Statistics

Problem Statement for "SemifinalAssignment"

Problem Statement

You have advanced to Online Round 5 of the 2010 CodeTopper Open! There are N people competing in this round and the k highest scoring competitors will advance to the Onsite Semifinal Rounds.

The competitors are numbered from 0 to N - 1. In Online Round 5, competitor i will score an integer point value between worst[i] and best[i], inclusive. Every integer point value in this range has the same probability. If two or more competitors get the same score, the lower-numbered competitors are preferred when determining the top k.

After the k advancers are determined, they will be assigned to either Semifinal 1 or Semifinal 2. In order of increasing competitor number, the advancers are assigned to the Semifinal rounds in the following order: 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, ... Note that the scores of the advancers are not considered when determining the Semifinal assignment.

Return a double[] containing 2N elements where the (2i+j)-th (1-based) element is the probability that competitor i is assigned to Semifinal j.

Definition

Class:
SemifinalAssignment
Method:
getProbability
Parameters:
int[], int[], int
Returns:
double[]
Method signature:
double[] getProbability(int[] worst, int[] best, int k)
(be sure your method is public)

Notes

  • Each element of the returned value must have an absolute or relative error less than 1e-9.
  • You can assume that scores of the competitors are mutually independent uniform random variables.

Constraints

  • worst will contain between 1 and 25 elements, inclusive.
  • worst and best will contain the same number of elements.
  • Each element of worst and best will be between 0 and 1,000, inclusive.
  • For each index i, worst[i] will be less than or equal to best[i].
  • k will be between 1 and the number of elements in worst, inclusive.

Examples

  1. { 1, 0, 1, 1, 1, 1 }

    { 1, 3, 1, 1, 1, 1 }

    4

    Returns: {1.0, 0.0, 0.0, 0.75, 0.0, 1.0, 0.75, 0.25, 0.25, 0.0, 0.0, 0.0 }

    There are two possible outcomes of this round: Competitor 1 scores positive points with 75% probability. Then the advancers are competitors 0, 1, 2 and 3. Competitors 0 and 3 are assigned to Semifinal 1, and competitors 1 and 2 are assigned to Semifinal 2. Competitor 1 scores zero points with 25% probability. Then the advancers are competitors 0, 2, 3 and 4. Competitors 0 and 4 are assigned to Semifinal 1, and competitors 2 and 3 are assigned to Semifinal 2.

  2. { 11, 11, 11, 10 }

    { 12, 12, 12, 11 }

    2

    Returns: {0.875, 0.0, 0.125, 0.625, 0.0, 0.375, 0.0, 0.0 }

    Competitor 0 will fail to advance only when he/she scores 11 points and each of competitors 1 and 2 scores 12 points.

  3. { 0 }

    { 1000 }

    1

    Returns: {1.0, 0.0 }

    This is a meaningless round.

  4. { 1, 2 }

    { 10, 9 }

    2

    Returns: {1.0, 0.0, 0.0, 1.0 }

    This is also meaningless because the assignment is based on competitor numbers, not on their scores.

  5. { 1, 1, 1, 2, 2, 2, 3, 3, 3 }

    { 4, 5, 6, 4, 5, 6, 4, 5, 6 }

    1

    Returns: {0.02041666666666667, 0.0, 0.11527777777777776, 0.0, 0.25810185185185186, 0.0, 0.011435185185185187, 0.0, 0.0875925925925926, 0.0, 0.23171296296296295, 0.0, 0.005046296296296296, 0.0, 0.0625, 0.0, 0.2079166666666667, 0.0 }

  6. { 1, 2, 5, 4 }

    { 9, 7, 8, 9 }

    3

    Returns: {0.6527777777777779, 0.0, 0.34722222222222227, 0.21296296296296297, 0.0, 0.9305555555555559, 0.0, 0.856481481481482 }

  7. { 3, 317, 25, 447, 96, 333, 361, 103 }

    { 947, 773, 601, 544, 594, 399, 786, 954 }

    6

    Returns: {0.6649201903354007, 0.0, 0.32850646461892563, 0.6163949837246063, 0.006573345045673984, 0.4544927900216218, 0.2180181176461977, 0.7769069045939901, 0.3815407626549669, 0.15220532165978432, 0.6601865341758356, 8.501235695949892E-4, 0.7402545855229999, 0.2430210789578823, 0.0, 0.756128797472523 }

  8. { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    { 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000 }

    25

    Returns: {0.9999999999999972, 0.0, 0.0, 0.9999999999999966, 0.0, 0.9999999999999964, 1.0, 0.0, 0.9999999999999958, 0.0, 0.0, 0.9999999999999979, 0.0, 0.9999999999999952, 0.999999999999996, 0.0, 0.9999999999999962, 0.0, 0.0, 0.9999999999999969, 0.0, 0.9999999999999948, 0.9999999999999996, 0.0, 0.9999999999999989, 0.0, 0.0, 0.999999999999997, 0.0, 0.9999999999999954, 0.9999999999999956, 0.0, 0.9999999999999949, 0.0, 0.0, 0.999999999999996, 0.0, 0.9999999999999962, 0.999999999999995, 0.0, 0.999999999999997, 0.0, 0.0, 0.9999999999999971, 0.0, 0.9999999999999966, 0.9999999999999949, 0.0, 0.9999999999999966, 0.0 }

  9. { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    { 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000 }

    12

    Returns: {0.4804995004994997, 0.0, 0.2599996673323346, 0.22045820812554034, 0.1355108663395381, 0.34490538407671256, 0.10697863817621485, 0.37339598719841055, 0.14437930174126143, 0.3359536985917397, 0.20876710682578675, 0.2715242684655878, 0.2666343739593718, 0.2136153762903776, 0.29760622276967236, 0.18260190243845345, 0.2963610446433059, 0.18380545552319152, 0.27020588612143936, 0.2099189890034362, 0.2339884669492024, 0.24609478313404687, 0.20404030878887205, 0.2760013162527512, 0.19266360534586707, 0.2873363946541306, 0.2043427935326649, 0.2756155814257091, 0.23442462638502454, 0.24549212353172445, 0.2705118095401391, 0.20936331533498717, 0.29629842480222734, 0.18353507503127142, 0.29708348318471955, 0.1827083916071544, 0.2657746613381112, 0.2139755884121372, 0.20787979699151077, 0.27182882771711275, 0.14382085356350574, 0.3358461461034955, 0.10693520212657258, 0.3726901724988015, 0.13579319221031794, 0.3437905573734317, 0.2599996673323355, 0.21954245720978988, 0.47950049950049867, 0.0 }

  10. { 5, 7, 4, 4, 8, 9, 7, 2, 2, 6, 6, 0, 4, 8, 7, 5, 0, 3, 9, 5, 5, 7, 7, 0, 0 }

    { 992, 997, 996, 994, 992, 997, 997, 996, 998, 991, 998, 991, 991, 997, 998, 996, 994, 995, 1000, 996, 1000, 993, 998, 992, 993 }

    18

    Returns: {0.71968720029694, 0.0, 0.2109182318945752, 0.5117130848941968, 0.054316273716049086, 0.6657081666424485, 0.254893880183398, 0.46449994588280696, 0.4880687193285374, 0.23373295363112126, 0.5273512138906106, 0.19663365817226516, 0.3940806755216387, 0.3283400395073568, 0.26101464790909085, 0.45729276131079893, 0.25262375540203047, 0.46623055969567484, 0.34993642557381216, 0.3698344555444364, 0.4455804585055318, 0.27620598398166507, 0.4425256405596637, 0.27262645564645377, 0.3585780033411132, 0.3595482655061356, 0.27480804017266725, 0.4480782685845263, 0.2779134239068774, 0.4444627713768742, 0.3727330225169678, 0.34750110873525614, 0.46495103994938264, 0.25088613688568795, 0.4553316273670259, 0.2630143674169117, 0.32606536874028547, 0.39824317506784795, 0.19552971445838097, 0.5245366796197889, 0.23657474312486418, 0.4846207784924914, 0.46864306016080226, 0.25197270639850816, 0.6651270723887642, 0.056913426322092966, 0.502747761090979, 0.2121998078732454, 0.0, 0.7152044428113851 }

  11. { 0 }

    { 0 }

    1

    Returns: {1.0, 0.0 }

  12. { 206 }

    { 323 }

    1

    Returns: {0.9999999999999989, 0.0 }

  13. { 282 }

    { 420 }

    1

    Returns: {0.9999999999999998, 0.0 }

  14. { 283, 896 }

    { 580, 914 }

    1

    Returns: {0.0, 0.0, 1.0, 0.0 }

  15. { 227, 412 }

    { 898, 717 }

    1

    Returns: {0.4977678571428572, 0.0, 0.5022321428571428, 0.0 }

  16. { 171, 43 }

    { 630, 461 }

    2

    Returns: {1.0, 0.0, 0.0, 1.0 }

  17. { 155, 48 }

    { 653, 669 }

    2

    Returns: {1.0, 0.0, 0.0, 1.0 }

  18. { 279, 788, 362 }

    { 698, 906, 792 }

    1

    Returns: {0.0, 0.0, 0.999805026418919, 0.0, 1.9497358107976322E-4, 0.0 }

  19. { 816, 492, 275 }

    { 879, 989, 537 }

    1

    Returns: {0.715863453815261, 0.0, 0.28413654618473905, 0.0, 0.0, 0.0 }

  20. { 121, 121, 527 }

    { 272, 656, 530 }

    2

    Returns: {0.14272388059701488, 0.0, 0.8572761194029865, 0.0, 0.0, 1.0 }

  21. { 217, 802, 862 }

    { 971, 855, 953 }

    2

    Returns: {0.19006622516556287, 0.0, 0.8099337748344376, 0.0, 0.0, 1.0 }

  22. { 499, 143, 523 }

    { 973, 603, 881 }

    3

    Returns: {0.999999999999998, 0.0, 0.0, 0.9999999999999978, 0.0, 0.999999999999998 }

  23. { 245, 55, 100 }

    { 645, 191, 574 }

    3

    Returns: {0.9999999999999997, 0.0, 0.0, 0.9999999999999998, 0.0, 0.9999999999999998 }

  24. { 39, 708, 28, 5 }

    { 986, 781, 852, 366 }

    1

    Returns: {0.2480533179900264, 0.0, 0.6478103823040527, 0.0, 0.10413629970592005, 0.0, 0.0, 0.0 }

  25. { 272, 711, 516, 353 }

    { 515, 738, 690, 794 }

    1

    Returns: {0.0, 0.0, 0.8427601809954752, 0.0, 0.0, 0.0, 0.1572398190045248, 0.0 }

  26. { 225, 197, 2, 216 }

    { 666, 357, 181, 792 }

    2

    Returns: {0.8881206290994111, 0.0, 0.11187937090058923, 0.09974414810700928, 0.0, 0.0, 0.0, 0.9002558518929912 }

  27. { 397, 954, 221, 74 }

    { 844, 993, 515, 969 }

    2

    Returns: {0.5895263671874998, 0.0, 0.4104736328124998, 0.5895263671874998, 0.0, 0.023894391741071417, 0.0, 0.3865792410714285 }

  28. { 504, 14, 541, 84 }

    { 994, 270, 830, 338 }

    3

    Returns: {0.9999999999999997, 0.0, 0.0, 0.26822308690012947, 0.0, 0.999999999999999, 0.0, 0.7317769130998705 }

  29. { 53, 249, 640, 227 }

    { 495, 700, 680, 505 }

    3

    Returns: {0.34425607174215456, 0.0, 0.6557439282578464, 0.24886197011540742, 0.0, 0.9999999999999997, 0.0, 0.7511380298845924 }

  30. { 563, 47, 429, 187 }

    { 929, 553, 966, 324 }

    4

    Returns: {0.9999999999999991, 0.0, 0.0, 0.999999999999999, 0.0, 0.999999999999999, 0.999999999999999, 0.0 }

  31. { 261, 54, 329, 534 }

    { 312, 729, 484, 822 }

    4

    Returns: {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0 }

  32. { 170, 189, 273, 635, 0 }

    { 238, 566, 396, 721, 403 }

    1

    Returns: {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 }

  33. { 599, 139, 398, 311, 209 }

    { 664, 669, 753, 618, 272 }

    1

    Returns: {0.6093049365467171, 0.0, 0.049314975384252266, 0.0, 0.3363742195858591, 0.0, 0.005005868483171499, 0.0, 0.0, 0.0 }

  34. { 608, 490, 229, 201, 393 }

    { 967, 728, 765, 648, 967 }

    2

    Returns: {0.9191722299703551, 0.0, 0.04928958102108647, 0.2561575061550445, 0.030139519325255104, 0.13598915621024688, 0.0013986696833037354, 0.029801179416753573, 0.0, 0.578052158217955 }

  35. { 92, 242, 43, 520, 162 }

    { 932, 368, 553, 669, 811 }

    2

    Returns: {0.5308877400622385, 0.0, 0.03186108306366316, 0.0, 0.08580094305056557, 0.002173061574296274, 0.3514502338235334, 0.5072017038608351, 0.0, 0.49062523456486945 }

  36. { 501, 196, 289, 139, 379 }

    { 946, 517, 336, 534, 588 }

    3

    Returns: {0.9999736831658951, 0.0, 2.6316834104484118E-5, 0.4681462182447479, 0.0, 0.16093517995691908, 0.0, 0.4108869538074618, 0.0, 0.9600316479908716 }

  37. { 149, 83, 223, 481, 382 }

    { 653, 401, 574, 804, 724 }

    3

    Returns: {0.5101141896659804, 0.0, 0.05520041240257352, 4.947731034379116E-4, 0.4346853979314469, 0.0703599130036705, 0.0, 0.9930837653736223, 0.0, 0.9360615485192698 }

  38. { 202, 267, 527, 384, 501 }

    { 439, 442, 998, 618, 763 }

    4

    Returns: {0.36277418607675177, 0.0, 0.6372258139232481, 0.006593469109113663, 0.0, 1.0, 0.0, 0.9934065308908865, 0.9999999999999999, 0.0 }

  39. { 99, 685, 221, 53, 223 }

    { 552, 900, 600, 72, 818 }

    4

    Returns: {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.9999999999999998, 0.0 }

  40. { 206, 454, 183, 173, 161 }

    { 756, 568, 230, 250, 254 }

    5

    Returns: {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0 }

  41. { 449, 772, 393, 127, 651 }

    { 794, 921, 518, 370, 754 }

    5

    Returns: {0.9999999999999998, 0.0, 0.0, 0.9999999999999998, 0.0, 0.9999999999999998, 0.9999999999999998, 0.0, 0.9999999999999998, 0.0 }

  42. { 438, 388, 544, 351, 159, 457, 541, 187, 456, 54, 291, 480, 223, 275, 190, 224, 826, 406, 537, 138, 430, 50, 589, 295, 743 }

    { 675, 657, 576, 384, 888, 633, 780, 618, 903, 60, 293, 572, 226, 828, 608, 971, 890, 467, 569, 777, 859, 663, 787, 983, 791 }

    9

    Returns: {0.37953978307693137, 0.0, 0.17729359431570288, 0.08346725869618027, 0.11782512496520628, 0.10691489574679648, 0.0, 0.0, 0.17773412555850598, 0.23925361025458367, 0.06613453333548484, 0.20310098705964585, 0.17649640147316933, 0.6684587122234463, 0.023232110435791854, 0.050678938731894406, 0.3005718953480991, 0.42377392289929605, 0.0, 0.0, 0.0, 0.0, 0.034175518170953864, 0.015594623560945955, 0.0, 0.0, 0.29567153813016056, 0.14555913076006172, 0.04355854993378681, 0.013833683207778785, 0.4280457721800908, 0.09195049122529358, 0.6131287507462531, 0.38687124925374655, 6.279013630042694E-9, 3.712758432648056E-8, 0.0372047481241282, 0.0850699947776381, 0.09972243506877014, 0.1978114028296985, 0.03539930254572582, 0.6131788730815553, 0.0016147953792541294, 0.11746771592077329, 0.4095125192435958, 0.5570144726430838, 0.5831437988252589, 0.0, 0.9999946968641172, 0.0 }

  43. { 24, 338, 760, 15, 250, 157, 647, 463, 517, 71, 1, 826, 376, 12, 185, 380, 120, 738, 9, 46, 623, 212, 470, 339, 211 }

    { 47, 550, 894, 30, 411, 538, 876, 867, 881, 906, 147, 893, 830, 829, 456, 399, 378, 886, 52, 265, 770, 273, 575, 843, 493 }

    20

    Returns: {6.914343731255398E-6, 0.0, 0.9999930856562692, 6.914343731255398E-6, 0.0, 1.0, 0.0, 0.0, 6.914343731255398E-6, 0.9998707731464185, 0.9690665826959143, 1.223125098504155E-4, 0.9999930856562691, 6.914343731255398E-6, 0.030933417304085487, 0.9690665826959147, 6.914343731255398E-6, 0.9999930856562691, 0.8863323867595495, 0.030933417304085494, 0.03432439603186926, 0.0, 0.9758076095500596, 0.024192390449940187, 0.10352869331479041, 0.8964713066852087, 0.0035859550255188766, 0.8344961228592978, 0.7380392603967146, 0.24484018000555222, 0.9964140449744817, 0.0035859550255188753, 0.2619607396032853, 0.6122749032471255, 0.0, 1.0, 0.0, 4.463846131042018E-5, 0.0287010015507955, 0.38409450326604483, 0.9999999999999998, 0.0, 0.9712989984492046, 0.004554396933869174, 0.0, 1.0, 0.004554396933869175, 0.9954456030661311, 0.9954456030661311, 0.0 }

  44. { 603, 684, 529, 90, 338, 870, 388, 491, 644, 459, 985, 72, 809, 186, 124, 210, 249, 404, 756, 12, 880, 932, 782, 281, 594 }

    { 610, 711, 534, 104, 358, 872, 393, 519, 679, 479, 992, 76, 822, 189, 129, 239, 253, 418, 759, 25, 882, 932, 789, 306, 599 }

    14

    Returns: {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0 }

  45. { 706, 223, 764, 180, 661, 413, 5, 937, 889, 329, 532, 568, 967, 728, 803, 372, 282, 55, 98, 612, 496, 251, 152, 471, 851 }

    { 709, 232, 790, 181, 662, 419, 16, 947, 893, 349, 545, 568, 982, 729, 821, 393, 303, 57, 101, 622, 512, 278, 154, 479, 873 }

    14

    Returns: {1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0 }

  46. { 580, 98, 275, 813, 684, 546, 42, 108, 268, 899, 729, 290, 987, 890, 54, 393, 37, 618, 590, 54, 192, 758, 309, 145, 725 }

    { 892, 485, 293, 892, 908, 832, 436, 193, 396, 969, 911, 295, 987, 916, 470, 483, 499, 752, 625, 381, 424, 806, 402, 269, 772 }

    21

    Returns: {1.0, 0.0, 0.0, 0.6816099190732747, 0.0, 0.9441929447669617, 0.6316636631436656, 0.36833633685633416, 0.9941392006965706, 0.00586079930343011, 0.36833633685633416, 0.6316636631436656, 0.005860799303430111, 0.5255587755164867, 0.0022596110976451666, 0.029962924521167677, 0.3004290776994015, 0.6884740562123235, 0.8734006839106171, 0.12659931608938296, 0.6995700466859798, 0.30042995331401995, 0.12659931608938296, 0.8655277723563832, 0.29801023516527625, 0.7019897648347235, 0.867947490505127, 0.13205250949487296, 0.47446247580412576, 0.11490112385012162, 0.33937865783252824, 0.6606213421674718, 0.04264536942641028, 0.5508449300374864, 0.40829102122634825, 0.5917089787736521, 0.8956321460952654, 0.10436785390473419, 0.3993512162663636, 0.06488893654272486, 0.2720226521955297, 0.5924662366571873, 0.0, 1.0, 0.6820581374164054, 0.31794186258359497, 0.31794186258359497, 0.0, 1.0, 0.0 }

  47. { 544, 2, 748, 30, 606, 248, 571, 604, 764, 85, 669, 758, 783, 168, 177, 57, 129, 348, 5, 60, 857, 642, 17, 24, 650 }

    { 779, 290, 870, 302, 681, 394, 925, 875, 986, 134, 674, 867, 842, 274, 408, 163, 156, 372, 107, 105, 920, 673, 480, 91, 976 }

    1

    Returns: {0.0, 0.0, 0.0, 0.0, 0.003221613692061523, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.051308397932258026, 0.0, 0.0028467958623045984, 0.0, 0.37750589080153363, 0.0, 0.0, 0.0, 0.0, 0.0, 0.002040967934885751, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.36730890063589455, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.19576743314106154, 0.0 }

  48. { 447, 200, 698, 881, 794, 5, 509, 594, 397, 103, 931, 701, 195, 361, 877, 545, 776, 37, 280, 93, 972, 621, 293, 473, 20 }

    { 473, 226, 709, 902, 818, 81, 550, 638, 403, 160, 982, 726, 229, 379, 886, 554, 823, 60, 322, 125, 974, 629, 322, 496, 50 }

    16

    Returns: {1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 }

  49. { 669, 200, 354, 704, 948, 291, 749, 589, 334, 616, 85, 499, 17, 476, 972, 26, 499, 433, 257, 795, 198, 33, 146, 846, 857 }

    { 672, 214, 403, 707, 978, 305, 818, 637, 408, 623, 162, 545, 48, 497, 977, 35, 560, 442, 278, 804, 236, 46, 161, 858, 878 }

    24

    Returns: {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.5790178571428571, 0.0, 0.42098214285714286, 0.5790178571428571, 0.0, 1.0, 0.02053571428571429, 0.42098214285714286, 1.0, 0.0, 0.9794642857142858, 0.02053571428571429, 0.0, 1.0, 0.02053571428571429, 0.9794642857142858, 1.0, 0.0, 0.9794642857142858, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0 }

  50. { 489, 737, 36, 128, 95, 743, 888, 825, 891, 396, 30, 949, 395, 352, 216, 455, 565, 694, 237, 110, 119, 413, 230, 874, 390 }

    { 518, 774, 238, 249, 219, 852, 998, 903, 979, 647, 228, 985, 503, 417, 282, 532, 566, 995, 304, 146, 325, 629, 291, 975, 537 }

    1

    Returns: {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.25672605753956673, 0.0, 0.0, 0.0, 0.09494567459385478, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5256326548339526, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.07158665035870534, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0511089626739201, 0.0, 0.0, 0.0 }

  51. { 35, 925, 341, 859, 710, 683, 57, 782, 450, 862, 598, 373, 267, 514, 17, 227, 806, 363, 340, 166, 69, 104, 18, 708, 372 }

    { 313, 959, 652, 876, 766, 776, 301, 887, 595, 983, 643, 587, 296, 660, 324, 303, 930, 366, 556, 234, 146, 204, 78, 844, 524 }

    10

    Returns: {0.0, 0.0, 1.0, 0.0, 0.0, 0.2118400284396145, 0.0, 0.9999999999999997, 0.2118400284396145, 0.7881599715603856, 0.9999999999999997, 0.0, 0.0, 0.0, 0.7881599715603856, 0.2118400284396145, 0.0, 0.10420091251933412, 0.0, 0.9999999999999998, 0.2842076948399882, 0.683959059041052, 0.0480258129272825, 0.0, 0.0, 0.0, 0.658146693552523, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0092250305535889, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.947681266176716E-4, 0.9996052318733823, 0.0, 3.947681266176716E-4 }

  52. { 166, 280, 6, 767, 279, 630, 813, 522, 523, 511, 876, 291, 184, 412, 403, 440, 220, 937, 647, 922, 736, 9, 789, 79, 79 }

    { 248, 292, 70, 845, 304, 677, 814, 557, 538, 533, 902, 317, 242, 433, 406, 495, 230, 995, 678, 924, 744, 99, 825, 117, 104 }

    21

    Returns: {1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }

  53. { 659, 8, 129, 253, 511, 57, 858, 382, 545, 965, 460, 764, 532, 14, 753, 430, 159, 278, 911, 171, 630, 334, 939, 72, 656 }

    { 726, 85, 213, 318, 607, 79, 862, 409, 569, 965, 462, 831, 562, 71, 798, 451, 245, 346, 930, 195, 690, 369, 974, 118, 739 }

    8

    Returns: {0.9003535840565731, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09964641594342663, 0.9003535840565731, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9999999999999998, 0.0, 0.0, 0.9003535840565731, 0.09964641594342663, 0.0, 0.0, 0.0, 0.0, 0.9999999999999998, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09964641594342663, 0.9003535840565731, 0.0, 0.0, 0.0, 0.20693851311016218, 0.0, 0.0, 0.10729209716673559, 0.8927079028332641, 0.0, 0.0, 0.8927079028332641, 0.0 }

  54. { 259, 158, 855, 825, 30, 517, 584, 531, 370, 550, 366, 134, 259, 773, 756, 514, 11, 78, 782, 398, 275, 18, 579, 165, 843 }

    { 265, 236, 866, 841, 242, 622, 633, 673, 402, 633, 498, 151, 339, 979, 967, 526, 176, 218, 951, 476, 348, 84, 586, 184, 887 }

    10

    Returns: {0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.5151966154914268, 0.5142135773031998, 0.4848033845085732, 0.7956391564410437, 0.0, 0.0, 0.0, 0.6901472662557571, 0.14970388495152656, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.14970388495152653, 0.8502961150484737, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.8502961150484737, 0.0, 0.0, 0.0, 0.0, 1.0 }

  55. { 94, 165, 658, 66, 170, 277, 348, 959, 172, 57, 822, 796, 647, 643, 618, 848, 551, 760, 330, 614, 387, 31, 363, 860, 362 }

    { 205, 236, 729, 70, 218, 313, 377, 959, 242, 90, 927, 915, 691, 690, 657, 931, 699, 862, 443, 649, 431, 86, 422, 895, 392 }

    18

    Returns: {0.0, 0.0, 0.0, 0.0, 0.9999999999999987, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9999999999999987, 0.0, 0.9999999999999987, 0.9999999999999987, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9999999999999987, 0.0, 0.0, 0.9999999999999987, 0.0, 0.9999999999999987, 0.9999999999999987, 0.0, 0.9999999999999987, 0.0, 0.0, 0.9999999999999987, 0.0, 0.9999999999999987, 0.9999999999999987, 0.0, 0.9999999999999987, 0.0, 0.0, 0.9999999999999987, 0.0, 0.9999999999999987, 0.0, 0.0, 0.9999999999999987, 0.0, 0.9999999999999987, 0.0, 0.0, 0.9999999999999987 }

  56. { 337, 948, 355, 542, 34, 565, 401, 841, 31, 62, 611, 43, 205, 539, 843, 249, 479, 801, 256, 668, 85, 905, 703, 707, 195 }

    { 434, 994, 441, 642, 126, 615, 405, 980, 95, 97, 644, 57, 266, 543, 875, 267, 483, 807, 279, 816, 119, 955, 803, 796, 209 }

    3

    Returns: {0.0, 0.0, 0.9999999999999994, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.8714285714285702, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.12857142857142853, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9999999999999989, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }

  57. { 626, 221, 668, 615, 603, 269, 366, 858, 67, 74, 393, 367, 260, 401, 855, 200, 698, 24, 861, 519, 66, 723, 854, 776, 151 }

    { 630, 321, 678, 620, 607, 291, 418, 969, 146, 88, 470, 431, 324, 428, 942, 261, 708, 84, 899, 641, 93, 771, 995, 791, 151 }

    24

    Returns: {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.9784153005464483, 0.0, 0.02158469945355192, 0.948199648711944, 0.0, 1.0, 0.9481996487119438, 0.05180035128805623, 1.0, 0.0, 0.05180035128805623, 0.9481996487119438, 0.0, 1.0, 0.9481996487119438, 0.05180035128805623, 1.0, 0.0, 0.051800351288056254, 0.0969042740046839, 0.0, 1.0, 0.0969042740046839, 0.9030957259953163, 0.9030957259953163, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0 }

  58. { 927, 248, 436, 630, 221, 944, 467, 569, 465, 699, 844, 295, 663, 25, 49, 912, 258, 32, 58, 839, 691, 466, 239, 71, 618 }

    { 931, 338, 485, 787, 393, 950, 490, 582, 529, 731, 949, 348, 716, 179, 68, 939, 353, 143, 152, 971, 776, 573, 383, 194, 642 }

    22

    Returns: {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.47097919421342127, 0.0, 0.0026866359447004617, 0.0, 1.0, 0.4736658301581217, 0.5263341698418783, 0.2860655527997937, 0.0, 0.48033250432272173, 0.0, 0.7599361127193636, 0.24006388728063663, 0.0, 0.9999999999999999, 0.24006388728063663, 0.7599361127193636, 0.9999999999999999, 0.0, 0.7599361127193636, 0.0, 0.0, 1.0 }

  59. { 34, 877, 66, 603, 5, 468, 294, 990, 866, 283, 609, 820, 601, 253, 44, 39, 204, 721, 506, 878, 514, 464, 216, 574, 630 }

    { 53, 878, 133, 642, 198, 584, 297, 998, 879, 360, 788, 925, 641, 358, 173, 199, 263, 772, 547, 954, 543, 542, 336, 581, 733 }

    10

    Returns: {0.0, 0.0, 0.9999999999999996, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0 }

  60. { 499, 82, 359, 195, 712, 367, 22 }

    { 853, 996, 480, 229, 851, 785, 52 }

    6

    Returns: {1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0 }

  61. { 134, 161, 593, 464 }

    { 560, 564, 600, 602 }

    2

    Returns: {0.07294433889668023, 0.0, 0.08518541440180122, 0.0, 0.8418702467015183, 0.15812975329848147, 0.0, 0.8418702467015183 }

  62. { 164, 606, 33, 620, 526, 161, 314, 25, 100, 178, 613, 227, 153, 14, 198, 70 }

    { 253, 694, 491, 713, 614, 914, 825, 628, 330, 821, 652, 733, 455, 165, 344, 290 }

    8

    Returns: {8.766412083949611E-4, 0.0, 0.9991212887840025, 8.766412083949611E-4, 0.0, 0.21398543590403526, 5.7225336297883044E-5, 0.9999427746637024, 0.21480692178373467, 0.7817331311023269, 0.7290655316869986, 0.003470098744042965, 0.8050411708267231, 0.09860190751541947, 0.16695490460379778, 0.23477178347821542, 0.007186526060234957, 0.013562840367914167, 0.07318892140700749, 0.6374710200415574, 0.1594781049656562, 0.8405216399821882, 0.565716866287188, 0.16527637139712853, 0.21843671409590878, 0.009398222961968516, 0.0, 0.0, 0.056342038888691305, 3.8813263310650344E-4, 0.0037271440653616765, 0.0 }

  63. { 324, 967, 237, 138, 309, 782, 12, 239, 257, 74, 948, 606, 375, 477, 11, 888 }

    { 603, 994, 975, 945, 527, 830, 275, 855, 717, 716, 978, 846, 924, 976, 878, 890 }

    9

    Returns: {0.14728797356002227, 0.0, 0.8527120264399782, 0.14728797356002227, 0.0, 0.5574536748733343, 0.011656752972395072, 0.45416480916274643, 0.004181089264850478, 0.037298606839558, 0.3295407538628117, 0.6702715446368873, 0.0, 0.0, 0.3676284022083234, 0.0957758459865484, 0.264762201030538, 0.03613395383560644, 0.18663501131971907, 0.019364499030795727, 0.7028524273130006, 0.2971475726869988, 0.1470327127430479, 0.8133449609064347, 0.06649951521341448, 0.6005786548126465, 0.571870042073176, 0.2711779036684222, 0.3473410919987232, 0.0, 1.0, 0.0 }

  64. { 181, 417, 250, 204, 61, 468, 355, 296, 312, 130, 214, 449, 0, 481, 497, 17, 182, 517, 167 }

    { 309, 789, 465, 830, 698, 793, 515, 938, 313, 673, 637, 762, 93, 675, 695, 537, 829, 627, 244 }

    6

    Returns: {0.0, 0.0, 0.6294312098739151, 0.0, 7.225957164462815E-5, 1.1388412808725994E-5, 0.1812914540809915, 0.25013401088272114, 0.05363400828288479, 0.15459357033244966, 0.1373790161708993, 0.6032333845336332, 7.612815902304456E-4, 0.0061303579855159695, 0.13892569951468353, 0.4558734434769367, 0.0, 0.0, 0.07810187118971104, 0.11925083357489594, 0.07229649436163499, 0.09520601507049736, 0.40591884841479275, 0.2575890124388248, 0.0, 0.0, 0.5137977382014224, 0.09919124081402309, 0.5666676374431634, 0.1420547937466297, 0.006844547151977254, 6.014521785814787E-4, 0.21487793415204887, 0.19931358092818816, 0.0, 0.6168169156242936, 0.0, 0.0 }

  65. { 240, 572, 14, 717, 7, 243, 34, 667, 706, 38, 11, 600, 184, 714, 591, 35, 203, 410, 390, 352, 372, 199, 192 }

    { 572, 819, 975, 955, 696, 634, 919, 710, 743, 550, 935, 705, 737, 832, 711, 161, 392, 504, 716, 606, 959, 984, 270 }

    6

    Returns: {0.0, 0.0, 0.5283373159649298, 0.0, 0.1592997470543493, 0.1339139391405041, 0.3122256301470268, 0.684155615598479, 2.655292572424781E-4, 0.012595479264638224, 0.0, 4.5040681214590867E-4, 0.02373559281349411, 0.23047173472200846, 0.05017229671494346, 0.411132834545356, 0.474092283823251, 0.4527034895443855, 0.0, 0.0, 0.21193897007269133, 0.048506678621234964, 0.13845966181466302, 0.00992640440081118, 0.06491998382307573, 0.006917626906237903, 0.7738907082383724, 0.21579307164156392, 0.0764201072177824, 0.0862676602959703, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03001156196294665, 0.035620029579522774, 5.74108532960525E-7, 1.301828433292678E-5, 0.15623003698669777, 0.3003668796107412, 0.0, 0.3711651310320665, 0.0, 0.0 }

  66. { 354, 479, 573, 207, 149, 67 }

    { 928, 489, 655, 968, 881, 400 }

    3

    Returns: {0.7409076772364611, 0.0, 0.12485064962432171, 0.15290194371624466, 0.13424167313921748, 0.7713815015664114, 0.0, 0.5919248705526893, 0.0, 0.48336713960669453, 0.0, 4.2454455796059505E-4 }

  67. { 128, 166, 291 }

    { 509, 935, 983 }

    3

    Returns: {1.0, 0.0, 0.0, 1.0, 0.0, 1.0 }

  68. { 183, 856, 220, 648, 268, 237, 983, 15, 493, 221 }

    { 769, 894, 892, 741, 377, 871, 987, 578, 863, 250 }

    7

    Returns: {0.7205730267863146, 0.0, 0.2794269732136861, 0.7205730267863146, 0.0, 0.8223109571285641, 0.5616259928780815, 0.4383740071219202, 0.2610837392374748, 0.018742008963204455, 0.8392407636384374, 0.0, 0.338037634666683, 0.6619623653333196, 1.1869579327735052E-5, 0.339192300370567, 0.0, 0.9976617885492968, 0.0, 0.0011835457468220444 }

  69. { 260, 569, 556, 10, 793 }

    { 480, 827, 937, 447, 868 }

    1

    Returns: {0.0, 0.0, 0.02183983377149536, 0.0, 0.28038027004684485, 0.0, 0.0, 0.0, 0.6977798961816597, 0.0 }

  70. { 231, 215, 922, 330, 583, 585, 140, 146, 449, 444, 463, 119, 29, 136, 595, 376, 63, 434, 381, 370, 181 }

    { 269, 608, 950, 491, 963, 848, 937, 396, 466, 539, 633, 208, 869, 295, 993, 736, 808, 796, 837, 480, 435 }

    6

    Returns: {0.0, 0.0, 0.023111435243276347, 0.0, 0.9768885647567243, 0.023111435243276347, 0.0, 1.3464508075569268E-4, 2.6080741482582484E-6, 0.9082310551441282, 0.021602789326865005, 0.8449434348719307, 0.26619910332569835, 0.12284347165050521, 0.0, 0.0, 2.5153674561087972E-5, 0.0, 0.008308326547824083, 0.0, 0.11382264785785927, 0.01133385416719453, 0.0, 0.0, 0.23230643185296254, 0.049832454673125796, 0.0, 0.0, 0.8258386123240035, 0.10600431288046486, 0.2071062754703775, 0.08314644861886517, 0.1457418595708825, 0.08694284745332141, 0.17904143554286175, 0.29678786229775767, 4.756431959680308E-6, 0.46664394275129745, 0.0, 4.4235167380679696E-5, 0.0, 0.0 }

  71. { 661 }

    { 922 }

    1

    Returns: {1.0, 0.0 }

  72. { 52, 25, 101, 129, 37, 158, 495, 74, 43, 214, 90, 508, 526, 603 }

    { 866, 839, 118, 949, 890, 980, 655, 667, 172, 417, 895, 769, 712, 859 }

    8

    Returns: {0.5483162255611247, 0.0, 0.26651651226503464, 0.24504907383306018, 6.083960378282816E-7, 0.0, 0.1503124507825585, 0.5050193050809763, 0.0686107720616887, 0.4826815518775268, 0.1918314961904436, 0.5030610028439411, 0.6906135435891703, 0.2533263879747073, 0.37594226380501994, 0.02072260714378481, 2.009552407979051E-5, 4.725605272487449E-6, 0.14592651865945233, 0.0, 0.5619106953696796, 0.031866984191128316, 4.08978988619494E-5, 0.9777881251718337, 4.2917721051656294E-4, 0.9804802362777719, 0.9995287426863332, 0.0 }

  73. { 442, 328, 672, 474, 56, 173, 412, 92, 56, 294, 597, 56 }

    { 470, 773, 714, 875, 699, 603, 546, 222, 281, 667, 699, 518 }

    3

    Returns: {0.0, 0.0, 0.3348729951406577, 0.0, 0.6641745351431296, 0.32484372219003793, 9.524697162131718E-4, 0.6903983798239403, 0.0, 0.09901909689343633, 0.0, 0.014332539867510423, 0.0, 0.0076993201880671165, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09702888083861383, 0.0, 0.7662408826377158, 0.0, 4.3717756067946246E-4 }

  74. { 129, 652, 746, 422, 72, 629, 562, 250, 90, 371, 97, 191, 560 }

    { 868, 986, 785, 479, 371, 955, 721, 542, 202, 897, 894, 655, 788 }

    7

    Returns: {0.45920003073817856, 0.0, 0.5407990744522354, 0.4585746532544583, 8.948095862181221E-7, 0.999999105190415, 0.016468656461361086, 0.10373567648574203, 1.1553123373110441E-7, 0.0, 0.5603147285935032, 0.4376011279192373, 0.9285117081530295, 0.016558209142743585, 0.06388586397155753, 0.020722913528866498, 0.0, 0.0, 0.3796715251594085, 0.35763570518928106, 0.05114740212990621, 0.406373851355676, 0.0, 0.2359201798620835, 0.0, 0.9628785780714975 }

  75. { 849 }

    { 939 }

    1

    Returns: {0.9999999999999991, 0.0 }

  76. { 63, 408, 428, 73, 439, 672, 476, 51, 840, 577, 266, 345, 470, 468, 443, 600 }

    { 897, 408, 931, 417, 528, 847, 783, 374, 873, 750, 673, 663, 950, 748, 683, 678 }

    2

    Returns: {0.10446167389229097, 0.0, 0.0, 0.0, 0.25217891201949827, 0.006405093160993121, 0.0, 0.0, 0.0, 0.0, 0.3034793600107832, 0.0010410898410634262, 0.03198896515269811, 0.0, 0.0, 0.0, 0.30789108892472755, 0.6460482352902203, 0.0, 0.01902074044857667, 0.0, 4.871796378423594E-7, 0.0, 0.0, 0.0, 0.3172087056562628, 0.0, 0.010139821880210098, 0.0, 7.326486138080003E-5, 0.0, 6.256168165312686E-5 }

  77. { 10, 217, 490, 855, 439, 148, 688, 692, 60, 159, 238, 344, 312, 200 }

    { 135, 834, 563, 859, 734, 405, 956, 971, 974, 256, 380, 353, 569, 605 }

    2

    Returns: {0.0, 0.0, 0.017790904711025568, 0.0, 0.0, 0.0, 0.7715445645001215, 0.017790904711025568, 0.0, 8.32694541789701E-4, 0.0, 0.0, 0.17042920696830138, 0.331122419435926, 0.040235323820551464, 0.5063826635773044, 0.0, 0.14387131773395423, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: