Dada uma sequência de 625 números inteiros não assinados de 32 bits (ou seja, no intervalo [0, 2**32)), produza qual dos seguintes geradores de números pseudo-aleatórios gerou a sequência:
Especificamente, as implementações em C desses três geradores usadas para esse desafio são as seguintes:
#include <stdint.h>
/* all code adapted from the sample implementations on the following Wikipedia pages:
https://en.wikipedia.org/wiki/Linear_congruential_generator
https://en.wikipedia.org/wiki/Xorshift
https://en.wikipedia.org/wiki/Mersenne_Twister
*/
uint32_t lcg_seed;
uint32_t xor_x, xor_y, xor_z, xor_w;
void lcg_srand(uint32_t seed) {
lcg_seed = seed;
}
uint32_t lcg(void) {
lcg_seed = ((uint64_t) lcg_seed * 1103515245 + 12345) & ( (uint64_t) 0xFFFFFFFF );
return (uint32_t) lcg_seed;
}
void xorshift128_srand(uint32_t x, uint32_t y, uint32_t z, uint32_t w) {
xor_x = x;
xor_y = y;
xor_z = z;
xor_w = w;
}
uint32_t xorshift128(void) {
uint32_t t = xor_x;
t ^= t << 11;
t ^= t >> 8;
xor_x = xor_y; xor_y = xor_z; xor_z = xor_w;
xor_w ^= xor_w >> 19;
xor_w ^= t;
return xor_w;
}
enum {
// Assumes W = 32 (omitting this)
N = 624,
M = 397,
R = 31,
A = 0x9908B0DF,
F = 1812433253,
U = 11,
// Assumes D = 0xFFFFFFFF (omitting this)
S = 7,
B = 0x9D2C5680,
T = 15,
C = 0xEFC60000,
L = 18,
MASK_LOWER = (1ull << R) - 1,
MASK_UPPER = (1ull << R)
};
static uint32_t mt[N];
static uint16_t index;
// Re-init with a given seed
void mt_Initialize(const uint32_t seed) {
uint32_t i;
mt[0] = seed;
for ( i = 1; i < N; i++ ) {
mt[i] = (F * (mt[i - 1] ^ (mt[i - 1] >> 30)) + i);
}
index = N;
}
static void mt_Twist() {
uint32_t i, x, xA;
for ( i = 0; i < N; i++ ) {
x = (mt[i] & MASK_UPPER) + (mt[(i + 1) % N] & MASK_LOWER);
xA = x >> 1;
if ( x & 0x1 )
xA ^= A;
mt[i] = mt[(i + M) % N] ^ xA;
}
index = 0;
}
// Obtain a 32-bit random number
uint32_t mt_ExtractU32() {
uint32_t y;
int i = index;
if ( index >= N ) {
mt_Twist();
i = index;
}
y = mt[i];
index = i + 1;
y ^= (mt[i] >> U);
y ^= (y << S) & B;
y ^= (y << T) & C;
y ^= (y >> L);
return y;
}
Regras
- A entrada e a saída podem estar em qualquer formato consistente e inequívoco. Se você não tiver certeza se um formato seria permitido, não hesite em perguntar.
- Todas as entradas são garantidas para corresponder exatamente a uma saída do PRNG (nunca haverá um caso em que uma sequência de entrada corresponda a nenhuma ou mais de uma saída do PRNG).
Casos de teste
Devido aos limites de comprimento do post, apenas 3 casos de teste estão incluídos. Uma lista maior de casos de teste pode ser encontrada aqui . Observe que os valores são fornecidos em hexadecimal.
[CEE63876, DE7E2E77, 54EC3AE4, 92DEBB4D, D0756602, EE9D3B13, 04A42150, 0FE8BF49, 2BD7E04E, BB96756F, B9B2027C, B5750705, 9DD5B35A, E23EF98B, D15ACA68, C1C40E81, 35ABAB26, 2DA1A367, 36462514, 3CA211BD, E79753B2, A49B0F03, B3EA7E80, 64630CB9, BC22F8FE, D535985F, 14B902AC, EE9EBB75, A831A70A, 79C55B7B, F7099D98, 98AC99F1, D9CB29D6, 53C43457, 04C6FB44, 43DFE42D, 05A80D62, D86DBEF3, F9DA87B0, 99839629, 017D9DAE, 0B1B574F, A5586EDC, F2966BE5, B709E6BA, A160196B, D16B9CC8, FF46E161, 3BDFB486, 4CE4E147, BE01BD74, 6A2F329D, 99F29312, C7044AE3, 9A373CE0, 73515B99, 94E2CE5E, FA26B23F, 2883470C, 3ED31855, 7809726A, 64DE335B, 79A3C7F8, 5379E4D1, B9444B36, 92C2AA37, 6A496BA4, 84E6FD0D, FC81E4C2, 470DB2D3, 4F839E10, 45935D09, C40D8B0E, B4F6A92F, FDEC8B3C, 1C8BC0C5, D99B4A1A, E1CEA94B, 17951F28, BAECA441, 3C13EDE6, 0CDC8F27, 4CB105D4, ED1E437D, 1E210272, B8F8F6C3, FB02AB40, 63D09A79, 4178D3BE, B3EA3C1F, 58073B6C, 10B76535, BAEA6DCA, 37807B3B, 11E2A258, 93061FB1, EB299C96, 00719017, 130B8C04, EFAC05ED, 385AEC22, F6F516B3, D4B76470, 915013E9, D45FA86E, C5206B0F, 6C06579C, 4C0D05A5, 9BE1DD7A, 7702A92B, 3DEF5188, E0ED5721, DA205746, 0080AD07, 05EBFE34, 3D27445D, 7D7AA1D2, 44F112A3, 9B64C9A0, 7118C959, 08BD091E, FC7835FF, A1DCDFCC, 1B03A215, 4D2C992A, 9324331B, 0FDE2CB8, C1894A91, B9531DF6, DDC8E5F7, 38A55C64, 59E6FECD, C88B2382, 409BEA93, C48DDAD0, F5F1BAC9, DF4BF5CE, A3909CEF, C43DD3FC, 55D23A85, A035A0DA, 5074190B, CA9233E8, D980FA01, 85DCF0A6, 96C93AE7, B94AA694, 0E02353D, 4D577132, D1649E83, AC759800, D261E839, 7D876E7E, 29C89FDF, 309C342C, D06FCEF5, 1727F48A, 35415AFB, AFAE6718, C53B6571, 3998CF56, 47C0ABD7, C0AEDCC4, D54FE7AD, 486A8AE2, 187A2E73, C61F0130, E8B051A9, DDAA732E, 143F3ECF, 072B005C, CA935F65, 94EE943A, 799AF8EB, 2F95C648, 88DF8CE1, 7B21BA06, 1AAE38C7, E264FEF4, 4F67161D, AF0F7092, 60CB9A63, CB4D1660, BAE3F719, 7EB003DE, EDD379BF, 5ADD388C, 5FB3EBD5, 0D347FEA, F74FF2DB, 196B5178, 00547051, 4DD2B0B6, 3750E1B7, 3CC00D24, AF9EC08D, DF512242, 0F07E253, EC82D790, DAC3D889, 1453208E, 372450AF, 6165DCBC, F7087445, 3464B79A, 19EF48CB, CB1208A8, 4F410FC1, C1C6B366, B327A6A7, A8D30754, 2D0DE6FD, 4FFA9FF2, 919E0643, 010344C0, 59D6F5F9, 370EC93E, 5690C39F, A337ECEC, B387F8B5, 2FAA3B4A, CEC7FABB, 612CEBD8, 510C6B31, A3D8C216, 81718797, EA70ED84, 728B896D, 4096E9A2, 50BD0633, B6D15DF0, 39644F69, 141DFDEE, 8837D28F, 2B86691C, E3E97925, 44F00AFA, 74E908AB, E71EFB08, 08DD82A1, 2DA3DCC6, 632D8487, E02CBFB4, 0EAEA7DD, 6970FF52, 9E53E223, C2B02320, DA72E4D9, 1D7BBE9E, CDF87D7F, B844514C, 72A3F595, 8AE126AA, CD21729B, 870B3638, 119B5611, B5830376, D71A9D77, B3597DE4, E3CE424D, AB93E102, A6119A13, 10229450, 6DC9B649, B9E30B4E, DF71C46F, EA24A57C, 55EE6E05, 98E88E5A, EA00388B, B9D49D68, 0DECE581, 5E913626, 09B7D267, 080A2814, 980158BD, C0CA8EB2, 5D652E03, F16BB180, 63EFC3B9, F4CEE3FE, 1A02A75F, 749A65AC, FFBFE275, 3731420A, 1FD45A7B, 771E3098, 183930F1, C8A974D6, C5442357, 2D11BE44, 051EEB2D, EBA00862, 737D9DF3, 4F8E7AB0, DD2C0D29, 2E7A48AE, 70CA264F, 4DD891DC, CDCF52E5, 0EA641BA, F4ACD86B, 654AEFC8, 32A73861, C066BF86, 61BE9047, 4C034074, A8BDF99D, A75F4E12, 4149E9E3, DA4DEFE0, 19859299, CBE0395E, 5CA7413F, DED22A0C, 7993BF55, 58F28D6A, 1058B25B, 097DDAF8, B71DFBD1, EF241636, B4E61937, 9931AEA4, 1435840D, 58135FC2, B97911D3, 382D1110, E8C35409, E6BBB60E, CC38F82F, 333A2E3C, 884427C5, 9081251A, 2C66E84B, F799F228, C7447B41, 8AFC78E6, 0239BE27, 83B008D4, 5C9C8A7D, FA873D72, 587A15C3, 366EDE40, 1A6C5179, FD87BEBE, 13DE4B1F, 29839E6C, BAD78C35, 207D08CA, 04267A3B, 02423558, BC81B6B1, 06CAE796, EAF87F17, E5514F04, 8ACA0CED, D445E722, 147BF5B3, F9165770, EDC78AE9, A37F536E, DDB63A0F, A2E17A9C, 7E04ECA5, 14D1387A, 44A6682B, 6AD9A488, 97FCAE21, C22A6246, 5E215C07, 32A88134, 0B550B5D, 239A5CD2, 4D6DB1A3, 2AE67CA0, 81DC0059, 309D741E, 199FC4FF, B346C2CC, 5A434915, CA28B42A, 7CB5B21B, 11833FB8, 729C6191, B975E8F6, 887354F7, AB089F64, 1E9485CD, CF8F9E82, BCFE4993, 2D624DD0, 4570B1C9, 719D20CE, ED39EBEF, D16676FC, 63C9A185, 9DEE7BDA, 0CE3580B, A52206E8, ED07D101, 35C87BA6, C46D69E7, 8884A994, 489F7C3D, 17F0AC32, 669CBD83, 48CCCB00, 670C9F39, 57F9597E, A3E3AEDF, 06B3972C, AA8EF5F5, 9E4D8F8A, 177E59FB, D358FA18, 9FA5FC71, 7CFD1A56, 8A4E9AD7, 2FEF9FC4, C14CEEAD, 454885E2, 87780D73, DC28F430, 44F6C8A9, A9ED1E2E, 9EBC0DCF, 1F61235C, AA4A4665, 3A30EF3A, 7095B7EB, 788B1948, 8A9DE3E1, 81AEC506, 6015E7C7, 60DC81F4, E433DD1D, 58E22B92, 867F3963, 8D39C960, DD362E19, B2736EDE, 44A208BF, DA621B8C, BA7292D5, F1439AEA, 8DF871DB, CFDB6478, 85D68751, 93387BB6, C98250B7, 659E5024, A0AB478D, BCC89D42, E4614153, 78824A90, 3D91CF89, F1474B8E, F2349FAF, 19697FBC, 7E3EDB45, 03F0929A, 773587CB, A32CDBA8, B0F6E6C1, 0DB53E66, 3812D5A7, 43480A54, E9CA2DFD, F3C6DAF2, 2B8D2543, 614577C0, F390ACF9, CAE3B43E, E9D2D29F, 10EA4FEC, 54A61FB5, 2362D64A, B59BF9BB, 7B227ED8, E3660231, 0A000D16, FB067697, E9ACB084, 2667906D, 4967E4A2, E031E533, E18650F0, 7C79C669, 3883A8EE, 439BA18F, 78178C1C, C85F6025, 218565FA, 443AC7AB, CF1F4E08, 1C4AD9A1, 0DB3E7C6, 2F5C3387, 635F42B4, A11A6EDD, 81F6BA52, 703E8123, 9A07D620, B5541BD9, 7822299E, DD6E0C7F, B8E4344C, FFE19C95, A10341AA, 7FE0F19B, 35464938, F28C6D11, BB2BCE76, AFD30C77, 05B2C0E4, F839C94D, 8A7E5C02, 2361F913, 624D0750, 4AE6AD49, BC7A364E, 4AE9136F, 2003487C, 2D63D505, C547695A, 171D778B, 927A7068, 04D1BC81, 8182C126, 04EA0167, A0BA2B14, 8DDC9FBD, 28C9C9B2, 0B0B4D03, 7898E480, 29B87AB9, DD06CEFE, C56BB65F, 0CE7C8AC, FEDD0975, E27CDD0A, FA3F597B, 4A5EC398, 6981C7F1, 4C93BFD6, 54E01257, AF488144, F7D9F22D, AB640362, F2697CF3, B1EE6DB0, EE108429, 0602F3AE, 1C14F54F, 21C4B4DC, 0E0439E5, 2D8E9CBA, 4B55976B, 6F5642C8, 1EC38F61, 34F9CA86, 53B43F47, 86F0C374, 6FC8C09D, 99980912, 4E6B88E3, AA10A2E0, 53F5C999, 6869A45E, A3C3D03F, 738D0D0C, 50506655, 6C27A86A, 4E2F315B, F283EDF8, 7A7E12D1, 300FE136, 33258837, 8805F1A4, 43000B0D, 6370DAC2, 2DC070D3, F3828410, A72F4B09, E9F5E10E, 2717472F, B9F3D13C, 86F88EC5, A4B3001A, 585B274B, D3CAC528, 9A585241, BFF103E6, 92B2ED27, 4D9B0BD4, 4296D17D, 11B97872, 28D734C3, 47871140, 33440879, D522A9BE, D66E5A1F, 7F6C016C, AEF3B335, CE5BA3CA, C128793B, 51CDC858, D3B94DB1, A3783296, 6F9B6E17, DD831204, 336413ED, F5FCE222, 51DED4B3, B6214A70, B37B01E9, 892AFE6E, 37E8090F, 51289D9C, 70F8D3A5, 810C937A, D1A6272B, 19EFF788, 23C80521, 86406D46] -> LCG
[7D17504D, 9FED269B, 939C3D03, C8FCFA6C, 0FAE4E06, F9816896, 8B872680, A4878206, D92436EE, 2B133084, 9912A040, 011D96D6, F976435D, 4B53DBE7, 474F626D, AA09E774, E12E35C3, 347746E2, 0817160B, EDC0623A, 7DD0D26C, F31ECB62, 43093C44, AD3657AD, 568EB3D5, 53CE27BD, 592FDA9C, 46BB652B, 65886632, 475956F1, 60859FBC, FD8A3CBA, DB156CCF, 56764782, 1A424A8F, B681CA91, C682BB9A, 222CBE9F, 2A329E67, 925F0CF2, 41D22B48, 064DBDAB, B832DAA3, D26069CB, 023890A4, 69F3D5AD, 473AFDF2, 96C5EAEF, 50BEF523, A7171C24, 3752B059, 8E79B6CE, 29C95DCF, 362092EE, 94523C0B, D7DE2789, B49A3F98, 861F7C07, 83A8BAAB, A56C2738, C06FAAF2, BDED09BC, 7B568148, BFC73CFD, 024229CD, D73760D0, 18A4E7BF, 9E021082, 8D1D4ECE, E1408E5D, DEE614D5, 50EE898B, 37E2D666, D23584A1, 3C9B628E, 181D1647, 396DA2C4, 470339C4, A06BACB8, 503439DC, 041BCA9C, 5A881EC2, A77B7747, 567040AD, 8CE52FD5, 96814E85, EA3CD25D, 3E9D929F, 9BA3891E, 07CA0989, 0B689D17, D9B3FF8F, 5EDF76DE, 090EBACD, 46C11EDE, 00C8DE0E, A504314F, D9A02FF0, 97D9EDF4, D1A769AF, 55ADB49D, 8DAACE77, D544247B, 3F44C56D, 07759744, DC7738AB, 28E4B8A2, 31927F7E, 9AF601BF, FF21C02A, F20D56C4, 50C6AE74, 7A17A62A, 8BC619D2, 13E5C518, 76357C1E, B1D4A204, 0A673565, 3797FC34, EA9FA354, FE4FF881, CDB03630, 454E05EE, 52DC8B10, D3D6FA3A, 9F9B57C6, AACF50AE, 1CFDCAEC, 789EE463, 3DFEA9D1, ED64C4E0, 1F3CD90A, 900E9B72, 58761883, 93FE94A9, 6AF3FB55, 8EC22872, 66988B29, 01A4008F, F4787ABD, 6B665DF8, C905527E, E88493A9, DF1EB196, 86CEBE10, 65BB9A15, A96E54D0, 83D6D26A, 701BC23E, C9C9951A, 12DA9027, 27AA5594, 890E696D, 0CEA5C13, CA77AE01, BF04442E, 45BB17A2, 1BEFD1C2, 6C9F7318, F1276F91, 6CBC7010, 09B8DD84, 9E286818, 54B9C7AB, DB0A01DC, 1491B3C4, C92471E6, 533A73F6, D8B59CAC, 41231BED, AB62F96E, 2B478A37, 5F63230F, 06C6A77D, BAD38742, ADD2B41D, EBEF81F3, D8212EBC, FEEE4B6D, C6A47AF1, 51D39BCF, 80560B87, 0C6F8DC3, E9F90D4D, 2439FE5E, 1403C36D, 647255BB, 45C0AF1D, AEE062F5, A4F2C4EF, 52DB8247, 12237746, BF79483D, 8D9E3681, 03D954CF, 0A498AB5, 7F041361, 0352083E, CAE45BB7, 8CBE7C7C, D37EE991, 40FE1838, A82FCA73, D70D1E96, F31B5787, 4394AE04, 953E8857, 2A78CDC8, 03F6006F, E5F46A9B, 84E93A42, 6813B19A, DB55318F, 9DB338CC, 50453A12, A52FCEE1, D7844A82, D3F57DE6, AA195820, 719AD344, 84BF57AF, FCDD1093, 9C658F70, 3BC26F4B, 45BE45B3, 51F39C1F, E15D875E, C9CD1409, 7EE9435E, B3373BF8, BE5D3DB7, 1F911B29, 2B565836, 21B44E5F, 76537F5B, E18C6AEB, 78820904, FBC776FD, 16836779, 94DA8C70, FC787DC6, 3CC88C2A, 317D9C65, 71842F36, 4E2DFA8D, 36FC86BE, EBBFAAB0, BB12D56E, 9ACAA913, 48D10582, 5E2DCC02, 73B9DB0C, BCF46659, 7CC99950, 4CB40717, F168D436, EEB1A2EC, DE82A573, 32E28D0B, 859C2605, E6595298, 2D3BDA1D, 0B978064, 6F5F231D, 43BE71FC, B0A6A0A4, 07858274, 91540E52, 21D5BC15, A4F39B0B, 8F4E3BC3, BE5992E6, 32E0A42C, 0AF34AB8, F49DF806, 86218AD1, B1D79FFD, 21E1A5F5, 3AA73407, B05A4680, BD7F0F01, 919DDB56, 9299C26E, F095F8FB, B5D7E6EF, CAEFDC68, 9639FDE9, C9349DF5, C3DEFAA2, 7766722D, 2EE91F9D, 435FF480, 77601DA3, 33D3FE78, 55A01A68, E9E71FA8, 9E1D8A32, 329187B7, 67B7A8D7, B67CE1D6, C442A131, 7A502A31, A07BC4BC, F158F334, 20C28F07, DB38288C, A5184973, 93EFCFB7, A761D07A, BD07F052, DA336550, 374C9BD6, 9E077F45, 1C0089B7, 5D587682, 0E99C4D4, ABC16F15, B39406EB, 2DE69A7D, ED994471, 4D802710, 5E30D315, 471C9FDC, 6081E182, 2C75F225, F40524C5, 5744A7E6, 38A6D17D, BBC1E896, 663FD027, 14363091, 1A152653, AE24F8DF, 3602BBD4, 9315B73D, 20813CB2, A9EADA7D, 8A15088F, B487EAAF, 9DCA3421, 620C2CD7, 407F0169, CB26495B, 07810722, 04E8F991, BC24C42C, 45B12E62, 4A0689E1, 0961D541, 93FE75E5, 5FF09BC6, 21C75858, 260B4AFC, 463A4285, 9DCFCF2F, 86D14156, FAF1A7DA, 6E4BFC6B, 8D1EF03A, 81C9CB3E, F67163AA, C7E871AB, BD0DD64C, 72526AE8, 0F433B3B, 8BA27651, 58CE6EDF, B92A4A04, AFA624F9, 372EDFA2, 1CBDF70E, F72CE4F7, 69339707, 28A1864C, DB5701D1, 4BCC4D10, BEB260C1, 9A0502BD, F93FC1A5, D0B2B75F, FD2B71E0, 4F899412, 48BC46AF, 0DF108A8, ABF3DC87, A8D9E4EF, 02FA4665, 87CBBADA, B2E95940, D5702D6E, 056990CB, DFAEE7D6, 2775863A, 733AC4E7, 3A9CED83, 92A42D51, 196B2D69, BCD3CF5F, 61FEDDB3, D283BA78, 92C3C524, B0484914, 27CC09EB, E8532710, 643535DB, 96C7D0A0, D10310C2, A019C655, 6D4FA460, C5A53BB9, 0CE9A6CF, 62ACE269, 72D026F8, 9E44A3E8, DFDAB131, DA60BF09, 2974A55B, 9294187E, 98CD6024, 478A1CC3, CB583714, F93D91E9, 0A0202AA, 1D796B2D, 17931F01, 023476C3, 1839337D, CECF1354, 412B769B, E0089213, 317BF7B4, 8798177C, 9D1D36BA, 3921B700, D70921C7, 906DEFAD, E4B1B3FC, D01C81DD, 4E858500, B16A1BFA, D82D7078, EC0B10C9, 8EC425CD, 6F904A24, DC8D591E, 68B4971E, C7F13D88, 2ADD8E38, 9C2E67D4, 50EE1F28, 1EBD75C0, D8D79461, 37285868, 171F16FA, E2F972AC, 86E9860E, F37765A3, 1C3015F1, 357568C9, FF66419F, B77479AD, 2B776D2F, B5DA7BA8, 787DBE35, 6CD01986, FC5E1F26, 9A3F3C3E, 0F26B55A, E3D68111, EF7D1562, 8CC01A7F, B676E2D8, E1FF230E, E62EEC56, 6AB1010E, 6BD04EA2, 732FF785, E2F2E9EA, 00A93DCB, E9E5C622, E57A9744, 90B28FB8, D9BCBF00, 1EAFA6C3, 2F5ED2E5, 2B9557F9, 17EDA934, 74178CB4, AD07B129, 2CAC11EF, 5672B947, 9EC8ED11, 0ED68918, 42B9C244, 81C2F3D5, 58BB2699, E29FFADF, 6EB8AF2A, F872A573, 797CDB0A, 64289FF8, CF42ADA8, A276D00E, 3D4DEBC1, 1DBA64CF, C74FA53D, D3ADEB7A, 81EC012D, 4FBE91C3, F562B344, 492860A9, A82CE5C8, 13A74987, F3BF2024, F9983BD2, 3655838C, 1F971FB0, 1523A266, 2D5D4DBB, B78EE27F, 104301A1, 187BA15D, DF8C077C, 1FD19BE8, 1797DFBA, D223E55C, 6D2BAF83, FEB67715, 57750D76, 9AB10BC1, AAD6F8A3, E7953C33, 1874830A, 0A896CC6, 17879ED4, 59BD4CB3, E56DF85D, A4C3576A, 8F990C18, 3CF2118C, B6D7A95F, 0811C0E8, 4FAFF43E, E37DF236, E8EB2257, 6E7BA922, 5E45AED7, 52A50B6B, E3ED62F2, 506CF514, 232CDAD8, 59A87385, D1DA70B0, E629FBCA, A39607CD, B9B87C61, BBE5C416, 12BB8F0B, 01004AFE, 7B2165CB, EE71DBCD, 207CD2DF, 23283B94, 53570D07, 33981B13, F5B4DD95, 9722AC2C, 7CF6B4FA, 8F4578F4, DC4E44FC, 5E8FD095, 9717EEDA, 3331A614, 9DF66D2A, BDDD0D79, 95944526, 2B2B5086, 059AF7F4, 507984FB, 67F346A7, 162D85BF, C4DAF5D9, 5818EFE5, A5235C3F, DF593559, CC3E6756, 53C6DEF3, ECBBB210, FA5EA123, C5656DE9, A03102F0, 912B0FD4, 9E73F36B, 7097CF69, 58996509, 91059461, 90ECC581, 5ECEBC72, CDEC2B8F, 70F708CF, 86C10B9D, ADC71A1B, 01DBEC7F, C9A22DFB, 47B14AB1, D233979E, 0C5521B3, D4401837, 196924CC, 57A8CF18, F25524E7, 26001B3A, 761F1472, 67DEC5A6, 3CF7A7A6, 1A08B2C9, 943A897E, 05589DAA, 8413C030, DBD2B481, 9BE3A7FC, 5A97CCE7, 409F95C5, 0EA757EB, 88FDCD84] -> Xorshift
[4BB6DADF, 8EEF8EA3, 06E8FD49, 88A2AF49, E3269CD4, ECA4F09A, 3ADC8EFB, AA4DD059, AC3B1AAE, DA22C244, B67C2EC6, DFD9C12F, B4A6DBAF, 354C372C, 2C6CA407, 0AC93693, 725C7716, B439DF25, 7C04626F, 67824F17, 21EE364D, 77D8D72F, 4BF90371, 7BC3C716, 472A4204, B842AEFE, 38270462, 3B17B189, 22760085, 2A801D85, 8DE334B5, A72580F7, F187AA9B, 2E04DC0C, 8A701C0D, 471B61E6, 98F859D9, 9EBC2F45, 02544E96, C2785B15, 20623FAB, 8001F9B4, 0E438545, CFA2A2A5, 9DA35720, BAA84901, 908758C8, FCF5557F, F905B3B4, BE7DEBCD, FED08B1E, 7E9472CB, AC3A29C1, 5BED194F, B6932F25, 1C95E32D, 67E94371, D7CCB4CE, DF296D87, 6AAEF0F6, 8CFFF867, 093F9F79, FB280F6C, DE7735A8, 684C17B5, A0DA757E, 374EC162, 1764A62D, 82C244F6, 9E4583C7, 56F02388, 0018E400, 815A0F1E, FD80C932, 30EDD175, D37AF8D8, 7C8E4633, 7D8E4E5D, 660A7F79, 4C2C08BD, B6656A5B, CCFD6607, B0AA17FA, 060EE305, DEE9752F, B38BE439, F04EB964, D4E6C330, DCD4F7AB, DF7D83BF, 309047C6, 51FFC819, 9E59C7D6, 46821973, 01B47792, F800809B, 6050BB64, C13CB495, A305F788, 7AD27279, B7F9151F, 9F154C4F, D3F688F1, FF830866, A9C059A3, FFBF160E, EA8D827A, 1F1DA6E8, FDC52EFC, 5325CE11, 765B86EB, A852DC5C, 74ADAF62, 45BFACA5, 8E1FF6C3, 83ADCF0A, 91D6626E, 316008CC, 0DAD4110, C28EA37D, 5F077B03, AF70C5E3, 13A7C50C, 0A737B9D, E236FCBB, DDADB0C5, F4CAA3C8, 73679470, 87AE2E8E, EAA6ADA4, F30CCA79, 2B2FED65, 9B55A25D, 7317A6DB, D505929C, 0F90C693, 5CED397C, C1CB0AB9, C81895F1, 828D68BF, C2D0D855, 70585D86, 1ACD41B1, D8227B76, 1CB6DD69, B71EF185, 3EB11656, 6674378A, BA543682, 895A464E, B9E6CC48, FDAB6657, AB815F3B, A717AF55, 5826ABAB, 7CAF7DA1, 33EB26C0, 9367A48F, 32334888, 6BD35F76, 21F56A13, B7E72B51, 2B110FC2, A7A6ED6F, 1B2E72D1, 855EC1F3, A320F92E, 05609603, 5AA26082, 937BB417, F7A082EF, 370690A8, 074B4C00, EFB2EF14, A449B9F8, 9AA7E8A8, 3AEC4108, E5DDDB2A, C2CC4D30, 8589EB3D, 030ED83E, 4230E9B3, 619B03C0, E2B2BB64, 839A7C40, 2527B162, D03987D6, F8D66424, B950968F, F41E4D21, 9BAEEC89, DB8C65CD, D19F0371, 42507672, F133D6DC, 8FF10301, 6267E094, 339A1D5D, 3DD9DDE3, 139AA839, 440F8A94, 5E10CEAF, 60A1BA78, 02576968, 9AE7D81E, B9BF647E, F1698EC1, 5EC4890B, 88CF1A87, 9F3442AD, 4ED7DB9A, 08BD20C4, DA4B2F8E, 7EE018A9, 41968817, 519BE32C, 26CC3EFD, 1C3CBCBB, 551FC090, D06676D9, 02BF4E3F, 5B331917, AA121020, 840B84DD, 1C04DB26, 42DC049A, 58E92781, 95DA8984, CEDFF185, 149A43E5, 9B4CAAE7, 9E61CFFC, C33F9485, 2ABFE975, 75F8E915, 167D7A60, 1086ABF9, FE0B87DC, 095EFA20, 79FC720C, 99DB743E, 8F4B2F19, 00A9188A, B5DE7C2D, DAF3734B, CCAD1F47, 0C9DB549, 0158D55C, BCD5F151, 72A210D9, ABB80C09, 99934B39, F92DF281, A35193BD, C3CB4E8B, 322DBEE4, 26E2E30D, 36F25EDD, F1C8C5DC, 44B5C836, 878075ED, 1140849C, DEBA2848, 6B8D4AD7, 0209883A, AEFFDC8B, F7862944, F2CAE4AB, 77A1EB21, C77D6350, 4749AA23, 1ECDFD3C, 55D6943C, FC9B102A, 80363E80, C28E5369, 7E4BDC16, 8DDD321E, 46E4B844, 71169596, 6EC788CA, 508E25D4, A3249379, C5493848, 67ECFFDB, F6B03518, D4FE2A7D, D6C8D739, 7A93EC17, 84E2A797, 08CB6F22, D09D5BFF, 7FF783FD, 749A4AA7, 9EE69739, 01BB87ED, CDB15087, 32FE625F, 3C8E72C6, 2386A26E, 0F243847, F9E50890, D10F1EC5, 6E1C032D, CE27B59B, 84F2447B, 62AFD23B, 2361B77C, 1532E2F5, BC65F691, D8106771, BC9F8553, 94B67790, CE7F4B32, E36DAA85, D42336C1, 414ABF42, F5D5E7FA, B17620A4, D42A5D6C, E1118425, 17C4B3F2, EBDCB06E, 1F8F7F65, 0AD89423, 32848E5D, 0A5028D0, 463B71B1, E896017F, C1DA750C, DB89FC54, AF665A17, 11F5A446, 45F2DD58, 9C66340A, F4DB1D19, 87AFFD89, 75CA495D, DE608110, 78EC9F5C, 7840FE7C, 6F4DA231, 1CF2E830, CD521794, CE4F5EBA, 79B79437, 5A91D18E, 95F1D139, D9CA1102, E3822EB3, F7C52D20, F917AEEE, 5EDCD7BF, 4BD3725C, 94EE3441, 713CF5DF, 937E1AA9, 08926562, 084E8DD4, 41100547, 1C706FF6, 2ED60298, 0D2E30BA, 82FECB1F, 831BCCE8, 0CB829DB, 0C522998, E0AD92F6, F8969EA4, 386650CD, CA41F763, 7BB34065, D79B9F81, 967FBB17, 7C2F61B2, 7B4E9B33, 8359EDDA, 3201D25E, 5F41BAA6, D94A1FD8, 6E29F112, EDB7885C, C4F4380D, DAD428C7, 40609A88, 66DF9A6C, D61B84E4, C4C77436, D6F4B201, 1C0AD2D4, 3A69D216, 1DD70F43, C887E79C, 8579D94E, F2D069EA, 17B4926F, 55BE153C, A783F442, C03D53D2, 5ED56627, C114DB61, 9B0BFD2C, 825DDE34, 97523F35, EE476E00, EB2ED50C, 567BB078, 9B70520D, DC96668B, FCFD7253, 0197E3F8, 7785825E, 0B00322C, B510F809, 51FB92EE, B6F7D331, 2DE0AC32, 00B41A7B, A432B1FE, 94ED9578, 4B56F086, F8BEADE1, 8C899DF2, EAB17808, 240BF736, 7CBA75E0, E06E352C, 3BBD94E5, 427CB86A, 31CB345E, C1226EE3, F9F4697B, 8820CBB6, C3F9BB4C, 509D403F, 03990E8E, 6C5CCD8B, 24F235C0, C5FC6E59, 05E627C9, 4B0C0C96, 45A35E8E, BBF14335, 89B957A1, 3E272204, EC501927, 00ADCBC3, 13DC9199, A682B338, BE42D97C, F97E0F28, 8C1A6128, 76ED6951, D7D8B74F, 80A6C9D2, 87111413, 48268EB5, 69DDA6F7, 8900B2E1, DBF809E0, D50D7B42, 9716581E, A7AE9B6E, 52366624, 85BAF9A3, DE28F70A, 890E37EC, 7F82541D, 9BA2C144, 8766E737, EA8B0E73, 6BC46E1A, 04A2D3E8, F01716BB, 3D0F7338, 93282BAA, 3A9E51C0, 7B26AFBD, FA2B6A90, 36DD5832, 18161A71, FDE783A2, FF84185B, C251868E, 957CA33D, 6D2BD402, F7E61B15, BAAD0068, 8413463A, 63F0F132, 55FBBC6A, 58E3298D, 845AA664, 02D242A7, A456CEED, 2C198D04, 89A25422, 3A4CABFB, 9D24D792, DFBB850F, 76E30332, 58B59723, 1B1A6913, 9FB961E8, B363CA07, 9CC01B66, 00E9E1DF, 9AF48078, F67167D2, 5D8EBE54, F0819D2D, A003D04B, BD20E32A, 7647BD73, DE509593, E381BF67, BB5D56E0, 675636A1, 983C7C47, C7D92CF8, 335F0477, A6EE6787, F2A67D0E, 29D7F83A, 3DA85C1F, 8E31E016, 5FBEB7EA, 01F017A9, 021B93ED, 8E2AE731, 3391B82D, 6AFEC318, C1E9610D, B50DE358, 46E16C1F, D7A03E8A, 74E52044, 4797BCBC, 49FC24BC, 119F71CB, 51ADB9AC, 1F7A8641, 373911A6, 79424584, 2D69A297, 32859E0B, FF812B02, 2060307E, 6AD9173E, AFCB84DA, 4F5B70D0, 34A63D93, 6DBD6388, BBD76CFA, 94EE5483, 20214C3F, E45B9B77, 8B3192D9, 109D8CE6, 8EBA320B, 53FA8CE2, 56A4A45A, 61AB8FDB, 3ABFD0EB, F92E5F91, 3CBA25FE, C2E19318, 2E5DC1D6, 751C25DB, 572BBA47, DF53AB19, 407F623F, EB9E4EE6, C98E9BFD, DA77A48F, 79D4B4D2, E4320563, 2C1C4BA4, CDCCD4A9, 5B74662F, 3B74B8C1, B1792883, 88D53BDA, FDFAB951, D2D3F844, 199D47E1, 7500E432, B0C714BD, EC5CCDCB, EC949808, 9B39D67F, 15D138B8, 17FE54A4, AD28C768, FE473BF7, AE29CB10, C987A478, EE50D094, 10ED5447, E2BF7CCF, BDD93708, D57E6C1B, 01079D4B, 6C6C547F, 363A37F3, 6D4D828A, EE1622DE, AF1D8240, B068E4C1, 9C5901F8, 17822119, 3C7837B0, DEFFD993, 28FA9C3A, EAADDC4E, 05705400, 0046CB17, E843346D, 2F33C418, AF1A47BD, E4C12B9E, BC3F9B15, 01E90C74, DE0C8A00, 5D52587A] -> MT
Respostas:
Gelatina , 23 bytes
Toma uma matriz de números inteiros; retorna [0, 1] para LCG , [1, 0] para Xorshift e [0, 0] para MT .
Experimente online! (O link permanente pode ser muito longo para alguns navegadores.)
fundo
A coisa mais aleatória sobre o LCG é que ele é considerado um PRNG. Para iniciantes, os k bits inferiores do estado não são afetados pelos 32 k bits mais altos , tornando-o uma opção excepcionalmente ruim para a maioria dos aplicativos. Em particular, o LSB de um estado atualizado é afetado apenas pelo LSB do anterior, e como 1103515245 e 12345 são ímpares, os números gerados seguirão um padrão par-ímpar-ímpar-ímpar.
As falhas do Xorshift são mais sutis, mas os bits gerados ainda seguem equações lineares simples. Dadas cinco palavras consecutivas geradas w k , w k + 1 , w k + 2 , w k + 3 , w k + 4 , a (equação não linear)
w k + 4 = w k + 3 ⊕ w k + 3 > > 19 k w k ⊕ w k ≪ 11 ⊕ (w k ⊕ w k ) 11) ≫ 8 é mantido por definição. Se enumerarmos os bits das palavras ( 0 sendo o mais baixo, 31 sendo o mais alto), podemos observar que a equação (linear) w k, 20⊕ w k, 31 kw k + 3,31 ⊕ w k + 4,31 = 0 é mantido . Para verificar isso, basta observar que as palavras que foram deslocadas para a direita não podem afetar w k + 4,31 , o bit mais significativo de w k + 4 .
Isso deixa o Mersenne Twister. Embora existam PRNGs melhores (mais rápidos, menos tendenciosos ou ambos), identificar os dados gerados pelo MT19937 é muito mais complicado do que com LCG e Xorshift. Felizmente, não precisamos. Se os dados não se encaixam em nenhum dos dois padrões anteriores, foram gerados pelo Mersenne Twister.
Como funciona
fonte
^Ḋṫ4^^Por que vejo muita repetição aqui? Sinto o cheiro de algo, mas não tenho certeza se existe um caminho mais curto que o XOR [...] XOR XOR.