Statistics

Problem Statement for "FizzBuzzTurbo"

Problem Statement

Fizz Buzz is a simple game used to teach kids about divisibility. The goal of the game is to say positive integers in increasing order, with a twist: You don't say the numbers divisible by 3 and 5. Instead, whenever a number was divisible by 3 you say "fizz" and for a number divisible by 5 you say "buzz". (Thus, if a number was divisible by 15, you say "fizzbuzz".)

Here is how the game starts: 1, 2, fizz, 4, buzz, fizz, 7, 8, fizz, buzz, 11, fizz, 13, 14, fizzbuzz, 16, 17, fizz, 19, buzz, fizz, 22, 23, fizz, buzz, 26, fizz, 28, 29, fizzbuzz, 31, 32, fizz, 34, buzz, fizz, ...

Fizz Buzz has also become a traditional programming interview question. However, in this problem we have a more tricky assignment for you.

You are given longs A and B. Consider the part of the game that corresponds to integers from A to B, inclusive. During this part of the game, you will say "fizz" X times, "buzz" Y times, and "fizzbuzz" Z times. Return a long[] with three elements: {X,Y,Z}.

Definition

Class:
FizzBuzzTurbo
Method:
counts
Parameters:
long, long
Returns:
long[]
Method signature:
long[] counts(long A, long B)
(be sure your method is public)

Notes

  • The return value can be quite large. Make sure to use the appropriate data type.

Constraints

  • A will be between 1 and 10^18, inclusive.
  • B will be between A and 10^18, inclusive.

Examples

  1. 1

    4

    Returns: {1, 0, 0 }

    This is the sequence "1, 2, fizz, 4".

  2. 2

    6

    Returns: {2, 1, 0 }

    This is the sequence "2, fizz, 4, buzz, fizz".

  3. 150

    165

    Returns: {4, 2, 2 }

    This sequence begins and ends with a "fizzbuzz". There are some "fizz"es and some "buzz"es inbetween.

  4. 474747

    747474

    Returns: {72728, 36363, 18182 }

  5. 1

    1

    Returns: {0, 0, 0 }

  6. 2

    2

    Returns: {0, 0, 0 }

  7. 3

    3

    Returns: {1, 0, 0 }

  8. 10

    10

    Returns: {0, 1, 0 }

  9. 15

    15

    Returns: {0, 0, 1 }

  10. 29

    29

    Returns: {0, 0, 0 }

  11. 30

    30

    Returns: {0, 0, 1 }

  12. 31

    31

    Returns: {0, 0, 0 }

  13. 40

    40

    Returns: {0, 1, 0 }

  14. 47

    47

    Returns: {0, 0, 0 }

  15. 1

    961574729077486878

    Returns: {256419927753996501, 128209963876998250, 64104981938499125 }

  16. 1

    969690745985575352

    Returns: {258584198929486760, 129292099464743380, 64646049732371690 }

  17. 2

    932572744790738365

    Returns: {248686065277530231, 124343032638765116, 62171516319382557 }

  18. 2

    942493741554318791

    Returns: {251331664414485011, 125665832207242506, 62832916103621252 }

  19. 2

    956161331128091222

    Returns: {254976354967490992, 127488177483745496, 63744088741872748 }

  20. 3

    916644652962961635

    Returns: {244438574123456436, 122219287061728218, 61109643530864109 }

  21. 1

    903634696377824051

    Returns: {240969252367419747, 120484626183709874, 60242313091854936 }

  22. 1

    997897124971294393

    Returns: {266105899992345172, 133052949996172586, 66526474998086292 }

  23. 2

    920481086823903147

    Returns: {245461623153040840, 122730811576520420, 61365405788260209 }

  24. 4

    964058125459890556

    Returns: {257082166789304147, 128541083394652074, 64270541697326037 }

  25. 3

    931653762392195762

    Returns: {248441003304585536, 124220501652292768, 62110250826146384 }

  26. 4

    955444493333250458

    Returns: {254785198222200121, 127392599111100061, 63696299555550030 }

  27. 397478970173037155

    539466146345280224

    Returns: {37863246979264819, 18931623489632410, 9465811744816204 }

  28. 419288862274313963

    790969176712720462

    Returns: {99114750516908400, 49557375258454200, 24778687629227100 }

  29. 161780629001183449

    792845347608024286

    Returns: {168283924961824223, 84141962480912112, 42070981240456056 }

  30. 434696931263743538

    444647743199529483

    Returns: {2653549849542919, 1326774924771459, 663387462385730 }

  31. 321413177499911855

    649669244483624756

    Returns: {87534951195656774, 43767475597828388, 21883737798914193 }

  32. 139242337281418962

    860605271493493969

    Returns: {192363449123220002, 96181724561610000, 48090862280805001 }

  33. 167206637142521893

    346688750102520063

    Returns: {47861896789332845, 23930948394666422, 11965474197333212 }

  34. 290368704958546069

    457487148054284990

    Returns: {44564918158863712, 22282459079431857, 11141229539715928 }

  35. 359791099760826346

    642920662487020178

    Returns: {75501216726985022, 37750608363492511, 18875304181746255 }

  36. 722912705312276976

    911866031060439261

    Returns: {50387553532843277, 25193776766421638, 12596888383210819 }

  37. 853427743008756103

    879888482135011683

    Returns: {7056197100334821, 3528098550167410, 1764049275083706 }

  38. 299387440688073929

    348413117061600967

    Returns: {13073513699607210, 6536756849803605, 3268378424901803 }

  39. 326580842749285661

    909699510083828883

    Returns: {155498311289211526, 77749155644605762, 38874577822302882 }

  40. 192441344361172571

    933187129330394372

    Returns: {197532209325125813, 98766104662562906, 49383052331281454 }

  41. 314629682787953603

    764176844988746931

    Returns: {119879243253544888, 59939621626772444, 29969810813386222 }

  42. 267545852315582004

    297985012303716089

    Returns: {8117109330169090, 4058554665084545, 2029277332542272 }

  43. 142081782556603160

    413837186186015024

    Returns: {72468107634509831, 36234053817254916, 18117026908627457 }

  44. 664219828511882442

    692370293763552053

    Returns: {7506790733778563, 3753395366889281, 1876697683444641 }

  45. 378563365237109259

    761899675828236788

    Returns: {102223016157634008, 51111508078817004, 25555754039408502 }

  46. 49151622844844413

    488242673204329915

    Returns: {117090946762529467, 58545473381264734, 29272736690632367 }

  47. 306007182394072344

    518835169807946873

    Returns: {56754129977033208, 28377064988516604, 14188532494258302 }

  48. 195616889028066345

    478903385241094354

    Returns: {75543065656807469, 37771532828403734, 18885766414201868 }

  49. 67445786431842557

    626112604768032264

    Returns: {148977818222983923, 74488909111491961, 37244454555745980 }

  50. 101238876615718648

    480743165053709728

    Returns: {101201143583464288, 50600571791732144, 25300285895866072 }

  51. 82451605275412784

    415325919307210627

    Returns: {88766483741812758, 44383241870906379, 22191620935453190 }

  52. 208223567685839269

    372594759786848683

    Returns: {43832317893602511, 21916158946801256, 10958079473400627 }

  53. 838740078257909273

    931180210957050015

    Returns: {24650702053104198, 12325351026552099, 6162675513276050 }

  54. 252361299542933329

    495535777509654126

    Returns: {64846527457792213, 32423263728896107, 16211631864448053 }

  55. 709302378159832689

    834851837874070572

    Returns: {33479855923796770, 16739927961898385, 8369963980949192 }

  56. 487924215477189966

    529348735718046729

    Returns: {11046538730895138, 5523269365447568, 2761634682723784 }

  57. 21857780802393468

    477351058865690896

    Returns: {121464874150212648, 60732437075106324, 30366218537553162 }

  58. 186632354130213084

    742376154314155338

    Returns: {148198346715717935, 74099173357858967, 37049586678929484 }

  59. 539640619758087395

    924674358693185075

    Returns: {102675663716026048, 51337831858013025, 25668915929006512 }

  60. 700317928484694715

    745791327586173994

    Returns: {12126239760394474, 6063119880197237, 3031559940098619 }

  61. 13173508402927929

    236913933996190656

    Returns: {59664113491536728, 29832056745768364, 14916028372884182 }

  62. 668230156617098997

    739271183936145495

    Returns: {18944273951745733, 9472136975872866, 4736068487936434 }

  63. 479061995247225973

    883329982691655739

    Returns: {107804796651847937, 53902398325923968, 26951199162961985 }

  64. 254595297271140395

    767046507505855292

    Returns: {136653656062590639, 68326828031295320, 34163414015647660 }

  65. 662315051377427551

    926459760700470193

    Returns: {70438589152811372, 35219294576405686, 17609647288202842 }

  66. 279550177551909522

    314286211699960353

    Returns: {9262942439480222, 4631471219740110, 2315735609870056 }

  67. 63524787742327251

    419228954663410715

    Returns: {94854444512288924, 47427222256144462, 23713611128072231 }

  68. 474896471944502178

    650353451230197547

    Returns: {46788527809518766, 23394263904759383, 11697131952379691 }

  69. 502596589167164656

    595932444826925350

    Returns: {24889561509269519, 12444780754634760, 6222390377317379 }

  70. 560240637400990012

    707254615545708373

    Returns: {39203727505258230, 19601863752629115, 9800931876314557 }

  71. 59447034043076949

    144897967789338044

    Returns: {22786915665669626, 11393457832834813, 5696728916417406 }

  72. 510327613223700161

    585834264851678456

    Returns: {20135107100794212, 10067553550397106, 5033776775198553 }

  73. 669372155538435004

    776734092865104488

    Returns: {28629849953778529, 14314924976889265, 7157462488444632 }

  74. 395501921694716987

    456119285092003500

    Returns: {16164630239276404, 8082315119638202, 4041157559819101 }

  75. 151606123488146145

    439548322064777662

    Returns: {76784586287101738, 38392293143550869, 19196146571775435 }

  76. 996287155999621052

    997183739489986253

    Returns: {239088930764054, 119544465382027, 59772232691013 }

  77. 1

    1000000000000000000

    Returns: {266666666666666667, 133333333333333334, 66666666666666666 }

  78. 1000000000000000

    1000000000000000000

    Returns: {266400000000000000, 133200000000000001, 66600000000000000 }

  79. 1

    999999999999999990

    Returns: {266666666666666664, 133333333333333332, 66666666666666666 }

  80. 1

    100000000000000000

    Returns: {26666666666666667, 13333333333333334, 6666666666666666 }

  81. 1

    1000000000000

    Returns: {266666666667, 133333333334, 66666666666 }

  82. 1

    10000000000000

    Returns: {2666666666667, 1333333333334, 666666666666 }

  83. 15

    1000000000000000000

    Returns: {266666666666666663, 133333333333333332, 66666666666666666 }

  84. 3

    1234567890123456

    Returns: {329218104032922, 164609052016461, 82304526008230 }

  85. 7

    999999999999999991

    Returns: {266666666666666662, 133333333333333331, 66666666666666666 }

  86. 1

    10000000000000000

    Returns: {2666666666666667, 1333333333333334, 666666666666666 }

  87. 2

    100000000000

    Returns: {26666666667, 13333333334, 6666666666 }

  88. 5

    18518518368518518

    Returns: {4938271564938271, 2469135782469136, 1234567891234567 }

  89. 150000000000000003

    150000000000000003

    Returns: {1, 0, 0 }

  90. 1

    1000000000

    Returns: {266666667, 133333334, 66666666 }

  91. 1

    100000000000

    Returns: {26666666667, 13333333334, 6666666666 }

  92. 1

    1000000000000000

    Returns: {266666666666667, 133333333333334, 66666666666666 }

  93. 1000000000000

    2000000000000

    Returns: {266666666666, 133333333334, 66666666667 }

  94. 1

    999999999999999999

    Returns: {266666666666666667, 133333333333333333, 66666666666666666 }

  95. 15

    9000000000000000

    Returns: {2399999999999996, 1199999999999998, 600000000000000 }

  96. 1

    100000000000000

    Returns: {26666666666667, 13333333333334, 6666666666666 }

  97. 15

    250157725494998535

    Returns: {66708726798666272, 33354363399333136, 16677181699666569 }

  98. 17

    1000000000000000000

    Returns: {266666666666666663, 133333333333333332, 66666666666666665 }

  99. 1

    10000000000

    Returns: {2666666667, 1333333334, 666666666 }

  100. 1

    123456789123456

    Returns: {32921810432922, 16460905216461, 8230452608230 }

  101. 7

    9

    Returns: {1, 0, 0 }

  102. 10000

    10000000000

    Returns: {2666664000, 1333332001, 666666000 }

  103. 7

    987654321987654321

    Returns: {263374485863374484, 131687242931687242, 65843621465843621 }

  104. 1

    99999999999999999

    Returns: {26666666666666667, 13333333333333333, 6666666666666666 }

  105. 1

    1111111111111111

    Returns: {296296296296296, 148148148148148, 74074074074074 }

  106. 10000000000000

    6666666666666666

    Returns: {1775111111111111, 887555555555556, 443777777777778 }

  107. 21

    39

    Returns: {6, 2, 1 }

  108. 1000000000000

    5000000000000

    Returns: {1066666666666, 533333333334, 266666666667 }

  109. 3

    5

    Returns: {1, 1, 0 }

  110. 15

    16

    Returns: {0, 0, 1 }

  111. 3

    7

    Returns: {2, 1, 0 }

  112. 15

    35

    Returns: {5, 3, 2 }

  113. 1234567890

    999888777666555444

    Returns: {266637007048530015, 133318503524265007, 66659251762132504 }

  114. 5546

    85910293850192845

    Returns: {22909411693383280, 11454705846691640, 5727352923345820 }

  115. 3

    1000000000000000000

    Returns: {266666666666666667, 133333333333333334, 66666666666666666 }

  116. 1

    15

    Returns: {4, 2, 1 }

  117. 10000000000000

    10000000050000

    Returns: {13333, 6667, 3334 }

  118. 100000000000000000

    1000000000000000000

    Returns: {240000000000000000, 120000000000000001, 60000000000000000 }

  119. 15

    31

    Returns: {4, 2, 2 }

  120. 30

    46

    Returns: {4, 2, 2 }

  121. 3

    8

    Returns: {2, 1, 0 }

  122. 351435665634543

    7432653265436326

    Returns: {1888324693280476, 944162346640238, 472081173320119 }

  123. 2

    1000000000000000000

    Returns: {266666666666666667, 133333333333333334, 66666666666666666 }

  124. 10

    12

    Returns: {1, 1, 0 }

  125. 10

    15

    Returns: {1, 1, 1 }

  126. 99999999999999

    999999999999999999

    Returns: {266640000000000001, 133320000000000000, 66660000000000000 }

  127. 3

    4

    Returns: {1, 0, 0 }

  128. 15

    29

    Returns: {4, 2, 1 }

  129. 14

    31

    Returns: {4, 2, 2 }

  130. 15

    18

    Returns: {1, 0, 1 }

  131. 222

    225

    Returns: {1, 0, 1 }

  132. 1

    11

    Returns: {3, 2, 0 }

  133. 4

    6

    Returns: {1, 1, 0 }

  134. 2

    300000000000000000

    Returns: {80000000000000000, 40000000000000000, 20000000000000000 }

  135. 1242543221516688

    337457997509021202

    Returns: {89657454476667872, 44828727238333936, 22414363619166967 }

  136. 1

    10000000000000129

    Returns: {2666666666666701, 1333333333333350, 666666666666675 }

  137. 2119855817433555

    2119855817434086

    Returns: {142, 71, 36 }

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