Statistics

Problem Statement for "FoxIntegerLevelThree"

Problem Statement

Fox Jiro likes to ponder integers. Today he thought about the following things.


First, he defines a function s(n) for positive integers n. s(n) indicates the sum of all digits of n in base 10. For example, s(58) = 5+8 = 13.


Next, he defines another function d(n) for positive integers n. d(n) applies function s for n repeatedly until the result has only one digit. For example, consider d(58). First, we calculate s(58) and get 13. 13 has two digits, so we calculate s(13) and get 4. So, d(58) = 4.


He says an integer x is representable if and only if there is at least one positive integer y such that y * d(y) = x. You are given a long min, a long max. Return the number of representable integers between min and max, inclusive.

Definition

Class:
FoxIntegerLevelThree
Method:
count
Parameters:
long, long
Returns:
long
Method signature:
long count(long min, long max)
(be sure your method is public)

Constraints

  • min will be between 1 and 10,000,000,000 (10^10), inclusive.
  • max will be between min and 10,000,000,000 (10^10), inclusive.

Examples

  1. 10

    16

    Returns: 2

    The representable numbers are 10 (= 10 * d(10)) and 16 (= 4 * d(4)).

  2. 123

    123

    Returns: 0

    123 is not representable.

  3. 160

    160

    Returns: 1

    160 can be represented by two ways: 160 = 40 * d(40) 160 = 32 * d(32)

  4. 47

    58

    Returns: 4

  5. 123456789

    9876543210

    Returns: 2618024258

  6. 1

    10000000000

    Returns: 2684303353

  7. 999477818

    9877080056

    Returns: 2383017742

  8. 332166888

    9720981883

    Returns: 2520242758

  9. 670369725

    9623023062

    Returns: 2403163736

  10. 67295660

    9923624519

    Returns: 2645737658

  11. 198003508

    9211619920

    Returns: 2419528075

  12. 785596202

    9993068237

    Returns: 2471564804

  13. 817861566

    9971342423

    Returns: 2457071933

  14. 655192803

    9201809355

    Returns: 2294171144

  15. 477448418

    9752058168

    Returns: 2489586604

  16. 806589382

    9401817655

    Returns: 2307220007

  17. 59444182

    9708983773

    Returns: 2590229148

  18. 28720789

    9623684788

    Returns: 2575579402

  19. 489364295

    9125384290

    Returns: 2318169740

  20. 849876378

    9836197613

    Returns: 2412201220

  21. 488877314

    9564105275

    Returns: 2436066483

  22. 672258198

    9109463696

    Returns: 2264801898

  23. 846115616

    9695343579

    Returns: 2375401226

  24. 219964909

    9318301126

    Returns: 2442269439

  25. 523686203

    9863098114

    Returns: 2506981471

  26. 778543113

    9858805920

    Returns: 2437417987

  27. 1

    1

    Returns: 1

  28. 4

    4

    Returns: 1

  29. 9

    9

    Returns: 1

  30. 1

    10

    Returns: 4

  31. 16

    16

    Returns: 1

  32. 10

    20

    Returns: 3

  33. 25

    25

    Returns: 1

  34. 26

    26

    Returns: 0

  35. 22

    22

    Returns: 1

  36. 159

    161

    Returns: 1

  37. 255

    256

    Returns: 1

  38. 300

    300

    Returns: 0

  39. 100

    200

    Returns: 27

  40. 200

    300

    Returns: 26

  41. 1156

    1156

    Returns: 1

  42. 3947463168

    3947463177

    Returns: 1

  43. 9949512048

    9949512074

    Returns: 6

  44. 4568024301

    4568024323

    Returns: 7

  45. 4982974413

    4982974419

    Returns: 1

  46. 6819413246

    6819413259

    Returns: 5

  47. 9523533014

    9523533042

    Returns: 8

  48. 1146416416

    1146416419

    Returns: 3

  49. 6063024735

    6063024749

    Returns: 3

  50. 2292078287

    2292078298

    Returns: 3

  51. 3190179329

    3190179341

    Returns: 5

  52. 5668805265

    5668805289

    Returns: 7

  53. 9816236349

    9816236362

    Returns: 5

  54. 6443306251

    6443306258

    Returns: 2

  55. 449647452

    449647455

    Returns: 2

  56. 8827643011

    8827643017

    Returns: 2

  57. 5511960170

    5511960174

    Returns: 2

  58. 7697863017

    7697863042

    Returns: 7

  59. 8958655844

    8958655872

    Returns: 9

  60. 4836304053

    4836304078

    Returns: 6

  61. 7042996490

    7042996515

    Returns: 8

  62. 8668559056

    8668559066

    Returns: 2

  63. 9411908146

    9411908173

    Returns: 9

  64. 9354088835

    9354088839

    Returns: 1

  65. 7766621218

    7766621228

    Returns: 3

  66. 4627928072

    4627928085

    Returns: 2

  67. 9720982243

    9720982246

    Returns: 2

  68. 8351055098

    8351055100

    Returns: 1

  69. 1301888651

    1301888652

    Returns: 0

  70. 7273215326

    7273215339

    Returns: 2

  71. 8894604672

    8894604687

    Returns: 3

  72. 1552743063

    9204446072

    Returns: 2053949203

  73. 7596064634

    9118563234

    Returns: 408684811

  74. 6908572064

    6921749334

    Returns: 3537179

  75. 3811510941

    5233839820

    Returns: 381796217

  76. 1907313831

    7970217868

    Returns: 1627467364

  77. 1908568255

    8606281986

    Returns: 1797869541

  78. 7491468460

    8494492492

    Returns: 269242078

  79. 5548693208

    7403980686

    Returns: 498015439

  80. 4509679052

    6709365812

    Returns: 590462653

  81. 1585614290

    6008458245

    Returns: 1187225485

  82. 2947141895

    4695550575

    Returns: 469325927

  83. 5000260874

    5865812984

    Returns: 232340445

  84. 940675466

    1891227030

    Returns: 255156875

  85. 7695156273

    7714679180

    Returns: 5240541

  86. 1817727697

    8215813141

    Returns: 1717440221

  87. 9835014505

    9927716728

    Returns: 24884089

  88. 7247339191

    8689742920

    Returns: 387184918

  89. 61122089

    4056811127

    Returns: 1072564146

  90. 163896270

    1760398980

    Returns: 428549758

  91. 2597232719

    8393932997

    Returns: 1556010196

  92. 5305631812

    5952340264

    Returns: 173596168

  93. 1947026426

    7337767647

    Returns: 1447038472

  94. 9046834479

    9428494298

    Returns: 102449073

  95. 3461169585

    9167168768

    Returns: 1531663273

  96. 6550820100

    7682188585

    Returns: 303693622

  97. 1498849063

    7035508172

    Returns: 1486207261

  98. 4197962301

    8630996804

    Returns: 1189960937

  99. 2701462299

    4198827287

    Returns: 401938186

  100. 5720653227

    8760773941

    Returns: 816060621

  101. 2465991158

    4342926116

    Returns: 503826280

  102. 1

    9999999999

    Returns: 2684303352

  103. 2

    10000000000

    Returns: 2684303352

  104. 3

    9999999997

    Returns: 2684303350

  105. 4

    10000000000

    Returns: 2684303352

  106. 79

    9999999912

    Returns: 2684303306

  107. 13

    9999999995

    Returns: 2684303347

  108. 22

    9999999898

    Returns: 2684303318

  109. 159

    9999999814

    Returns: 2684303261

  110. 46682

    9999974115

    Returns: 2684283872

  111. 9999999999

    10000000000

    Returns: 2

  112. 1

    1000000000

    Returns: 268430337

  113. 12032214

    9542358756

    Returns: 2558228747

  114. 1000000000

    10000000000

    Returns: 2415873017

  115. 213908

    9999999993

    Returns: 2684245930

  116. 43

    353224343

    Returns: 94816118

  117. 1

    100000000

    Returns: 26843035

  118. 5000000000

    10000000000

    Returns: 1342151676

  119. 1312

    999999999

    Returns: 268429983

  120. 1

    9876543210

    Returns: 2651163805

  121. 7900

    10000000000

    Returns: 2684301232

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: