Statistics

Problem Statement for "MostLikely"

Problem Statement

In a contest, we know the scores of all our competitors, and we estimate that our own score is equally likely to be any integer value between low and high, inclusive. We want to know what our rank will most likely be. We define our rank to be 1 + the number of competitors that beat us, so our rank will be number 1 if no one beats us (even if several tie us).

Given a int[] scores, the scores of our competitors, and ints low and high, return our most likely rank. If there is more than one most likely rank, return -1.

Definition

Class:
MostLikely
Method:
likelyRank
Parameters:
int[], int, int
Returns:
int
Method signature:
int likelyRank(int[] sc, int low, int high)
(be sure your method is public)

Constraints

  • scores will contain between 1 and 50 elements, inclusive.
  • Each element of scores will be between 0 and 1,000,000,000, inclusive.
  • low will be between 0 and 1,000,000,000, inclusive.
  • high will be between low and 1,000,000,000, inclusive.

Examples

  1. {3,12,4}

    8

    8

    Returns: 2

    It is certain that only the 12 will beat us, giving us a rank of 2.

  2. {3,4,5}

    3

    7

    Returns: 1

    Our score is equally likely to be 3 or 4 or 5 or 6 or 7. One of those scores (the 3) gives us a rank of 3. Similarly, one of those scores gives us a rank of 2. And the remaining 3 scores all give us a rank of 1 which is thus the most likely.

  3. {3,4,5}

    2

    5

    Returns: -1

    Each of our possible scores gives us a different rank, so all those ranks are tied for most likely.

  4. {121,120,119}

    120

    120

    Returns: 2

  5. {5}

    1

    1

    Returns: 2

  6. {11,11}

    0

    0

    Returns: 3

  7. {199999900}

    201000000

    201000000

    Returns: 1

  8. {117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117}

    117

    122

    Returns: 1

  9. {117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117,117}

    112

    117

    Returns: 51

  10. {234,1000000000,333333333,444444444,555555555,0,1,999999999,333333333,222222234}

    0

    922222222

    Returns: 3

  11. {1,6,6,7,9}

    5

    7

    Returns: -1

  12. {1,6,6,8,9}

    5

    7

    Returns: 3

  13. {422000000,1,6,6,8,9,422000000}

    0

    843999989

    Returns: 3

  14. {422000000,1,6,6,8,9,422000000}

    0

    843999989

    Returns: 3

  15. {422000000,1,6,6,8,9,422000000}

    0

    843999990

    Returns: -1

  16. {422000000,1,6,6,8,9,422000000}

    0

    843999991

    Returns: 1

  17. {470428639, 509959133, 414860692, 413242890, 780165405, 239767459, 464007868, 371070014, 731943922, 689269959, 509784042, 654399067, 673028214, 294088218, 583790801, 770657866, 255898284, 627206520, 656746207, 303561142, 336677693, 387914137, 594557748}

    388802647

    549772527

    Returns: 15

  18. {735997929, 796517922, 765116916, 750996250, 718838311, 731876524, 784419099, 792820808, 783012578, 694657742, 666018239, 749974911, 663954650, 792498123, 741457712, 652988147, 777263549}

    684463254

    775314794

    Returns: 14

  19. {972170909, 969360620, 956557123, 951869529, 967431645, 961003682, 953501467, 968825402, 970138014, 952141397, 973178141, 952489767, 959058216, 963463212}

    975020158

    975271776

    Returns: 1

  20. {787448972, 556899633, 740187190, 628565409, 779751361, 732770537, 761591015, 580617684, 694032886, 422852946, 628015314, 566198244, 522997061, 645300169, 784475698, 491649245, 598151186, 383768572, 544066096, 555808458, 433856273, 467170256, 526359360, 663033582, 505661062, 410581086, 528955273, 459387443, 713890682}

    613213859

    739130371

    Returns: 9

  21. {410219923, 412221335, 385628651, 387987771, 413824751, 402226607, 376662458, 372231719, 360389205, 391025015, 368724278, 366110168, 381046179, 389819789, 396887877, 404964913, 398433009, 380810947, 369685929, 374033383, 366106213, 409732468, 365583264, 394508006, 365575318, 368499656, 411957453, 363730225, 405742629, 358293294, 414919512, 400159842, 395553353, 400990739, 400054521}

    375741981

    407888967

    Returns: 21

  22. {597807872, 610128932, 666677511, 576034341, 694394295, 682182214, 553738342, 710612125, 512842605, 522380423}

    606761675

    665991627

    Returns: 5

  23. {808120420, 853775370, 886587813, 704737127, 735027988, 795800300, 745042651, 730720416}

    686025710

    753499745

    Returns: 8

  24. {391502477, 362307576, 366869628, 349181249, 356079764, 364982905, 385258069, 344042740, 360864208, 350243073, 395215253, 347824732, 343361880, 372562812, 356376215, 385484332, 377757702, 374368255, 392105119, 356058583}

    396539029

    397466982

    Returns: 1

  25. {750869392, 742121543, 942379694, 913553270, 858208943, 822595946, 830142438, 786923935, 818653037, 922931697, 924631189, 920045175, 893129938, 886766297, 744152314, 924871798, 773827640, 762210234, 832432895, 801184249, 732958478, 743111992, 915309368, 830576861, 867532362, 951191084, 826004517, 751734319, 944439243}

    764696499

    896293839

    Returns: 14

  26. {821958858, 813788242, 821821675, 818787706, 817253541, 815523732, 819954085, 819032527, 815199700, 820075582, 813417698, 817820658, 813121139, 814801658, 815430308, 813480791, 815889472, 821794717}

    820139607

    822415366

    Returns: 4

  27. {701692403, 672656048, 631758149, 625908343, 716914442, 591012775, 708656593, 597298584, 628557999, 772506793, 666135170, 589177229, 571226468, 663516177, 709605533, 716235409, 605165522, 651885665, 764774147, 759133911, 755415842, 633261186, 732755564, 721072863, 633733698, 665875056, 713832675, 739997386, 696304904, 607849099, 739843125, 623242671, 581431892, 748215203, 600132575, 776036103, 769275693, 633708700, 765144376, 750487651, 661528843, 592587419, 745124914, 657177690, 752087369, 680725409, 583142588}

    769569841

    775990050

    Returns: 2

  28. {464124194, 481355145, 503857876, 427482292, 477145267, 460390544, 486184582, 453634629, 454893310, 478980178, 487790265, 436874876, 516127764, 449068463, 510239757, 437446953, 463590162}

    451253563

    471720992

    Returns: 9

  29. {333820877, 465542724, 170156947, 153580744, 369262072}

    384758295

    434790696

    Returns: 2

  30. {941547037, 928672511, 949917052, 928246223, 936420656, 943167343, 933334299, 934193011, 946481145, 939866067, 928582142, 946185877, 934617100, 948350888}

    944039707

    947198360

    Returns: 5

  31. {677437941, 563423024, 110888814, 121957020, 122691838, 699218935, 470696364, 744435297, 617960739, 439666422}

    622355331

    695005699

    Returns: 4

  32. {541102735, 457482036, 468394345, 508312459, 342685763, 431136835, 492751351, 356401731, 350142359, 536661046, 354655363, 383081309, 339148472, 463057557, 358742615, 344732856, 534271086, 539762132, 409035801}

    547325714

    549925137

    Returns: 1

  33. {922559787, 961158697, 932628777, 917747531, 960370091, 966391680, 910148897, 960568575, 914220516, 945528416, 951623746, 947013052, 920585795, 962333250, 919852828, 909973200, 908505420, 917287982, 934549272, 966424234, 948049841, 918709869, 942713487, 940080268, 960638492, 954280750, 943052277}

    908301379

    949705183

    Returns: 18

  34. {601338069, 604929518, 594309071, 584048644, 575518463, 580765054, 605165269, 605785274}

    583984683

    584052855

    Returns: 7

  35. {572651212, 540414388, 533767644, 589888606, 568398210, 594848493, 500977420, 459750174, 471213340}

    505844436

    574502588

    Returns: 5

  36. {497331608, 505901179, 417827011, 503740508, 502087603, 498789877, 426939952, 493433356, 447840670, 426076026, 495652811, 488402523, 503103972, 444886247, 492976610, 421789063, 442599325, 509106644, 497268363, 428446452, 434095611, 493524262, 465341752, 410629563, 477644768, 449634212, 483343843, 508204226, 454543597, 469132580, 443386308, 421843460, 479401798, 457631202, 405478850, 501333868, 474990833, 434959740, 423841398, 488115139, 430532477, 513636989, 435388203}

    487972720

    503343927

    Returns: 16

  37. {689371991, 468801824, 461017224, 474708669, 480747521, 416977571, 598759841, 622378900, 602354896, 435569359, 643950177, 668480503, 925259564, 656217145, 591558095, 674111557, 540195996, 519192082, 747285813, 804915657, 484560734, 670090277, 569801608, 527374083}

    766976358

    939161028

    Returns: 2

  38. {533374732, 536428260, 499256478, 520143343, 605173842, 628768973, 608691311, 712696301, 583222739, 631630443, 653883252, 559777539, 703107480, 747490344, 638968084, 509223538, 542108202, 681364280, 556000376, 648370212, 626849889, 683470856, 606279591, 657897046, 584012021, 524318626}

    730982666

    736554607

    Returns: 2

  39. {561117130, 597158716, 563991039, 579148710, 597217699, 568405016, 523382587, 514470369, 523659332, 551178965, 530565593, 509247529, 592868936, 556293402, 572789799, 512117605, 589607002, 594792824, 541096516, 543877713, 553840557, 572271809, 524818830, 540242473, 518511981, 517231160, 504563693, 532711822, 596449803, 575470498, 529169101, 559691903, 611967872}

    539934762

    583435587

    Returns: 19

  40. {312718624, 632145508, 80604731, 531076041, 513376744, 566142578, 272373144, 580203595, 84671389, 468016512, 633989070, 437068938, 133726344, 251985819, 270909156, 415338466, 606288945, 528752110, 675335435, 398247835, 469882557, 554533133, 234349982, 545696236, 528622687, 480233537, 359713859, 263916580}

    568615714

    631281173

    Returns: 5

  41. {527644094, 766735751, 788958718, 658948429, 753001505, 713708488, 539677203, 724538734, 596278771, 747645753, 837804087, 827512786}

    698065592

    830071307

    Returns: 3

  42. {539447447, 814704703, 880562244, 753270189, 646389313, 484066732, 690330392, 793501532, 420117367, 741638385, 595249276, 862568944, 798777088, 591803805, 721866077, 398786242, 690124226, 403899333, 484220510, 495259104, 559369067, 526384875, 450200610, 473769742, 423433746, 635792953, 787914014, 611459461, 511571772, 347375859, 812220111, 739793955, 337904865, 386082046, 853079302, 334722628, 735351601, 322235141, 661879820, 650337453, 805110635, 681196550, 555408574, 631788650, 459338870, 493132689, 333465903}

    789328330

    794822353

    Returns: 9

  43. {208955096, 117205214, 211527151, 206524899, 81909079, 202684263, 87346933, 194350652, 85422498, 186027450, 217857534, 102245837, 295311176, 170221012, 235910668, 272361876, 130451683, 202926087, 213267153, 268396222, 126806953, 171706471, 90077248, 274983399, 271855236, 255150855, 266823996, 106519962, 78983026, 146669059, 83401422, 132034677, 77317774, 224074263, 179854644, 240426029}

    124269762

    278104200

    Returns: 23

  44. {383377355, 374653939, 347497026, 384672986, 292295495, 160680168, 308600371, 484818859, 430975587, 399676591, 524770056, 137227188, 169950024, 234851728, 305449780, 344704382, 244526411, 136736838, 327817020, 477127285, 382110124, 240339090, 264035691, 156262674, 241961200, 246935107, 414509827, 357930086, 413735845, 318709254, 181474484, 177599588, 325735316, 488114703, 281284631, 547791770, 156090945, 282057405, 317891223, 150587760, 487825090, 169493560, 143916496, 371569500, 236392674, 546884073, 174192568}

    205544729

    289760482

    Returns: 36

  45. {848664536}

    904882354

    918264787

    Returns: 1

  46. {581438554, 557054610, 619879460}

    552144048

    605547702

    Returns: 3

  47. {443306060, 250641150, 612389273, 275078406, 278875045, 212408078, 223972631, 571729722, 213141018, 526276909, 400801488, 224925519, 566413491, 266707113, 450939822, 558140376, 330923786, 660575623, 518524986, 646991316, 279530000, 71217053, 243955535, 268700581, 162905398, 660261972, 162617187, 369028223, 463244903, 450555019, 405477748, 348562074, 658247431, 122826277, 681834661}

    421165858

    460866835

    Returns: 16

  48. {526503303, 690614289, 369298884, 349790082, 576429685, 449557340, 283541322, 495004428, 583308235, 439619071, 469560254, 290555829, 301239044, 282502089, 400708934, 304144340, 242722222, 316497637, 418459455, 381412351, 663969044, 407358369, 229054239, 628616453, 647379706, 530814345, 636746855, 708967215, 434218292, 467612786, 358474910, 621599403, 419582025, 380599372, 675369155, 698746423, 232727565, 704201554, 251275734, 605977955, 613412566, 287704759, 369930710, 545411249, 441103376, 447731981, 669096856}

    622384553

    697681413

    Returns: 8

  49. {870134703, 656505685, 339548016, 253321652, 553082102, 413587576, 634428398, 149660572, 311484298, 650812582, 458525490}

    107054094

    819587539

    Returns: 2

  50. {1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 }

    0

    1000000000

    Returns: 2

  51. {0, 10, 100, 200, 300, 400, 500, 1000, 2000, 3000, 4000, 5000, 10000, 20000, 30000, 40000, 50000, 100000, 200000, 300000, 400000, 500000, 600000, 700000, 1000000, 2000000, 3000000, 4000000, 5000000, 6000000, 7000000, 20000000, 30000000, 40000000, 50000000, 60000000, 10000000, 100000000, 555555555, 888888888, 999999999, 1000000000 }

    1

    1000000000

    Returns: 5

  52. {3, 4, 5 }

    2

    5

    Returns: -1

  53. {499999999, 500000000 }

    1

    1000000000

    Returns: 1

  54. {3, 4, 5 }

    1

    2

    Returns: 4

  55. {3, 4, 5 }

    1

    1000000000

    Returns: 1

  56. {1, 2, 222, 33, 333, 333, 44, 44, 444, 444, 4, 55555, 555, 55, 6, 66, 666, 666, 666, 66, 6 }

    0

    1000000000

    Returns: 1

  57. {400, 1000, 2000, 3000 }

    450

    2500

    Returns: 3

  58. {5, 5, 5, 5, 5 }

    1

    7

    Returns: 6

  59. {1, 2, 66, 1000000000 }

    1

    1000000000

    Returns: 2

  60. {1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 999999999, 99999999, 9999999, 99900011 }

    0

    1000000000

    Returns: 2

  61. {1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6 }

    0

    1000000000

    Returns: 1

  62. {1324, 321111111, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000 }

    0

    1000000000

    Returns: 12

  63. {200, 200, 200, 300, 300, 1000000000 }

    1

    500000000

    Returns: 2

  64. {0, 1, 2, 1000000000 }

    0

    1000000000

    Returns: 2

  65. {0, 10, 20, 30 }

    11

    28

    Returns: -1

  66. {3, 4, 5 }

    2

    1000000000

    Returns: 1

  67. {7, 8, 9 }

    6

    7

    Returns: -1

  68. {1, 100, 50000, 532333, 53323, 646463, 345566, 5000000, 50000000, 500000000, 1000000000, 52345, 523462, 378554, 233342, 6678888, 325, 552234, 623454, 6235252, 7453663, 236676, 34777788, 532355, 735778383, 32822356, 23567772, 2355666, 23312333, 4234555, 35626266, 523523523, 62562353, 342523627, 7, 7457735, 5235532, 3552, 42344, 266666, 635453, 5235, 845635, 234555, 23577, 8, 86477463, 523521, 2344 }

    10

    1000000000

    Returns: 2

  69. {999999999, 999923999, 999999999, 999990000, 999999999, 1, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999, 999999999 }

    0

    1000000000

    Returns: 48

  70. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 }

    0

    1000000000

    Returns: 1

  71. {3, 3, 3 }

    1

    4

    Returns: -1

  72. {1000000000, 999993101, 999997852, 999995393, 999992118, 999991877, 999993731, 999997869, 999993680, 999991420, 999998058, 999999856, 999991800, 999991815, 999992776, 999990749, 999990245, 999996578, 999998155, 999992124, 999997897, 999995505, 999990762, 999996760, 999990254, 999999716, 999992705, 999999388, 999999401, 999991844, 999999116, 999991159, 999999920, 999995588, 999998166, 999998726, 999999390, 999997909, 999995430, 999990565, 999998599, 999994033, 999992383, 999997700, 999998423, 999990137, 999996972, 999993349, 999997431, 1000000000 }

    0

    1000000000

    Returns: 51

  73. {1, 10 }

    8

    11

    Returns: -1

  74. {3, 12, 4, 3, 4, 12, 12 }

    8

    8

    Returns: 4

  75. {5, 5, 5, 5, 5 }

    1

    3

    Returns: 6

  76. {2, 3, 4 }

    1

    2

    Returns: -1

  77. {2, 2 }

    1

    2

    Returns: -1

  78. {1, 15, 4000, 5000, 9000, 1000, 10000, 100000, 200000, 300000, 2, 3, 4, 999999, 1000000, 1000001, 1000002, 1000004, 1000005, 1000008, 1000009, 90000000, 90000001, 10000000 }

    0

    1000000000

    Returns: 1

  79. {9, 234534534, 345345, 43534536, 546457657, 7867867, 4362, 34523, 423, 4, 23, 5, 34, 5, 4, 6, 546, 45, 66, 57567, 656, 756, 5656, 756, 999999900, 999990000 }

    1

    99999999

    Returns: 5

  80. {9, 234534534, 345345, 43534536, 546457657, 7867867, 4362, 34523, 423, 4, 23, 5, 34, 5, 4, 6, 546, 45, 66, 57567, 656, 756, 5656, 756, 1000000000 }

    1

    1000000000

    Returns: 2

  81. {3, 12, 4 }

    1

    1000000000

    Returns: 1

  82. {3, 4, 5, 2, 3, 4, 5, 10 }

    2

    5

    Returns: -1

  83. {1, 5, 200000000, 999999999 }

    1

    1000000000

    Returns: 2

  84. {1, 5 }

    2

    6

    Returns: 2

  85. {3, 4, 6, 3, 4, 5, 76, 3, 3, 4, 3, 4, 43, 43, 34, 34, 34, 45, 54, 3, 23, 45, 5, 3, 23, 34, 34, 45, 45, 45, 45, 56, 4, 43, 2, 23, 5, 4, 45, 23, 345, 6, 56, 45, 43, 43, 34, 34 }

    0

    1000000000

    Returns: 1

  86. {4343, 22, 1, 10000 }

    0

    1000000000

    Returns: 1

  87. {8, 8, 8, 8 }

    8

    8

    Returns: 1

  88. {1, 11, 111, 111, 2, 33, 55, 44, 88, 33, 5, 44, 77, 88, 899, 6, 66, 333, 22, 1, 55, 4, 54, 545, 45, 4 }

    0

    1000000000

    Returns: 1

  89. {5, 8, 11 }

    2

    13

    Returns: -1

  90. {3, 12, 4, 0, 1000000000 }

    0

    1000000000

    Returns: 2

  91. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 30, 1231, 213, 214, 123, 123 }

    1

    1000000000

    Returns: 1

  92. {3, 12, 4 }

    8

    8

    Returns: 2

  93. {9383, 10886, 12777, 16915, 7793, 18335, 5386, 492, 16649, 1421, 2362, 10027, 8690, 59, 17763, 13926, 540, 3426, 9172, 15736, 5211, 15368, 2567, 16429, 5782, 1530, 2862, 5123, 14067, 3135, 13929, 19802, 14022, 3058, 13069, 18167, 1393, 18456, 15011, 18042, 16229, 17373, 4421, 4919, 13784, 18537, 15198, 14324, 18315, 4370 }

    0

    999999999

    Returns: 1

  94. {1, 56456, 45645, 12654, 544, 546456, 456456, 4, 4, 4, 5, 6, 6, 7, 8, 9, 6456, 654645 }

    15

    1000

    Returns: 9

  95. {3, 12, 4 }

    8

    1000000000

    Returns: 1

  96. {1, 5, 5, 5, 7 }

    6

    6

    Returns: 2

  97. {3, 4, 5, 500000000, 1000000000 }

    0

    99999999

    Returns: 3

  98. {1, 2, 3, 100, 1000000000, 1000000000 }

    999999999

    1000000000

    Returns: -1

  99. {1, 1, 1, 1, 12, 2, 2, 3, 55, 5, 5, 510, 1000000, 3434343, 434343 }

    0

    1000000000

    Returns: 1

  100. {10, 20, 30, 30, 30, 10, 10, 10 }

    10

    10

    Returns: 5

  101. {3, 4, 5, 1, 1000000000 }

    1

    1000000000

    Returns: 2

  102. {1, 2, 3 }

    1

    1000000000

    Returns: 1

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