Statistics

Problem Statement for "Hyperbox"

Problem Statement

  • The boundary of a two-dimensional rectangle is one-dimensional (a collection of line segments), and we can measure its length.
  • The boundary of a three-dimensional box is two-dimensional (a collection of rectangles), and we can measure its area.
  • In the same sense, the boundary of a four-dimensional hyperbox is three-dimensional, and we can measure its volume.

You are given the int volume (in cubic meters). Return the number of distinct hyperboxes with positive integer sides (in meters) and this exact surface volume.

Two hyperboxes are distinct if they are not congruent. (In other words, they are distinct if we cannot rearrange the dimensions of one to get the dimensions of the other.)

Definition

Class:
Hyperbox
Method:
count
Parameters:
int
Returns:
int
Method signature:
int count(int volume)
(be sure your method is public)

Constraints

  • volume will be between 1 and 200,000,000, inclusive.

Examples

  1. 8

    Returns: 1

    The smallest possible hyperbox (i.e., the 1 x 1 x 1 x 1 hyperbox) is the only one with surface volume 8.

  2. 1234567

    Returns: 0

    There are no hyperboxes with integer sides and this exact surface volume.

  3. 120

    Returns: 3

    One of the three distinct hyperboxes with this surface volume has side lengths 1, 2, 2, and 7.

  4. 1

    Returns: 0

  5. 2

    Returns: 0

  6. 4

    Returns: 0

  7. 6

    Returns: 0

  8. 8

    Returns: 1

  9. 12

    Returns: 0

  10. 16

    Returns: 0

  11. 36

    Returns: 0

  12. 46

    Returns: 0

  13. 48

    Returns: 1

  14. 52

    Returns: 0

  15. 54

    Returns: 1

  16. 56

    Returns: 2

  17. 58

    Returns: 0

  18. 62

    Returns: 2

  19. 64

    Returns: 2

  20. 68

    Returns: 1

  21. 74

    Returns: 2

  22. 76

    Returns: 1

  23. 82

    Returns: 0

  24. 88

    Returns: 2

  25. 2452361

    Returns: 0

  26. 4077592

    Returns: 119

  27. 8929267

    Returns: 0

  28. 9470116

    Returns: 74

  29. 10766894

    Returns: 41

  30. 26064724

    Returns: 105

  31. 26292468

    Returns: 148

  32. 29567012

    Returns: 160

  33. 30584374

    Returns: 69

  34. 33688540

    Returns: 139

  35. 40051182

    Returns: 93

  36. 45713384

    Returns: 247

  37. 52608872

    Returns: 344

  38. 55589302

    Returns: 78

  39. 58667620

    Returns: 138

  40. 59307330

    Returns: 143

  41. 60923520

    Returns: 1734

  42. 61752760

    Returns: 431

  43. 63818340

    Returns: 282

  44. 64053852

    Returns: 181

  45. 64151500

    Returns: 355

  46. 64974488

    Returns: 299

  47. 67869752

    Returns: 372

  48. 67951406

    Returns: 83

  49. 69858652

    Returns: 127

  50. 70219948

    Returns: 146

  51. 76857988

    Returns: 135

  52. 83807334

    Returns: 268

  53. 84712198

    Returns: 67

  54. 89638134

    Returns: 124

  55. 89888012

    Returns: 171

  56. 91781778

    Returns: 146

  57. 94770874

    Returns: 138

  58. 94879204

    Returns: 183

  59. 95816226

    Returns: 166

  60. 96390371

    Returns: 0

  61. 97398754

    Returns: 75

  62. 100439752

    Returns: 486

  63. 101969844

    Returns: 207

  64. 102966122

    Returns: 126

  65. 106160286

    Returns: 154

  66. 111846388

    Returns: 188

  67. 114809691

    Returns: 0

  68. 118707796

    Returns: 162

  69. 119154840

    Returns: 884

  70. 126441214

    Returns: 91

  71. 129908276

    Returns: 213

  72. 130298248

    Returns: 392

  73. 136447292

    Returns: 189

  74. 137963137

    Returns: 0

  75. 139425126

    Returns: 217

  76. 140464113

    Returns: 0

  77. 142991378

    Returns: 150

  78. 144989600

    Returns: 1191

  79. 146750383

    Returns: 0

  80. 146832216

    Returns: 568

  81. 149053092

    Returns: 327

  82. 149730732

    Returns: 386

  83. 149798542

    Returns: 90

  84. 150577697

    Returns: 0

  85. 151058874

    Returns: 179

  86. 151769030

    Returns: 174

  87. 152355432

    Returns: 610

  88. 154378054

    Returns: 131

  89. 155250198

    Returns: 300

  90. 161323161

    Returns: 0

  91. 162006192

    Returns: 1106

  92. 162310888

    Returns: 463

  93. 162764456

    Returns: 367

  94. 168351146

    Returns: 106

  95. 168418334

    Returns: 141

  96. 174163200

    Returns: 2121

  97. 181154904

    Returns: 769

  98. 184576584

    Returns: 507

  99. 187692292

    Returns: 198

  100. 192396339

    Returns: 0

  101. 194309033

    Returns: 0

  102. 195729420

    Returns: 373

  103. 196014538

    Returns: 160

  104. 199764026

    Returns: 207

  105. 200000000

    Returns: 1414

  106. 123456

    Returns: 52

  107. 196028000

    Returns: 1626

  108. 8000000

    Returns: 598

  109. 100000000

    Returns: 1524

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