Statistics

Problem Statement for "ExtendedHappyNumbers"

Problem Statement

Given a positive integer N, raise each of its digits to the K-th power and sum those values to get SK(N). For example, S2(65) = 62 + 52 = 61. Now, consider a sequence N, SK(N), SK(SK(N)) and so on. The happiness of N with respect to K is the smallest number in this sequence.

You will be given three ints A, B and K. Calculate the happiness of each integer between A and B, inclusive, with respect to K and return their sum.

Definition

Class:
ExtendedHappyNumbers
Method:
calcTheSum
Parameters:
int, int, int
Returns:
long
Method signature:
long calcTheSum(int A, int B, int K)
(be sure your method is public)

Constraints

  • A will be between 1 and 1,000,000, inclusive.
  • B will be between A and 1,000,000, inclusive.
  • K will be between 1 and 6, inclusive.

Examples

  1. 13

    13

    2

    Returns: 1

    The sequence for 13 is 13, 10, 1, 1...

  2. 1

    5

    2

    Returns: 14

    The sequences for numbers 1 to 5 are: 1: 1, 1, 1... 2: 2, 4, 16, 37, 58, 89, 145, 42, 20, 4... 3: 3, 9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, 16, 37... 4: 4, 16, 37, 58, 89, 145, 42, 20, 4... 5: 5, 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58, 89...

  3. 10

    99

    1

    Returns: 450

  4. 535

    538

    3

    Returns: 820

  5. 72637

    74236

    5

    Returns: 11789917

  6. 100000

    400000

    6

    Returns: 5169721292

  7. 1

    1000000

    1

    Returns: 4999996

  8. 1

    1000000

    2

    Returns: 3449108

  9. 1

    1000000

    3

    Returns: 160104496

  10. 1

    1000000

    4

    Returns: 662296074

  11. 1

    1000000

    5

    Returns: 6399861874

  12. 1

    1000000

    6

    Returns: 17031865483

  13. 1

    1

    6

    Returns: 1

  14. 2

    2

    6

    Returns: 2

  15. 999999

    999999

    6

    Returns: 5619

  16. 999999

    999999

    5

    Returns: 309

  17. 568625

    621730

    6

    Returns: 978533935

  18. 670270

    810950

    4

    Returns: 95153223

  19. 854744

    971170

    6

    Returns: 2194469088

  20. 476423

    491337

    3

    Returns: 2515259

  21. 242739

    840550

    5

    Returns: 3872455375

  22. 222558

    543391

    5

    Returns: 1970098456

  23. 112843

    445295

    5

    Returns: 2009503692

  24. 822402

    909381

    3

    Returns: 14099100

  25. 943019

    986251

    4

    Returns: 28690265

  26. 772328

    982900

    3

    Returns: 33823866

  27. 664486

    775299

    6

    Returns: 1955466546

  28. 984799

    994910

    5

    Returns: 62963877

  29. 176725

    731853

    2

    Returns: 1913156

  30. 343782

    559543

    6

    Returns: 3801037388

  31. 95563

    615898

    3

    Returns: 82927342

  32. 853244

    963813

    3

    Returns: 17628851

  33. 786558

    978964

    6

    Returns: 3672572090

  34. 233616

    869623

    6

    Returns: 11428330857

  35. 190015

    738105

    5

    Returns: 3479382561

  36. 984572

    986912

    4

    Returns: 1518223

  37. 95506

    769624

    3

    Returns: 107923684

  38. 854990

    874785

    3

    Returns: 3197612

  39. 713111

    916052

    3

    Returns: 33160169

  40. 103454

    105991

    6

    Returns: 37842086

  41. 940911

    962628

    6

    Returns: 393226747

  42. 720841

    726017

    1

    Returns: 25884

  43. 408088

    628656

    5

    Returns: 1402436454

  44. 367107

    695991

    1

    Returns: 1644426

  45. 239072

    742764

    3

    Returns: 80655956

  46. 232040

    396659

    3

    Returns: 25972811

  47. 441925

    709354

    2

    Returns: 923870

  48. 288411

    590095

    5

    Returns: 1894517320

  49. 835746

    837884

    4

    Returns: 1331533

  50. 190918

    261935

    3

    Returns: 10742235

  51. 436115

    500637

    1

    Returns: 322610

  52. 314423

    520705

    3

    Returns: 33337440

  53. 110706

    532823

    3

    Returns: 67225380

  54. 50425

    647687

    3

    Returns: 95469633

  55. 381832

    496887

    6

    Returns: 2029335895

  56. 818648

    983398

    1

    Returns: 823752

  57. 811629

    876592

    5

    Returns: 449437168

  58. 402757

    950032

    4

    Returns: 367974407

  59. 577260

    665132

    6

    Returns: 1609236767

  60. 753721

    836741

    6

    Returns: 1553958826

  61. 125945

    817759

    5

    Returns: 4422341415

  62. 588950

    787112

    4

    Returns: 134018239

  63. 740923

    940171

    6

    Returns: 3728420695

  64. 518554

    753707

    6

    Returns: 4143643049

  65. 896686

    958314

    4

    Returns: 40923299

  66. 905439

    909645

    4

    Returns: 2756821

  67. 106031

    133842

    4

    Returns: 17282141

  68. 197709

    270506

    3

    Returns: 10926867

  69. 757551

    982135

    3

    Returns: 36135598

  70. 6033

    895106

    4

    Returns: 590240188

  71. 743729

    761411

    4

    Returns: 12385279

  72. 640808

    932547

    5

    Returns: 2005740356

  73. 338590

    959556

    5

    Returns: 4123964502

  74. 438681

    488244

    6

    Returns: 833657679

  75. 624270

    902896

    4

    Returns: 186194394

  76. 50932

    291683

    6

    Returns: 3774424464

  77. 57390

    86673

    6

    Returns: 413438186

  78. 764470

    968857

    5

    Returns: 1408164454

  79. 133902

    648198

    6

    Returns: 8967071180

  80. 668710

    768987

    4

    Returns: 67997327

  81. 233089

    880967

    3

    Returns: 104160405

  82. 376023

    799495

    3

    Returns: 68335942

  83. 914477

    921696

    5

    Returns: 53547104

  84. 507348

    831313

    6

    Returns: 5761884357

  85. 425434

    817104

    5

    Returns: 2595407649

  86. 656264

    978002

    4

    Returns: 214593087

  87. 809028

    970012

    5

    Returns: 1103920660

  88. 570006

    653284

    6

    Returns: 1530539059

  89. 93836

    389691

    4

    Returns: 191564227

  90. 137067

    282771

    3

    Returns: 23019783

  91. 408112

    998188

    5

    Returns: 3928835167

  92. 671649

    713051

    6

    Returns: 786593034

  93. 142632

    998611

    5

    Returns: 5561378008

  94. 831133

    987534

    6

    Returns: 2976784946

  95. 222714

    240056

    5

    Returns: 90342843

  96. 590077

    923592

    3

    Returns: 54316662

  97. 25678

    25678

    6

    Returns: 5619

  98. 117888

    117888

    5

    Returns: 309

  99. 234556

    234556

    4

    Returns: 99

  100. 3

    3

    6

    Returns: 3

  101. 7

    7

    5

    Returns: 7

  102. 100000

    400000

    6

    Returns: 5169721292

  103. 1

    1000000

    6

    Returns: 17031865483

  104. 1234

    926134

    6

    Returns: 15675272554

  105. 1

    999999

    6

    Returns: 17031865482

  106. 999999

    999999

    6

    Returns: 5619

  107. 1000000

    1000000

    6

    Returns: 1

  108. 10

    99

    1

    Returns: 450

  109. 1

    998765

    6

    Returns: 17014040712

  110. 1

    100000

    6

    Returns: 1120996038

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: