2756591965, 804169437, 1610259885, 1727659540, 3804671151, 2651460465, 3679117113, 3392652401, 4291100134, 3315401681, 4150630548, 3255282492, 1793428708, 4213220288, 1275054855, 3395683809, 126422719, 747072718] -> 529806420
[3795382423, 2318193600, 2941259533, 1429473204, 3841712189, 908410440, 2163447895, 2266401416, 1962272288, 2172290597, 903602965, 2493475709, 1557270830, 1269693466, 1882416966, 1675172531, 2727910931, 67882201, 982110502, 922191612, 1147478737, 1527639226, 1162436584, 3427111171, 1012039523, 775426178, 2235111095, 838473449, 3547292154, 2331447259, 2482093779, 3522096001, 978885775, 911597256, 4199754157, 884328339, 3958245046, 3701693539, 2205845644, 737996384] -> 594670421
[2281257517, 3184614238, 760843542, 2349085191, 3946149756, 3843515781, 357391440, 280771960, 1523563345, 1988608601, 3428233753, 100999796, 1858706576, 3053822297, 2013347998, 2869736987, 3049191880, 2683304507, 2165662057, 1644801829, 3174344328, 516799881, 2817748912, 680940874, 60488796, 440310808, 4238771580, 3333869324, 3437732706, 2291819087, 2904810286, 643100619, 2444662123, 2814934785, 3198564042, 3050641347, 2644737611, 1044358220, 2729428974, 2696207835, 1949284287, 2602160488, 4077269219, 843097934] -> 608761482
[2459044101, 3628291690, 21901316, 1607776779, 574126446, 2632595613, 1898457307, 1993218217, 2268071755, 2262630078, 1334308000, 2756814507, 1322265974, 493521136, 3513003023, 1998755513, 501729387, 461623974, 2703701229, 3074392802, 2895338933, 1257991758, 1147599903, 2188879650, 2802233695, 1049885503, 67969151, 3855902849, 1481701505, 2592817148, 3215907335, 3924969407, 91996333, 857125517, 3408363147, 4006870634, 998389513, 1316925910, 1621658875, 2583060764, 3809067813, 4122609293, 3970592027, 529557207, 1717219729, 2504378950, 418151974, 1944676036, 4136632810, 2747386509] -> 672575322
[58833619, 2580439730, 3693390914, 2286941505, 2380251005, 860188183, 1775128121, 1286129564, 1885665593, 2208299577, 4157266729, 3426550994, 3918528183, 4277973044, 3399609402, 1027156209, 2127983039, 4014806283, 1680366681, 2338809246, 2450101289, 2369487851, 2470761981, 4146252501] -> 758102662
[1228778451, 3161629785, 956090791, 2661866534, 3797423759, 387813121, 686718911, 1671912681, 3122216050, 3708361254, 2450007821, 562470295, 2371567740, 594715145, 1539207036, 1044745741, 3799733486, 3957279143, 3072889407, 43156136, 564713293, 3478075046, 3706967146, 3687044887, 992776898, 3807405066] -> 829276193
[4181681092, 472808862, 2820379353, 1971138909, 957029949, 383690688, 1619203644, 40060279, 799380031, 2522476881, 3052161194, 1101783645, 550394884, 1003243703, 1139176364, 637909704, 1746995412, 3569010375, 2962331845, 1221693446, 1622613434, 2503259347, 1956882342, 3173044265, 1239439145, 842693462, 2538205226, 2451274505, 4212820092, 3591867315, 1233020299, 978021001, 3148810648, 1811827712, 2638973530, 815364991, 1169900461, 1109925685, 856009157, 3254416301, 2037813477, 3945026418, 1535198958, 4259784019, 573350683, 1682977388, 1817703645, 2576589136] -> 898248134
[3182465441, 38281954, 424174823, 2654611156, 2877159272, 723093605, 1443837986, 3392781854, 2463922103, 4286449851, 538962217, 2130457280, 2178815165, 3486677232, 4058242555, 491907811, 162839736, 1759357975, 870141283, 1495756753, 1216746993, 1937724479, 1514235325, 4184006461, 3436845854, 2401877503, 610797147] -> 913459250
[1149034119, 2642531102, 1662163608, 3290983280, 819699523, 515983953, 2696922239, 2166479741, 1179733281, 2022256392, 1626594590, 543353369, 3692263091, 2392093428, 4014491227, 1041518429, 1713650051, 3538550903, 3376348599, 4277108217, 2867735513, 82177527, 10764183, 2126826329, 1028783725, 2271873691, 213268477, 2609718986, 3495904404, 913207638, 1265558725, 2980124058, 303469040, 253105205, 495410356] -> 931867201
[1077541173, 465200833, 3196368211, 1288748206, 2815478016, 1065298665, 2884065004, 392702413, 3587996620, 2894220485, 3226548573, 145951050, 956741233, 2456765795, 3978933657, 1007424556, 2169150234, 3651822773, 1565891297, 510586439, 2219790712, 422126653, 1640535295, 2992880885, 3691821384, 1555208492, 2642710071, 2625348100, 578265950, 592730275, 2092195932, 2504727970, 2149376041, 3179917702, 141987426, 2680075044, 656985656, 2153196909, 4149347932, 2216899428, 2639954700, 3190665042, 2786390314, 2974431514, 1505784370, 3602363995, 1699665616, 327189341, 335160466] -> 945442081
[1284631810, 3717268552, 2270237312, 1334241593, 1477854231, 3138477902, 3837857694, 3586498067, 1959233909, 3891506078, 2756512687, 2553842301, 964459746, 1395510385, 1185295577, 3096625618, 3145085801, 2953203657, 412902939, 3850708910, 2893328412, 2046860068, 86811187, 1188173782, 1294786028, 3044338056, 1040690464, 2128428491, 2571424043, 467837042, 3752155615, 4020048256, 3119445970, 2240289832, 1491368301, 3651270856, 2456196179, 378459336, 188104463, 777143930, 1824526143, 4060407078, 3866701738] -> 1005490735
[329511653, 2198540059, 2154958918, 378488687, 1460553211, 2529097663, 2295211009, 68583162, 1430570391, 1601101442, 1075009348, 2795773614, 833830658, 903181786, 633114581, 3292534356, 3245176784, 2582500259, 3943169203, 1130082435, 3079387854, 3150805871, 1721482617, 2291158702, 3225790458, 1468813727, 862011357, 4268175908, 3661137987, 464141661, 3956758980, 353701536, 1341361227, 809582799, 3968372465, 4111098095, 2898048807, 1509470117, 3255194829, 1330296075, 3520527115, 3736908846, 168999059] -> 1056211089
[1981947965, 3374825360, 3953254353, 1846368367, 1512467473, 3858309918, 4274851313, 787575622, 1876080592, 73919936, 3951066372, 730226758, 3289279637, 768907525, 1773361296, 821210337, 823248190, 869737395, 1360958003, 37854528, 426098214, 2732039516, 64754302, 3276807872, 3816769165, 991587659, 2262236344, 2500333010, 544193426, 1576372318, 2228843007, 2361635236, 2149913894, 3651360213, 2399010654, 4269441712, 1500948518, 3962883634, 1885037482, 2608182179, 3516218188, 513897987, 4242749462, 3892663321, 3922003874, 2123606394, 1383207752, 2867973529, 3840556114, 2969243741] -> 1071722183
[2514263486, 742731713, 3234620175, 3101660088, 2571087369, 3985627296, 3534135449, 2957356517, 2720311929, 2985074784, 2621199558, 3407431088, 2711831197, 1247421057, 3794320157, 1180925811, 1569942151, 2629267152, 173488457, 1406704148, 3969219352, 291552269, 1333806964, 2203738485, 1554560925, 496218017, 1379546509, 2539796280, 4118468566, 2328295795, 884528669, 123600717, 1597383076] -> 1093875318
[1521547521, 982639096, 3108583938, 3860926389, 1477036165, 2087376039, 953332718, 1432039007, 836148138, 3081500185, 396473811, 1621365414, 3796659618, 3939606659, 4248871833, 2917576264, 2729341943, 2981171481, 2311970081, 150264587, 2215220955, 995666639, 452785817, 758560294, 2134005122, 39617150, 1283053470, 4198921194, 2492185018, 595457083, 1042642207, 545670342, 4068770955, 749869737, 984770127, 663196981, 1849907933, 1443537561, 3860175505, 1016163998, 3260982442, 3769639327, 2728953690, 1556597597, 1877966580] -> 1155984918
[1198705327, 1935517658, 503589232, 1577874702, 627636752, 3338218922, 1157893341, 3491377096, 158028724, 2472091015, 1488124620, 2401465711, 3064309912, 1501000204, 3549612642, 2584717560, 1744885213, 4114571438, 1885581118, 2912594621, 3206412254, 4218195409, 2855464167, 2517461088, 685010709, 2000660923, 3562767265, 1193468772, 1470300123, 819551295, 2007863203, 980161306, 717575858, 2022655390, 1011703442, 1190149434, 182438707, 4158211886, 2175561856, 3060913999, 1239412823, 2397907962, 3942897187, 2435381198, 4007365042, 1591831562, 1664232451] -> 1198085477
[3487615865, 4016084043, 1447817513, 2774535999, 1987172957, 3906060658, 3082008686, 88752056, 1947416015, 3376238098, 3503927625, 342228658, 2709452172, 1070052314, 3791872618, 1290870698, 587900606, 1133043554, 671196454, 3876594873, 526665632, 165876551, 3122917378, 4053700531, 1298948490, 1351144611, 563691115, 322287271, 2461185743, 3663527460, 4222266716, 3553092834, 4168116886, 1291668088, 2033147092, 17653398, 3675413239, 2758765766, 2242336270, 734645239] -> 1234710497
[4199109099, 1728109096, 1057011054, 312030739, 490158329, 2571270959, 1337574406, 3037342898, 2943362559, 468588625, 1215641907, 891368463, 3446982561, 146537280, 1406572684, 1996341215, 1239450385, 3239123491, 2654855274, 584040319, 664433665, 3282777560, 3498456462, 398718226, 3318895203, 4109932784, 435092929, 3761442422] -> 1281039914
[330441100, 3682376585, 1548511518, 1012361554, 1641750013, 1347050521, 2746331107, 363031882, 3664742187, 263887825, 3045968855, 4047861721, 4201376344, 2013802400, 43925321, 2057073856, 974221675, 1240944962, 3823005386, 3154676709, 1649841356, 3211264096, 355417272, 2640980835, 2706339938, 987877841, 110633642, 4200784138, 3756125284, 471091914, 3370617977] -> 1307906352
[3242988428, 4255969082, 867271806, 415292052, 3609803438, 416630352, 3232953772, 4269951801, 350204559, 4181264343, 2332795572, 2668659134, 2628956236, 3596517643, 2454368561, 1369266677, 3672701863, 388613580, 1479812495, 2141142524, 2486572053, 2320908196, 393062185, 1938229604, 231136143, 1626064567, 1493467817, 1983339349, 894785483, 44315897, 1514887732, 1864793575, 3953707615, 3492718672, 3522516821, 289358385, 2227856486, 256540739, 4213343606, 200728817, 3396994332, 3845507785, 220892851] -> 1358830177
[3696325595, 95369954, 135918350, 487636311, 825705453, 3049392697, 841126004, 1979734631, 507462131, 1964376824, 3031319264, 3487421046, 2192402845, 3792297163, 3808487536, 1516405605, 664293073, 613658148, 4063050354, 1921745034, 2258497732, 3473698642, 3256102715, 1916456581, 1185919167, 3315712023, 2955859300, 1784025278, 2641317925] -> 1394873382
[2775177776, 3943074566, 1008831348, 423577731, 2936039382, 3419907541, 3346657170, 1767888023, 2549910502, 1510292917, 609091982, 3619041655, 1071140841, 4210891014, 4197129534, 4002247218, 1785145415, 773140313, 850187206, 3695148850, 1699963321, 2029501148, 2273345989, 2045294772, 2490424114, 3670522622, 1903814852, 2845243988, 547217989, 814736327, 1178316093, 3421797242, 583834194, 560861293, 1728122240, 1143281622] -> 1418337751
[3909221229, 1543378013, 3578599386, 1821301593, 382025872, 3090149061, 2799832135, 2969167740, 3214053618, 2459088339, 61851869, 2988154510, 3405155263, 1143312722, 3055626916, 1306722473, 2424970867, 3838250998, 2541260784, 3634562987, 91009990, 228167376, 144739158, 69758376, 1416179539, 175832649, 1058618668, 3141319060, 2603813691, 3448922532, 3563483339, 2187253777, 3939459963, 729053170, 348198400, 2818894106, 4163690148, 4269596985, 1550179869, 2888474224, 977138852, 2267335031, 1039633247, 331897176, 3493431132] -> 1440945260
[548460784, 2008846553, 4095226690, 2537987040, 1412322911, 295388541, 388770296, 2073124976, 4254588769, 2032785043, 3714052855, 653890260, 3378524009, 4169809326, 1850329785, 2009334592, 2701527530, 260935905, 1081271463, 3349408130, 187425716, 588199859, 1037983019, 3586620795, 4254384458, 3345512384, 1424865889, 1577623131, 3897199153, 2727265103, 3204931862, 4089210973, 1909632078, 3588030047, 1946727191, 502364265, 2290334448, 2873594561, 1542446006, 3459132329, 4292608386, 3741690622, 165647068, 1253913368, 1993997790, 2812680991, 2352267270] -> 1500826128
[888893887, 2614777345, 2033163377, 4036989271, 3569896418, 1268962278, 1146226964, 107044610, 2147272927, 3436615686, 1202308143, 1325516848, 2994121867, 973196789, 3793281340, 3099942299, 2472036270, 1798140896, 2858254867, 2204354371, 3472459738, 826142039, 4066377434, 2519409484, 1777413266, 3493671143, 551412865, 886786197, 3882384707, 1172607108, 636563066, 190968362, 3994307050, 3757375918, 2755608252] -> 1566530912
[2820693508, 1716694240, 2268887698, 1296436510, 2916995305, 3041798596, 3096982293, 177546898, 3065170162, 933607211, 102294817, 1801218436, 102569645, 2901869379, 2714886480, 119387632, 656198271, 1388322584, 2775933520, 255861774, 653410879, 121504271, 3607745288, 2230556561, 2594802791, 1189055855, 1111240008, 2530579856, 936965766, 3263165681, 1646076782, 3215192313, 2313499990, 1836078863, 76222274, 3537625615, 3448299995, 1142686967, 2783169043, 1481999457, 407759227] -> 1596242054
[2829936706, 3129475899, 3747369794, 3436426639, 2221019177, 2711897885, 2281503984, 3142203725, 1105679393, 2240453588, 21256724, 1976207648, 2233823367, 3867572431, 883054004, 3828587385, 55294132, 3869553795, 815613304, 1561650320, 1751491302, 3021430621, 3344018026, 1092797427, 2270330908, 872186202, 1096541534, 2148792176, 3302750004, 1221765447, 2805795772, 779878772, 758662454, 4154291008, 1400703216, 2661407119, 3653090591, 674866675, 688479370, 757212805, 2546987102, 3742892714] -> 1598478846
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